Parental Beliefs about Returns to Educational Investments—The Later the Better?

Parental Beliefs about Returns to Educational Investments—The Later the Better? Abstract In this paper, we study parental beliefs about the returns to parental investments made during different periods of childhood. Using two independent samples, we document that parents perceive the returns to different late investments to be higher than the returns to early investments, and that they perceive investments in different time periods as substitutes rather than complements. We show that parental beliefs about the returns to investments vary substantially across the population and that individual beliefs are predictive of actual investment decisions. Moreover, we document that parental beliefs about the productivity of investments differ significantly across socioeconomic groups. Perceived returns to early parental investments are positively associated with household income, thereby potentially contributing to the intergenerational persistence in earnings. 1. Introduction It has been well documented that the amount of time and financial resources parents allocate toward their children varies considerably across families, and that differences in parental investments are highly predictive of test scores and important life outcomes such as educational attainment, earnings, and health (e.g., Todd and Wolpin 2007; Lareau 2011; Attanasio et al. 2013; Carneiro, Meghir, and Parey 2013; Gayle, Golan, and Soytas 2015; Putnam 2015). Moreover, more educated and wealthier parents do not only spend more financial resources on their children, but they also spend more time with their children despite facing a higher opportunity cost in terms of foregone earnings (Guryan, Hurst, and Kearney 2008; Ramey and Ramey 2010; Deckers et al. 2015). This raises the question of why we observe such a large and systematic variation in parental investments. Although differences in preferences or available resources might explain part of this variation (e.g., Caucutt and Lochner 2012; Lee and Seshadri forthcoming), parental beliefs about the productivity of investments are likely to play a crucial role in parental investment decisions. To investigate the role of beliefs in human capital investment decisions it is not possible to rely on choice data alone. The reason is that observed choices may be consistent with many different alternative specifications of preferences and beliefs (Manski 2004). To overcome this identification problem, we need direct measures of individual beliefs about the returns to human capital investments. One useful way to measure perceived returns, which was pioneered by Dominitz and Manski (1996), is to construct hypothetical educational investment scenarios and ask respondents about the likely outcomes of these scenarios. By constructing hypothetical scenarios it is possible to vary one input at a time while keeping other factors constant, which allows the researcher to elicit individual perceived returns to a specific educational input.1 In recent work, Cunha, Elo, and Culhane (2013) make an important contribution to the literature by developing a method that relies on the use of hypothetical investment scenarios to elicit parental beliefs about the returns to parental investments. In a sample of parents with low socioeconomic status, they document beliefs about the returns to parental investments made in children aged 0–2. In this paper, we build on the seminal work by Cunha et al. (2013) and make two contributions to the literature. Motivated by the empirical work that investigates the optimal timing of investments and the dynamic properties of the skill production function (e.g., Cunha, Heckman, and Schennach 2010; Del Boca, Flinn, and Wiswall 2014; Heckman and Kautz 2014, Chap. 9; Attanasio et al. 2015a; Attanasio, Meghir, and Nix 2015b; Attanasio et al. 2017), we document parental beliefs about the returns to parental investments made during different periods of childhood. More specifically, we document parental beliefs about the returns to parental investments made during early stages of a child’s school life (henceforth referred to as early investments) and later stages of a child’s school life (henceforth referred to as late investments). We also investigate how parents perceive the dynamic properties of the skill production function, that is, whether parents perceive investments in different time periods as complements or substitutes. Recent empirical evidence suggests that skills acquired at earlier ages increase the productivity of later investments because of dynamic complementarities in the skill accumulation process (“skills beget skills”) (e.g., Cunha et al. 2010; Caucutt and Lochner 2012; Heckman and Mosso 2014; Attanasio et al. 2015a; Attanasio et al. 2017). In addition, we document individual heterogeneity in perceived returns and investigate whether this heterogeneity is systematic. In particular, we are interested in whether parents from different socioeconomic groups hold different beliefs about the returns to parental investments. To our knowledge, this is the first paper to document how parents perceive the dynamic properties of the skill production function and how parental beliefs about the returns to parental investments in different time periods differ across socioeconomic groups. To investigate these questions, we conduct two separate surveys with 538 and 1909 parents of both primary and secondary school children in the United Kingdom. We collect detailed information on parental beliefs, parental investment activities, and parent and child characteristics. To elicit beliefs about the productivity of investments, we build on and extend the approach developed in Cunha et al. (2013). In particular, we present parents with hypothetical investment scenarios that vary along three dimensions: (i) the level of early parental investments, (ii) the level of late parental investments, and (iii) the initial human capital level of the child. For each scenario, parents are asked to state what the future earnings of the child will be at age 30.2 In the scenarios of the first survey, early investments refer to investments made during school years 3–6, whereas late investments refer to investments made during school years 7–10. Here we focus on a particular type of parental investment that is relevant to all school-age children: the number of hours parents spend every week helping their child with school work. The chosen metric, that is, the number of hours spent on a specific activity, has the advantage that it is comparable across time periods. In the second survey, we construct the scenarios by replicating the types of parental investments included in the British Cohort Study (BCS). Information on parental investments is collected as part of the BCS when children are 5 and 10 years old and the investments are age-specific (e.g., reading to child at age 5, talking to child about school at age 10). In the hypothetical scenarios we construct, we use the same age-specific investments as in the BCS and vary the levels of investments made at age 5 and at age 10. The results are remarkably consistent across the two surveys and reveal that parents perceive the returns to early and late investments to be different. In particular, we find that parents perceive late investments in the scenarios to be significantly more productive than early investments. Moreover, we find that parents perceive the early and late investments as substitutes rather than complements. We further document that parents differ substantially in their beliefs about the returns to parental investments. We show that individual beliefs about the productivity of parental investments are predictive of parents’ current investment decisions and document that the heterogeneity in perceived returns is systematic. Compared to parents with high socioeconomic status, parents with low socioeconomic status perceive the returns to early investments to be significantly lower. We do not detect significant socioeconomic differences in the perceived returns to late investments. We also provide evidence from a supplementary questionnaire in which we elicit parental beliefs about the malleability of children’s skills and the capability of children to acquire skills given they are provided with professional support. We find that beliefs about returns to parental investments, which we elicit using the hypothetical investment scenarios, are positively correlated with these two supplementary measures of parental beliefs. Moreover, when we examine the heterogeneity of responses in these two supplementary belief measures, we also find that parents with low socioeconomic status are less likely to believe that children’s skills are malleable and that children have the capability of acquiring skills. An important question that emerges is whether parents’ perceptions of the returns to early and late investments are correct. In Boneva and Rauh (2017), we estimate a dynamic latent factor model using the BCS data and the estimation technique developed by Agostinelli and Wiswall (2016). Using the estimated model, we simulate how increases in investments in the two different time periods translate into increased earnings at age 30. For early investments, we find that the estimated returns are very close to what parents perceive them to be. For late investments, we find that parents overestimate the returns by a factor of two, which suggests that parents overestimate the relative importance of late relative to early investments. The second interesting question that emerges is whether parents with low socioeconomic status only perceive the returns to early investments to be lower or whether the returns to investments are actually lower in families of low socioeconomic status. In Boneva and Rauh (2017) we investigate whether the production function parameters differ across families with different characteristics to shed some light on this question. Interestingly, we cannot reject the null that the returns to parental time investments are the same across households with different parent or child characteristics. These results suggest that interventions that target parental beliefs about returns to investments may be effective at raising child outcomes and narrowing the socioeconomic gap in achievement. Our study relates to the growing literature that documents the importance of individual beliefs about the returns to education for students’ educational investment decisions.3 Attanasio and Kaufmann (2014) analyze the link between students’ beliefs and parents’ beliefs about the returns to formal education and students’ decisions to spend more time in formal education. Kaufmann (2014) documents differences in student beliefs by socioeconomic groups and shows that poor students require higher expected returns to be induced to attend college than students from rich families. Jensen (2010) shows that the perceived returns to schooling can differ from actual measured returns and that an intervention that informs students about actual returns increases school attendance. Our work also relates to the literature that investigates the role of individual beliefs in explaining students’ choice of major and students’ choice of which university to attend (Montmarquette, Cannings, and Mahseredjian 2002; Arcidiacono 2004; Arcidiacono, Hotz, and Kang 2012; Beffy, Fougere, and Maurel 2012; Stinebrickner and Stinebrickner 2012, 2014; Zafar 2013; Delavande and Zafar 2014; Wiswall and Zafar 2015; Giustinelli 2016). The literature on parental investments in children, pioneered by Becker and Tomes (1979, 1986), traditionally assumes that parents are endowed with perfect information concerning the human capital production function. Recent studies have relaxed this assumption and have drawn attention to the importance of parental beliefs in the skill accumulation process.4 Caucutt, Lochner, and Park (2017) provide a theoretical framework in which they explore how information-based frictions can lead to inefficiently low investments. Dizon-Ross (2014) finds that parents tailor financial educational investments according to their (inaccurate) beliefs about their children’s academic achievements, and that in response to an educational intervention, parents reallocate their financial investments. As mentioned previously, our study most closely relates to Cunha et al. (2013) who use hypothetical scenarios to elicit maternal beliefs about the productivity of investments made in children aged 0–2. Using the same data, Cunha (2014) investigates the relative role of heterogeneity in budget sets, preferences, beliefs about the technology of skill formation, and human capital at birth to explain the black-white gap in early parental investments, and concludes that the racial gaps in early investments are primarily produced by differences in beliefs and differences in preferences. Although Cunha et al. (2013) and Cunha (2014) elicit parental beliefs about how parental investments in very early childhood (age 0–2) map into increased skill levels at age 2, we elicit parental beliefs about how parental investments in different periods of childhood map into later-life outcomes, which allows us to investigate how parents perceive the dynamic nature of the skill production function. Our rich data set also allows us to gain further insights into differences in beliefs across socioeconomic groups. This paper proceeds as follows: Section 2 presents a stylized model of the production technology that incorporates parental beliefs and that highlights which (perceived) characteristics of the production technology are likely to be critical for parents’ investment decisions. Section 3 presents the survey design we use to elicit parental beliefs about the characteristics of the production technology as well as details about the data collection and the characteristics of the sample. Section 4 presents the main results, whereas Section 5 presents additional analyses using the two supplementary measures of parental beliefs. Section 6 compares perceived returns to estimated returns, whereas Section 7 concludes. 2. Theoretical Framework In the following, we present a theoretical framework that describes the technology that maps parental investments into future child outcomes as well as the parents’ decision problem. We use this theoretical framework to highlight which parental beliefs are likely to be critical for their investment decisions and to motivate our survey design. The model is based on the general framework developed in Cunha et al. (2010).5 Consider a model with two periods of childhood t ∈ {1, 2}, followed by one period of working life (t = 3). Each child i enters period t with a set of skills or initial conditions, denoted as θ$$\mathit{ti}$$. In every period of childhood, parents choose how much to invest in their child (I$$\mathit{ti}$$). The technology of skill production depends on the stock of skills θ$$\mathit{ti}$$, parental investments I$$\mathit{ti}$$, and the production function f in period t:   \begin{equation*} \theta _{t+1,i}=f_{t}(\theta _\mathit{ti},I_\mathit{ti}). \end{equation*} Assume that f is monotone increasing in its arguments, twice continuously differentiable and concave in I$$\mathit{ti}$$. Adult outcome yi is produced by the set of skills with which the child enters working life, θ3i, via the following function: yi = g(θ3i). Taken together, adult outcome yi depends on the child’s initial conditions θ1i, early investments I1i, late investments I2i, and the function h that maps these inputs into adult outcome yi:   \begin{equation*} y_i=h(\theta _{1i},I_{1i},I_{2i}). \end{equation*} In any given time period, parent i can allocate her total available leisure time, L$$\mathit{ti}$$, to activities that help child i accumulate skills (I$$\mathit{ti}$$) and activities that do not directly promote the child’s human capital, which we henceforth refer to as “own” leisure time (l$$\mathit{ti}$$). Suppose that parental preferences are a function of own leisure time in period 1, l1i, own leisure time in period 2, l2i, as well as child outcome yi:   \begin{equation*} u_i(l_{1i},l_{2i},y_i)=\ln l_{1i} + \alpha _i \ln l_{2i} + \beta _i \ln y_i, \end{equation*} where αi captures how much parent i values own leisure time in period 2 relative to own leisure time in period 1, and βi captures how much parent i values child outcome yi relative to own leisure time in period 1. Parent i chooses I1i and I2i so as to maximize utility ui(l1i, l2i, yi) subject to the following within period time budget constraints,   \begin{equation*} l_\mathit{ti}+I_\mathit{ti}=L_\mathit{ti} \, \, \forall t\in \lbrace 1,2\rbrace , \end{equation*} as well as the perceived technological constraint,   \begin{equation*} \tilde{y}_{i} = h_{i}(\theta _{1i},I_{1i},I_{2i}). \end{equation*} Note that parents base their decisions on the perceived technological constraint hi(.), which may or may not coincide with the “true” technological constraint h(.). Given the complex nature of the human capital accumulation process, it seems unlikely that parents have complete information about how inputs map into future child outcomes.6 As a result, the investment levels chosen by parent i may or may not actually be optimal, that is, the investment levels chosen might differ from the investment levels that would be chosen by parent i if the parent was fully informed about the ‘true’ function h(.). From the first order conditions to this problem it becomes apparent that parental beliefs about the partial derivatives of this production technology are critical for parental investment decisions:   \begin{equation} \frac{\partial h_{i}(\cdot )}{\partial I_{1i}},\frac{\partial h_{i}(\cdot )}{\partial I_{2i}}. \end{equation} (1) Notice that these (perceived) marginal returns may depend on the levels of the other inputs. It is therefore equally important to investigate parental beliefs about the cross derivatives of the production function. For example, a question that has been much debated in the literature is whether late investments are more productive if they are preceded by high early investments. We are therefore interested in how parents perceive the degree of complementarity between investments in the two different time periods:   \begin{equation} \frac{\partial ^2 h_{i}(\cdot )}{\partial I_{2i}\partial I_{1i}}\lesseqqgtr 0. \end{equation} (2) Moreover, the (perceived) marginal returns to investments may depend on the initial level of human capital of the child, which is why it is interesting to investigate how parents perceive the degree of complementarity between investments and the child’s initial skill level:7  \begin{equation} \frac{\partial ^2 h_{i}(\cdot )}{\partial I_\mathit{ti}\partial \theta _{1i}}\lesseqqgtr 0\,\forall t\epsilon \lbrace 1,2\rbrace . \end{equation} (3) Although the literature has been emphasizing the importance of these partial and cross derivatives for parental investment decisions, little is known about parents’ beliefs about these derivatives. To gain a better understanding of how parents perceive these characteristics of the production function, we elicit parental beliefs using a novel survey design. 