TY - JOUR
AU - Carozzi,, Felipe
AB - Abstract During the housing bust of 2008–2009, housing prices and transaction volumes fell across the United Kingdom. Although the drop in prices was similar across housing types, transaction volumes fell more for units at the lower end of the market. I document this fact and provide panel and instrumental variable estimates showing its link with tightening credit conditions in England and Wales during 2008. I then use an overlapping-generation framework to relate the change in the composition of sales with the reduction in loan-to-value ratios by British banks and to derive additional predictions. As down-payment requirements increase, young households with scarce financial resources are priced out by older owners who retain their previous houses as rental properties when trading up. Recent changes in aggregate housing tenure, disaggregated changes in renting, and sales in areas with different age compositions, are consistent with these predictions. The results presented here show how the composition of sales changes over the housing cycle and may inform ongoing policy discussions about reduced access to home-ownership by the young. 1. Introduction House prices and transaction volumes fall during recessions and rise during expansions.1 This paper begins by showing that these changes feature a previously overlooked heterogeneity across different quality segments of the housing market. During the housing bust of 2008–2009, housing prices and transaction volumes fell across the entire United Kingdom. Although the initial reduction in prices was similar across housing types, transaction volumes fell more for houses at the lower end of the market. To document this, I use an administrative data set containing all private housing market transactions in England and Wales. Figure 1 illustrates the finding. The left panel plots the median percentage change in prices between 2007 and 2009 against a measure of housing quality. We see that the relationship is slightly positive but close to flat. The right panel shows the same plot for the percentage change in transactions, where we see that the drop in sales was substantially larger for lower-quality houses. This differential decrease in transactions affected the composition of sales in subsequent years. Figure 1. View largeDownload slide Change in prices and transactions by housing quality. The vertical axis represents the proportional change in prices between 2007 and 2009 and the horizontal axis measures within-city quality rank calculated as shown in Section 3. The line represents a polynomial fitted using a median regression of changes in prices on the quality rank (correlation equal to 4%). Right: the vertical axis represents the change in transactions between 2007 and 2009 and the horizontal axis measures within-city quality ranks. The line represents a polynomial fitted using a median regression of changes in transactions on the quality rank (correlation equal to 19%). Figure 1. View largeDownload slide Change in prices and transactions by housing quality. The vertical axis represents the proportional change in prices between 2007 and 2009 and the horizontal axis measures within-city quality rank calculated as shown in Section 3. The line represents a polynomial fitted using a median regression of changes in prices on the quality rank (correlation equal to 4%). Right: the vertical axis represents the change in transactions between 2007 and 2009 and the horizontal axis measures within-city quality ranks. The line represents a polynomial fitted using a median regression of changes in transactions on the quality rank (correlation equal to 19%). In this paper I show that these changes are the result of the tightening of credit conditions in the United Kingdom during 2008, which lead to a sharp reduction of the loan-to-value ratios (LTVs) on mortgages offered by British banks to first-time buyers (FTBs). I use city-level data on changes in LTVs to estimate the effect of this tightening of credit conditions on transaction volumes and prices across segments of the housing market. My findings indicate that a 1 percentage point reduction in mean loan-to-value ratios reduced transactions of average quality housing by up to 1.2%. However, for housing with quality a standard deviation below the mean, the same change in LTVs generated a reduction of 3% in volumes. This heterogeneous effect is consistent with the changing composition of sales after 2008. In order to explore the mechanisms in operation behind this finding and to derive additional implications, I propose a tractable housing ladder model with borrowing constraints and renting in which credit conditions affect the composition of sales. In the model, greater down-payment requirements hinder house purchases by young households with lower levels of wealth. In turn, older and wealthier households facing lower prices become “accidental landlords”, who keep their previous properties and rent them out when moving up the housing ladder. The fact that these entry-level houses are rented instead of being sold drives the change in the composition of transactions: sales of lower quality houses make up a smaller fraction of the total when down-payment requirements increase. In addition to reproducing the stylized fact outlined previously, the model delivers additional predictions that are tested empirically: tighter credit leads to an increase in private renting, a negative cross-sectional correlation between renting and transactions, and less purchases by the young. I exploit the high level of geographical disaggregation in my transactions data set to test these implications and find support for the underlying mechanism. The last decade has seen a consistent reduction in home-ownership rates for young households in the United Kingdom. Although these households still aspire to become owners, high prices and deposit constraints stand in the way of these aspirations. By examining the evolution of transactions in different segments of the housing market, this paper sheds light on the mechanism leading to this change by tying the composition of sales, credit conditions and the supply of rented housing. In doing so, I also provide a mechanism that explains why young generations in England and Wales have been priced out of owner-occupation after 2008. This study contributes to the empirical literature studying the heterogeneity of housing cycles across different market segments. Previous studies have documented how the prices for housing of different quality change over the cycle, particularly during boom periods such as the early 2000s in the United States.2 For example, several studies seek to explain within-city changes in prices during the housing boom (e.g., Ferreira and Gyourko 2011; Glaeser et al. 2012; Genesove and Han 2013; Guerrieri et al. 2013). In recent work, Landvoigt et al. (2015) focus on matching the joint distributions of wealth, income and qualities using an assignment model that takes the quality distribution of traded units as given. Relative to this literature, my paper focuses specifically on understanding and explaining changes in the composition of transactions. Incorporating transactions into the analysis is relevant because, in the recent UK housing bust, the disparity between segments is larger in the evolution of transaction volumes than in the evolution of prices. My contribution is also related to the empirical and theoretical literatures on the effects of credit constraints on housing prices and transaction volumes. Stein (1995) presents a partial equilibrium model linking down-payment requirements to the number of sales. Its mechanism is integrated into a housing model with endogenous prices in Ortalo-Magne and Rady (1999, 2006). In these studies the change in the time series for transactions emerges from capital gains (or losses) on starter homes. I propose an alternative mechanism relating borrowing constraints and sales by emphasizing the link between housing ladder transitions and the supply of housing in the rental market. In this sense, I draw attention to the relationship between the composition of sales and changes in home-ownership rates. Moreover, the qualitative predictions from my model refer to the variation in the impact of borrowing constraints on sale volumes across housing types rather than on the time series of total transactions.3 Recent work has documented the effect of credit supply shocks on residential and other markets. Mian and Sufi (2009) use spatially disaggregated credit demand measures to study the effect of a credit expansion on the growth in housing prices during the boom and defaults during the bust. Mondragon (2017) and Kleiner (2015) use different methods to identify how lender level shocks can impact the housing, credit, and labour markets. My contribution to this literature is to focus specifically on the impact of changing credit conditions on different segments of the housing market, tenure choice and the composition of sales. Finally, this paper informs the literature on house price indices. It is broadly acknowledged that changes in composition must be taken into account when constructing housing price indices (see, e.g., Case 1986; Case and Shiller 1989, see also Hill 2013 for a survey). Gatzlaff and Haurin (1997) argue that traditional hedonic or repeat sales methods that use characteristics to adjust for changes in composition may still face selection problems that yield biased measures of the price of the housing stock at any point in time. Kleiner (2014) documents a change in composition in the United States in the period between 2000 and 2006 and provides a method to construct a repeat-sales price index that is robust to these changes. Despite the variety of methods available to deal with changes in composition, little is known about how and why the composition of transactions actually changes over the cycle. This paper describes these changes and provides evidence relating them to credit conditions. The documented change in the composition of sales after 2008 implies that mean prices undervalue the extent of the housing slump