3. Eliciting Parental Beliefs To collect information on parental beliefs as well as current parental investment decisions, we administer two different surveys to two independent samples (referred to as sample A and sample B). This allows us to document parental beliefs about the production technology and to investigate whether parental beliefs about the returns to investments are predictive of current parental investment decisions. In addition, we collect information on background characteristics, which allows us to examine whether parents with different characteristics hold systematically different beliefs about the returns to parental investments. We collect all survey data online. Both surveys are distributed via the parental mailing lists of schools in England that agreed to participate (see maps in Online Appendix D).8 survey A was distributed to parents via the mailing lists of 5 primary and 5 secondary schools in May–June 2015 (sample A), whereas survey B was distributed via the mailing lists of 11 primary and 24 secondary schools in May–June 2016 (sample B).9 In each sample, we incentivize parental participation through a prize draw of a voucher worth £100. As motivated in Section 2, parental beliefs about several partial and cross derivatives of the production function are likely to be critical for the level, timing and allocation of parental investments. We build on Cunha et al. (2013) and use hypothetical investment scenarios to elicit parental beliefs about the characteristics of the production function.10 Hypothetical Scenarios We present parents with different hypothetical scenarios and ask them to state what they expect the earnings of the child in the scenario to be at age 30. The scenarios vary along three key dimensions: (i) the initial human capital level of the child, (ii) the level of early investments, and (iii) the level of late investments. A comparison of the parents’ responses across the different scenarios allows us to infer how parents perceive the importance of the initial human capital level of the child, the returns to early and late investments (derivative (1)), and the complementarity or substitutability between the different inputs (cross derivatives (2) and (3)). More specifically, all parents are presented with two hypothetical families (the “Jones” and the “Smiths”). In both hypothetical families there is one child of primary school age. Parents are told that although the Jones and the Smiths live in the same neighborhood and are very similar in many different respects (e.g., in terms of income and education), there is one difference between the two families. In particular, they are told that the children of the two families differ in their initial level of human capital.11 For each of these two hypothetical families, parents are then presented with four different investment scenarios that vary in the levels of investments the Smiths and the Jones could make during the following time periods. The four different investment scenarios are (1) low early investments/low late investments, (2) low early investments/high late investments, (3) high early investments/low late investments, and (4) high early investments/high late investments.12 Therefore, each parent is in total presented with eight different scenarios, which are illustrated in Table 1. For each of these eight scenarios j, parents are asked to state the expected gross annual earnings of the child at age 30 ($$\tilde{y}_{j}$$).13 Table 1. Overview of different scenarios. The Jones  The Smiths  High initial human capital  Low initial human capital    Low late investment  High late investment    Low late investment  High late investment    $$\tilde{y}_{1}$$  $$\tilde{y}_{2}$$    $$\tilde{y}_{5}$$  $$\tilde{y}_{6}$$  Low early  Low early/  Low early/  Low early  Low early/  Low early/  investment  low late  high late  investment  low late  high late    $$\tilde{y}_{3}$$  $$\tilde{y}_{4}$$    $$\tilde{y}_{7}$$  $$\tilde{y}_{8}$$  High early  High early/  High early/  High early  High early/  High early/  investment  low late  high late  investment  low late  high late  The Jones  The Smiths  High initial human capital  Low initial human capital    Low late investment  High late investment    Low late investment  High late investment    $$\tilde{y}_{1}$$  $$\tilde{y}_{2}$$    $$\tilde{y}_{5}$$  $$\tilde{y}_{6}$$  Low early  Low early/  Low early/  Low early  Low early/  Low early/  investment  low late  high late  investment  low late  high late    $$\tilde{y}_{3}$$  $$\tilde{y}_{4}$$    $$\tilde{y}_{7}$$  $$\tilde{y}_{8}$$  High early  High early/  High early/  High early  High early/  High early/  investment  low late  high late  investment  low late  high late  View Large Table 1. Overview of different scenarios. The Jones  The Smiths  High initial human capital  Low initial human capital    Low late investment  High late investment    Low late investment  High late investment    $$\tilde{y}_{1}$$  $$\tilde{y}_{2}$$    $$\tilde{y}_{5}$$  $$\tilde{y}_{6}$$  Low early  Low early/  Low early/  Low early  Low early/  Low early/  investment  low late  high late  investment  low late  high late    $$\tilde{y}_{3}$$  $$\tilde{y}_{4}$$    $$\tilde{y}_{7}$$  $$\tilde{y}_{8}$$  High early  High early/  High early/  High early  High early/  High early/  investment  low late  high late  investment  low late  high late  The Jones  The Smiths  High initial human capital  Low initial human capital    Low late investment  High late investment    Low late investment  High late investment    $$\tilde{y}_{1}$$  $$\tilde{y}_{2}$$    $$\tilde{y}_{5}$$  $$\tilde{y}_{6}$$  Low early  Low early/  Low early/  Low early  Low early/  Low early/  investment  low late  high late  investment  low late  high late    $$\tilde{y}_{3}$$  $$\tilde{y}_{4}$$    $$\tilde{y}_{7}$$  $$\tilde{y}_{8}$$  High early  High early/  High early/  High early  High early/  High early/  investment  low late  high late  investment  low late  high late  View Large The parents’ responses to the eight different scenarios allow us to infer parental beliefs about the characteristics of the production technology. First, we can infer the parents’ beliefs about the importance of the initial human capital level of the child by comparing the parents’ responses to the scenarios in which the level of human capital is high to the corresponding scenarios in which the level of human capital is low. Second, the design allows us to investigate parental beliefs about the partial derivatives of the production function with respect to early and late investments (derivative (1)). Intuitively, by comparing parents’ responses in the scenarios in which early (late) investments are high to the corresponding scenarios in which early (late) investments are low, we can obtain an estimate of parental beliefs about the returns to early (late) investments.14 The design also allows us to obtain insights into parental beliefs about the complementarity or substitutability of different inputs or, put differently, parental beliefs about the cross derivatives of the production technology (cross derivatives (2) and (3)). By comparing perceived returns to late investments when early investments are low to perceived returns to late investments when early investments are high, we can learn something about the perceived complementarity/substitutability between early and late investments. More specifically, if investments in different time periods are perceived as complements, we expect perceived returns to late investments to be higher when early investments are high, that is, we expect $$(\log \tilde{y}_{4}- \log \tilde{y}_{3})>(\log \tilde{y}_{2}- \log \tilde{y}_{1})$$ and $$(\log \tilde{y}_{8}- \log \tilde{y}_{7})>(\log \tilde{y}_{6}- \log \tilde{y}_{5})$$. If instead investments in the different time periods are perceived as substitutes, we expect perceived returns to late investments to be lower when early investments are high. Similarly, a comparison between perceived returns to investments when human capital is low to perceived returns to investments when human capital is high informs us about the perceived complementarity/substitutability between parental investments and the initial human capital level of the child. Empirical Specification. To estimate the partial and cross derivatives of interest, we estimate an ordinary least squares regression in which we allow for interactions between the different inputs. Given that we have eight responses for each parent, this gives us a pseudo-panel for each parent, which allows us to include parental fixed effects. In particular, we estimate the β coefficients in the following specification:   \begin{eqnarray} \log \tilde{y}_{ji} &=& \alpha + \beta _{1}I_{1j}+\beta _{2}I_{2j}+\beta _{3}\theta _{1j}+\beta _{4} I_{1j}\times I_{2j}\nonumber\\ &&+ \,\beta _{5} I_{1j}\times \theta _{1j}+\beta _{6} I_{2j}\times \theta _{1j} + \gamma _{i} + \epsilon _{ji}, \end{eqnarray} (4)where j indicates the scenario, $$\tilde{y}_{ji}$$ are the earnings parent i expects in scenario j, α is the intercept, I1j and I2j are dummy variables indicating whether early and late investments are high, respectively, θ1j is a dummy variable indicating whether the initial level of human capital is high, and γi are parent fixed effects. β1 and β2 reveal how parents perceive the returns to early and late investments in the scenarios, whereas β3 reveals how parents perceive the returns to the child’s initial human capital level. If parents perceive the early and late investments as complements (substitutes), we expect β4 > 0 (β4 < 0). If parents perceive early/late investments and initial human capital as complements (substitutes), we expect β5 > 0 (β5 < 0) and β6 > 0 (β6 < 0), respectively.15 Types and Levels of Investments. The structure of the hypothetical scenarios is the same across the two surveys, that is, in both surveys we present all parents with eight different scenarios, which vary in the level of initial human capital, as well as in the level of early and late investments (see Table 1). The main difference between the two surveys is that we use different types and levels of investments. In survey A, the children of the two families are in year 3 of primary school (7–8 years old), and they differ in their prior achievement in the national curriculum test which children in the United Kingdom have to take at the end of year 2. In particular, although the child of the Jones managed to achieve the level that is expected of children in this age group, the child of the Smiths did not.16 We then vary the level of investments the two families make in school years 3–6 (i.e., the level of early investments) and the level of investments the two families make in school years 7–10 (i.e., the level of late investments). In this survey, we hold the type of investments fixed across time periods. More specifically, in both time periods we vary the amount of time the Jones and the Smiths spend helping their child with his school work. To additionally investigate whether parents perceive the returns to investments as diminishing as investment levels rise, we randomize respondents into two different conditions. In particular, for half the respondents “high” and “low” investments refer to spending 4 and 1 h every week helping the child with his school work, respectively. For the other half of the respondents “high” investments refer to 3 h whereas “low” investments refer to 0 h. Although there are advantages to keeping the type of investment fixed across the different time periods, a potential concern with this design is that in different time periods different types of investments might be relevant for the production of human capital. We provide evidence that our results are not merely driven by the specific type of investment we choose by conducting a second survey (survey B) in which we use the British Cohort Study (BCS) to replicate questions about investments relevant for children of different ages.17 We choose the descriptions of the scenarios in survey B so that the types of investments described in the scenarios match those collected as part of the BCS. The children of the two families in sample B are 5 years old, and they differ in how intelligent they are. In particular, on an intelligence test the child of the Jones scored better than 70% of all children in the same age group, whereas the child of the Smiths scored worse than 70%. We then vary the level of age-specific investments parents make at age 5 and the level of age-specific investments parents make at age 10.18 When choosing the levels of low and high investments, we choose values that are ±0.5 standard deviations from the mean response of parents who are part of the BCS. More specifically, we use the data on the actual investments parents in the BCS make and first extract a factor from the three age-specific investments (separately for each time period). We then compute the average level of each investment for parents whose predicted factor is −0.5 standard deviations below the mean, and +0.5 standard deviations above the mean, and use these values to construct our scenarios. The resulting scenarios are as follows. In scenarios in which age 5 investments are low, the parents in the hypothetical scenario read to their child every second day, they rarely take their child to the playground, and they let their child watch TV for 2 h every day. In contrast, in scenarios in which the level of age 5 investments is high, parents read to their child every day, they take their child to the playground once every fortnight, and they let their child watch TV for 1 h every day. In scenarios in which age 10 investments are low, parents show moderate interest in their child’s education, they do not talk to their child very much, and they sometimes engage in activities together (e.g., go out for walks, have breakfast or tea together). In contrast, in scenarios in which age 10 investments are high, parents show a lot of interest in their child’s education, they talk to their child quite a lot, and they often engage in activities together. Gender of Child in Scenario. While in sample A all parents are presented with hypothetical scenarios in which the child is a boy (“John” or “Simon”), we present a subset of the respondents in sample B with hypothetical scenarios in which the child is a girl (“Jessica” or “Sarah”). More specifically, all parents in sample B who received the invitation to participate via their daughter’s school were presented with scenarios that featured girls, while all parents who received the invitation to participate via their son’s school were presented with scenarios that featured boys. This allows us to compare how parents with daughters perceive the returns to investments in girls to how parents with sons perceive the returns to investments in boys. Additional Outcome. In addition to asking about the likely future earnings of the child at age 30, we also ask a random subset of parents in sample A (N = 266) to state how likely they think it is that the child will graduate from university in each of the eight scenarios. We ask parents to report their response on a 0–100% scale. Although our main analysis focuses on using the likely future earnings as the outcome variable, we use the respondents’ answers to these additional questions to investigate whether we find similar results if we use a different outcome measure. 3.1. Summary Statistics Sample A consists of 538 parents who completed the survey. The characteristics of the sample are reported in Panel A of Table 2. 85% of the respondents in our sample are female. Out of the 85% who are employed, 60% work full-time whereas 40% work part-time. A university degree is held by 45% of the respondents and the average annual household income of the families is £55,771. Fourteen percent of the respondents in sample A are single parent households. The parents in sample A on average have 1.96 children. The children for whom the parents completed the survey are on average 13 years old.19 Table 2. Descriptive statistics.   sample A  sample B  FRS    Mean  [SD]  Mean  [SD]  Mean  [SD]  Female respondent  0.85  [0.36]  0.75  [0.43]  0.77  [0.42]  Employed  0.85  [0.35]  0.82  [0.39]  0.70  [0.46]   Part-time  0.40  [0.49]  0.31  [0.46]  0.37  [0.49]   Full-time  0.60  [0.49]  0.69  [0.46]  0.61  [0.49]  University graduate  0.45  [0.50]  0.60  [0.49]  0.32  [0.47]  Single parent  0.14  [0.34]  0.14  [0.34]  0.30  [0.46]  Number of children  1.96  [0.88]  2.28  [0.94]  1.84  [0.88]  Age of child  13.39  [3.58]  12.99  [3.33]  10.43  [4.15]  Female child  0.56  [0.50]  0.32  [0.47]  0.50  [0.50]  Household incomea  55,771  [27,019]  78,996  [37,546]  45,679  [28,031]  Observations  538    1909    3381      sample A  sample B  FRS    Mean  [SD]  Mean  [SD]  Mean  [SD]  Female respondent  0.85  [0.36]  0.75  [0.43]  0.77  [0.42]  Employed  0.85  [0.35]  0.82  [0.39]  0.70  [0.46]   Part-time  0.40  [0.49]  0.31  [0.46]  0.37  [0.49]   Full-time  0.60  [0.49]  0.69  [0.46]  0.61  [0.49]  University graduate  0.45  [0.50]  0.60  [0.49]  0.32  [0.47]  Single parent  0.14  [0.34]  0.14  [0.34]  0.30  [0.46]  Number of children  1.96  [0.88]  2.28  [0.94]  1.84  [0.88]  Age of child  13.39  [3.58]  12.99  [3.33]  10.43  [4.15]  Female child  0.56  [0.50]  0.32  [0.47]  0.50  [0.50]  Household incomea  55,771  [27,019]  78,996  [37,546]  45,679  [28,031]  Observations  538    1909    3381    Notes: For the FRS we present the averages of 1,000 randomly drawn samples resembling a convex combination of samples A and B in terms of share of female respondents that had at least one child aged 5–19 in the household. a. Household income refers to the gross annual income of all household members. View Large Table 2. Descriptive statistics.   sample A  sample B  FRS    Mean  [SD]  Mean  [SD]  Mean  [SD]  Female respondent  0.85  [0.36]  0.75  [0.43]  0.77  [0.42]  Employed  0.85  [0.35]  0.82  [0.39]  0.70  [0.46]   Part-time  0.40  [0.49]  0.31  [0.46]  0.37  [0.49]   Full-time  0.60  [0.49]  0.69  [0.46]  0.61  [0.49]  University graduate  0.45  [0.50]  0.60  [0.49]  0.32  [0.47]  Single parent  0.14  [0.34]  0.14  [0.34]  0.30  [0.46]  Number of children  1.96  [0.88]  2.28  [0.94]  1.84  [0.88]  Age of child  13.39  [3.58]  12.99  [3.33]  10.43  [4.15]  Female child  0.56  [0.50]  0.32  [0.47]  0.50  [0.50]  Household incomea  55,771  [27,019]  78,996  [37,546]  45,679  [28,031]  Observations  538    1909    3381      sample A  sample B  FRS    Mean  [SD]  Mean  [SD]  Mean  [SD]  Female respondent  0.85  [0.36]  0.75  [0.43]  0.77  [0.42]  Employed  0.85  [0.35]  0.82  [0.39]  0.70  [0.46]   Part-time  0.40  [0.49]  0.31  [0.46]  0.37  [0.49]   Full-time  0.60  [0.49]  0.69  [0.46]  0.61  [0.49]  University graduate  0.45  [0.50]  0.60  [0.49]  0.32  [0.47]  Single parent  0.14  [0.34]  0.14  [0.34]  0.30  [0.46]  Number of children  1.96  [0.88]  2.28  [0.94]  1.84  [0.88]  Age of child  13.39  [3.58]  12.99  [3.33]  10.43  [4.15]  Female child  0.56  [0.50]  0.32  [0.47]  0.50  [0.50]  Household incomea  55,771  [27,019]  78,996  [37,546]  45,679  [28,031]  Observations  538    1909    3381    Notes: For the FRS we present the averages of 1,000 randomly drawn samples resembling a convex combination of samples A and B in terms of share of female respondents that had at least one child aged 5–19 in the household. a. Household income refers to the gross annual income of all household members. View Large In sample B, we have information on 1909 parents who completed the survey (see Panel B of Table 2). 68% are female and 82% are employed either full-time or part-time. 60% of the responding parents have a university degree and the average annual household income is £78,996. 