relative to quality-adjusted indices. The data used in the empirical sections of this paper is presented in Section 2. To measure transaction volumes and prices, I use the Price Paid Dataset from the English and Welsh Land Registry. This data set covers all regular residential transactions in England and Wales. High coverage is essential in order to study possible changes in transactions for different qualities over time. In Section 3, I document how housing prices and transactions changed between 2007 and 2009 for different segments within English and Welsh metropolitan areas. To do so, I propose two different estimates of unobserved quality, both yielding similar results. Housing of different qualities experienced a similar fall in prices. In contrast, transactions fell substantially more for lower quality units, changing the composition of sales. The findings are interpreted in the context of recent academic and policy discussions highlighting the role of credit conditions in housing markets and their effect on young households. In Section 4, I use data from a mortgage provider and exploit heterogeneity across cities in the change of loan-to-value ratios to estimate the effect of credit tightening on the composition of sales. Panel and instrumental variable estimates show that the reduction in LTVs to first-time buyers had a large negative effect on transactions of low quality dwellings. I do not observe a heterogeneous effect of changes in LTVs on prices. Section 5 presents a housing ladder model with renting and credit constraints in which households differ in age and income. I use this to show that steady states with tighter lending conditions have a lower number of first-time buyers, a right-shifted composition of traded qualities and higher levels of renting. In addition, tighter credit leads to more let-to-buy (households that keep their starter houses and rent these when trading up). These results are driven by the pricing out of young buyers by wealthier, older households when credit is tighter. Evidence supporting the underlying mechanism is presented in Section 6. Using disaggregated information on the evolution of housing tenure, I show a strong negative correlation between the fall in transactions and the increase in renting. Using data on changes in LTV by city, I relate credit tightening to changes in rental markets. Finally, I show that the change in transactions had a clear age profile. Other explanations that could also account for the change in composition of housing sales are discussed in Section 7. Finally, Section 8 concludes by discussing policy implications and avenues for further research. 2. Data Throughout most of this paper I use the Land Registry’s Price Paid data set covering the vast majority of residential transactions in England and Wales.4 It includes market transactions for the 1995–2013 period recording the transaction price, address, an indicator of dwelling type (detached, semidetached, terrace, or flat), contract type (freehold or leasehold) and whether the house is a new build. The Price Paid data for the 1995–2013 period includes a total of 18,744,353 transactions. Given that leasehold transactions do not include information on the lease term I exclude them from the analysis. I also exclude new build sales as they are related to construction activity. As will be shown in what follows, neither of these restrictions have a qualitative effect on my findings. Finally, I drop all transactions missing location data. These sample restrictions are summarized in Table A.1 in Online Appendix A. The final transactions data set encompasses a total of 12,537,180 transactions for the 1995–2013. I also build a repeat-sales sample of units sold at least twice over my sample period. There are a total of 9,4342,390 transactions in my repeat-sales data set. I complement this with information from other sources. Disaggregated population counts by age group are obtained from the Office for National Statistics (ONS). Data on labour market performance is obtained from the Annual Population Survey and the Annual Survey of Hours and Earnings.5 Disaggregated data on housing tenure distributions is taken from the 2001 and 2011 census, whereas aggregate tenure is obtained from the English Housing Survey. Internal migration data is obtained from the ONS. With respect to information on credit market conditions, I use data on mortgages granted by Nationwide—one of the largest mortgage providers in the United Kingdom—to measure LTV ratios to first time buyers in 1999, 2007, and 2009. Figures A.8 and A.7 in Online Appendix A, show that this data set is broadly representative of the spatial distribution of transactions and the trends in lending behaviour over the 2007 to 2009 period. 2.1. Geographies Throughout the paper I use data at different levels of geographical disaggregation. Aggregate quantities refer to England and Wales only. My definition of spatial housing markets or cities is based on Travel-to-Work Areas (TTWAs). TTWAs are analogous to commuting zones for the United States and are built using information on commuting patterns. There are a total of 186 travel-to-work areas in England and Wales. Throughout the paper I use the terms city and TTWA interchangeably. Within-TTWAs I use information at the lower super output area (LSOA), postcode sector and postcode district levels. LSOAs are spatial units defined for the collection and publication of data by the ONS. They represent the smallest area at which the 2011 census data was disclosed. There are 34,753 LSOAs in England and Wales, of which 34,374 have at least one transaction in the Land Registry data set. Postcode sectors (PS) and postcode districts are aggregations of postcodes.6 I use the National Statistics Postcode Lookup Directory (PLD) to match this geographical information with the Land Registry data set. The PLD links postcodes with all the relevant geographies in the United Kingdom. 2.2. The Housing Market of England and Wales Figure 2 shows the series of deseasonalized housing transactions and prices for the 1995–2013 period. Before the financial crisis, the monthly number of sales increased from around 70,000 in 1995 to 100,000 after 1998 and then oscillated around this figure until the last quarter of 2007. Figure 2. View largeDownload slide Evolution of transactions and prices. Data for England and Wales. Left vertical axis corresponds to transaction volumes and right vertical axis corresponds to prices. Number of transactions in thousands. The price index is the repeat-sales index built by the Land Registry (base set to June 2003). Figure 2. View largeDownload slide Evolution of transactions and prices. Data for England and Wales. Left vertical axis corresponds to transaction volumes and right vertical axis corresponds to prices. Number of transactions in thousands. The price index is the repeat-sales index built by the Land Registry (base set to June 2003). After a brief period of stagnation house prices began to drop steadily and by April 2009 the Land Registry’s index reached its trough.7 This supposed a 17% drop in nominal housing prices (20.4% in real terms). Simultaneously, 2008 saw a fast decrease in transaction volumes: December 2008 recorded 51% less housing purchases than the same month in 2007. The change in transactions was coupled with a sharp decrease in listings during 2008 and an increase in time on the market for listed houses (see Figure A.1 in Online Appendix A) . More than six years after the bust started, prices and transactions had not fully recovered. In 2013, yearly sales were still lower than in every year between 1997 and 2007. Regarding trends in housing tenure, the 1981–2001 period saw an increase in home-ownership from 59% to 69%. Several studies point to the relaxation of credit conditions over the 1980s and 1990s, as the source of this change in tenure (see Muellbauer and Murphy 1997; Ortalo-Magne and Rady 1999; Stephens et al. 2005). However, in 2001 the rate of home-ownership started to decrease and private renting recovered. Between 2002 and 2008, the percentage of households living as renters increased from 10% to 12.8%, mainly through increases in rented stock resulting from purchases by home-owners for investment purposes. Renting increased faster during the crisis, going from 12.8% to 16.4% in 2012. Rented units usually have lower selling prices than owner-occupied units. This owes in large part to differences in physical characteristics, as reported in Halket et al. (2015) and shown in Figure A.2 in Online Appendix A. 3. Stylized Fact: The Bust by Housing Qualities In this section I study how the downturn affected different segments of the housing market. In particular, I study how prices and transactions fell between 2007 and 2009 for houses of different quality levels. In order to study how transactions and prices of different qualities evolved during the crisis I first need a definition of quality that can be applied to my transaction data. I will define the quality of a house as a fixed, unobservable attribute that is desirable for households seeking to reside there and, hence, will be positively correlated with prices in equilibrium. Note that I am not seeking to estimate quality as a structural parameter in household preferences but rather to obtain a classification of houses in terms of this unobservable trait. For this purpose, suppose the price for a unit i sold in quarter t can be decomposed as follows: \begin{equation*} p_{it}=\delta ^{\textit{TTWA}}_{it}+\alpha _{i}+\xi _{it}. \end{equation*} Where |$\mathit {p_{it}} $| is the logarithm of the transaction price and |$\delta ^{\textit{TTWA}}_{t}$| is a set of (TTWA specific) time dummies. The error term ξ|$\mathit {it} $| captures random variation in the transaction price that is not fixed or unit specific (e.g., specific to the buyer–seller match). Quality is defined as αi and is fixed and unobservable. In the estimation of quality, I will only use data from the benchmark (1997–2007) period.8 The challenge is to obtain an estimate for this parameter. For this purpose I follow two methods, both of them inspired in the house price index literature. The first follows a hedonic approach, estimating quality using location—housing type groups. The second uses repeated sales of the same unit (matched using address). 