14% of the respondents are single parent households, and on average the parents in this sample have 2.28 children. The children for whom the parent completed this survey are also on average 13 years old. Compared to a representative sample of parents in England with at least one child aged 5–19, the parents in our sample have higher levels of education, they are less likely to be single parents, are more likely to be employed and report higher annual household incomes.20 Figure D.3 in the Online Appendix D shows the distribution of annual household incomes for parents in our two samples and parents in the Family Resources Survey (FRS). We note that although parents in our samples have higher levels of income compared to the parents in the representative sample, there is still a substantial amount of variation in parental income, which allows us to estimate differences in parental beliefs across different socioeconomic groups. There are two different reasons why the characteristics of parents who participated in our survey are different from the characteristics of a representative sample of parents in England (see Table 2). First, it was the decision of the head teacher whether or not to distribute our survey among parents, so the schools included in our sample are not representative of the population of English schools (see Table A.1 in the Appendix  A for a comparison). For example, the schools in our sample have a lower share of students eligible for free school meals (FSM) compared to the national average. Second, participation in the survey was voluntary and the response rate to our survey was 7% so the characteristics of participating parents may differ from the characteristics of the full sample of parents that was contacted via the participating schools.21 Although the administrative school data does not contain information on parental income or education, which would allow us to assess whether parents in our surveys self-select on these characteristics within the participating schools, we note that 8% of the parents who participated in survey A report that their children are eligible for Free School Meals, which corresponds to the actual percentage of students on FSM in these schools (8.2%).22 Although we can only speculate whether or not we would find similar results if we surveyed a representative sample of parents in England, we note that we find the same results when we reweigh our observations in order to resemble a representative population in terms of household income (see Table C.1 in the Online Appendix C). Parental Investments. To investigate whether parental beliefs about the productivity of investments are predictive of current parental investments, we ask parents to provide detailed information on the investments they currently make in their child. In sample A, we ask all parents to provide information on (i) the time they spend every week on certain activities (e.g., “help child with homework, check workbooks”), (ii) the frequency at which they engage in certain activities with their child during the year (e.g., “visit museum/art gallery”), and (iii) the financial resources they spend every month on different categories related to their child’s education (e.g., “Sport clubs/music lessons/other societies”).23 Tables A.2–A.4 in the Appendix  A present the summary statistics of the responses to these three questionnaires, respectively. In sample B, we replicate the questions from the British Cohort Study, and ask about the same age-specific investments that we vary in the hypothetical investment scenarios. In particular, we ask parents of children aged 3–9 to provide information on (i) how many days their child has been read to at home in the past 7 days, (ii) how many hours per day the child usually watches TV, and (iii) whether the child has been taken to a park or playground during the past 7 days. Parents of children aged 10 or above are asked about (i) the frequency of different activities they do together with their child (e.g., have breakfast or tea together), (ii) how interested they are in their child’s education, and (iii) how much time they usually spend talking to their child every day. Tables A.5–A.6 in the Appendix  A present the summary statistics of the responses to these different questions. To investigate whether the results are susceptible to the order in which the survey modules are presented, we randomize the order in which perceptions and investments are elicited in sample B.24 4. Results 4.1. Parental Beliefs about the Production Technology In both surveys, all parents are presented with eight hypothetical investment scenarios and are asked to state the expected earnings of the child at age 30 in each scenarios (see Table 1). Figure 1 depicts the child’s expected earnings ($$\tilde{y}_{j}$$) in the eight scenarios for sample A and sample B, respectively, averaged across respondents. Although the left panels depict the average expected earnings for the child with low initial human capital, the right panels depict the average expected earnings for the child with high initial human capital. For each level of human capital, we show the average expected earnings by the level of early investments (low vs. high) and by the level of late investments (low vs. high). Figure 1. View largeDownload slide Expected earnings at age 30. This figure depicts the expected earnings of the child at age 30 in each of the eight hypothetical investment scenarios (see Table 1) for sample A and sample B, respectively, averaged across all respondents in a given sample (with 95% confidence intervals). LL: low early, low late investments; HL: high early, low late investments; LH: low early, high late investments; HH: high early, high late investments. Figure 1. View largeDownload slide Expected earnings at age 30. This figure depicts the expected earnings of the child at age 30 in each of the eight hypothetical investment scenarios (see Table 1) for sample A and sample B, respectively, averaged across all respondents in a given sample (with 95% confidence intervals). LL: low early, low late investments; HL: high early, low late investments; LH: low early, high late investments; HH: high early, high late investments. There are several patterns that are worth noting. First, parents give meaningful responses to the questions in the sense that higher levels of initial human capital or higher levels of investments are also associated with higher expected earnings of the child in the scenario. Moreover, parents are on average remarkably close in their estimates to the true average.25 Using the Family Resources Survey of 2013–2014, we find the average annual earnings of 25–34 year-old men in England to be £30,977 and the average annual earnings of 25–34 year-old women to be £25,630 (conditional on working full-time, that is, at least 30 h per week). In sample A, in which we present all parents with scenarios in which the children are male, the average estimates across the four scenarios in which the child achieved the expected level in the national curriculum test (“high initial human capital”) is £31,550, whereas the average estimates across the four scenarios in which the child did not achieve the expected level (“low initial human capital”) is about £26,480. Given that about 80% of all students in the United Kingdom achieve the expected level, the weighted average of parental estimates in sample A is about £30,540, which is remarkably close to the actual average earnings of men in the specified age group. In sample B, in which we present some parents with girls and other parents with boys, parents believe that a child who is more intelligent than 70% of the children in their age group (“high initial human capital”) will earn about £36,750, whereas a child who is less intelligent than 70% of the children in their age group (“low initial human capital”) will earn about £27,560. Averaging across these two numbers gives us an estimate of £32,155, which is again very close to the true average, albeit slightly higher than the average across the two genders in the FRS (£28,303). Another pattern that emerges in both samples is that parents believe, irrespective of the initial human capital level of the child, that the earnings of a child will be higher when early investments are low and late investments are high (bar 3) compared to when early investments are high and late investments are low (bar 2). This indicates that parents perceive returns to the late investments in the scenarios to be higher than returns to the early investments.26 To investigate the perceived returns to the different inputs in more detail, we pool the parents’ responses to the eight hypothetical investment scenarios and estimate variants of the empirical specification presented in Section 3 (equation 4). We first regress the log expected earnings of the child at age 30 as reported by parent i ($$\log \tilde{y}_{ij}$$) on (i) a dummy variable that takes a value of 1 if early investments in the scenario are high (I1j), (ii) a dummy variable that equals 1 if late investments in the scenario are high (I2j), and (iii) a dummy variable that takes a value of 1 if the child in the scenario has high initial human capital (θ1j). In sample A, the difference between scenarios in which investments are high and scenarios in which investments are low is that the parents spend an additional 3 h every week helping their child with school work.27 In sample B, low levels of investments are described as being 0.5 standard deviations below the actual mean investments made by panel members of the BCS, whereas high levels of investments are described as being 0.5 standard deviations above the mean (see Section 3). The difference between low and high levels of investments for sample B is therefore one standard deviation in age-specific investments. The regression results are presented in Table 3. Table 3. Determinants of perceived log earnings at age 30 (1). Dependent variable: Perceived log earnings at age 30    sample A    sample B    (1)  (2)  (3)    (4)  (5)  (6)  Scenarios                Early investmentsa  0.154***  0.155***  0.154***    0.100***  0.100***  0.100***    (0.008)  (0.008)  (0.008)    (0.003)  (0.003)  (0.003)  Late investmentsb  0.255***  0.255***  0.254***    0.316***  0.315***  0.315***    (0.010)  (0.010)  (0.010)    (0.006)  (0.006)  (0.006)  High human capitalc  0.185***  0.190***  0.185***    0.277***  0.290***  0.288***    (0.009)  (0.009)  (0.010)    (0.007)  (0.006)  (0.006)  High baselined  0.210***  0.192***              (0.034)  (0.032)            Female childe            −0.083***                (0.018)    Respondent characteristics                Log(HH income)    0.184***        0.111***        (0.042)        (0.016)    Employedf    0.055        −0.033        (0.055)        (0.021)    University graduate    −0.045        0.010        (0.033)        (0.017)    Number of children    0.015        0.009        (0.021)        (0.009)    Female respondent    −0.078        −0.059***        (0.051)        (0.017)    Single parent    0.107        0.040        (0.072)        (0.025)    Constant  9.777***  7.514***  9.749***    9.924***  8.445***  9.485***    (0.028)  (0.493)  (0.010)    (0.009)  (0.173)  (0.005)  School fixed effects  No  Yes  No    No  Yes  No  Parent fixed effects  No  No  Yes    No  No  Yes  Observations  4069  3771  4069    16251  13551  16251  R2  0.181  0.275  0.827    0.204  0.332  0.782  Dependent variable: Perceived log earnings at age 30    sample A    sample B    (1)  (2)  (3)    (4)  (5)  (6)  Scenarios                Early investmentsa  0.154***  0.155***  0.154***    0.100***  0.100***  0.100***    (0.008)  (0.008)  (0.008)    (0.003)  (0.003)  (0.003)  Late investmentsb  0.255***  0.255***  0.254***    0.316***  0.315***  0.315***    (0.010)  (0.010)  (0.010)    (0.006)  (0.006)  (0.006)  High human capitalc  0.185***  0.190***  0.185***    0.277***  0.290***  0.288***    (0.009)  (0.009)  (0.010)    (0.007)  (0.006)  (0.006)  High baselined  0.210***  0.192***              (0.034)  (0.032)            Female childe            −0.083***                (0.018)    Respondent characteristics                Log(HH income)    0.184***        0.111***        (0.042)        (0.016)    Employedf    0.055        −0.033        (0.055)        (0.021)    University graduate    −0.045        0.010        (0.033)        (0.017)    Number of children    0.015        0.009        (0.021)        (0.009)    Female respondent    −0.078        −0.059***        (0.051)        (0.017)    Single parent    0.107        0.040        (0.072)        (0.025)    Constant  9.777***  7.514***  9.749***    9.924***  8.445***  9.485***    (0.028)  (0.493)  (0.010)    (0.009)  (0.173)  (0.005)  School fixed effects  No  Yes  No    No  Yes  No  Parent fixed effects  No  No  Yes    No  No  Yes  Observations  4069  3771  4069    16251  13551  16251  R2  0.181  0.275  0.827    0.204  0.332  0.782  Notes: Standard errors in parentheses. Standard errors are clustered at the parent level. For each sample, the regressions are performed using the parents’ responses to all eight hypothetical investment scenarios. a. Dummy variable for high parental time investments in the early period; b. Dummy variable for high parental time investments in the late period; c. Dummy variable that equals 1 if the child in the scenario has high initial human capital; d. Dummy variable indicating that the responding parent was randomized into the group that saw 1 h/4 h (rather than 0 h/3 h) for low/high levels of investments; e. Child in the scenario is female (for sample B only); f. Coded 0 if not employed, 0.5 if part-time employed, 1 if full-time employed. ***p < 0.01. View Large Table 3. Determinants of perceived log earnings at age 30 (1). Dependent variable: Perceived log earnings at age 30    sample A    sample B    (1)  (2)  (3)    (4)  (5)  (6)  Scenarios                Early investmentsa  0.154***  0.155***  0.154***    0.100***  0.100***  0.100***    (0.008)  (0.008)  (0.008)    (0.003)  (0.003)  (0.003)  Late investmentsb  0.255***  0.255***  0.254***    0.316***  0.315***  0.315***    (0.010)  (0.010)  (0.010)    (0.006)  (0.006)  (0.006)  High human capitalc  0.185***  0.190***  0.185***    0.277***  0.290***  0.288***    (0.009)  (0.009)  (0.010)    (0.007)  (0.006)  (0.006)  High baselined  0.210***  0.192***              (0.034)  (0.032)            Female childe            −0.083***                (0.018)    Respondent characteristics                Log(HH income)    0.184***        0.111***        (0.042)        (0.016)    Employedf    0.055        −0.033        (0.055)        (0.021)    University graduate    −0.045        0.010        (0.033)        (0.017)    Number of children    0.015        0.009        (0.021)        (0.009)    Female respondent    −0.078        −0.059***        (0.051)        (0.017)    Single parent    0.107        0.040        (0.072)        (0.025)    Constant  9.777***  7.514***  9.749***    9.924***  8.445***  9.485***    (0.028)  (0.493)  (0.010)    (0.009)  (0.173)  (0.005)  School fixed effects  No  Yes  No    No  Yes  No  Parent fixed effects  No  No  Yes    No  No  Yes  Observations  4069  3771  4069    16251  13551  16251  R2  0.181  0.275  0.827    0.204  0.332  0.782  Dependent variable: Perceived log earnings at age 30    sample A    sample B    (1)  (2)  (3)    (4)  (5)  (6)  Scenarios                Early investmentsa  0.154***  0.155***  0.154***    0.100***  0.100***  0.100***    (0.008)  (0.008)  (0.008)    (0.003)  (0.003)  (0.003)  Late investmentsb  0.255***  0.255***  0.254***    0.316***  0.315***  0.315***    (0.010)  (0.010)  (0.010)    (0.006)  (0.006)  (0.006)  High human capitalc  0.185***  0.190***  0.185***    0.277***  0.290***  0.288***    (0.009)  (0.009)  (0.010)    (0.007)  (0.006)  (0.006)  High baselined  0.210***  0.192***              (0.034)  (0.032)            Female childe            −0.083***                (0.018)    Respondent characteristics                Log(HH income)    0.184***        0.111***        (0.042)        (0.016)    Employedf    0.055        −0.033        (0.055)        (0.021)    University graduate    −0.045        0.010        (0.033)        (0.017)    Number of children    0.015        0.009        (0.021)        (0.009)    Female respondent    −0.078        −0.059***        (0.051)        (0.017)    Single parent    0.107        0.040        (0.072)        (0.025)    Constant  9.777***  7.514***  9.749***    9.924***  8.445***  9.485***    (0.028)  (0.493)  (0.010)    (0.009)  (0.173)  (0.005)  School fixed effects  No  Yes  No    No  Yes  No  Parent fixed effects  No  No  Yes    No  No  Yes  Observations  4069  3771  4069    16251  13551  16251  R2  0.181  0.275  0.827    0.204  0.332  0.782  Notes: Standard errors in parentheses. Standard errors are clustered at the parent level. For each sample, the regressions are performed using the parents’ responses to all eight hypothetical investment scenarios. a. Dummy variable for high parental time investments in the early period; b. Dummy variable for high parental time investments in the late period; c. Dummy variable that equals 1 if the child in the scenario has high initial human capital; d. Dummy variable indicating that the responding parent was randomized into the group that saw 1 h/4 h (rather than 0 h/3 h) for low/high levels of investments; e. Child in the scenario is female (for sample B only); f. Coded 0 if not employed, 0.5 if part-time employed, 1 if full-time employed. ***p < 0.01. View Large In sample A, three additional weekly hours of investments made in school years 3–6 translate into an increase in expected earnings by 15.4%, whereas three additional weekly hours of investments made in school years 7–10 translate into an increase in expected earnings by 25.5%. High initial human capital is associated with an earnings increase of 18.5% (column (1)). In sample B, a one standard deviation increase in the level of age-specific investment in the early period is associated with an earnings increase of 10.0%, whereas a one standard deviation increase in the level of age-specific investment in the later time period is associated with 31.6% higher earnings (column (4)). The results are robust to the inclusion of household characteristics and school fixed effects (columns (2) and (5)), as well as to the inclusion of parent fixed effects (columns (3) and (6)). The inclusion of parent fixed effects allows us to estimate the coefficients using within-parent variation only. A result that is worth noting is that in all specifications the coefficient on late investments is significantly larger than the coefficient on early investments (at the 1% level), indicating that parents perceive the late investments in the scenarios as significantly more productive. Table 4 explores additional features of the perceived function that maps investments into future outcomes. In particular, we first examine whether parents perceive early and late investments as substitutes or complements (see cross derivative (2)). When we allow for an interaction between early and late investments, we find that in both samples the coefficient on the interaction term is significantly negative (at the 1% level), indicating that parents perceive the returns to late investments as less productive if they are preceded by high early investments (columns (1) and (4)). For sample A every three additional hours invested early reduce the returns to 3 h invested late by 10.4%, or −2.8 percentage points of earnings at age 30. In sample B, high early investments reduce the returns to high late investments by 22%, or −7.7 percentage points of future earnings. Next we investigate whether parents perceive investments as more productive if the initial human capital of the child is high (see cross derivative (3)). In sample A, we find that neither early nor late investments are perceived as more productive if the child in the hypothetical scenario has a high level of initial human capital (column (2)). In sample B, parents perceive early investments as more productive and late investments as less productive if the initial human capital level of the child is high (column (5)). When we simultaneously control for all interaction terms we obtain similar results (columns (3) and (6)). Table 4. Determinants of perceived log earnings at age 30 (2). Dependent variable: Perceived log earnings at age 30    sample A    sample B  Early investmentsa  0.168***  0.149***  0.163***    0.138***  0.090***  0.129***    (0.009)  (0.009)  (0.010)    (0.004)  (0.004)  (0.005)  Late investmentsb  0.268***  0.257***  0.271***    0.353***  0.325***  0.364***    (0.012)  (0.011)  (0.013)    (0.007)  (0.007)  (0.009)  High human capitalc  0.185***  0.183***  0.183***    0.288***  0.288***  0.288***    (0.010)  (0.012)  (0.012)    (0.006)  (0.008)  (0.008)  Early × Late  −0.028**    −0.027**    −0.077***    −0.077***    (0.011)    (0.011)    (0.006)    (0.006)  Early × High HC    0.011  0.011      0.018***  0.018***      (0.008)  (0.008)      (0.005)  (0.005)  Late × High HC    −0.006  −0.006      −0.019***  −0.019***      (0.010)  (0.010)      (0.006)  (0.006)  Parent fixed effects  Yes  Yes  Yes    Yes  Yes  Yes  Observations  4069  4069  4069    16251  16251  16251  R2  0.827  0.827  0.827    0.784  0.782  0.784  Dependent variable: Perceived log earnings at age 30    sample A    sample B  Early investmentsa  0.168***  0.149***  0.163***    0.138***  0.090***  0.129***    (0.009)  (0.009)  (0.010)    (0.004)  (0.004)  (0.005)  Late investmentsb  0.268***  0.257***  0.271***    0.353***  0.325***  0.364***    (0.012)  (0.011)  (0.013)    (0.007)  (0.007)  (0.009)  High human capitalc  0.185***  0.183***  0.183***    0.288***  0.288***  0.288***    (0.010)  (0.012)  (0.012)    (0.006)  (0.008)  (0.008)  Early × Late  −0.028**    −0.027**    −0.077***    −0.077***    (0.011)    (0.011)    (0.006)    (0.006)  Early × High HC    0.011  0.011      0.018***  0.018***      (0.008)  (0.008)      (0.005)  (0.005)  Late × High HC    −0.006  −0.006      −0.019***  −0.019***      (0.010)  (0.010)      (0.006)  (0.006)  Parent fixed effects  Yes  Yes  Yes    Yes  Yes  Yes  Observations  4069  4069  4069    16251  16251  16251  R2  0.827  0.827  0.827    0.784  0.782  0.784  Notes: Standard errors in parentheses. Standard errors are clustered at the parent level. For each sample, the regressions are performed using the parents’ responses to all eight hypothetical investment scenarios. a. Dummy variable for high parental time investments in the early period; b. Dummy variable for high parental time investments in the late period; c. Dummy variable that equals 1 if the child in the scenario has high initial human capital (High HC). **p < 0.05; ***p < 0.01. View Large Table 4. Determinants of perceived log earnings at age 30 (2). Dependent variable: Perceived log earnings at age 30    sample A    sample B  Early investmentsa  0.168***  0.149***  0.163***    0.138***  0.090***  0.129***    (0.009)  (0.009)  (0.010)    (0.004)  (0.004)  (0.005)  Late investmentsb  0.268***  0.257***  0.271***    0.353***  0.325***  0.364***    (0.012)  (0.011)  (0.013)    (0.007)  (0.007)  (0.009)  High human capitalc  0.185***  0.183***  0.183***    0.288***  0.288***  0.288***    (0.010)  (0.012)  (0.012)    (0.006)  (0.008)  (0.008)  Early × Late  −0.028**    −0.027**    −0.077***    −0.077***    (0.011)    (0.011)    (0.006)    (0.006)  Early × High HC    0.011  0.011      0.018***  0.018***      (0.008)  (0.008)      (0.005)  (0.005)  Late × High HC    −0.006  −0.006      −0.019***  −0.019***      (0.010)  (0.010)      (0.006)  (0.006)  Parent fixed effects  Yes  Yes  Yes    Yes  Yes  Yes  Observations  4069  4069  4069    16251  16251  16251  R2  0.827  0.827  0.827    0.784  0.782  0.784  Dependent variable: Perceived log earnings at age 30    sample A    sample B  Early investmentsa  0.168***  0.149***  0.163***    0.138***  0.090***  0.129***    (0.009)  (0.009)  (0.010)    (0.004)  (0.004)  (0.005)  Late investmentsb  0.268***  0.257***  0.271***    0.353***  0.325***  0.364***    (0.012)  (0.011)  (0.013)    (0.007)  (0.007)  (0.009)  High human capitalc  0.185***  0.183***  0.183***    0.288***  0.288***  0.288***    (0.010)  (0.012)  (0.012)    (0.006)  (0.008)  (0.008)  Early × Late  −0.028**    −0.027**    −0.077***    −0.077***    (0.011)    (0.011)    (0.006)    (0.006)  Early × High HC    0.011  0.011      0.018***  0.018***      (0.008)  (0.008)      (0.005)  (0.005)  Late × High HC    −0.006  −0.006      −0.019***  −0.019***      (0.010)  (0.010)      (0.006)  (0.006)  Parent fixed effects  Yes  Yes  Yes    Yes  Yes  Yes  Observations  4069  4069  4069    16251  16251  16251  R2  0.827  0.827  0.827    0.784  0.782  0.784  Notes: Standard errors in parentheses. Standard errors are clustered at the parent level. For each sample, the regressions are performed using the parents’ responses to all eight hypothetical investment scenarios. a. Dummy variable for high parental time investments in the early period; b. Dummy variable for high parental time investments in the late period; c. Dummy variable that equals 1 if the child in the scenario has high initial human capital (High HC). **p < 0.05; ***p < 0.01. View Large Overall, parents seem to believe that the late investments in the scenarios have a greater payoff compared to the early investments in the scenarios and that foregone early investments can at least partially be made up for during later time periods due to their perceived substitutability with late investments. We note that we find very similar patterns when we use the perceived probability of graduating from university as the main outcome variable (see Table A.7 in the Appendix  A). Again parents perceive the returns to later investments to be significantly higher than the returns to earlier investments. We also find a negative but insignificant coefficient on the interaction term between early and late investments. Since parental beliefs about the returns to investments in different time periods are likely to determine the inter-temporal allocation of parental investments, this raises the question of whether parents might misperceive the optimal timing of investments that could prevent parents from optimally investing in their children. We provide a discussion of this question in Section 6. 4.2. Heterogeneity in Perceived Returns The estimated regression coefficients mask a substantial degree of heterogeneity across respondents. In the following, we separately calculate the perceived returns to the different inputs for each respondent i. To obtain a measure of individual perceived returns to early investments, $$r_{i}^{ {\mathit {early}}}$$, we first calculate the perceived differences in log earnings by comparing a parent’s responses in the four scenarios in which early investments are high to the parent’s responses in the corresponding four scenarios in which early investments are low. We average across these differences to obtain the average perceived return to early investments:   \begin{multline*} r_{i}^{ {\mathit {early}}}=\\ \frac{(\log y_{3i}- \log y_{1i})+(\log y_{4i}- \log y_{2i})\!+\!(\log y_{7i}- \log y_{5i})+(\log y_{8i}- \log y_{6i})}{4} \end{multline*} We apply the same procedure to calculate individual perceived returns to late investments, which we denote as $$r_{i}^{ {\mathit {late}}}$$:28  \begin{multline*} r_{i}^{ {\mathit {late}}}=\\ \frac{(\log y_{2i}- \log y_{1i})+(\log y_{4i}- \log y_{3i})\!+\!(\log y_{6i}- \log y_{5i})+(\log y_{8i}- \log y_{7i})}{4}. \end{multline*} Moreover, we also calculate the perceived return to high initial human capital by averaging across the following differences:   \begin{multline*} r_{i}^{HC}=\\ \frac{(\log y_{5i}- \log y_{1i})+(\log y_{6i}- \log y_{2i})\!+\!(\log y_{7i}- \log y_{3i})+(\log y_{8i}- \log y_{4i})}{4}. \end{multline*} Figure 2 plots the cumulative distribution of perceived returns to early and late investments separately for sample A and sample B respondents. The figure exhibits a high degree of heterogeneity in perceived returns in both samples. It is also visible that the distribution of perceived returns to early investments contains lower values than the distribution of perceived returns to late investments, indicating that parents perceive the early investments in the scenarios to be less productive than the late investments. In both samples, a Kolmogorov–Smirnov test for equality of distributions rejects the null of having equal distributions (p-value = 0.00). Figure A.1 in the Appendix  A shows the joint distribution of perceived returns to both early and late investments separately for each sample. Although there are some parents who perceive the early investments in the scenarios to be more productive than the late investments, most parents perceive the late investments as more productive. Figure 2. View largeDownload slide Cumulative distribution of individual perceived returns. This figure shows the cumulative distribution of individual perceived returns to early and late investments separately for each sample. In both samples, a Kolmogorov–Smirnov test for equality of distributions rejects the null of having equal distributions (p-value = 0.00). Figure 2. View largeDownload slide Cumulative distribution of individual perceived returns. This figure shows the cumulative distribution of individual perceived returns to early and late investments separately for each sample. In both samples, a Kolmogorov–Smirnov test for equality of distributions rejects the null of having equal distributions (p-value = 0.00). Next we investigate whether the perceived returns to the different inputs vary with the characteristics of the respondent. The results of this analysis are presented in Table 5, separately for sample A and sample B. We are specifically interested in which characteristics predict the perceived returns to high initial human capital (columns (1) and (5)), the perceived returns to early investments (columns (2) and (6)), the perceived returns to late investments (columns (3) and (7)), and the ratio of perceived returns to early versus late investments (columns (4) and (8)).29 Table 5. Determinants of perceived returns.   sample A    sample B    HC  Early  Late  Ratio    HC  Early  Late  Ratio  2nd income quartile  0.034  0.019  0.007  0.131    0.023  −0.013  −0.013  −0.059*    (0.024)  (0.022)  (0.028)  (0.211)    (0.018)  (0.009)  (0.017)  (0.034)  3rd income quartile  0.020  0.061**  0.060*  −0.025    0.049**  0.018*  0.013  0.038    (0.029)  (0.026)  (0.033)  (0.249)    (0.020)  (0.010)  (0.019)  (0.036)  4th income quartile  0.073**  0.056*  0.056  0.346    0.072***  0.023**  0.001  0.037    (0.034)  (0.031)  (0.039)  (0.295)    (0.019)  (0.010)  (0.018)  (0.035)  University graduate  0.007  0.016  −0.027  0.052    0.027*  0.005  −0.016  0.046*    (0.018)  (0.016)  (0.021)  (0.156)    (0.014)  (0.007)  (0.013)  (0.026)  Number of children  −0.007  0.007  0.014  −0.125    −0.004  −0.006  −0.004  −0.010    (0.010)  (0.009)  (0.012)  (0.088)    (0.007)  (0.004)  (0.007)  (0.014)  Female respondent  0.063***  0.010  0.019  −0.010    0.055***  −0.009  0.025*  −0.099***    (0.024)  (0.022)  (0.028)  (0.212)    (0.015)  (0.008)  (0.014)  (0.028)  Single parent  −0.039  −0.007  0.031  −0.124    −0.010  0.001  −0.005  −0.011    (0.028)  (0.025)  (0.032)  (0.240)    (0.019)  (0.010)  (0.019)  (0.036)  Age of child  0.004*  −0.000  −0.004  0.005              (0.002)  (0.002)  (0.003)  (0.020)            Age of parent            0.002**  0.000  −0.001  0.000              (0.001)  (0.001)  (0.001)  (0.002)  Age oldest child            −0.001  −0.001  −0.000  0.001              (0.002)  (0.001)  (0.002)  (0.004)  Female childa            0.006  −0.002  −0.016  −0.012              (0.014)  (0.007)  (0.013)  (0.026)  Constant  0.075  0.132***  0.264***  1.133***    0.098*  0.118***  0.401***  0.412***    (0.046)  (0.042)  (0.053)  (0.404)    (0.050)  (0.026)  (0.048)  (0.094)  Sample mean  0.19  0.18  0.27  1.04    0.29  0.1  0.32  0.38  Observations  470  474  474  449    1682  1682  1682  1553  R2  0.044  0.025  0.021  0.012    0.033  0.019  0.007  0.023    sample A    sample B    HC  Early  Late  Ratio    HC  Early  Late  Ratio  2nd income quartile  0.034  0.019  0.007  0.131    0.023  −0.013  −0.013  −0.059*    (0.024)  (0.022)  (0.028)  (0.211)    (0.018)  (0.009)  (0.017)  (0.034)  3rd income quartile  0.020  0.061**  0.060*  −0.025    0.049**  0.018*  0.013  0.038    (0.029)  (0.026)  (0.033)  (0.249)    (0.020)  (0.010)  (0.019)  (0.036)  4th income quartile  0.073**  0.056*  0.056  0.346    0.072***  0.023**  0.001  0.037    (0.034)  (0.031)  (0.039)  (0.295)    (0.019)  (0.010)  (0.018)  (0.035)  University graduate  0.007  0.016  −0.027  0.052    0.027*  0.005  −0.016  0.046*    (0.018)  (0.016)  (0.021)  (0.156)    (0.014)  (0.007)  (0.013)  (0.026)  Number of children  −0.007  0.007  0.014  −0.125    −0.004  −0.006  −0.004  −0.010    (0.010)  (0.009)  (0.012)  (0.088)    (0.007)  (0.004)  (0.007)  (0.014)  Female respondent  0.063***  0.010  0.019  −0.010    0.055***  −0.009  0.025*  −0.099***    (0.024)  (0.022)  (0.028)  (0.212)    (0.015)  (0.008)  (0.014)  (0.028)  Single parent  −0.039  −0.007  0.031  −0.124    −0.010  0.001  −0.005  −0.011    (0.028)  (0.025)  (0.032)  (0.240)    (0.019)  (0.010)  (0.019)  (0.036)  Age of child  0.004*  −0.000  −0.004  0.005              (0.002)  (0.002)  (0.003)  (0.020)            Age of parent            0.002**  0.000  −0.001  0.000              (0.001)  (0.001)  (0.001)  (0.002)  Age oldest child            −0.001  −0.001  −0.000  0.001              (0.002)  (0.001)  (0.002)  (0.004)  Female childa            0.006  −0.002  −0.016  −0.012              (0.014)  (0.007)  (0.013)  (0.026)  Constant  0.075  0.132***  0.264***  1.133***    0.098*  0.118***  0.401***  0.412***    (0.046)  (0.042)  (0.053)  (0.404)    (0.050)  (0.026)  (0.048)  (0.094)  Sample mean  0.19  0.18  0.27  1.04    0.29  0.1  0.32  0.38  Observations  470  474  474  449    1682  1682  1682  1553  R2  0.044  0.025  0.021  0.012    0.033  0.019  0.007  0.023  Notes: Standard errors in parentheses. The dependent variables (in order) are the individual perceived returns to high initial human capital (HC), early and late investments, and the ratio of early/late, that is, the relative importance of early investments. For sample B, we also control for the order in which the survey modules were presented. a. It refers to whether the child in the scenario is female (for sample B only). *p < 0.10; **p < 0.05; ***p < 0.01. View Large Table 5. Determinants of perceived returns.   sample A    sample B    HC  Early  Late  Ratio    HC  Early  Late  Ratio  2nd income quartile  0.034  0.019  0.007  0.131    0.023  −0.013  −0.013  −0.059*    (0.024)  (0.022)  (0.028)  (0.211)    (0.018)  (0.009)  (0.017)  (0.034)  3rd income quartile  0.020  0.061**  0.060*  −0.025    0.049**  0.018*  0.013  0.038    (0.029)  (0.026)  (0.033)  (0.249)    (0.020)  (0.010)  (0.019)  (0.036)  4th income quartile  0.073**  0.056*  0.056  0.346    0.072***  0.023**  0.001  0.037    (0.034)  (0.031)  (0.039)  (0.295)    (0.019)  (0.010)  (0.018)  (0.035)  University graduate  0.007  0.016  −0.027  0.052    0.027*  0.005  −0.016  0.046*    (0.018)  (0.016)  (0.021)  (0.156)    (0.014)  (0.007)  (0.013)  (0.026)  Number of children  −0.007  0.007  0.014  −0.125    −0.004  −0.006  −0.004  −0.010    (0.010)  (0.009)  (0.012)  (0.088)    (0.007)  (0.004)  (0.007)  (0.014)  Female respondent  0.063***  0.010  0.019  −0.010    0.055***  −0.009  0.025*  −0.099***    (0.024)  (0.022)  (0.028)  (0.212)    (0.015)  (0.008)  (0.014)  (0.028)  Single parent  −0.039  −0.007  0.031  −0.124    −0.010  0.001  −0.005  −0.011    (0.028)  (0.025)  (0.032)  (0.240)    (0.019)  (0.010)  (0.019)  (0.036)  Age of child  0.004*  −0.000  −0.004  0.005              (0.002)  (0.002)  (0.003)  (0.020)            Age of parent            0.002**  0.000  −0.001  0.000              (0.001)  (0.001)  (0.001)  (0.002)  Age oldest child            −0.001  −0.001  −0.000  0.001              (0.002)  (0.001)  (0.002)  (0.004)  Female childa            0.006  −0.002  −0.016  −0.012              (0.014)  (0.007)  (0.013)  (0.026)  Constant  0.075  0.132***  0.264***  1.133***    0.098*  0.118***  0.401***  0.412***    (0.046)  (0.042)  (0.053)  (0.404)    (0.050)  (0.026)  (0.048)  (0.094)  Sample mean  0.19  0.18  0.27  1.04    0.29  0.1  0.32  0.38  Observations  470  474  474  449    1682  1682  1682  1553  R2  0.044  0.025  0.021  0.012    0.033  0.019  0.007  0.023    sample A    sample B    HC  Early  Late  Ratio    HC  Early  Late  Ratio  2nd income quartile  0.034  0.019  0.007  0.131    0.023  −0.013  −0.013  −0.059*    (0.024)  (0.022)  (0.028)  (0.211)    (0.018)  (0.009)  (0.017)  (0.034)  3rd income quartile  0.020  0.061**  0.060*  −0.025    0.049**  0.018*  0.013  0.038    (0.029)  (0.026)  (0.033)  (0.249)    (0.020)  (0.010)  (0.019)  (0.036)  4th income quartile  0.073**  0.056*  0.056  0.346    0.072***  0.023**  0.001  0.037    (0.034)  (0.031)  (0.039)  (0.295)    (0.019)  (0.010)  (0.018)  (0.035)  University graduate  0.007  0.016  −0.027  0.052    0.027*  0.005  −0.016  0.046*    (0.018)  (0.016)  (0.021)  (0.156)    (0.014)  (0.007)  (0.013)  (0.026)  Number of children  −0.007  0.007  0.014  −0.125    −0.004  −0.006  −0.004  −0.010    (0.010)  (0.009)  (0.012)  (0.088)    (0.007)  (0.004)  (0.007)  (0.014)  Female respondent  0.063***  0.010  0.019  −0.010    0.055***  −0.009  0.025*  −0.099***    (0.024)  (0.022)  (0.028)  (0.212)    (0.015)  (0.008)  (0.014)  (0.028)  Single parent  −0.039  −0.007  0.031  −0.124    −0.010  0.001  −0.005  −0.011    (0.028)  (0.025)  (0.032)  (0.240)    (0.019)  (0.010)  (0.019)  (0.036)  Age of child  0.004*  −0.000  −0.004  0.005              (0.002)  (0.002)  (0.003)  (0.020)            Age of parent            0.002**  0.000  −0.001  0.000              (0.001)  (0.001)  (0.001)  (0.002)  Age oldest child            −0.001  −0.001  −0.000  0.001              (0.002)  (0.001)  (0.002)  (0.004)  Female childa            0.006  −0.002  −0.016  −0.012              (0.014)  (0.007)  (0.013)  (0.026)  Constant  0.075  0.132***  0.264***  1.133***    0.098*  0.118***  0.401***  0.412***    (0.046)  (0.042)  (0.053)  (0.404)    (0.050)  (0.026)  (0.048)  (0.094)  Sample mean  0.19  0.18  0.27  1.04    0.29  0.1  0.32  0.38  Observations  470  474  474  449    1682  1682  1682  1553  R2  0.044  0.025  0.021  0.012    0.033  0.019  0.007  0.023  Notes: Standard errors in parentheses. The dependent variables (in order) are the individual perceived returns to high initial human capital (HC), early and late investments, and the ratio of early/late, that is, the relative importance of early investments. For sample B, we also control for the order in which the survey modules were presented. a. It refers to whether the child in the scenario is female (for sample B only). *p < 0.10; **p < 0.05; ***p < 0.01. View Large For both samples, the results reveal that parents with higher levels of income perceive the returns to high initial human capital and the returns to early investments to be significantly higher.30 In sample A, parents with higher levels of income also perceive the returns to late investments to be higher although the coefficients are less precisely estimated. In sample B, we find no association between parental income and the perceived returns to late investments. When we investigate what predicts the ratio of perceived returns to early versus late investments, we find no clear relationship between parental income and parental beliefs. We do note, however, that respondents with a university degree in sample B perceive the ratio to be higher, that is, they are more likely to believe that early investments matter relatively more compared to late investments. Figures A.2 and A.3 in the Appendix  A visualize the differences in perceived returns by income quartile as well as by parental education.31 Another interesting question is whether the age of the respondent’s own child predicts perceived returns to early and/or late investments. In sample A, we include the age of the target child (i.e., the child for whom the parent completed the survey) as a control variable, and we find no significant association between the age of the child and the perceived returns to early investments, the perceived returns to late investments or the ratio of perceived returns. In sample B, we perform the same analysis this time controlling for the age of the respondent’s oldest child. Again we find similar results, that is, we find no significant association between the age of the oldest child and perceived returns to parental investments in any given time period. We further investigate whether parents differ in their perceptions about the substitutability of the different inputs. For this purpose, we obtain individual measures of perceived substitutability/complementarity and regress them on parental characteristics (see details in Online Appendix F). In sample B we find some evidence that more educated parents perceive investments across periods to be less substitutable indicated by the positive and significant coefficient of the university dummy (see Table F.1 in the Online Appendix F). We do not find any significant associations between household income and the perceived substitutability/complementarity of early and late investments. We also find no significant associations between the socioeconomic background of the respondent and the perceived substitutability/complementarity between investments and the initial human capital of the child. We also investigate heterogeneity in beliefs with regard to the gender of the child in the scenario. Recall that in sample B all parents with daughters are asked about the likely earnings of girls, whereas all parents with sons are asked about the likely earnings of boys. Consistent with the literature that documents a gender gap in earnings (e.g., Altonji and Blank 1999; Bayard et al. 2003; Bertrand 2011), we find that parents who are asked about girls perceive the earnings of the child at age 30 to be lower compared to parents who are asked about boys (see Table 3). Interestingly, we find that parents underestimate the actual gender gap in earnings that we document using the representative sample of 25–34 year old men and women in the Family Resources Survey. Although parents believe that girls will earn 8.3% less than boys at age 30, the true gender gap we find in the FRS data is 21%. One potential reason for this difference is that parents may misperceive the current gender gap in earnings. Alternatively, it may be that parents believe that the gender gap in earnings will diminish over time. The second interesting result that emerges from our data is that although we find differences in the perceived levels of earnings, we do not find that parents perceive the returns to initial human capital or the returns to investments to differ depending on the gender of the child in the scenario (see Table 5). Finally, we can use the responses in sample A to investigate whether parents differ in their beliefs about the returns to additional weekly time investments depending on whether the levels of low and high investments they are presented with are 0 and 3 h or 1 and 4 h.32 As expected, we do find evidence for perceived diminishing returns as parents in the 0–3 group perceive the returns to be higher than parents in the 1–4 group (see Figure A.4 in the Appendix  A). 4.3. Do Perceived Returns Predict Current Parental Investments? In both surveys, we also ask parents to provide information on their current investment decisions. We use this information to investigate whether parental beliefs about the returns to current investments are predictive of parents’ current investment choices while controlling for a range of parent and child characteristics. In sample A, we pool all respondents and regress different measures of current parental time and financial investments on the parents’ perceived returns to one additional hour of weekly time investments in the given time period. We regress parental investments on the perceived returns to early investments if the child of the respondent is in primary school and on the parents’ perceived returns to late investments if the child of the respondent is in secondary school.33 The results are presented in Table 6. Table 6. Beliefs and time investments—sample A. Dependent variable: Reported investment    Weekly time investments  Acti-  Expend-    Total  School  Homework  Stories  Play  vities  iture  Perceived returnst  1470.1***  321.2**  507.4***  227.3**  360.9***  1.8**  115.0**    (346.6)  (160.7)  (127.2)  (101.3)  (128.5)  (0.7)  (55.4)  Age of child  2.0  11.1**  −3.7  −7.1**  −5.6  −0.0  −0.6    (11.5)  (5.3)  (4.1)  (3.3)  (4.2)  (0.0)  (1.8)  Female child  −15.3  −5.8  3.9  −3.5  −7.4  0.2**  13.3*    (46.6)  (21.3)  (16.4)  (13.2)  (17.1)  (0.1)  (7.3)  Log(HH income)  −83.0*  −8.0  −17.0  −17.6  −43.3***  0.1  19.7***    (44.4)  (20.6)  (16.1)  (12.7)  (16.3)  (0.1)  (7.0)  University degree  38.8  25.0  7.8  16.9  −3.9  0.2**  24.1***    (44.0)  (20.1)  (15.8)  (12.7)  (16.2)  (0.1)  (7.0)  Employment  145.2**  27.2  43.2*  13.5  65.1***  −0.0  8.3    (66.4)  (30.5)  (23.7)  (18.9)  (24.4)  (0.1)  (10.5)  Number of children  1.0  7.8  −1.0  −5.8  1.7  0.0  −3.0    (24.2)  (11.3)  (8.7)  (6.9)  (8.8)  (0.1)  (3.9)  Female respondent  120.2**  37.5  48.6**  24.8  33.1  0.0  9.3    (59.7)  (27.6)  (21.8)  (17.4)  (22.0)  (0.1)  (9.7)  Single parent  −40.1  −1.6  −26.5  −15.7  39.1  −0.1  −17.7    (72.6)  (34.0)  (25.6)  (20.9)  (26.3)  (0.1)  (11.3)  Foreign languagea  −146.9  −15.5  −47.7  −64.4**  −51.7  −0.2  −10.2    (106.4)  (47.7)  (36.5)  (29.3)  (38.6)  (0.2)  (16.3)  School fixed effect  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Observations  368  412  412  395  385  461  432  R2  0.159  0.056  0.105  0.326  0.130  0.113  0.156  Dependent variable: Reported investment    Weekly time investments  Acti-  Expend-    Total  School  Homework  Stories  Play  vities  iture  Perceived returnst  1470.1***  321.2**  507.4***  227.3**  360.9***  1.8**  115.0**    (346.6)  (160.7)  (127.2)  (101.3)  (128.5)  (0.7)  (55.4)  Age of child  2.0  11.1**  −3.7  −7.1**  −5.6  −0.0  −0.6    (11.5)  (5.3)  (4.1)  (3.3)  (4.2)  (0.0)  (1.8)  Female child  −15.3  −5.8  3.9  −3.5  −7.4  0.2**  13.3*    (46.6)  (21.3)  (16.4)  (13.2)  (17.1)  (0.1)  (7.3)  Log(HH income)  −83.0*  −8.0  −17.0  −17.6  −43.3***  0.1  19.7***    (44.4)  (20.6)  (16.1)  (12.7)  (16.3)  (0.1)  (7.0)  University degree  38.8  25.0  7.8  16.9  −3.9  0.2**  24.1***    (44.0)  (20.1)  (15.8)  (12.7)  (16.2)  (0.1)  (7.0)  Employment  145.2**  27.2  43.2*  13.5  65.1***  −0.0  8.3    (66.4)  (30.5)  (23.7)  (18.9)  (24.4)  (0.1)  (10.5)  Number of children  1.0  7.8  −1.0  −5.8  1.7  0.0  −3.0    (24.2)  (11.3)  (8.7)  (6.9)  (8.8)  (0.1)  (3.9)  Female respondent  120.2**  37.5  48.6**  24.8  33.1  0.0  9.3    (59.7)  (27.6)  (21.8)  (17.4)  (22.0)  (0.1)  (9.7)  Single parent  −40.1  −1.6  −26.5  −15.7  39.1  −0.1  −17.7    (72.6)  (34.0)  (25.6)  (20.9)  (26.3)  (0.1)  (11.3)  Foreign languagea  −146.9  −15.5  −47.7  −64.4**  −51.7  −0.2  −10.2    (106.4)  (47.7)  (36.5)  (29.3)  (38.6)  (0.2)  (16.3)  School fixed effect  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Observations  368  412  412  395  385  461  432  R2  0.159  0.056  0.105  0.326  0.130  0.113  0.156  Notes: Standard errors in parentheses. The weekly time investments are measured in minutes. Activities is an extracted factor with mean 0 and standard deviation 1 from the activities questionnaie, and Expenditure refers to the total monthly expenditure parents devote to their children. School refers to the time parents spend talking to their child about their experiences at school. Homework refers to the time parents help their child with homework/check workbooks. Stories refers to the time parents spend reading/telling stories and Play refers to the time parents spend playing board/card games. Perceived Returnt refers to the perceived return to 1 h of weekly early investments for parents with primary school children, and to the perceived return to 1 h of weekly late investments for parents with secondary school children. The top and bottom 1% of perceived returns were excluded from the sample. a. Dummy for households speaking a foreign language at home. *p < 0.10; **p < 0.05; ***p < 0.01. View Large Table 6. Beliefs and time investments—sample A. Dependent variable: Reported investment    Weekly time investments  Acti-  Expend-    Total  School  Homework  Stories  Play  vities  iture  Perceived returnst  1470.1***  321.2**  507.4***  227.3**  360.9***  1.8**  115.0**    (346.6)  (160.7)  (127.2)  (101.3)  (128.5)  (0.7)  (55.4)  Age of child  2.0  11.1**  −3.7  −7.1**  −5.6  −0.0  −0.6    (11.5)  (5.3)  (4.1)  (3.3)  (4.2)  (0.0)  (1.8)  Female child  −15.3  −5.8  3.9  −3.5  −7.4  0.2**  13.3*    (46.6)  (21.3)  (16.4)  (13.2)  (17.1)  (0.1)  (7.3)  Log(HH income)  −83.0*  −8.0  −17.0  −17.6  −43.3***  0.1  19.7***    (44.4)  (20.6)  (16.1)  (12.7)  (16.3)  (0.1)  (7.0)  University degree  38.8  25.0  7.8  16.9  −3.9  0.2**  24.1***    (44.0)  (20.1)  (15.8)  (12.7)  (16.2)  (0.1)  (7.0)  Employment  145.2**  27.2  43.2*  13.5  65.1***  −0.0  8.3    (66.4)  (30.5)  (23.7)  (18.9)  (24.4)  (0.1)  (10.5)  Number of children  1.0  7.8  −1.0  −5.8  1.7  0.0  −3.0    (24.2)  (11.3)  (8.7)  (6.9)  (8.8)  (0.1)  (3.9)  Female respondent  120.2**  37.5  48.6**  24.8  33.1  0.0  9.3    (59.7)  (27.6)  (21.8)  (17.4)  (22.0)  (0.1)  (9.7)  Single parent  −40.1  −1.6  −26.5  −15.7  39.1  −0.1  −17.7    (72.6)  (34.0)  (25.6)  (20.9)  (26.3)  (0.1)  (11.3)  Foreign languagea  −146.9  −15.5  −47.7  −64.4**  −51.7  −0.2  −10.2    (106.4)  (47.7)  (36.5)  (29.3)  (38.6)  (0.2)  (16.3)  School fixed effect  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Observations  368  412  412  395  385  461  432  R2  0.159  0.056  0.105  0.326  0.130  0.113  0.156  Dependent variable: Reported investment    Weekly time investments  Acti-  Expend-    Total  School  Homework  Stories  Play  vities  iture  Perceived returnst  1470.1***  321.2**  507.4***  227.3**  360.9***  1.8**  115.0**    (346.6)  (160.7)  (127.2)  (101.3)  (128.5)  (0.7)  (55.4)  Age of child  2.0  11.1**  −3.7  −7.1**  −5.6  −0.0  −0.6    (11.5)  (5.3)  (4.1)  (3.3)  (4.2)  (0.0)  (1.8)  Female child  −15.3  −5.8  3.9  −3.5  −7.4  0.2**  13.3*    (46.6)  (21.3)  (16.4)  (13.2)  (17.1)  (0.1)  (7.3)  Log(HH income)  −83.0*  −8.0  −17.0  −17.6  −43.3***  0.1  19.7***    (44.4)  (20.6)  (16.1)  (12.7)  (16.3)  (0.1)  (7.0)  University degree  38.8  25.0  7.8  16.9  −3.9  0.2**  24.1***    (44.0)  (20.1)  (15.8)  (12.7)  (16.2)  (0.1)  (7.0)  Employment  145.2**  27.2  43.2*  13.5  65.1***  −0.0  8.3    (66.4)  (30.5)  (23.7)  (18.9)  (24.4)  (0.1)  (10.5)  Number of children  1.0  7.8  −1.0  −5.8  1.7  0.0  −3.0    (24.2)  (11.3)  (8.7)  (6.9)  (8.8)  (0.1)  (3.9)  Female respondent  120.2**  37.5  48.6**  24.8  33.1  0.0  9.3    (59.7)  (27.6)  (21.8)  (17.4)  (22.0)  (0.1)  (9.7)  Single parent  −40.1  −1.6  −26.5  −15.7  39.1  −0.1  −17.7    (72.6)  (34.0)  (25.6)  (20.9)  (26.3)  (0.1)  (11.3)  Foreign languagea  −146.9  −15.5  −47.7  −64.4**  −51.7  −0.2  −10.2    (106.4)  (47.7)  (36.5)  (29.3)  (38.6)  (0.2)  (16.3)  School fixed effect  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Observations  368  412  412  395  385  461  432  R2  0.159  0.056  0.105  0.326  0.130  0.113  0.156  Notes: Standard errors in parentheses. The weekly time investments are measured in minutes. Activities is an extracted factor with mean 0 and standard deviation 1 from the activities questionnaie, and Expenditure refers to the total monthly expenditure parents devote to their children. School refers to the time parents spend talking to their child about their experiences at school. Homework refers to the time parents help their child with homework/check workbooks. Stories refers to the time parents spend reading/telling stories and Play refers to the time parents spend playing board/card games. Perceived Returnt refers to the perceived return to 1 h of weekly early investments for parents with primary school children, and to the perceived return to 1 h of weekly late investments for parents with secondary school children. The top and bottom 1% of perceived returns were excluded from the sample. a. Dummy for households speaking a foreign language at home. *p < 0.10; **p < 0.05; ***p < 0.01. View Large Parental beliefs about the returns to investments are associated with the amount of time parents spend talking to their child about school, helping their child with their homework, reading/telling stories to their child, and playing games with the child. More specifically, an increase in the perceived return by 10 percentage points is associated with parents spending 147 min more every week on these activities.34 We also extract the first principal component from the questionnaire that asks parents to report how often they engage in certain less regular activities with their children and regress the extracted factor on perceived returns to weekly time investments (column (6)).35 Again we find a significant positive association between perceived returns and parental investment behavior. Finally, we regress the total monthly expenditures of the parents on the parents’ perceived returns to weekly time investments and we find that an increase in perceived returns by 10 percentage points is associated with parents spending £11.50 more every month (column (7)).36 In sample B, we ask parents to report investments that are specific to their child’s age group (see Section 3.1). We separately regress the investments of parents with young children on the parents’ beliefs about the returns to early investments (see Table 7), and the investments of parents with older children on the parents’ beliefs about the returns to late investments (see Table 8). Again we document that parental beliefs are associated with parental investments. Parents who perceive the returns to early investments to be high are also more likely to spend more time reading to their child and let their child watch less TV. Moreover, parents who perceive the returns to late investments to be high are more likely to engage in different activities with their child (e.g., chat with their child, have meals together), and they are more likely to be interested in their child’s education.37 Table 7. Beliefs and time investments at age 5—sample B.   Read  TV  Park  Perceived returnsta  2.382*  −2.000***  −0.248    (1.261)  (0.611)  (0.215)  Log(HH Income)  0.243  −0.176  0.011    (0.327)  (0.159)  (0.056)  Employed  0.181  0.039  0.127**    (0.377)  (0.183)  (0.064)  University graduate  0.179  0.205  −0.020    (0.366)  (0.177)  (0.063)  Number of children  −0.504***  −0.048  0.021    (0.164)  (0.079)  (0.028)  Female respondent  0.017  −0.041  −0.047    (0.369)  (0.179)  (0.063)  Age of parent  0.017  0.009  −0.007    (0.029)  (0.014)  (0.005)  Single parent  0.461  −0.500*  0.071    (0.560)  (0.272)  (0.096)  Female child  0.290  0.057  −0.038    (0.288)  (0.140)  (0.049)  Order effectb  −0.107  −0.288**  0.031    (0.286)  (0.139)  (0.049)  School fixed effects  Yes  Yes  Yes  Observations  221  221  221  R2  0.191  0.267  0.197    Read  TV  Park  Perceived returnsta  2.382*  −2.000***  −0.248    (1.261)  (0.611)  (0.215)  Log(HH Income)  0.243  −0.176  0.011    (0.327)  (0.159)  (0.056)  Employed  0.181  0.039  0.127**    (0.377)  (0.183)  (0.064)  University graduate  0.179  0.205  −0.020    (0.366)  (0.177)  (0.063)  Number of children  −0.504***  −0.048  0.021    (0.164)  (0.079)  (0.028)  Female respondent  0.017  −0.041  −0.047    (0.369)  (0.179)  (0.063)  Age of parent  0.017  0.009  −0.007    (0.029)  (0.014)  (0.005)  Single parent  0.461  −0.500*  0.071    (0.560)  (0.272)  (0.096)  Female child  0.290  0.057  −0.038    (0.288)  (0.140)  (0.049)  Order effectb  −0.107  −0.288**  0.031    (0.286)  (0.139)  (0.049)  School fixed effects  Yes  Yes  Yes  Observations  221  221  221  R2  0.191  0.267  0.197  Notes: Standard errors in parentheses. “Read” refers to the number of days during the past week the parent has read to the child, “TV” refers to the number of hours the child watches TV during a typical day, and “Park” indicates whether the child has been taken to the park or playground during the past week. The top and bottom 1% of perceived returns are excluded from the sample. a. Perceived return to investments in children at age 5; b. Dummy variable that takes the value 1 if respondents first saw the hypothetical scenarios before reporting own investments (and zero otherwise). *p < 0.10; ** p < 0.05; ***p < 0.01. View Large Table 7. Beliefs and time investments at age 5—sample B.   Read  TV  Park  Perceived returnsta  2.382*  −2.000***  −0.248    (1.261)  (0.611)  (0.215)  Log(HH Income)  0.243  −0.176  0.011    (0.327)  (0.159)  (0.056)  Employed  0.181  0.039  0.127**    (0.377)  (0.183)  (0.064)  University graduate  0.179  0.205  −0.020    (0.366)  (0.177)  (0.063)  Number of children  −0.504***  −0.048  0.021    (0.164)  (0.079)  (0.028)  Female respondent  0.017  −0.041  −0.047    (0.369)  (0.179)  (0.063)  Age of parent  0.017  0.009  −0.007    (0.029)  (0.014)  (0.005)  Single parent  0.461  −0.500*  0.071    (0.560)  (0.272)  (0.096)  Female child  0.290  0.057  −0.038    (0.288)  (0.140)  (0.049)  Order effectb  −0.107  −0.288**  0.031    (0.286)  (0.139)  (0.049)  School fixed effects  Yes  Yes  Yes  Observations  221  221  221  R2  0.191  0.267  0.197    Read  TV  Park  Perceived returnsta  2.382*  −2.000***  −0.248    (1.261)  (0.611)  (0.215)  Log(HH Income)  0.243  −0.176  0.011    (0.327)  (0.159)  (0.056)  Employed  0.181  0.039  0.127**    (0.377)  (0.183)  (0.064)  University graduate  0.179  0.205  −0.020    (0.366)  (0.177)  (0.063)  Number of children  −0.504***  −0.048  0.021    (0.164)  (0.079)  (0.028)  Female respondent  0.017  −0.041  −0.047    (0.369)  (0.179)  (0.063)  Age of parent  0.017  0.009  −0.007    (0.029)  (0.014)  (0.005)  Single parent  0.461  −0.500*  0.071    (0.560)  (0.272)  (0.096)  Female child  0.290  0.057  −0.038    (0.288)  (0.140)  (0.049)  Order effectb  −0.107  −0.288**  0.031    (0.286)  (0.139)  (0.049)  School fixed effects  Yes  Yes  Yes  Observations  221  221  221  R2  0.191  0.267  0.197  Notes: Standard errors in parentheses. “Read” refers to the number of days during the past week the parent has read to the child, “TV” refers to the number of hours the child watches TV during a typical day, and “Park” indicates whether the child has been taken to the park or playground during the past week. The top and bottom 1% of perceived returns are excluded from the sample. a. Perceived return to investments in children at age 5; b. Dummy variable that takes the value 1 if respondents first saw the hypothetical scenarios before reporting own investments (and zero otherwise). *p < 0.10; ** p < 0.05; ***p < 0.01. View Large Table 8. Beliefs and time investments at age 10—sample B.   