3.1. House Groups I first use data on type of dwelling (detached, semidetached, terrace, flat) and location to group houses and then take mean prices within these groups as proxies for αi. In using this information I follow the spirit of hedonic or spatial house price indices that control for unit characteristics to eliminate changes in the composition of sales (see Hill 2013 for a survey). Formally, the method proceeds by estimating the following specification by OLS: \begin{equation*} p_{it}=\delta ^{\textit{TTWA}}_{it}+\mu _{j}+\xi _{it}. \end{equation*} Again |${p_{it}}$| corresponds to the log of price for house i sold at quarter t. Parameter μj is a dummy for location or location-type group j, |$\delta ^{\textit{TTWA}}_{it}$| is a set of city specific time effects, and ξ|${it} $| is an error term. The set of city-by-quarter dummies in |$\delta ^{\textit{TTWA}}_{it}$| filters out city-wide variation in prices. The set of dummies μj captures price variation between dwellings within cities. Location and dwelling types are important determinants of housing prices and explain a large fraction (over 70%) of their cross-sectional variance. Moreover, location-dwelling type groups have stable price rankings within each TTWA. Both of these conditions make them reasonable proxies for αi. I use |$\widehat{\mu _{j}}$| as proxies for quality in each group j. As an initial illustration, I focus on the case of the London TTWA and group houses by postcode district. There are roughly 270 postcode districts in this metropolitan area and fixed effects at this level explain 77% of the cross-sectional variance in log prices. Once I estimate |$\widehat{\mu _{j}}$|⁠, I assign postcode districts into estimated quality quintiles. I then compare these quality quantiles to the change in transactions and house prices at the postcode district level. In both cases the change is taken over the 2007–2009 period. I illustrate the results in the map shown in Figure 3. The upper panel displays a map of London’s postcode districts in which darker shades correspond to higher quality (more expensive) areas. We observe that central London and the South West are high quality areas whereas the East is cheaper. In the middle panel I portray the change in transactions in each district with darker shades corresponding to larger decreases in the number of sales between 2009 and 2007. Finally, the bottom panel displays the change in prices for each area with darker shades corresponding to larger declines. Figure 3. View largeDownload slide Postcode districts in London TTWA. Figure 3. View largeDownload slide Postcode districts in London TTWA. The comparison between these maps is illustrative of the stylized fact documented in this paper. Comparing the top and middle panels we can observe that places with higher quality experienced more moderate reductions in transactions. Take, for example, the case of central London and the South West. In both cases we observe a corridor of high quality areas with some of the smallest declines in transaction volumes. The opposite happens in the more affordable areas in East London, which experienced a sharper reduction in sales. The picture for prices is less clear. In the third panel, we observe that several districts in the South West rank high in the distribution of price reductions. The correlation between price drops and low quality is only clear in the east and less so than in the case of transactions. I now turn to a detailed analysis, combining more disaggregated location data with information on dwelling types in my estimation of quality and extending the analysis beyond London. For this purpose I define groups at the postcode sector—dwelling type level. A postcode sector dwelling-type group identifies a type of house in a specific location.9 A total of 36,085 postcode sector—dwelling type (PS-DT) groups had at least one sale during the benchmark (1997–2007) period. I now re-estimate the price previous equation using this definition of groups. Parameter μj now corresponds to a PS-DT dummy for group j. I obtain |$\widehat{\mu _{j}}$| as proxies for quality in each group. For all PS-DT pairs having positive sales in 2007 and 2009, I compute the percent difference in mean prices between peak (2007) and trough (2009) as well as the difference in average yearly transactions between both years. Figure 4 plots these differences against the within-TTWA rank of estimated quality. The figure represents contours for a kernel density estimated over the underlying scatter plot of housing groups. Contour lines correspond to different quantiles of the estimated density. Figure 4. View largeDownload slide Change in prices and transactions by quality—postcode sector—dwelling type pairs. Top: the change in prices between 2007 and 2009 against the within-TTWA quality rank. Bottom: the change in yearly transactions between the 2007 and 2009 periods against the within-TTWA quality rank. In both cases the units are the postcode sector-dwelling type pairs with positive sales in both years. The figure plots the contour plot of a Normal kernel density estimate with bandwidth chosen according to Silverman’s rule-of-thumb. Contour lines chosen using quantiles of the density estimate. Figure 4. View largeDownload slide Change in prices and transactions by quality—postcode sector—dwelling type pairs. Top: the change in prices between 2007 and 2009 against the within-TTWA quality rank. Bottom: the change in yearly transactions between the 2007 and 2009 periods against the within-TTWA quality rank. In both cases the units are the postcode sector-dwelling type pairs with positive sales in both years. The figure plots the contour plot of a Normal kernel density estimate with bandwidth chosen according to Silverman’s rule-of-thumb. Contour lines chosen using quantiles of the density estimate. The change in prices is shown in the top panel. We can see it was on average negative, as expected, and that it was fairly homogeneous across qualities. The correlation on the kernel density estimate appears close to 0 or slightly positive.10 Turning to transactions, the bottom panel of Figure 4 displays a clear positive correlation: the percentage drop in transactions was lower for houses higher up in the quality distribution with the correlation being roughly 17%. The pattern is observed consistently in the vast majority of TTWAs including the 10 largest ones (not shown). The fact that the number of transactions fell more for lower quality houses implies a change in composition: the fraction of total transactions corresponding to these units was lower after 2008. Alternatively, I estimate the change in prices and transactions for different location-type groups by estimating the following specifications using OLS and data for years 2007 and 2009 only \begin{align*} \log (\overline{\textit{price}})_{jt}&=\beta ^{\textit{price}}_{1}\textit{Quality}_{j}+\beta ^{\textit{price}}_{2} \textit{Quality}_{j} \times d_{2009}+\eta ^{\textit{price}}_{t}+\epsilon ^{\textit{price}}_{jt}, \\ \log (\textit{trans}_{jt})&=\beta ^\textit{trans}_{1}\textit{Quality}_{j}+\beta ^\textit{trans}_{2}\textit{Quality}_{j} \times d_{2009}+\eta ^\textit{trans}_{t}+\epsilon ^\textit{trans}_{jt}. \end{align*} The dependent variables |$\log (\overline{\textit{price}})_{jt}$| and |$\log (\textit{trans}_{jt})$| correspond to the logarithms of the mean price and the number of transactions for group j in year t, respectively. In both cases the variables are normalized so that the relevant coefficient can be interpreted in terms of 2007 standard deviations of the dependent variable. Variable d2009 is a dummy taking value 1 in 2009. The coefficients of interest in this context are |$\beta ^{\textit{price}}_{2}$| and |$\beta ^\textit{trans}_{2}$| that measure the respective changes in the slopes of the quality–price and quality–transaction relationships. Estimates for |$\beta ^{\textit{price}}_{2}$| and |$\beta ^{\textit{trans}}_{2}$| are presented in the second row of Table 1. We can see that in all cases the coefficients of interest are positive. The coefficient on the time effect d2009 in column (1) indicates that the price of a unit of average quality declined by a 2.3% of the cross-sectional standard deviation between 2007 and 2009. The coefficient on the interaction term indicates that the decline in prices was only slightly larger for properties with quality a standard deviation below the average (−(0.023 + 0.006) = 2.9%). Including TTWA-year effects in column (2) makes the interaction term indistinguishable from 0. In the case of transactions, we also find the coefficient on the time dummy is negative and significant (i.e., transactions dropped for units of average quality). But the coefficient for the interaction term in column (3) indicates that properties with qualities one standard deviation below the average experienced a 2/3 larger drop in transactions than properties of average quality. Note that this result is robust to controlling for year-TTWA effects. Table 1. Stylized fact—quality estimated by groups. |$\log (\overline{\textit{price}})$| |$\log (\overline{\textit{price}})$| |$\log (\textit{trans})$| |$\log (\textit{trans})$| (1) (2) (3) (4) Quality 1.082*** 1.084*** −0.158*** −0.163*** (0.0322) (0.0339) (0.0148) (0.0199) Quality × d2009 0.00672** 0.00302 0.110*** 0.121*** (0.00318) (0.00581) (0.0267) (0.0111) d2009 −0.0233*** −0.161*** (0.00353) (0.0187) Observations 48,442 48,442 48,442 48,442 R-squared 0.910 0.911 0.079 0.082 TTWA Effects Yes Yes Yes Yes TTWA - Year Effects No Yes No Yes |$\log (\overline{\textit{price}})$| |$\log (\overline{\textit{price}})$| |$\log (\textit{trans})$| |$\log (\textit{trans})$| (1) (2) (3) (4) Quality 1.082*** 1.084*** −0.158*** −0.163*** (0.0322) (0.0339) (0.0148) (0.0199) Quality × d2009 0.00672** 0.00302 0.110*** 0.121*** (0.00318) (0.00581) (0.0267) (0.0111) d2009 −0.0233*** −0.161*** (0.00353) (0.0187) Observations 48,442 48,442 48,442 48,442 R-squared 0.910 0.911 0.079 0.082 TTWA Effects Yes Yes Yes Yes TTWA - Year Effects No Yes No Yes Notes: In columns (1) and (2) the dependent variable is the standardized logarithm of mean prices. In columns (3) and (4) it is the standardized number of transactions. In both cases the standardization amounts to subtracting the mean and dividing by the standard deviation, both calculated within the TTWA. All columns estimated via OLS over the sample of location type groups with positive sales in both 2007 and 2009. Standard errors are clustered at the postcode district level in all cases. **Significant at 5%; ***significant at 1%. View Large Table 1. Stylized fact—quality estimated by groups. |$\log (\overline{\textit{price}})$| |$\log (\overline{\textit{price}})$| |$\log (\textit{trans})$| |$\log (\textit{trans})$| (1) (2) (3) (4) Quality 1.082*** 1.084*** −0.158*** −0.163*** (0.0322) (0.0339) (0.0148) (0.0199) Quality × d2009 0.00672** 0.00302 0.110*** 0.121*** (0.00318) (0.00581) (0.0267) (0.0111) d2009 −0.0233*** −0.161*** (0.00353) (0.0187) Observations 48,442 48,442 48,442 48,442 R-squared 0.910 0.911 0.079 0.082 TTWA Effects Yes Yes Yes Yes TTWA - Year Effects No Yes No Yes |$\log (\overline{\textit{price}})$| |$\log (\overline{\textit{price}})$| |$\log (\textit{trans})$| |$\log (\textit{trans})$| (1) (2) (3) (4) Quality 1.082*** 1.084*** −0.158*** −0.163*** (0.0322) (0.0339) (0.0148) (0.0199) Quality × d2009 0.00672** 0.00302 0.110*** 0.121*** (0.00318) (0.00581) (0.0267) (0.0111) d2009 −0.0233*** −0.161*** (0.00353) (0.0187) Observations 48,442 48,442 48,442 48,442 R-squared 0.910 0.911 0.079 0.082 TTWA Effects Yes Yes Yes Yes TTWA - Year Effects No Yes No Yes Notes: In columns (1) and (2) the dependent variable is the standardized logarithm of mean prices. In columns (3) and (4) it is the standardized number of transactions. In both cases the standardization amounts to subtracting the mean and dividing by the standard deviation, both calculated within the TTWA. All columns estimated via OLS over the sample of location type groups with positive sales in both 2007 and 2009. Standard errors are clustered at the postcode district level in all cases. **Significant at 5%; ***significant at 1%. View Large Hence, although there was only a small increase in the difference in prices between the lower and higher ends of the market in 2009, the difference in transaction volumes between segments changed substantially. This is another expression of the stylized fact documented above. Although the fall in prices between 2007 and 2009 was fairly similar for units of different quality, transactions fell much more in the lower end of the market. 3.2. Repeat-Sales The second approach used to estimate housing qualities is inspired by the repeat-sales method proposed initially by Bailey et al. (1963) and popularized after Case and Shiller (1989). For this purpose, I focus on the sub-sample of units that had been sold at least twice between 1995 and 2013. Having more than one sale allows me to estimate quality from historical selling prices at the dwelling level. To do so, I estimate |$p_{it}=\pi ^{\textit{TTWA}}_{t}+\alpha _{i}+\xi _{it}$| by fixed effects to obtain an estimate for αi. I next use these estimates to compute deciles of the αi distribution for each TTWA and classify houses using these estimated deciles. Finally, I compute the change in transactions and prices for each of these groups. Results are presented in Figure 5. Figure 5. View largeDownload slide Change in prices and transactions by quality. Left-panel: change in average prices between 2007 and 2009 (peak and trough of the aggregate price index series) for within-TTWA quality deciles. Right-panel: average change in yearly transactions between 2007 and 2009 for within-TTWA quality deciles. Quality estimated at the level of individual houses in the repeat-sales sample. Figure 5. View largeDownload slide Change in prices and transactions by quality. Left-panel: change in average prices between 2007 and 2009 (peak and trough of the aggregate price index series) for within-TTWA quality deciles. Right-panel: average change in yearly transactions between 2007 and 2009 for within-TTWA quality deciles. Quality estimated at the level of individual houses in the repeat-sales sample. The results are qualitatively the same as those obtained estimating quality using PS-DT groups. The change in prices across the quality distribution (pictured on the top left panel) shows no clear pattern and is fairly homogeneous, between −10% and −5% for all deciles. On the other hand, transactions (pictured on the bottom right panel) fell more for relatively lower quality units (60% against 40% at the upper end of the market), confirming the change in composition discussed previously. This shift is present in the overwhelming majority of TTWAs (not shown). Both the housing group and repeat-sales methods yield similar result so I conclude that between 2007 and 2009 the drop in transaction volumes was larger at the lower end of the market. But was this change in the composition of sales specific to this period or does it happen regularly? To answer this question I construct a panel of PS-DT pairs at the quarterly frequency. For each pair I use the quality estimates described previously and then calculate the correlation between quality and the number of transactions for each quarter. These correlations are plotted in Figure 6. Figure 6. View largeDownload slide Correlation between quality and transactions. Plot of the cross-sectional correlation between estimated quality and the number of transactions for each semester between 2000 and 2013. Units are the 36,085 postcode sector—dwelling type pairs with positive sales in the 1997–2007 period. Figure 6. View largeDownload slide Correlation between quality and transactions. Plot of the cross-sectional correlation between estimated quality and the number of transactions for each semester between 2000 and 2013. Units are the 36,085 postcode sector—dwelling type pairs with positive sales in the 1997–2007 period. We can see that over the 2000–2007 period, the correlation between the quality of traded units and transactions was relatively stable around 0. Correlations increased abruptly in late 2008 and oscillated around 0.2 thereafter. The timing of this shift largely coincides with the change in borrowing conditions in UK credit markets. Further results on the change in this correlation are presented in Figure A.3 in Online Appendix A. Although, admittedly, this time-series evidence is not conclusive, it is consistent with the hypothesis that the stylized fact was related to the reduction in the supply of high LTV mortgages on offer by British banks during 2008. 3.3. Robustness I have run several complementary tests to confirm the robustness of the empirical results given previously. First, I can show that my housing quality estimates are stable over time: a unit that has a high estimated quality over a given period is very likely to have a high estimated quality for a different period. Note that this is not necessarily the case, as units may be remodelled or upgraded, neighbourhoods may experience change in demographic composition, become gentrified or enter a phase of decay. Fortunately, the assumption that quality is (approximately) fixed can be tested. For this purpose, I compute quality estimates for the same unit in different time periods. I then check whether these estimates fall in similar quantiles of the cross-sectional quality distribution. The corresponding rank correlation plots are provided in Figure A.4 of Online Appendix A. The quality correlations for these different periods are all comfortably above 0.9, indicating that the fixed quality assumption may be a reasonable approximation. Next, I test whether the stylized facts reported previously can be detected using a simpler definition of quality. To do so, I look at the evolution of sales and prices for different dwelling types, as recorded in the Land Registry source. I compare observed changes in volumes and prices for the highest quality type (detached dwellings) and the lowest quality type (terraced housing). Studying how these houses fared during the crisis confirms the results obtained for more refined definitions of quality. The share of total transactions of higher quality detached houses increased abruptly in 2008, whereas that of terraced units fell. Prices dropped for both units in the 2007–2009 period, with the decline in the price of terraced units being only slightly larger than that for detached houses (15.1% vs 13.6 %). These results are reported in Figure A.5 of Online Appendix A. Finally, I report that the previous findings are robust to the inclusion of leaseholds and new-builds in the analysis. When using this extended sample to detect changes in the composition of sales, the qualitative picture is very similar: average yearly transactions after 2008 fell more for relatively lower quality housing. This result is documented in Figure A.6 of Online Appendix A. I conclude that the stylized facts reported in this section are robust to some key methodological choices on how to measure quality or transaction volumes. The next section investigates the economic origin of these facts. 