Walks  Meals  Chat  Interest  Time  Perceived returnsta  0.136  0.325***  0.246***  0.469***  0.510***    (0.115)  (0.099)  (0.071)  (0.079)  (0.100)  Log(HH Income)  −0.000  0.087**  0.105***  −0.021  −0.042    (0.047)  (0.040)  (0.029)  (0.032)  (0.041)  Employed  0.063  0.018  −0.010  −0.099**  −0.085    (0.069)  (0.059)  (0.042)  (0.047)  (0.059)  University graduate  −0.058  −0.032  −0.029  0.067*  −0.002    (0.058)  (0.049)  (0.035)  (0.040)  (0.050)  Number of children  0.021  0.003  −0.030*  −0.037*  −0.076***    (0.027)  (0.024)  (0.017)  (0.019)  (0.024)  Female respondent  0.129**  0.290***  0.220***  −0.042  0.206***    (0.059)  (0.051)  (0.036)  (0.041)  (0.051)  Age of respondent  0.008**  0.007*  0.005*  0.007**  0.006*    (0.004)  (0.003)  (0.002)  (0.003)  (0.004)  Single parent  0.003  0.003  −0.053  −0.081  −0.128*    (0.076)  (0.065)  (0.047)  (0.052)  (0.066)  Female child  0.017  −0.068  0.002  −0.032  0.080    (0.067)  (0.058)  (0.042)  (0.046)  (0.058)  Order effectb  0.166***  0.112***  0.095***  −0.050  0.143***    (0.050)  (0.043)  (0.031)  (0.034)  (0.043)  School fixed effects  Yes  Yes  Yes  Yes  Yes  Observations  1432  1433  1433  1433  1433  R2  0.047  0.069  0.071  0.074  0.080    Walks  Meals  Chat  Interest  Time  Perceived returnsta  0.136  0.325***  0.246***  0.469***  0.510***    (0.115)  (0.099)  (0.071)  (0.079)  (0.100)  Log(HH Income)  −0.000  0.087**  0.105***  −0.021  −0.042    (0.047)  (0.040)  (0.029)  (0.032)  (0.041)  Employed  0.063  0.018  −0.010  −0.099**  −0.085    (0.069)  (0.059)  (0.042)  (0.047)  (0.059)  University graduate  −0.058  −0.032  −0.029  0.067*  −0.002    (0.058)  (0.049)  (0.035)  (0.040)  (0.050)  Number of children  0.021  0.003  −0.030*  −0.037*  −0.076***    (0.027)  (0.024)  (0.017)  (0.019)  (0.024)  Female respondent  0.129**  0.290***  0.220***  −0.042  0.206***    (0.059)  (0.051)  (0.036)  (0.041)  (0.051)  Age of respondent  0.008**  0.007*  0.005*  0.007**  0.006*    (0.004)  (0.003)  (0.002)  (0.003)  (0.004)  Single parent  0.003  0.003  −0.053  −0.081  −0.128*    (0.076)  (0.065)  (0.047)  (0.052)  (0.066)  Female child  0.017  −0.068  0.002  −0.032  0.080    (0.067)  (0.058)  (0.042)  (0.046)  (0.058)  Order effectb  0.166***  0.112***  0.095***  −0.050  0.143***    (0.050)  (0.043)  (0.031)  (0.034)  (0.043)  School fixed effects  Yes  Yes  Yes  Yes  Yes  Observations  1432  1433  1433  1433  1433  R2  0.047  0.069  0.071  0.074  0.080  Notes: Standard errors in parentheses. The dependent variables are measured on a 5-point Likert scale. “Walks” refers to going out for walks together, “Meals” to having breakfast or tea together, “Chat” to having a chat or talk with the child (for more than 5 min), “Interest” to how interested or concerned the parent is interested in the child’s education, and “Time” to the time the parent spends talking to the child each day. The top and bottom 1% of perceived returns are excluded from the sample. a. Perceived return to investments in children at age 10; b. Dummy variable that takes the value 1 if respondents first saw the hypothetical scenarios before reporting own investments (and zero otherwise). *p < 0.10; **p < 0.05; ***p < 0.01. View Large Table 8. Beliefs and time investments at age 10—sample B.   Walks  Meals  Chat  Interest  Time  Perceived returnsta  0.136  0.325***  0.246***  0.469***  0.510***    (0.115)  (0.099)  (0.071)  (0.079)  (0.100)  Log(HH Income)  −0.000  0.087**  0.105***  −0.021  −0.042    (0.047)  (0.040)  (0.029)  (0.032)  (0.041)  Employed  0.063  0.018  −0.010  −0.099**  −0.085    (0.069)  (0.059)  (0.042)  (0.047)  (0.059)  University graduate  −0.058  −0.032  −0.029  0.067*  −0.002    (0.058)  (0.049)  (0.035)  (0.040)  (0.050)  Number of children  0.021  0.003  −0.030*  −0.037*  −0.076***    (0.027)  (0.024)  (0.017)  (0.019)  (0.024)  Female respondent  0.129**  0.290***  0.220***  −0.042  0.206***    (0.059)  (0.051)  (0.036)  (0.041)  (0.051)  Age of respondent  0.008**  0.007*  0.005*  0.007**  0.006*    (0.004)  (0.003)  (0.002)  (0.003)  (0.004)  Single parent  0.003  0.003  −0.053  −0.081  −0.128*    (0.076)  (0.065)  (0.047)  (0.052)  (0.066)  Female child  0.017  −0.068  0.002  −0.032  0.080    (0.067)  (0.058)  (0.042)  (0.046)  (0.058)  Order effectb  0.166***  0.112***  0.095***  −0.050  0.143***    (0.050)  (0.043)  (0.031)  (0.034)  (0.043)  School fixed effects  Yes  Yes  Yes  Yes  Yes  Observations  1432  1433  1433  1433  1433  R2  0.047  0.069  0.071  0.074  0.080    Walks  Meals  Chat  Interest  Time  Perceived returnsta  0.136  0.325***  0.246***  0.469***  0.510***    (0.115)  (0.099)  (0.071)  (0.079)  (0.100)  Log(HH Income)  −0.000  0.087**  0.105***  −0.021  −0.042    (0.047)  (0.040)  (0.029)  (0.032)  (0.041)  Employed  0.063  0.018  −0.010  −0.099**  −0.085    (0.069)  (0.059)  (0.042)  (0.047)  (0.059)  University graduate  −0.058  −0.032  −0.029  0.067*  −0.002    (0.058)  (0.049)  (0.035)  (0.040)  (0.050)  Number of children  0.021  0.003  −0.030*  −0.037*  −0.076***    (0.027)  (0.024)  (0.017)  (0.019)  (0.024)  Female respondent  0.129**  0.290***  0.220***  −0.042  0.206***    (0.059)  (0.051)  (0.036)  (0.041)  (0.051)  Age of respondent  0.008**  0.007*  0.005*  0.007**  0.006*    (0.004)  (0.003)  (0.002)  (0.003)  (0.004)  Single parent  0.003  0.003  −0.053  −0.081  −0.128*    (0.076)  (0.065)  (0.047)  (0.052)  (0.066)  Female child  0.017  −0.068  0.002  −0.032  0.080    (0.067)  (0.058)  (0.042)  (0.046)  (0.058)  Order effectb  0.166***  0.112***  0.095***  −0.050  0.143***    (0.050)  (0.043)  (0.031)  (0.034)  (0.043)  School fixed effects  Yes  Yes  Yes  Yes  Yes  Observations  1432  1433  1433  1433  1433  R2  0.047  0.069  0.071  0.074  0.080  Notes: Standard errors in parentheses. The dependent variables are measured on a 5-point Likert scale. “Walks” refers to going out for walks together, “Meals” to having breakfast or tea together, “Chat” to having a chat or talk with the child (for more than 5 min), “Interest” to how interested or concerned the parent is interested in the child’s education, and “Time” to the time the parent spends talking to the child each day. The top and bottom 1% of perceived returns are excluded from the sample. a. Perceived return to investments in children at age 10; b. Dummy variable that takes the value 1 if respondents first saw the hypothetical scenarios before reporting own investments (and zero otherwise). *p < 0.10; **p < 0.05; ***p < 0.01. View Large Overall, the parents’ perceived returns to parental investments, which we elicit with the help of the hypothetical investment scenarios, are predictive of the investments parents report to make. Although this evidence is of a correlational nature, the results are consistent with a model in which parents’ investment choices are influenced by parental beliefs about the productivity of investments.38 Combining the findings that parental beliefs about returns to investments are positively correlated with household income as well as with actual investments provides suggestive evidence that beliefs about returns to investments could be contributing to the intergenerational persistence in earnings, which is particularly high in the United Kingdom compared to other developed countries (Corak 2013). 5. Supplementary Measures of Parental Beliefs In addition to using hypothetical scenarios to elicit parental beliefs about the production technology, we also administer two supplementary surveys in sample A, which allow us to shed further light on why parents might differ in their beliefs about the productivity of parental investments. First, we present parents with a series of items that pertain to the malleability of children’s skills through the home environment, and ask parents to rate these items on a Likert-type scale (e.g., “My child develops at his/her own pace and there is not much I can do about that”).39 We use this information to investigate whether parents who believe that the development of children’s skills cannot be affected through the home environment are also more likely to perceive the returns to parental investments to be low. Second, we elicit parents’ beliefs about the capability of their child to acquire different skills. More specifically, we ask parents to state how likely it is that their child can learn how to (i) speak a new foreign language, (ii) program a software, and (iii) manage a company (over the course of their lives). Since we are interested in parental beliefs about the predisposition of their child to acquire a specific skill (rather than the availability of resources that might be necessary to acquire the skill), we make it explicit that parents should imagine a situation in which their child is provided with maximum support.40 We use this information to explore whether parents who believe that their children do not have the capabilities to acquire different skills, even if they are provided with maximum support, are also less likely to believe that the returns to parental investments are high. We extract factors from the parents’ responses to each supplementary questionnaire.41 Table 9 shows the Spearman rank correlations between these two measures and the parents’ perceived returns to early and late investments (see Section 4.2). As we would expect, the parental belief measures are positively correlated. In particular, parents who believe that their own children’s skills are malleable through the home environment are also more likely to perceive the returns to both early and late investments to be high (significant at the 1% level). Moreover, parents who believe their children are likely to acquire new skills given they are provided with maximum support are also more likely to believe that parental investments pay off, though the correlations are less strong. Table 9. Spearman rank correlations between different measures.   Early  Late  Malleability  Capability  Perceived returns early  1        Perceived returns late  0.379***  1      Beliefs about malleability of skills  0.150***  0.129***  1    Beliefs about capability  0.092**  0.023  0.108**  1    Early  Late  Malleability  Capability  Perceived returns early  1        Perceived returns late  0.379***  1      Beliefs about malleability of skills  0.150***  0.129***  1    Beliefs about capability  0.092**  0.023  0.108**  1  Notes: **p < 0.05; ***p < 0.01. View Large Table 9. Spearman rank correlations between different measures.   Early  Late  Malleability  Capability  Perceived returns early  1        Perceived returns late  0.379***  1      Beliefs about malleability of skills  0.150***  0.129***  1    Beliefs about capability  0.092**  0.023  0.108**  1    Early  Late  Malleability  Capability  Perceived returns early  1        Perceived returns late  0.379***  1      Beliefs about malleability of skills  0.150***  0.129***  1    Beliefs about capability  0.092**  0.023  0.108**  1  Notes: **p < 0.05; ***p < 0.01. View Large There is also a substantial degree of heterogeneity in individual responses, and this heterogeneity seems to be systematically related to the socioeconomic characteristics of the respondent. In particular, parents with lower levels of income are less likely to believe that their children’s skills are malleable through the home environment. The extracted factor has a value of −0.1 for parents with below median income, whereas it has a value of 0.25 for parents with above median income.42 The differences are even more pronounced when we compare parents in the bottom and the top income quartile. We illustrate these differences graphically in Panel A of Figure 3.43 These results are consistent with the findings in the literature that document that parents with lower socioeconomic status have a lower locus of control (Becker et al. 2012). Similarly, parents with lower income are less likely to believe that their children can acquire skills given they are provided with maximum support. For parents with below median income the extracted factor from the capabilities questionnaire has a value of −0.12, compared to a value of 0.29 for parents with above median income.44 Again we illustrate the relationship graphically by comparing bottom and top income quartile respondents, for whom the differences are even more extreme (Panel (b) of Figure 3).45 These results are consistent with the findings in Section 4 in which we document socioeconomic differences in perceived returns to parental investments that we elicit with the help of the hypothetical investment scenarios.46 Figure 3. View largeDownload slide Perceived malleability of skills and capabilities of children by income quartile. Bottom quartile refers to the parent being in the bottom quartile of the household income distribution, whereas top quartile refers to the parent being in the top income quartile. Panel (a) shows the distribution of the extracted factor from the beliefs about malleability questionnaire, whereas Panel (b) shows the distribution of the extracted factor from the beliefs about capability questionnaire (see Online Appendix B for a list of all questions). Figure 3. View largeDownload slide Perceived malleability of skills and capabilities of children by income quartile. Bottom quartile refers to the parent being in the bottom quartile of the household income distribution, whereas top quartile refers to the parent being in the top income quartile. Panel (a) shows the distribution of the extracted factor from the beliefs about malleability questionnaire, whereas Panel (b) shows the distribution of the extracted factor from the beliefs about capability questionnaire (see Online Appendix B for a list of all questions). Figure A.1. View largeDownload slide Distribution of individual perceived returns. This figure shows the joint distributions of individual perceived returns to early and late investments. The left panels show contour plots whereas the right panels show density distributions. Figure A.1. View largeDownload slide Distribution of individual perceived returns. This figure shows the joint distributions of individual perceived returns to early and late investments. The left panels show contour plots whereas the right panels show density distributions. Figure A.2. View largeDownload slide Distribution of perceived returns by income quartile. Panels show kernel densities of perceived returns to high human capital, high early investments, high late investments, and perceived ratio of returns. Top panels show results for sample A, bottom panels show results for sample B. All densities are depicted separately for bottom and top income quartile respondents. Reported p-values are from Kolmogorov–Smirnov tests for equality of distributions. Figure A.2. View largeDownload slide Distribution of perceived returns by income quartile. Panels show kernel densities of perceived returns to high human capital, high early investments, high late investments, and perceived ratio of returns. Top panels show results for sample A, bottom panels show results for sample B. All densities are depicted separately for bottom and top income quartile respondents. Reported p-values are from Kolmogorov–Smirnov tests for equality of distributions. Figure A.3. View largeDownload slide Distribution of perceived returns by parental education. Panels show kernel densities of perceived returns to high human capital, high early investments, high late investments, and perceived ratio of returns. Top panels show results for sample A, bottom panels show results for sample B. All densities are depicted separately for respondents with and without university degree. Reported p-values are from Kolmogorov–Smirnov tests for equality of distributions. Figure A.3. View largeDownload slide Distribution of perceived returns by parental education. Panels show kernel densities of perceived returns to high human capital, high early investments, high late investments, and perceived ratio of returns. Top panels show results for sample A, bottom panels show results for sample B. All densities are depicted separately for respondents with and without university degree. Reported p-values are from Kolmogorov–Smirnov tests for equality of distributions. Figure A.4. View largeDownload slide Beliefs in sample a by scenario group. Panels depict kernel densities of perceived return to early investments, late investments, and high human capital, as well as the perceived intercept, which captures the perceived earnings of a child with low human capital, and low early and late investments. The densities are depicted separately for respondents who saw 0 and 3 h (0–3 group) and respondents who saw 1 and 4 h (1–4 group). Reported p-values are from Kolmogorov–Smirnov tests for equality of distributions. Figure A.4. View largeDownload slide Beliefs in sample a by scenario group. Panels depict kernel densities of perceived return to early investments, late investments, and high human capital, as well as the perceived intercept, which captures the perceived earnings of a child with low human capital, and low early and late investments. The densities are depicted separately for respondents who saw 0 and 3 h (0–3 group) and respondents who saw 1 and 4 h (1–4 group). Reported p-values are from Kolmogorov–Smirnov tests for equality of distributions. 6. Comparison to Estimated Returns Having documented how parents perceive the returns to early and late investments, a natural question that arises is whether parents are correct in their beliefs. Estimating the true returns to parental investments is an important yet challenging task. First, it requires a longitudinal data set that contains detailed information on investments made by parents during different stages of childhood as well as information on children’s skills and later-life outcomes. Second, it is important to recognize that investments and skills are measured with error, which is why it is useful to have multiple measures of investments and skills in the data. Third, one needs to account for the endogeneity of parental investments when parents make investment decisions in response to the characteristics of the child that may change over time (Cunha et al. 2010). The British Cohort Study data is a longitudinal data set that follows all individuals born in a specific week in 1970. It contains multiple measures of investments at age 5 and age 10, multiple measures of children’s skills at ages 5, 10 and 16, as well as detailed information on later-life outcomes (including earnings at age 30). In Boneva and Rauh (2017) we use this rich data and estimate a dynamic latent factor model of human capital production using the estimation technique developed by Agostinelli and Wiswall (2016). The approach accounts for the fact that the data only contains imperfect proxies of investments and skills, and explicitly models the investments of parents as a function of different parent and child characteristics.47 To estimate the returns to parental investments, we use the estimated model to simulate earnings at age 30 for children exposed to low and high levels of investments. To make it comparable to the hypothetical scenarios we use to elicit beliefs, low and high levels of investment are 0.5 standard deviations below and above the mean. Using the simulated data we can then estimate a reduced form regression similar to our benchmark specification of which we present the results in Table 3. In Table 10 we compare the estimated “true” returns to the perceived returns of parents in our survey sample B.48 We find that the estimated returns to early investments are very close to what parents perceive them to be (believed 10.0% vs. 11.1% in the BCS). However, for the returns to late investments we find that parents overestimate these returns almost by a factor of two (believed 31.5% vs. 17.3% in the BCS), suggesting that they overestimate the relative importance of late relative to early investments. Regarding the importance of initial human capital for earnings, we find that parental beliefs are fairly close to the data estimate. Table 10. Data estimate versus survey beliefs about returns to time investment. Dependent variable: Log earnings at age 30    (BCS)  (Survey)  Early investments  0.111***  0.100***    (0.001)  (0.003)  Late investments  0.173***  0.315***    (0.001)  (0.006)  High human capital  0.250***  0.290***    (0.001)  (0.006)  Controlsa  Yes  Yes  School FE  No  Yes  Datasource  BCS  Survey  Observations  800,000  13,551  R2  0.165  0.332  Dependent variable: Log earnings at age 30    (BCS)  (Survey)  Early investments  0.111***  0.100***    (0.001)  (0.003)  Late investments  0.173***  0.315***    (0.001)  (0.006)  High human capital  0.250***  0.290***    (0.001)  (0.006)  Controlsa  Yes  Yes  School FE  No  Yes  Datasource  BCS  Survey  Observations  800,000  13,551  R2  0.165  0.332  Notes: This table is adopted from Boneva and Rauh (2017). Standard errors in parentheses. All regressions include a constant. The left column contains the estimated returns from simulated data based on a dynamic latent factor model using data from the BCS. This sample is composed of simulations from 100 drawn synthetic samples with 100,000 individuals. For the simulated data initial human capital is considered low for a child at the 30th and high at the 70th percentile of the cognitive skill distribution. Controls include parental cognitive and noncognitive skills. The right column is based on