4. Credit Conditions and the Composition of Sales: Direct Evidence A large and arguably unexpected change in credit conditions affected British housing markets in 2008, when banks removed high LTV mortgages from offer in the midst of the Great Recession. Trends in UK mortgage markets around this year can be observed in Figure 7, which was constructed using data from Nationwide mortgages to first-time buyers.11 The left panel shows that, before 2008, the typical FTB could buy a house by paying a deposit of 10% of the total value and obtaining a loan on the remaining 90%. With the advent of the financial crisis, median LTVs for this group decreased abruptly from 90% in early 2007 to roughly 75% by 2009. This change in median coincided with a broader change in the whole distribution of LTVs. The right panel of Figure 7, shows how the cumulative distribution of mortgage LTVs to first-time buyers changed between 2005 and 2011. We can see that much of the mass of the distribution shifted to the left. By 2009, LTVs above 90% had become a negligible fraction of total loans. The change in LTV ratios implies increased down-payment requirements became necessary for prospective FTBs.12 Survey evidence from British banks indicates this change in credit conditions was largely supply driven.13 Figure 7. View largeDownload slide Loan-to-value ratios—nationwide mortgages. Left: evolution of median loan-to-value ratio on mortgages granted to first-time buyers by Nationwide (in percentage terms). Right: cumulative distributions of LTVs for first time buyers for years 2005, 2007, 2009, and 2011 in the Nationwide data set. Figure 7. View largeDownload slide Loan-to-value ratios—nationwide mortgages. Left: evolution of median loan-to-value ratio on mortgages granted to first-time buyers by Nationwide (in percentage terms). Right: cumulative distributions of LTVs for first time buyers for years 2005, 2007, 2009, and 2011 in the Nationwide data set. This section tests whether this change in credit conditions affected the composition of sales. The fact that this was an aggregate shock complicates the empirical analysis because all areas of the country were affected by this change in lending. However, although the removal of high LTV mortgages from offer occurred at the national level, its effects are likely to be heterogeneous across markets. Relatively unaffordable markets, where first-time buyers typically purchase houses using high LTV mortgages, experienced a sharper tightening of credit conditions than markets where LTV were initially low to begin with. This provides cross-sectional variation in the change in credit conditions across markets and motivates the empirical strategy employed. The intuition is that the size of the shock is larger in cities where households typically needed high LTV loans to become home-owners. I build a lower super output area (LSOA) level panel covering 2007 and 2009 and use it to estimate the effect of the change in credit conditions on sale volumes using specification 1: \begin{align} &\Delta \log (\textit{trans})_{i2009}=\beta _{1} \Delta LTV_{j2009}+\beta _{2} \Delta LTV_{j2009} \nonumber \\ &\quad {}\times \textit{Quality}_{i}+\beta _{3} \textit{Quality}_{i}+\phi \Delta X_{i2009}+\Delta \epsilon _{i2009}, \end{align} (1) where log (trans)it is the natural logarithm of the number transactions in LSOA i in time t with t = {2007, 2009}, αi is an LSOA fixed effect, LTV|$\mathit {jt} $| is the average loan-to-value ratio of first-time buyer mortgages in city j and period t (measured in percentage points), |$\textit{Quality}_{i}$| is the LSOA specific housing quality, estimated as in Section 3.1 and normalized to have mean zero and standard deviation 1, X|${it} $| is a set of city and area specific controls, and ϵ|${it} $| is an error term.14 Time differencing, indicated by Δ, is taken between 2009 and 2007. The set of controls include the city-level unemployment, employment, participation, and youth unemployment rates as well as the fraction of workers in professional occupations, obtained from the Annual Population Survey. I also include the fraction of jobseeker’s benefit claimants, at the LSOA-level, and mean and median wages.15 Under the assumption of strict exogeneity of ΔLTVj2009 and |$\Delta LTV_{j2009} \times \textit{Quality}_{i}$|⁠, β1 measures the effect of LTV on transaction volumes and β2 measures the differential impact of credit conditions across segments of the housing market. β3 captures whether different segments experienced different changes in transactions between 2007 and 2009 for other reasons. Results for OLS estimation of equation (1) are presented in columns (1) and (2) of Table 2. Column (1) presents results without controls, whereas column (2) includes both city level and area level controls. In the first place, we can observe that in both columns the effect of credit conditions on transaction volumes is small and not significantly different from 0. This means that the effect of credit tightening on transactions of houses of average quality is negligible. Our main coefficient of interest is the one corresponding to |$\Delta LTV_{j2009} \times \textit{Quality}_{i}$|⁠, which is negative and significant. Because the quality variable is standardized, this indicates that changes in credit conditions will have different effects on the upper and lower segments of the housing market. For units with quality 1 s.d. below the mean, a 1 percentage point drop in LTVs reduced transactions by roughly 1% (0.7% in column (2)). Taking a 10% drop as an approximation for the average change in LTVs, this would roughly translate into a 10 percentage point larger drop in transactions at the low end of the market. Table 2. Change in Loan-to-Value and transactions (OLS and IV). OLS IV (⁠|$ltv\_{t-1}$|⁠) IV (⁠|$ltv\_{1999}$|⁠) IV (both) (1) (2) (3) (4) (5) (6) (7) Δ LTV × Quality −0.010** −0.007** −0.018*** −0.009** −0.046*** −0.010** −0.009** (0.01) (0.00) (0.00) (0.00) (0.01) (0.01) (0.00) Δ LTV −0.001 −0.001 0.012** −0.010 (0.00) (0.00) (0.00) (0.03) Quality 0.183*** 0.133*** 0.129*** 0.181*** 0.149*** 0.181*** 0.181*** (0.03) (0.02) (0.02) (0.01) (0.02) (0.01) (0.01) Δ Job Seekers −12.892*** −12.428*** −8.193*** −10.916*** −8.161*** −8.201*** (0.73) (0.82) (0.97) (0.95) (0.97) (0.97) Δ Unemp. −0.025*** −0.019** −0.012 −0.025 −0.012 −0.012 (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) F-stat 1 − − 68 − 17 − − F-stat 2 − − 47 46 33 35 47 Controls No Yes Yes Yes Yes Yes Yes TTWA Effects No No No Yes No Yes Yes R2 0.12 0.14 0.13 0.20 0.10 0.20 0.20 Observations 33573 33572 33572 33572 33555 33555 33555 OLS IV (⁠|$ltv\_{t-1}$|⁠) IV (⁠|$ltv\_{1999}$|⁠) IV (both) (1) (2) (3) (4) (5) (6) (7) Δ LTV × Quality −0.010** −0.007** −0.018*** −0.009** −0.046*** −0.010** −0.009** (0.01) (0.00) (0.00) (0.00) (0.01) (0.01) (0.00) Δ LTV −0.001 −0.001 0.012** −0.010 (0.00) (0.00) (0.00) (0.03) Quality 0.183*** 0.133*** 0.129*** 0.181*** 0.149*** 0.181*** 0.181*** (0.03) (0.02) (0.02) (0.01) (0.02) (0.01) (0.01) Δ Job Seekers −12.892*** −12.428*** −8.193*** −10.916*** −8.161*** −8.201*** (0.73) (0.82) (0.97) (0.95) (0.97) (0.97) Δ Unemp. −0.025*** −0.019** −0.012 −0.025 −0.012 −0.012 (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) F-stat 1 − − 68 − 17 − − F-stat 2 − − 47 46 33 35 47 Controls No Yes Yes Yes Yes Yes Yes TTWA Effects No No No Yes No Yes Yes R2 0.12 0.14 0.13 0.20 0.10 0.20 0.20 Observations 33573 33572 33572 33572 33555 33555 33555 Notes: LSOA (Census-area) level regressions. Dependent Variable in all columns is the difference in the logarithm of transactions in a census area between 2007 and 2009. Columns (1) and (2) report OLS estimates for coefficients in equation (1). Columns (3) and (4) correspond to IV estimates using the initial (2007) average LTV to first-time buyers as an instrument. Columns (5) and (6) use this average for 1999. Column (7) combines both instruments. The list of controls is reported in the text. Only the coefficients for the change in claimants for the job seeker allowance and changes in unemployment reported in the table. F-statistics for first-stage regressions included as indicated in the table. **Significant at 5%; ***significant at 1% View Large Table 2. Change in Loan-to-Value and transactions (OLS and IV). OLS IV (⁠|$ltv\_{t-1}$|⁠) IV (⁠|$ltv\_{1999}$|⁠) IV (both) (1) (2) (3) (4) (5) (6) (7) Δ LTV × Quality −0.010** −0.007** −0.018*** −0.009** −0.046*** −0.010** −0.009** (0.01) (0.00) (0.00) (0.00) (0.01) (0.01) (0.00) Δ LTV −0.001 −0.001 0.012** −0.010 (0.00) (0.00) (0.00) (0.03) Quality 0.183*** 0.133*** 0.129*** 0.181*** 0.149*** 0.181*** 0.181*** (0.03) (0.02) (0.02) (0.01) (0.02) (0.01) (0.01) Δ Job Seekers −12.892*** −12.428*** −8.193*** −10.916*** −8.161*** −8.201*** (0.73) (0.82) (0.97) (0.95) (0.97) (0.97) Δ Unemp. −0.025*** −0.019** −0.012 −0.025 −0.012 −0.012 (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) F-stat 1 − − 68 − 17 − − F-stat 2 − − 47 46 33 35 47 Controls No Yes Yes Yes Yes Yes Yes TTWA Effects No No No Yes No Yes Yes R2 0.12 0.14 0.13 0.20 0.10 0.20 0.20 Observations 33573 33572 33572 33572 33555 33555 33555 OLS IV (⁠|$ltv\_{t-1}$|⁠) IV (⁠|$ltv\_{1999}$|⁠) IV (both) (1) (2) (3) (4) (5) (6) (7) Δ LTV × Quality −0.010** −0.007** −0.018*** −0.009** −0.046*** −0.010** −0.009** (0.01) (0.00) (0.00) (0.00) (0.01) (0.01) (0.00) Δ LTV −0.001 −0.001 0.012** −0.010 (0.00) (0.00) (0.00) (0.03) Quality 0.183*** 0.133*** 0.129*** 0.181*** 0.149*** 0.181*** 0.181*** (0.03) (0.02) (0.02) (0.01) (0.02) (0.01) (0.01) Δ Job Seekers −12.892*** −12.428*** −8.193*** −10.916*** −8.161*** −8.201*** (0.73) (0.82) (0.97) (0.95) (0.97) (0.97) Δ Unemp. −0.025*** −0.019** −0.012 −0.025 −0.012 −0.012 (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) F-stat 1 − − 68 − 17 − − F-stat 2 − − 47 46 33 35 47 Controls No Yes Yes Yes Yes Yes Yes TTWA Effects No No No Yes No Yes Yes R2 0.12 0.14 0.13 0.20 0.10 0.20 0.20 Observations 33573 33572 33572 33572 33555 33555 33555 Notes: LSOA (Census-area) level regressions. Dependent Variable in all columns is the difference in the logarithm of transactions in a census area between 2007 and 2009. Columns (1) and (2) report OLS estimates for coefficients in equation (1). Columns (3) and (4) correspond to IV estimates using the initial (2007) average LTV to first-time buyers as an instrument. Columns (5) and (6) use this average for 1999. Column (7) combines both instruments. The list of controls is reported in the text. Only the coefficients for the change in claimants for the job seeker allowance and changes in unemployment reported in the table. F-statistics for first-stage regressions included as indicated in the table. **Significant at 5%; ***significant at 1% View Large The strict exogeneity assumption needed to give causal interpretation to the OLS estimates in Table 2 is strong. There may be three sources of endogeneity at play. In the first place, reverse causality could exist if banks change their lending criteria in response to other shocks to housing markets. This issue is especially important if we take into account that transaction volumes are known to be a leading indicator of housing market performance (see Miller and Sklarz 1986; De Wit et al. 2013). A second problem may arise due to measurement error. The ΔLTVj2009 measure used here is based on data for a sample of mortgages from one lender only. Although the data is quite representative of total sales (see Figure A.7 in Online Appendix A), LTV averages will contain some degree of measurement error and this could bias coefficients towards zero. Finally, local economic shocks associated to the Great Recession could affect credit and labour markets to produce a drop in LTVs and sales (e.g., due to changing incomes for the young, a channel emphasized, for example, in Muellbauer and Murphy 1997; Ortalo-Magne and Rady 1999). Although controls are included to help deal with some of these confounders, it is likely that part of the shock operates via unobservable channels. I propose two alternative solutions to this problem. The first is to use precrisis measures of LTVs to first-time buyers as instruments for ΔLTVj2009. The second is to include travel-to-work area fixed effects to account for city wide shocks. If we relax the strict exogeneity assumption invoked previously and instead assume that variable LTVjt is predetermined, we can allow for contemporaneous correlation between this variable and the error term (see Arellano 2003). Under this assumption, E(LTVj2007ϵj2009) = 0, and I can use LTVj2007 as an instrument for ΔLTVj2009 in estimating equation 1. Moreover, given that |$\textit{Quality}_{i}$| is fixed, we can construct an additional instrument |$LTV_{j2007} \textit{Quality}_{i}$| for the interaction term. One issue with this instrument is that cross-sectional variation in lending conditions at the onset of the crisis are themselves related to changes in risk taking behaviour by banks during the pre-crisis boom.16 In order to avoid this problem, I consider an alternative, LTV1999, which measures average LTVs in loans to first-time buyers at the TTWA level in 1999. This will still be related to affordability in English cities (and to the need of high LTV mortgages by FTBs) but not to changes in credit conditions in the run-up to the crisis. The relevance condition for these instruments is satisfied as can be seen in the F-statistics reported in Table 2. Results for the IV estimation of equation (1) using instruments LTV2007 and LTV1999 are provided in columns (3) and (5) of Table 2, respectively. For both instruments, we observe that the coefficient on |$\Delta LTV \times \textit{Quality}$| is negative and significant. The coefficient on ΔLTV is significant and has the expected sign in the case of the first instrument, but is not significantly different from 0 when instrumenting with LTV1999. I can use these coefficients to calculate the effect of a change in LTVs on sales of properties with qualities 1 s.d. below the mean. In the case of column (3), the combined effect of a percentage point reduction in LTVs on these properties would be a 3% reduction in transactions (0.0125 − (−0.0181) = 3.06%) and is significant at all conventional levels. For column (5), the same effect would be 4.62%. These are large effects, which could account for much of the observed heterogeneity in the evolution of sales between 2007 and 2009. The coefficients are larger than those for OLS, perhaps due to the fact that IV estimates are less likely to be rigged with measurement error. I conclude from these results that credit tightening had a substantial impact on the reduction of transaction volumes at the lower end of the market. The assumptions required to give causal interpretation to the IV estimates in Table 2 are still relatively strong and deserve further discussion. If markets with initially high LTV ratios experienced large negative economic shocks in 2008–2009, these assumptions would be violated. To test whether this is the case, I run a series of balancing checks by estimating univariate regressions of the instruments on city-level variables measuring changes in economic conditions. Estimates from these regressions are reported in Table 3. We observe that in all but one case there is no statistically significant relationship between the instruments and the covariates, which is reassuring. I do find a significant partial correlation between the IVs and the fraction of population receiving the job-seeker allowance. Recall I have included this fraction as a control in all specifications. Table 3. Balancing tests. D. Unemp D. Employ D. Inactive D. SelfEmp D. Profess LTVt−1 0.0303 −0.0116 −0.00580 −0.0397 0.0248 (0.02) (0.05) (0.05) (0.03) (0.04) Observations 186 186 186 186 185 D. High Edu D. YouthUnemp D. Seekers D. Mean W D. Median W LTVt−1 0.0459 −0.00980 0.0191*** 0.300 0.440 (0.07) (0.04) (0.00) (0.64) (0.44) Observations 186 186 186 186 186 D. Unemp D. Employ D. Inactive D. SelfEmp D. Profess LTV1999 0.0504 0.0775 −0.154* −0.0484 −0.00418 (0.03) (0.10) (0.08) (0.04) (0.04) Observations 185 185 185 185 184 D. High Edu D. YouthUnemp D. Seekers D. Mean W D. Median W LTV1999 0.0287 −0.00183 0.0297*** 0.540 0.868 (0.08) (0.06) (0.01) (0.83) (0.64) Observations 185 185 185 185 185 D. Unemp D. Employ D. Inactive D. SelfEmp D. Profess LTVt−1 0.0303 −0.0116 −0.00580 −0.0397 0.0248 (0.02) (0.05) (0.05) (0.03) (0.04) Observations 186 186 186 186 185 D. High Edu D. YouthUnemp D. Seekers D. Mean W D. Median W LTVt−1 0.0459 −0.00980 0.0191*** 0.300 0.440 (0.07) (0.04) (0.00) (0.64) (0.44) Observations 186 186 186 186 186 D. Unemp D. Employ D. Inactive D. SelfEmp D. Profess LTV1999 0.0504 0.0775 −0.154* −0.0484 −0.00418 (0.03) (0.10) (0.08) (0.04) (0.04) Observations 185 185 185 185 184 D. High Edu D. YouthUnemp D. Seekers D. Mean W D. Median W LTV1999 0.0287 −0.00183 0.0297*** 0.540 0.868 (0.08) (0.06) (0.01) (0.83) (0.64) Observations 185 185 185 185 185 Notes: Balancing checks for the instrumental variables used in this section. TTWA level regressions in all specifications suing univariate regressions of selected controls on the instruments. Robust standard errors in parenthesis. 186 TTWAs in total (1 missing LTV data in 1999). *Significant at 10%; ***significant at 1% View Large Table 3. Balancing tests. D. Unemp D. Employ D. Inactive D. SelfEmp D. Profess LTVt−1 0.0303 −0.0116 −0.00580 −0.0397 0.0248 (0.02) (0.05) (0.05) (0.03) (0.04) Observations 186 186 186 186 185 D. High Edu D. YouthUnemp D. Seekers D. Mean W D. Median W LTVt−1 0.0459 −0.00980 0.0191*** 0.300 0.440 (0.07) (0.04) (0.00) (0.64) (0.44) Observations 186 186 186 186 186 D. Unemp D. Employ D. Inactive D. SelfEmp D. Profess LTV1999 0.0504 0.0775 −0.154* −0.0484 −0.00418 (0.03) (0.10) (0.08) (0.04) (0.04) Observations 185 185 185 185 184 D. High Edu D. YouthUnemp D. Seekers D. Mean W D. Median W LTV1999 0.0287 −0.00183 0.0297*** 0.540 0.868 (0.08) (0.06) (0.01) (0.83) (0.64) Observations 185 185 185 185 185 D. Unemp D. Employ D. Inactive D. SelfEmp D. Profess LTVt−1 0.0303 −0.0116 −0.00580 −0.0397 0.0248 (0.02) (0.05) (0.05) (0.03) (0.04) Observations 186 186 186 186 185 D. High Edu D. YouthUnemp D. Seekers D. Mean W D. Median W LTVt−1 0.0459 −0.00980 0.0191*** 0.300 0.440 (0.07) (0.04) (0.00) (0.64) (0.44) Observations 186 186 186 186 186 D. Unemp D. Employ D. Inactive D. SelfEmp D. Profess LTV1999 0.0504 0.0775 −0.154* −0.0484 −0.00418 (0.03) (0.10) (0.08) (0.04) (0.04) Observations 185 185 185 185 184 D. High Edu D. YouthUnemp D. Seekers D. Mean W D. Median W LTV1999 0.0287 −0.00183 0.0297*** 0.540 0.868 (0.08) (0.06) (0.01) (0.83) (0.64) Observations 185 185 185 185 185 Notes: Balancing checks for the instrumental variables used in this section. TTWA level regressions in all specifications suing univariate regressions of selected controls on the instruments. Robust standard errors in parenthesis. 186 TTWAs in total (1 missing LTV data in 1999). *Significant at 10%; ***significant at 1% View Large Perhaps some remaining unobserved variation in city-level economic performance could still be correlated with the instruments. In order to further explore this, I modify equation (1) to include interaction terms |$\Delta X_{i2009} \times \textit{Quality}$|⁠. Coefficient estimates for these interacted controls can indicate whether business cycle shocks have a differential effect on transactions across segments of the housing market and threaten instrument validity through this channel. Estimates and joint significance test statistics are provided in Table A.3 in Online Appendix B. Almost all of the coefficients on these interaction terms are insignificant. Importantly, they are jointly insignificant at all conventional levels. I interpret these estimates as indicating that economic performance did not have a substantial heterogeneous effect on the change in transaction volumes. I also re-estimate equation (1) including TTWA fixed effects. These will account for any city level shocks over the 2007–2009 period. Variable Δ LTV will be subsumed by these fixed effects, but we can still estimate the differential effect of credit tightening on transactions for different segments of the housing market. Results are provided in columns (4) and (6) of Table 2. I obtain very similar coefficients on variable |$\Delta LTV \times \textit{Quality}$| in both columns. Column (4) indicates that for properties with a quality 1 standard deviation below the mean, a 1% reduction in LTV ratios leads to a 0.9% reduction in transaction volumes. In the case of column (6), this effect is 1%. We can also combine both instruments in one specification, as reported in column (7). The effect is now 0.9%.17 Note that the resulting coefficients are now quite close to those obtained under OLS. Thus far this section has discussed the link between credit conditions and transaction volumes, I now briefly turn my attention to the case of housing prices. I re-estimate equation (1), but now using |$\Delta \textit{price}_{j2009}$| as the dependent variable. In this way, I try to capture whether credit conditions had a differential effect on prices across different segments of the housing market. OLS and IV estimates for these coefficients are provided in