sample B as presented in Table 3. a. Controls include log household income, number of children, and dummies for gender of the child and respondent, single parenthood, employment, and whether the respondent has a university degree. *p < 0.10; **p < 0.05; ***p < 0.01. View Large Table 10. Data estimate versus survey beliefs about returns to time investment. Dependent variable: Log earnings at age 30    (BCS)  (Survey)  Early investments  0.111***  0.100***    (0.001)  (0.003)  Late investments  0.173***  0.315***    (0.001)  (0.006)  High human capital  0.250***  0.290***    (0.001)  (0.006)  Controlsa  Yes  Yes  School FE  No  Yes  Datasource  BCS  Survey  Observations  800,000  13,551  R2  0.165  0.332  Dependent variable: Log earnings at age 30    (BCS)  (Survey)  Early investments  0.111***  0.100***    (0.001)  (0.003)  Late investments  0.173***  0.315***    (0.001)  (0.006)  High human capital  0.250***  0.290***    (0.001)  (0.006)  Controlsa  Yes  Yes  School FE  No  Yes  Datasource  BCS  Survey  Observations  800,000  13,551  R2  0.165  0.332  Notes: This table is adopted from Boneva and Rauh (2017). Standard errors in parentheses. All regressions include a constant. The left column contains the estimated returns from simulated data based on a dynamic latent factor model using data from the BCS. This sample is composed of simulations from 100 drawn synthetic samples with 100,000 individuals. For the simulated data initial human capital is considered low for a child at the 30th and high at the 70th percentile of the cognitive skill distribution. Controls include parental cognitive and noncognitive skills. The right column is based on sample B as presented in Table 3. a. Controls include log household income, number of children, and dummies for gender of the child and respondent, single parenthood, employment, and whether the respondent has a university degree. *p < 0.10; **p < 0.05; ***p < 0.01. View Large We would also like to note that unlike some influential studies that have concluded that earlier investments are more productive than late investments (e.g., Cunha et al. 2010; Del Boca et al. 2014), our estimates using the BCS suggest that the returns to an increase of one standard deviation in age-specific early investments are lower than the returns to an increase of one standard deviation in age-specific late investments (11.1% vs. 17.3%). Although previous studies have mainly focused on comparing the productivity of investments in children below age 5 to the productivity of investments in children above age 5, we consider two later time periods in our study (age 5 vs. age 10). Not much is known about whether the returns to investments are linearly decreasing in age, or which types of investments are most productive in any given time period. In fact, there are recent studies that suggest that shifting resources from middle periods of childhood to adolescence might indeed be optimal. For example, Carneiro et al. (2015) use registry data from Norway and find that shifting parental income from child ages 6–11 to ages 12–17 improves schooling outcomes, increases a child’s earnings at age 30, and reduces the prevalence of teenage pregnancies. More research will be needed to fully understand which types of investments are most productive in any given time period, and how to optimally allocate resources over time. Another question that emerges from our study is whether parents with different socioeconomic background only perceive the returns to parental investments to be different or whether the returns to parental investments really differ across families of different socioeconomics status. In Boneva and Rauh (2017) we further investigate whether the production function parameters differ significantly with parent or child characteristics. Interestingly, we cannot reject the null that the returns to parental time investments are the same across households with different socioeconomic status, that is, we find no evidence that high SES parents are more productive than low SES parents or that investments are more productive for children with high initial skill levels. In the model we estimate, investments lead to increases in skill levels and increased skill levels lead to increases in earnings. An interesting related question is how parents of different socioeconomic status perceive the mapping of investments into skills as well as the mapping of skills into earnings. Could it be that parents of different socioeconomic status perceive the mapping of investments into skills as similar but that they differ in their beliefs about the returns to skills in the labor market? Although our research design does not allow us to disentangle the two channels, we provide suggestive evidence in Table A.7 in the Appendix  A that the results are not merely driven by differences in beliefs about the returns to skills in the labor market. Compared to high SES parents, low SES parents also perceive the returns to early investments to be lower when we use the probability of graduating from university as an outcome variable. More research will be needed to shed some further light on this question. 7. Conclusion In this paper, we use hypothetical investment scenarios to elicit parental beliefs about the technology that maps parental investments in different time periods into future child outcomes. Our first main result is that parents perceive the returns to parental investments in early periods of a child’s school life as less productive compared to parental investments in later periods of childhood. Moreover, we find that parents perceive the investments in the different time periods as substitutes rather than complements, that is, they perceive the returns to late investments to be lower if these investments are preceded by high early investments. Our second main finding is that parents differ in their beliefs about the productivity of investments and that this heterogeneity is systematic. In particular, parents with low socioeconomic status perceive the returns to early investments to be lower. We also document that parental beliefs are predictive of current investment decisions made by parents. These results are robust across two independently conducted surveys and raise important questions that need to be addressed to further our understanding of which policies might be most effective in raising child outcomes, especially among families of low socioeconomic status. First, a question that emerges is whether parents are on average correct in their beliefs about the returns to investments in the different periods of childhood. A comparison to the estimated returns we obtain in Boneva and Rauh (2017) suggests that parents may in fact overestimate the relative importance of late investments, which might lead to a misallocation of resources across time periods. Although there is some recent work on the optimal timing of investments (e.g., Cunha et al. 2010; Del Boca et al. 2014; Attanasio et al. 2015b; Carneiro et al. 2015), more research will be needed on which parental investments are most effective in a given time period and how to optimally allocate resources over time. Second, the results raise important questions concerning which bottlenecks need to be overcome to promote parental investments and child development in disadvantaged families. Although traditional models of parental investments have pointed to the importance of credit constraints in explaining differences in investments across socioeconomic groups (Restuccia and Urrutia 2004; Caucutt and Lochner 2012; Cunha 2013; Lee and Seshadri forthcoming), the findings in this paper suggest that socioeconomic differences in parental investments might also be driven by socioeconomic differences in parental beliefs about the returns to parental investments. If parents from low socioeconomic groups underestimate the returns to parental investments and/or if they misperceive the malleability of their children’s skills and the capability of their children to acquire new skills, then interventions that target parental beliefs may be effective in raising parental investments and child outcomes. In related work, Alan, Boneva, and Ertac (2015) provide evidence from a randomized educational intervention that targets students’ beliefs about the malleability of skills and find that treated students are significantly more likely to engage in skill accumulating activities and more likely to accumulate skills as a result. Whether a similar intervention targeted at parents has the potential to increase parental investments and child outcomes is an important policy-relevant question that future research should address. Appendix A: Tables and figures Table A.1. Characteristics of schools in sample.   sample A  sample B  National average    P  S  P  S  P  S  % students on free school meals  10.6  7.4  10.3  11.7  25.4  29.3  % English not first language  3.6  11.0  24.0  15.0  20.0  15.7  % students meeting standard  49.4  –  49.6  –  53.0  –  Attainment 8 score  –  54.6  –  54.8  –  48.5  Number of schools  5  5  11  24      Total number of students  2,304  4,901  5,534  22,502      Number of parents in sample  140  398  214  1,695      Response rate  6.1%  8.1%  3.9%  7.5%        sample A  sample B  National average    P  S  P  S  P  S  % students on free school meals  10.6  7.4  10.3  11.7  25.4  29.3  % English not first language  3.6  11.0  24.0  15.0  20.0  15.7  % students meeting standard  49.4  –  49.6  –  53.0  –  Attainment 8 score  –  54.6  –  54.8  –  48.5  Number of schools  5  5  11  24      Total number of students  2,304  4,901  5,534  22,502      Number of parents in sample  140  398  214  1,695      Response rate  6.1%  8.1%  3.9%  7.5%      Notes: Averages shown for all schools within each sample (weighted by total number of students in each school). Data shown reflects the period in which schools were sampled (2015 for sample A and 2016 for sample B) with the exception of performance scores that are shown for 2016. For primary schools (entries “P”), the performance score is the percentage of students meeting the expected standards in reading, writing, and Maths in the Key Stage 2 examinations, whereas for secondary schools (entries “S”) it is the attainment 8 score, which measures students’ average GCSE grade across eight subjects, including English and Maths. National averages shown for 2016. View Large Table A.1. Characteristics of schools in sample.   sample A  sample B  National average    P  S  P  S  P  S  % students on free school meals  10.6  7.4  10.3  11.7  25.4  29.3  % English not first language  3.6  11.0  24.0  15.0  20.0  15.7  % students meeting standard  49.4  –  49.6  –  53.0  –  Attainment 8 score  –  54.6  –  54.8  –  48.5  Number of schools  5  5  11  24      Total number of students  2,304  4,901  5,534  22,502      Number of parents in sample  140  398  214  1,695      Response rate  6.1%  8.1%  3.9%  7.5%        sample A  sample B  National average    P  S  P  S  P  S  % students on free school meals  10.6  7.4  10.3  11.7  25.4  29.3  % English not first language  3.6  11.0  24.0  15.0  20.0  15.7  % students meeting standard  49.4  –  49.6  –  53.0  –  Attainment 8 score  –  54.6  –  54.8  –  48.5  Number of schools  5  5  11  24      Total number of students  2,304  4,901  5,534  22,502      Number of parents in sample  140  398  214  1,695      Response rate  6.1%  8.1%  3.9%  7.5%      Notes: Averages shown for all schools within each sample (weighted by total number of students in each school). Data shown reflects the period in which schools were sampled (2015 for sample A and 2016 for sample B) with the exception of performance scores that are shown for 2016. For primary schools (entries “P”), the performance score is the percentage of students meeting the expected standards in reading, writing, and Maths in the Key Stage 2 examinations, whereas for secondary schools (entries “S”) it is the attainment 8 score, which measures students’ average GCSE grade across eight subjects, including English and Maths. National averages shown for 2016. View Large Table A.2. Parental time spent with children every week (in min)—sample A.   Weekday  Weekend day  Week total  SD  Min  Max  Median  Talk about school  25.75  23.34  175.11  189.73  0  1980  120  Help with homework  19.19  25.58  144.39  148.06  0  1060  110  Reading-telling stories  10.14  12.66  76.01  137.01  0  1320  0  Play board-card games  6.86  31.06  89.76  152.88  0  1400  45  Total time  58.74  87.9  462.36  408.26  0  3630  360    Weekday  Weekend day  Week total  SD  Min  Max  Median  Talk about school  25.75  23.34  175.11  189.73  0  1980  120  Help with homework  19.19  25.58  144.39  148.06  0  1060  110  Reading-telling stories  10.14  12.66  76.01  137.01  0  1320  0  Play board-card games  6.86  31.06  89.76  152.88  0  1400  45  Total time  58.74  87.9  462.36  408.26  0  3630  360  View Large Table A.2. Parental time spent with children every week (in min)—sample A.   Weekday  Weekend day  Week total  SD  Min  Max  Median  Talk about school  25.75  23.34  175.11  189.73  0  1980  120  Help with homework  19.19  25.58  144.39  148.06  0  1060  110  Reading-telling stories  10.14  12.66  76.01  137.01  0  1320  0  Play board-card games  6.86  31.06  89.76  152.88  0  1400  45  Total time  58.74  87.9  462.36  408.26  0  3630  360    Weekday  Weekend day  Week total  SD  Min  Max  Median  Talk about school  25.75  23.34  175.11  189.73  0  1980  120  Help with homework  19.19  25.58  144.39  148.06  0  1060  110  Reading-telling stories  10.14  12.66  76.01  137.01  0  1320  0  Play board-card games  6.86  31.06  89.76  152.88  0  1400  45  Total time  58.74  87.9  462.36  408.26  0  3630  360  View Large Table A.3. Share of parents engaging in activities with their children (in %)—sample A.     Once  Every  Every  Once  Every  Every    Never  a year  6 months  3 months  a month  2 weeks  week  Watch theatre or circus  7.3  36.3  29.3  19.8  5.2  1.3  0.7  Visit museum/art gallery  12.9  34.8  31.3  17.8  2.4  0.4  0.4  Outdoor activities  1.9  1.1  3.2  4.9  16.6  12.5  59.8      Once  Every  Every  Once  Every  Every    Never  a year  6 months  3 months  a month  2 weeks  week  Watch theatre or circus  7.3  36.3  29.3  19.8  5.2  1.3  0.7  Visit museum/art gallery  12.9  34.8  31.3  17.8  2.4  0.4  0.4  Outdoor activities  1.9  1.1  3.2  4.9  16.6  12.5  59.8  View Large Table A.3. Share of parents engaging in activities with their children (in %)—sample A.     Once  Every  Every  Once  Every  Every    Never  a year  6 months  3 months  a month  2 weeks  week  Watch theatre or circus  7.3  36.3  29.3  19.8  5.2  1.3  0.7  Visit museum/art gallery  12.9  34.8  31.3  17.8  2.4  0.4  0.4  Outdoor activities  1.9  1.1  3.2  4.9  16.6  12.5  59.8      Once  Every  Every  Once  Every  Every    Never  a year  6 months  3 months  a month  2 weeks  week  Watch theatre or circus  7.3  36.3  29.3  19.8  5.2  1.3  0.7  Visit museum/art gallery  12.9  34.8  31.3  17.8  2.4  0.4  0.4  Outdoor activities  1.9  1.1  3.2  4.9  16.6  12.5  59.8  View Large Table A.4. Monthly expenditures of parents—sample A.   Mean  SD  Min  Max  Median  Books (nonschool)  10.27  9.56  0  60  10  Toys, games, DVDs, etc.  11.93  17.67  0  300  10  Sports, music lessons  47.56  54.17  0  500  30  Private tuition  11.54  44.78  0  700  0  Total money  79.3  86.82  0  1201.5  60    Mean  SD  Min  Max  Median  Books (nonschool)  10.27  9.56  0  60  10  Toys, games, DVDs, etc.  11.93  17.67  0  300  10  Sports, music lessons  47.56  54.17  0  500  30  Private tuition  11.54  44.78  0  700  0  Total money  79.3  86.82  0  1201.5  60  View Large Table A.4. Monthly expenditures of parents—sample A.   Mean  SD  Min  Max  Median  Books (nonschool)  10.27  9.56  0  60  10  Toys, games, DVDs, etc.  11.93  17.67  0  300  10  Sports, music lessons  47.56  54.17  0  500  30  Private tuition  11.54  44.78  0  700  0  Total money  79.3  86.82  0  1201.5  60    Mean  SD  Min  Max  Median  Books (nonschool)  10.27  9.56  0  60  10  Toys, games, DVDs, etc.  11.93  17.67  0  300  10  Sports, music lessons  47.56  54.17  0  500  30  Private tuition  11.54  44.78  0  700  0  Total money  79.3  86.82  0  1201.5  60  View Large Table A.5. Time investments (age 5)—sample B.   Mean  SD  Min  Max  Median  Visits park with child in a given week  0.86  0.35  0  1  1  Hours TV child watches per day  1.47  1.03  0  7  1  Days parent reads to child per week  5.17  2.04  0  7  6    Mean  SD  Min  Max  Median  Visits park with child in a given week  0.86  0.35  0  1  1  Hours TV child watches per day  1.47  1.03  0  7  1  Days parent reads to child per week  5.17  2.04  0  7  6  View Large Table A.5. Time investments (age 5)—sample B.   Mean  SD  Min  Max  Median  Visits park with child in a given week  0.86  0.35  0  1  1  Hours TV child watches per day  1.47  1.03  0  7  1  Days parent reads to child per week  5.17  2.04  0  7  6    Mean  SD  Min  Max  Median  Visits park with child in a given week  0.86  0.35  0  1  1  Hours TV child watches per day  1.47  1.03  0  7  1  Days parent reads to child per week  5.17  2.04  0  7  6  View Large Table A.6. Family activities (age 10)—sample B.   1  2  3  4  5  Go for walks together  0.02  0.11  0.40  0.33  0.14  Have breakfast/tea together  0  0.03  0.10  0.25  0.61  Have a chat with the child  0  0.01  0.04  0.22  0.73  Interested in child’s education  0  0.01  0.06  0.45  0.47  Time spent talking to child  0  0.03  0.30  0.41  0.26    1  2  3  4  5  Go for walks together  0.02  0.11  0.40  0.33  0.14  Have breakfast/tea together  0  0.03  0.10  0.25  0.61  Have a chat with the child  0  0.01  0.04  0.22  0.73  Interested in child’s education  0  0.01  0.06  0.45  0.47  Time spent talking to child  0  0.03  0.30  0.41  0.26  Notes: Parents were asked to give their responses on a 5-point Likert scale. For items 1–3, the Likert scale ranged from “Never” (1) to “Very often” (5). For item 4, the scale ranged from “Not interested at all” (1) to “Extremely interested” (5), whereas for item 5 the scale ranged from “None at all” (1) to “A great deal” (5). The numbers reported are fractions of overall responses. View Large Table A.6. Family activities (age 10)—sample B.   1  2  3  4  5  Go for walks together  0.02  0.11  0.40  0.33  0.14  Have breakfast/tea together  0  0.03  0.10  0.25  0.61  Have a chat with the child  0  0.01  0.04  0.22  0.73  Interested in child’s education  0  0.01  0.06  0.45  0.47  Time spent talking to child  0  0.03  0.30  0.41  0.26    1  2  3  4  5  Go for walks together  0.02  0.11  0.40  0.33  0.14  Have breakfast/tea together  0  0.03  0.10  0.25  0.61  Have a chat with the child  0  0.01  0.04  0.22  0.73  Interested in child’s education  0  0.01  0.06  0.45  0.47  Time spent talking to child  0  0.03  0.30  0.41  0.26  Notes: Parents were asked to give their responses on a 5-point Likert scale. For items 1–3, the Likert scale ranged from “Never” (1) to “Very often” (5). For item 4, the scale ranged from “Not interested at all” (1) to “Extremely interested” (5), whereas for item 5 the scale ranged from “None at all” (1) to “A great deal” (5). The numbers reported are fractions of overall responses. View Large Table A.7. Determinants of probability of graduating from university—sample A. Dependent variable: Expected probability of graduating from universitya  Early investmentsb  11.020***  11.970***  11.156***    (0.716)  (0.737)  (0.734)  Late investmentsc  14.268***  15.219***  14.507***    (0.783)  (1.010)  (0.810)  High human capitald  13.925***  13.927***  14.149***    (0.817)  (0.817)  (0.833)  Early × Late    −0.161        (0.102)    Incomee × Early      1.547**        (0.772)  Incomee × Late      0.898        (0.915)  Incomee × High HC      1.183        (0.871)  Parent fixed effects  Yes  Yes  Yes  Observations  2132  2132  2030  R2  0.735  0.736  0.734  Dependent variable: Expected probability of graduating from universitya  Early investmentsb  11.020***  11.970***  11.156***    (0.716)  (0.737)  (0.734)  Late investmentsc  14.268***  15.219***  14.507***    (0.783)  (1.010)  (0.810)  High human capitald  13.925***  13.927***  14.149***    (0.817)  (0.817)  (0.833)  Early × Late    −0.161        (0.102)    Incomee × Early      1.547**        (0.772)  Incomee × Late      0.898        (0.915)  Incomee × High HC      1.183        (0.871)  Parent fixed effects  Yes  Yes  Yes  Observations  2132  2132  2030  R2  0.735  0.736  0.734  Notes: Standard errors in parentheses. Standard errors are clustered at the parent level. The regressions are performed using the parents’ responses to all eight hypothetical investment scenarios. a. In percentage points, that is, 0–100; b. Dummy variable for high early parental investments; c. Dummy variable for high late parental investments; d. Dummy variable for scenario with high initial human capital (High HC); e. Standardized household income of the respondent (mean 0, standard deviation 1). *p < 0.10; **p < 0.05; ***p < 0.01. View Large Table A.7. Determinants of probability of graduating from university—sample A. Dependent variable: Expected probability of graduating from universitya  Early investmentsb  11.020***  11.970***  11.156***    (0.716)  (0.737)  (0.734)  Late investmentsc  14.268***  15.219***  14.507***    (0.783)  (1.010)  (0.810)  High human capitald  13.925***  13.927***  14.149***    (0.817)  (0.817)  (0.833)  Early × Late    −0.161        (0.102)    Incomee × Early      1.547**        (0.772)  Incomee × Late      0.898        (0.915)  Incomee × High HC      1.183        (0.871)  Parent fixed effects  Yes  Yes  Yes  Observations  2132  2132  2030  R2  0.735  0.736  0.734  Dependent variable: Expected probability of graduating from universitya  Early investmentsb  11.020***  11.970***  11.156***    (0.716)  (0.737)  (0.734)  Late investmentsc  14.268***  15.219***  14.507***    (0.783)  (1.010)  (0.810)  High human capitald  13.925***  13.927***  14.149***    (0.817)  (0.817)  (0.833)  Early × Late    −0.161        (0.102)    Incomee × Early      1.547**        (0.772)  Incomee × Late      0.898        (0.915)  Incomee × High HC      1.183        (0.871)  Parent fixed effects  Yes  Yes  Yes  Observations  2132  2132  2030  R2  0.735  0.736  0.734  Notes: Standard errors in parentheses. Standard errors are clustered at the parent level. The regressions are performed using the parents’ responses to all eight hypothetical investment scenarios. a. In percentage points, that is, 0–100; b. Dummy variable for high early parental investments; c. Dummy variable for high late parental investments; d. Dummy variable for scenario with high initial human capital (High HC); e. Standardized household income of the respondent (mean 0, standard deviation 1). *p < 0.10; **p < 0.05; ***p < 0.01. View Large Acknowledgements We are very grateful to the editor and the five anonymous referees, Orazio Attanasio, Eva Berger, Betsy Caucutt, Flavio Cunha, Armin Falk, Christina Gravert, James J. Heckman, Stephanie Heger, Larry Katz, Daniel Kuehnle, Hamish Low, Bethan Morgan, Rajesh Ramachandran, and Anna Vignoles for providing us with valuable comments and suggestions. We further thank seminar participants at University of Zurich, NHH Bergen, King’s College London, Humboldt University, Freie University Berlin, CESifo Munich, and the EDePo group at IFS, as well as participants of the IZA workshop on education, interventions and experiments in Bonn, the workshop on intergenerational mobility in Madrid, the Early-Career Behavioral Economics conference in Bonn, the Royal Economics Society Conference in Bristol, the EALE conference in Ghent, the MISOC workshop on parental beliefs, information and investments in Essex, and the Ce2 Workshop in Warsaw. Boneva acknowledges financial support from the British Academy and Rauh acknowledges financial support from the INET Institute at the University of Cambridge. Notes The editor in charge of this paper was Daniele Paserman. Footnotes 1 This approach has been successfully used in a growing number of studies (e.g., Jensen 2010; Attanasio and Kaufmann 2014; Kaufmann 2014). In comparison, vaguely worded qualitative questions have been shown to provide little useful information about respondents’ expectations (see, e.g., Manski 1990; Juster 1966). See Manski (2004) for a review and discussion of different survey elicitation approaches. 2 Asking parents directly about the likely outcomes of these scenarios, and not about interim test scores, has the advantage that we can directly calculate expected returns without having to make assumptions about the returns of arbitrarily scaled test scores. 3 By analyzing patterns of belief-updating, Zafar (2011) provides evidence that subjective expectations can inform educational choice models. 4 In his recent EEA presidential address, Attanasio (2015) discusses the recent developments in the skill accumulation literature and stresses the importance of investigating the role of parental beliefs in understanding parental investment decisions and child outcomes. 5 For our purposes, we simplify the framework by Cunha et al. (2010) in several ways, for example, we only consider two periods of childhood and we do not distinguish between cognitive and noncognitive skills. 6 Note that there are different reasons why parents might differ in their beliefs about how investments map into the expected future outcome $$\tilde{y}$$. First, parents can differ in their beliefs about how investments translate into higher skill levels ( f ). Second, parents can differ in their beliefs about how an increase in the skill level translates into adult outcomes (g). Here we abstract from these two different channels and directly investigate how parents differ in their beliefs about how their investments map into adult outcomes (h). 7 The extent to which parents perceive investments to be complementary to initial skill levels can be especially important for the parents’ decisions of how to allocate limited resources across siblings with different initial ability levels. See, for example, Aizer and Cunha (2012) who find that parents invest more into children with higher human capital, consistent with strong complementarities in the production of human capital. 8 We used the same sampling procedure for sample A as well as for sample B. We did not use any specific selection criteria to select the schools we contacted. The Department for Education provides lists of all primary and secondary schools in England. We used these lists of potential schools and contacted the head teachers of a random subset of these schools in no specific order. 9 We set up the survey with the survey software Qualtrics. The invitation to participate asks the primary caregiver (referred to as the parent throughout this document) to complete the survey. The survey was advertised to take 15–20 min. The actual mean (median) time of completion was 14 (13) min in sample A and 20 (13) min in sample B. 10 Note that Cunha et al. (2013) do not elicit parental beliefs about returns to investments in different periods of childhood, which is why they cannot document how parents perceive the dynamic nature of the skill production function. Another important difference between the two studies is that although we elicit parental beliefs about how parental investments in different periods of the child’s school life map into later-life outcomes, Cunha et al. (2013) elicit parental beliefs about how parental investments in very early childhood (age 0–2) map into increased skill levels at age 2. 11 See Online Appendix B for the exact formulation. Although we cannot perfectly rule out that parents inferred other differences between the families from our description, we explicitly described the two hypothetical families as being very similar to each other (e.g., in terms of income, education, and the neighborhood they live in) and stressed that there was one difference between the two families, while at the same time avoiding the use of explicit economic jargon (e.g., “ceteris paribus” or “all else equal”). 12 Note that parents saw all four scenarios for each hypothetical family simultaneously on one screen, that is, they could compare across the four scenarios while responding to the questions. We chose this design to mitigate potential concerns that could arise from the order in which the scenarios are presented. 13 We chose to directly ask parents about the likely future earnings of the child, instead of asking about some interim test result, because this allows us to calculate expected returns without having to rely on assumptions about the returns of arbitrarily scaled test scores. 14 For the perceived returns to initial human capital, the differences of interest are $$(\log \tilde{y}_{5}- \log \tilde{y}_{1})$$, $$(\log \tilde{y}_{6}- \log \tilde{y}_{2})$$, $$(\log \tilde{y}_{7}- \log \tilde{y}_{3})$$, and $$(\log \tilde{y}_{8}- \log \tilde{y}_{4})$$. Similarly, for the perceived returns to early investments, the differences of interest are $$(\log \tilde{y}_{3}- \log \tilde{y}_{1})$$, $$(\log \tilde{y}_{4}- \log \tilde{y}_{2})$$, $$(\log \tilde{y}_{7}- \log \tilde{y}_{5})$$, and $$(\log \tilde{y}_{8}- \log \tilde{y}_{6})$$, whereas for the perceived returns to late investments, the differences of interest are $$(\log \tilde{y}_{2}- \log \tilde{y}_{1})$$, $$(\log \tilde{y}_{4}- \log \tilde{y}_{3})$$, $$(\log \tilde{y}_{6}- \log \tilde{y}_{5})$$, and $$(\log \tilde{y}_{8}- \log \tilde{y}_{7})$$. 15 Essentially, the empirical specification is similar to a difference-in-difference approach. The coefficients on the interaction terms indicate whether the perceived returns to investments I$$\mathit{tj}$$ are higher if the variable the investments I$$\mathit{tj}$$ are interacted with are also higher. 16 The expected level in the year 2 national curriculum test (Key Stage 1, age 6–7) is level 2. More than 80% of all students are successful in achieving the expected level (Source: National Pupil Database, 2014). 17 The BCS (1970) follows all children born in a specific week in 1970. More details on the BCS can be found on the following website http://www.cls.ioe.ac.uk as well as in Section 6. 18 Note that the BCS collects information on parental investments at age 5 and age 10, which is why we also chose these ages to make our survey consistent with the BCS. 19 Parents are asked to provide detailed information only about the child who is enrolled in the school through which the survey is distributed. If parents have several children enrolled in the school, they are instructed to provide information on only one of the children enrolled in this school. 20 We use the Family Resources Survey 2013–2014 to obtain the statistics for a representative sample of parents in England. We restrict the sample to parents who have at least one child aged 5–19. On average the respective households have 1.84 children. The average annual household income in this sample is £45,679. To make the sample comparable to our samples, we randomly draw 1,000 subsamples comprised of 77% females (the average from our samples) and find that on average 32% have a university degree, 30% are single parents, and 70% are employed. 21 Table A.1 in the Appendix  A also contains information on the response rates by school type (primary/secondary) and sample. The response rates were 6.1% (primary schools) and 8.1% (secondary schools) in sample A, and 3.9% (primary schools) and 7.5% (secondary schools) in sample B. We note that despite the similar response rates we have significantly more respondents whose children attend secondary schools because more head teachers of secondary schools agreed to participate and because secondary schools are, on average, much larger than primary schools. 22 Note that this information was not collected in sample B that is why we cannot make this comparison for the parents in this sample. 23 See Online Appendix B for more details on the specific questions, which were included in the questionnaire. 24 Note that in sample A the order of the survey modules was not randomized. 25 Note that we did not give parents any information on actual average earnings, that is, we did not anchor responses in any way. 26 The differences in means are significantly different from zero at the 1% level in all four cases. 27 As explained in Section 3, half the respondents in sample A are presented with investments of 1 h/week (low) and 4 h/week (high), whereas the other half of the respondents is presented with investments of 0 h/week (low) and 3 h/week (high). In the regressions that do not include parental fixed effects we additionally control for the dummy variable high baseline that equals 1 if the responding parent saw 1 h/4 h (rather than 0 h/3 h) for low/high levels of investments. 28 To make individual averages comparable in sample A, we account for the fact that the respondents are randomized into a group for whom low investments are 0 h whereas high investments are 3 h, and a group for whom low investments are 1 h whereas high investments are 4 h. For the latter group we remove the marginal effects of the first and last hour in the low and high scenario, respectively. The details can be found in Online Appendix E. The results without this harmonization are qualitatively unchanged. 29 To make the analysis robust to outliers, which are salient in Figure 2, we set the bottom and top 1% of responses to missing. The results remain qualitatively unchanged if we do not perform this correction. 30 We would also like to note that although there are significant differences in beliefs across socioeconomic groups a large share of the variation cannot be explained by observables. More research will be needed into which other observed and unobserved factors play a role in determining beliefs. 31 We would like to note that although all parents are presented with the same hypothetical scenarios, it may be that parents bring their own experiences to the survey and/or imagine families that have similar characteristics to their own. This can also be seen in Figure C.1 in the Online Appendix C that depicts the parents’ beliefs about the intercept, that is, the earnings of a child with low initial human capital, early and late investments. In both samples, top income quartile respondents perceive the earnings of the child in the baseline scenario to be higher compared to parents in the bottom income quartile. 32 We randomized respondents in sample A into two groups, the 0–3 group and the 1–4 group. Table D.1 in the Online Appendix D shows that the two subsamples are balanced in terms of observable characteristics. 33 Given the apparent outliers in Figure 2, we exclude the top and bottom 1% of perceived returns. Including these outliers leads to qualitatively similar results but comes at the cost of a loss in precision. 34 Note that the average perceived return to investment in any given time period is calculated using the differences in log earnings in the corresponding scenarios, that is, log yj − log yk (see Section 4.2). The perceived percentage point change in y, which is defined as (yj − yk)/yk, is approximately equal to log yj − log yk (log approximation rule), so $$r^{ {\mathit {early}}}_i$$ and $$r^{ {\mathit {late}}}_i$$ approximate the perceived percentage point difference in earnings between scenarios in which investments are high and scenarios in which investments are low. Because the difference between low and high investments is 3 h, we additionally divide the perceived returns variables by three, so that the perceived return variable in Table 6 is measured in percentage points (0–1). 35 The extracted factor from the activities questionnaire explains 47% of the variation in responses. 36 The R2 increases by 38% for total time when adding parental beliefs to a regression compared to only including household characteristics. On average it increases by 2 percentage points across the seven columns of Table 6. Similarly, the coefficients of perceived returns are robust to the inclusion of the two supplementary measures we introduce in Table 9 of Section 5. Also, perceived returns again on average add 1.9 percentage points to the R2 above and beyond what is explained by household characteristics and the two supplementary measures, with an increase of 39% for time spent helping with homework. 37 We also performed analyses in which we regress actual investments on the perceived returns to early and late investments, separately for parents whose children attend primary schools and parents whose children attend secondary schools. As one would expect, we find that perceived returns to late investments are predictive of late investments, whereas perceived returns to early investments are predictive of early investments, with the only exception that the positive coefficients on early investments in the sample of primary school parents in sample A do not reach significance, possibly because the sample size in this cell is small (n ≈100). Results are available upon request. 38 We note that although we cannot rule out that the correlations are driven by the respondents’ desire to provide consistent responses across the different survey modules (Cialdini 1984), our results are not driven by order effects. We find a positive correlation between investments and beliefs irrespective of the order in which the survey modules are presented. Within both subsamples we find that parents perceive returns to later investments to be higher than returns to earlier investments, that there are socioeconomic differences in perceived returns, and that parental beliefs are predictive of current investment choices. We do, however, note that there is a level effect, that is, parents on average report higher levels of investments when beliefs are elicited first, as indicated by the (for some cases) significant coefficient of Order effect. 39 This questionnaire is inspired by the growth-mindset questionnaire developed in Dweck (2006). All questions can be found in Online Appendix B. 40 We specify that this, for example, might involve that the child spends several hours every week with a professional teacher/coach. See Online Appendix B for exact wording. 41 The extracted factors from the malleability of skills and capabilities questionnaire explain 47% and 61% of the variation in item responses, respectively. 42 This difference is statistically significant at the 1% level. 43 The mean value of the factor for bottom income quartile respondents is −0.15 whereas the mean value of the factor for top income quartile respondents is 0.31. The difference between these two values is significant at the 1% level. The Kolmogorov–Smirnov test rejects the null of having equal distributions (p-value = 0.02). 44 This difference is statistically significant at the 1% level. 45 The mean value of the factor for bottom income quartile respondents is −0.2 whereas the mean value of the factor for top income quartile respondents is 0.4. The difference between these two values is significant at the 1% level. The Kolmogorov–Smirnov test rejects the null of having equal distributions (p-value = 0.00). 46 Note that it may well be that parents from different socioeconomic groups interpret the questions differently. It may for example be that parents from the top income quartile have a different understanding of what “maximum support” means compared to parents from the bottom income quartile. The study design does not allow us to investigate the underlying reasons for why parents from different income quartiles perceive the malleability of their children’s skills or the capability of their children to acquire new skills as different. 47 Parental investments may also respond to unobserved shocks correlated with observables. 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Parental Beliefs about Returns to Educational Investments—The Later the Better?