Table 4. Results are consistent with the descriptive patterns observed in Section 3. There is no evidence that relative prices of low quality housing decreased in places that experienced a sharper tightening in credit. Table 4. Change in loan-to-value and prices (OLS and IV) . OLS IV (⁠|$\textit{ltv}\_{t-1}$|⁠) IV (⁠|$\textit{ltv}\_{1999}$|⁠) IV (both) (1) (2) (3) (4) (5) (6) Δ LTV × Quality 0.0002 0.0002 0.0001 0.0016 0.0004 0.0002 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Δ LTV −0.0002 −0.0011* −0.0010 (0.00) (0.00) (0.00) Quality 0.0105*** 0.0110*** 0.0134*** 0.0106*** 0.0134*** 0.0134*** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Δ Job Seekers −1.0012*** −0.9971*** −0.7069** −1.0553*** −0.7138** −0.7068** (0.31) (0.31) (0.32) (0.33) (0.33) (0.32) Δ Unemp. −0.0060*** −0.0064*** −0.0058** −0.0064*** −0.0059** −0.0058** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) F-stat 1 – 68 – 17 – – F-stat 2 – 47 46 33 35 47 Controls Yes Yes Yes Yes Yes Yes TTWA Effects No No Yes No Yes Yes R2 0.01 0.01 0.02 0.01 0.02 0.02 Observations 33572 33572 33572 33555 33555 33555 OLS IV (⁠|$\textit{ltv}\_{t-1}$|⁠) IV (⁠|$\textit{ltv}\_{1999}$|⁠) IV (both) (1) (2) (3) (4) (5) (6) Δ LTV × Quality 0.0002 0.0002 0.0001 0.0016 0.0004 0.0002 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Δ LTV −0.0002 −0.0011* −0.0010 (0.00) (0.00) (0.00) Quality 0.0105*** 0.0110*** 0.0134*** 0.0106*** 0.0134*** 0.0134*** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Δ Job Seekers −1.0012*** −0.9971*** −0.7069** −1.0553*** −0.7138** −0.7068** (0.31) (0.31) (0.32) (0.33) (0.33) (0.32) Δ Unemp. −0.0060*** −0.0064*** −0.0058** −0.0064*** −0.0059** −0.0058** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) F-stat 1 – 68 – 17 – – F-stat 2 – 47 46 33 35 47 Controls Yes Yes Yes Yes Yes Yes TTWA Effects No No Yes No Yes Yes R2 0.01 0.01 0.02 0.01 0.02 0.02 Observations 33572 33572 33572 33555 33555 33555 Notes: LSOA (Census-area) level regressions. Dependent variable in all columns is the difference in the logarithm of average prices in a census area (cross sectional unit) between 2007 and 2009. Columns (1) and (2) report OLS estimates for coefficients in equation (1). Columns (3) and (4) correspond to IV estimates using the initial (2007) average LTV to first-time buyers as an instrument. Columns (5) and (6) use this measure for 1999. Column (7) combines both instruments. List of controls as highlighted in the text. Only the coefficients for the change in claimants for the job seeker allowance and changes in unemployment reported in the table. *Significant at 10%; **significant at 5%; ***significant at 1% View Large Table 4. Change in loan-to-value and prices (OLS and IV) . OLS IV (⁠|$\textit{ltv}\_{t-1}$|⁠) IV (⁠|$\textit{ltv}\_{1999}$|⁠) IV (both) (1) (2) (3) (4) (5) (6) Δ LTV × Quality 0.0002 0.0002 0.0001 0.0016 0.0004 0.0002 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Δ LTV −0.0002 −0.0011* −0.0010 (0.00) (0.00) (0.00) Quality 0.0105*** 0.0110*** 0.0134*** 0.0106*** 0.0134*** 0.0134*** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Δ Job Seekers −1.0012*** −0.9971*** −0.7069** −1.0553*** −0.7138** −0.7068** (0.31) (0.31) (0.32) (0.33) (0.33) (0.32) Δ Unemp. −0.0060*** −0.0064*** −0.0058** −0.0064*** −0.0059** −0.0058** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) F-stat 1 – 68 – 17 – – F-stat 2 – 47 46 33 35 47 Controls Yes Yes Yes Yes Yes Yes TTWA Effects No No Yes No Yes Yes R2 0.01 0.01 0.02 0.01 0.02 0.02 Observations 33572 33572 33572 33555 33555 33555 OLS IV (⁠|$\textit{ltv}\_{t-1}$|⁠) IV (⁠|$\textit{ltv}\_{1999}$|⁠) IV (both) (1) (2) (3) (4) (5) (6) Δ LTV × Quality 0.0002 0.0002 0.0001 0.0016 0.0004 0.0002 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Δ LTV −0.0002 −0.0011* −0.0010 (0.00) (0.00) (0.00) Quality 0.0105*** 0.0110*** 0.0134*** 0.0106*** 0.0134*** 0.0134*** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Δ Job Seekers −1.0012*** −0.9971*** −0.7069** −1.0553*** −0.7138** −0.7068** (0.31) (0.31) (0.32) (0.33) (0.33) (0.32) Δ Unemp. −0.0060*** −0.0064*** −0.0058** −0.0064*** −0.0059** −0.0058** (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) F-stat 1 – 68 – 17 – – F-stat 2 – 47 46 33 35 47 Controls Yes Yes Yes Yes Yes Yes TTWA Effects No No Yes No Yes Yes R2 0.01 0.01 0.02 0.01 0.02 0.02 Observations 33572 33572 33572 33555 33555 33555 Notes: LSOA (Census-area) level regressions. Dependent variable in all columns is the difference in the logarithm of average prices in a census area (cross sectional unit) between 2007 and 2009. Columns (1) and (2) report OLS estimates for coefficients in equation (1). Columns (3) and (4) correspond to IV estimates using the initial (2007) average LTV to first-time buyers as an instrument. Columns (5) and (6) use this measure for 1999. Column (7) combines both instruments. List of controls as highlighted in the text. Only the coefficients for the change in claimants for the job seeker allowance and changes in unemployment reported in the table. *Significant at 10%; **significant at 5%; ***significant at 1% View Large 5. Model I now present a deterministic overlapping generation framework in which credit conditions affect the composition of housing transactions. As in Ortalo-Magne and Rady (2004, 2006), the model features heterogeneity both in dwelling types and household incomes, and transactions are intergenerational transfers of houses. In my framework, older, wealthier households can become landlords of starter units and therefore compete for ownership with the young households. Some of these young households become renters and are effectively priced out of home-ownership. Affordability for younger households will be determined by credit conditions. With abundant credit, young households have more available resources to compete for ownership. Tighter credit will benefit wealth-rich landlords. I first show analytically that steady states (SS) with tighter credit constraints have a relatively smaller fraction of sales in the lower side of the market and a larger fraction of households living as renters. Importantly, changes in the composition of transactions arise because of changes in the number of units that are retained and rented out by wealthy households when moving up the housing ladder. In this way, I emphasize the role of let-to-buy (moving up without selling the starter home) in affecting housing sale volumes and the inter-generational competition for ownership.18 Depending on parameter values, the model can accommodate several different lifetime tenure transitions. I study steady state equilibria in which younger, poorer agents are renters and older, richer agents are landlords residing in high quality housing. I show credit tightening affects the composition of sales for these steady state allocations. In order to explore transition dynamics in response to a permanent, unexpected shock to credit conditions, I solve the model numerically for different sets of parameters. Convergence to the new steady state can take several periods, as prices and wealth levels are jointly and dynamically determined. I show that the model can feature transitions in which the short run impact of the credit shock coincides, qualitatively, with the prediction obtained from a steady state comparison. The model will yield a set of additional testable hypotheses at the micro-level that will be tested separately in Section 6. 5.1. Setup Incomes. Consider an overlapping generation economy with no uncertainty in which agents live for three periods. Agents are born without wealth but are heterogeneous in their incomes. At ages a = 1, 2, 3 agents of type i ∈ [0, 1] receive an endowment ea(i) where the functions |$e_{a}:[0,1] \rightarrow {\mathbb {R}}^{+}$| are continuous and strictly increasing. We can think of these functions as the inverse cdf of incomes for each age cohort. I assume that |$e_{a+1}(i)> e_{a}(i) \, \forall i$|⁠. To save on notation, I define function e(i) corresponding to the accumulated lifetime endowments on period 2, if all period 1 income is saved at interest rate r (i.e., e(i) ≡ e1(i)(1 + r) + e2(i)). Note that function e(i) is again continuous and strictly increasing. Housing Stock and Ownership. There is a fixed stock of housing units |$\bar{S}=S_{L}+S_{H}$| with SL and SH being the stock of low and high type dwellings, respectively. I assume |$\bar{S} < 2$| that ensures positive rental prices. I also assume SL > 1 and SH > 1/2. The housing stock owned by an agent of age a and type i at the beginning of period t is given by vector ht(i, a) = (hL, t, hH, t)′. Scalars hL, t and hH, t record the number of type L and H properties owned by the agent, respectively. Households can own more than one dwelling and rent it out in exchange for rental income. Prices for low and high houses in period t are pL, t and pH, t, respectively. Alternatively, agents can rent a house by paying Rt. Rents are paid in advance. These prices are determined endogenously in the model. Preferences. Households have preferences over housing and a numeraire consumption good. Their per period utility function is given by U(ct, ht) = ct + uh(τt), where ct indicates consumption of the numeraire and τt indicates residential choice at the beginning of the period. Utility from housing depends housing tenure τt = (τR, t, τL, t, τH, t)′ with the elements of vector τ taking value 1 depending on the type of residence (rental, home-ownership of an L or an H unit). The contribution of housing to individual utility is given by function uh(τt) taking values: \begin{equation*} u_{h}(\tau _{t})=\left\lbrace \begin{array}{@{}l@{\quad }l@{}}0 \,\,\,\,\,\,\qquad \text{if live with parents / social housing} \,\,(\tau _{t}=0) \\ \mu v_{L} \,\,\,\,\quad \text{if renting} \, L \,\,(\tau _{R,t}=1)\\ v_{L} \,\,\qquad \text{if owner occupier} \, L \,\,(\tau _{L,t}=1)\\ v_{H} \,\qquad \text{if owner occupier} \, H \,\,(\tau _{H,t}=1)\\ \end{array}\right. \end{equation*} Some agents may not be able to obtain access to a dwelling through the private market. We can think of these agents as residing in social housing or living with their parents, which provide minimal housing services at a price equal to the agent’s current income.19 They receive 0 utility from these housing services. Agents renting low or high type units receive utility μvL.20 Owner occupiers receive utilities vL and vH, respectively. Note that μ < 1 indicates utility from renting is lower than utility from owner-occupation. Housing ownership ht and tenure τt will be tightly related, as only agents owning a unit can be owner-occupiers. Agents discount future utility at rate β. The interest rate on borrowing and saving is r. I will assume |$\beta \, (1+r)\ge 1$|⁠. Combined with linearity of consumption in the utility function, this ensures we can assume without loss of generality that all consumption takes place in the last period. This feature is drawn from Ortalo-Magne and Rady (2006) and allows us to focus on the role of credit conditions on determining housing market decisions. Borrowing Constraints. Collateralized borrowing is available to households. Credit constraints enter the model via a minimum down-payment requirement. Agents can borrow up to |$\gamma \, p_{j,t}$| when buying a type j unit in period t and therefore have to pay a down-payment equal to |$p_{j,t}\, (1-\gamma )$|⁠. We can see γ as the maximum available LTV ratio on mortgages. Importantly, agents can only have a mortgage on one of their housing units so that mortgage debt does not scale with the number of dwellings owned. This assumption plays an important role in Proposition 1. I further assume r < min{γ, 1 − γ}. Combined with the assumption of increasing incomes by age, this ensures all households that take on debt can pay interest on this debt in steady state. There is no default on debt. Supply of Rented Dwellings. Rental supply is comprised of households owning more than one dwelling and renting these out as landlords. Define λt(i, a) as the number of properties rented out by an agent of age a and type i at the beginning of period t. By assumption, deep-pocketed investors do not participate in real estate markets. As a result, the typical no-arbitrage condition is not met and the present discounted value of rental income can be different from the price of low type housing in equilibrium, which allows pL, t and Rt to evolve independently.21 Together with the lower utility resulting from renting, this assumption is critical to ensure that credit constraints have an impact on prices and transactions. Timing. Timing is as follows. Within each period agents first derive housing utility, they receive their corresponding endowment ea(i), pay interests on debt, receive interest from savings, trade in the low-type housing market, trade in the high-type housing market and, finally, derive utility from consumption of the numeraire good. Because agents only enjoy housing utility at the beginning of the period (and they are born with no housing wealth) the maximum possible demand for housing is equal to 2: demand from age 1 and age 2 agents. I will sometimes refer to these two groups as young (age 1) and old (age 2) agents. Choice Variables, State Variables, and Inter-temporal Decisions. Every period, agents decide whether to buy units, whether to become landlords and where to reside at the beginning of the next period, as well as whether to consume or save. Hence, in principle they choose ct, ht+1, τt+1, λt+1. However, this can be simplified substantially. Households owning more than one property will always rent out additional properties to obtain Rt if Rt ≥ 0. Hence, the choice of λt+1 is given directly by ht+1. Formally \begin{eqnarray*} &&\lambda _{t+1}(i,a)\\ &&\quad= \left\lbrace \begin{array}{@{}l@{\quad }l@{}}\sum h_{L,t+1}(i,a)+h_{H,t+1}(i,a)-1 & \text{if $h_{L,t+1}(i,a)+h_{H,t+1}(i,a)> 0$.}\\ 0 & \text{otherwise.} \end{array}\right. \end{eqnarray*} Moreover, given ht + 1, some aspects of residential choice are known because the first home is always owner-occupied (if vH and vL are sufficiently high). Finally, as discussed previously, all consumption takes place in the last period of households’ lives so all resources not used in housing markets are saved by agents of ages 1 and 2. As a result, decisions over ht+1 and τt are sufficient to characterize all household choices. The state variables for this economy will be the amounts of nonhousing net wealth and housing wealth for every agent at the beginning of period t. Nonhousing net wealth is recorded as b(i, a) and maps agents’ type and age to the real line. In the case of housing wealth h(i, a), this will be a function from agent’s type and age to the set of feasible ownership combinations. In this context, agents’ value functions at age a are: \begin{equation*} V^{a}(b,h)=\underset{\tau^\prime ,h^\prime }{\text{max}}\,\, c+u_h(\tau )+\beta V^{a+1}(b^{\prime },h^{\prime }) \end{equation*} Policy functions τ′(i, x, a) and h′(i, x, a), map the state of the economy (x) and the household type and age to their optimal decisions. Agents can only choose the housing services they will enjoy at the beginning of the next period. The law of motion for individual nonhousing wealth at the beginning of a period is \begin{equation} b^{\prime }=(1+r)(e_{a}(i)(1-1\lbrace \tau ^{\prime }=0\rbrace )+b-c-P^{own}(h^{\prime }-h)+R(\lambda -\tau _{R})), \end{equation} (2) where τR takes value 1 if the agent lived in rented accommodation in period t and λ′ indicates the number of properties rented out as a landlord in that period. A full description of the value functions in each period, as well as a definition of the recursive equilibrium are provided in Online Appendix B. Equilibrium. Housing market equilibrium is a set of prices Pt = (Rt, pL, t, pH, t), gross savings bt(i, a) and housing allocations ht(i, a) in the age-type space [0, 1] × {1, 2}, as well as residential decisions τt(i, a), such that households make optimal choices given their budget and credit constraints, and housing markets clear. Housing market clearing is given by \begin{eqnarray*} D^{L}_{1}(P_{t})+D^{L}_{2}(P_{t})+S^{R}(P_{t})&=&S_{L}, \\ D^{H}_{1}(P_{t})+D^{H}_{1}(P_{t})&=&S_{H}, \\ D^{R}_{1}(P_{t})+D^{R}_{2}(P_{t})&=&S^{R}(P_{t}), \end{eqnarray*} where |$D^{h}_{a}$| is the demand of h tenure (rented, low-type home-owner, high-type home-owner) by age a agents buying or renting that period and SR is the supply of rented dwellings. Parameter Conditions. I will impose a set of parameter conditions to ensure that credit constraints are binding for all households (i.e., incentives to become a home-owner/landlord are always present). I will also impose a series of additional conditions to ensure the steady state equilibrium includes lifetime transitions following a housing ladder, where old potential landlords can outbid prospective young buyers for ownership of low type housing. The conditions imposed on preference parameters are the following: \begin{equation} v_{H} > v_{L}> \dfrac{r}{1-\gamma }e(1), \end{equation} (3.1) \begin{equation} \mu v_{L}> e_{1}(2-S_{L}-S_{H}), \end{equation} (3.2) \begin{equation} (1+\mu ) v_{L}> v_{H}, \end{equation} (3.3) \begin{equation} v_{H} -v_{L}> \dfrac{r}{1-\gamma }\left (e(1)-e_{1}(2-S_{L}-S_{H})\right ), \end{equation} (3.4) \begin{equation} e_{1}(2-S_{L}-S_{H})> r e_{1}(1)(1-\gamma )^{-1}. \end{equation} (3.5) These conditions ensure that owner occupation is always worth the user cost of housing (3.1), that renting is always worth the rental price (3.2), that households will not downsize housing consumption today to ensure better quality housing consumption in the future (3.3), that higher quality housing consumption is guaranteed to be worth the user cost in equilibrium (3.4), and that it is profitable to become a landowner of a type L unit (3.5). Additional conditions are imposed on other model parameters including conditions on the distribution of incomes by age. These are required to restrict steady state allocations to those displaying a ladder structure: \begin{equation} e_{2}(0)> e_{1}(2-S_{L}-S_{H}), \end{equation} (4.1) \begin{equation} e_{1}(1) < e(1-S_{H})-e_{1}(2-S_{L}-S_{H}), \end{equation} (4.2) \begin{equation} e(S_{H})-e(1-S_{H})> \dfrac{e_{1}(1-S_{H})}{1-\gamma } -e_{1}(2-S_{L}-S_{H}), \end{equation} (4.3) \begin{equation} e(1) < e(1-S_{H})+\dfrac{2+r}{1-\gamma }e_{1}(1-S_{H})-(2+r)e_{1}(2-S_{L}-S_{H}), \end{equation} (4.4) \begin{equation} \dfrac{2-\gamma }{1-\gamma } e_{1}(2-S_{L}-S_{H})> e(1-S_{H}). \end{equation} (4.5) These conditions ensure that only young agents priced out of the private market (4.1), that only old agents reside in type H properties (4.2), that rental markets exist and marginal owners of H units were renters when young (4.3), and that no landlords rent out two properties (4.4 and 4.5).22 I formally lay out the link between these statements and assumptions (3.1)–(4.5) in Online Appendix B. 5.2. Steady State Price Bounds. Under these assumptions, feasibility of housing choices will be determined by credit constraints and prices. We can use these constraints to obtain bounds on prices for H and L type units. We can also use household income directly to pin down the rental price when rental markets exist. These yield price bounds \begin{equation} p_{H} \le e(1-S_{H})(1-\gamma )^{-1}, \end{equation} (5.1) \begin{equation} p_{L} \ge e_{1}(2-S_{L}-S_{H})\, (1-\gamma )^{-1}, \end{equation} (5.2) \begin{align} & R = e_{1}(2-S_{L}-S_{H}) \quad \text{if rental markets exist.} \end{align} (5.3) Proofs for these statements are provided in the Theoretical Online Appendix. Intuitively, the first statement follows from the fact that otherwise pH would be so high that the richest SH mass of agents in the economy cannot afford an H unit and markets cannot clear. Statement (5.2) follows from the fact that if pL was lower than this level, more than SH + SL households will be able to afford a unit. The condition on rents is also determined by market clearing condition in residential markets. Allocations. Thresholds in the type distribution of households at every age will determine the steady state mass of homeless agents, demands for renting, owner-occupation of L units, owner-occupation of H units, and rental supply. Notation is as follows: |$i^{y}_{R}$| and |$i^{y}_{L}$| are the thresholds beyond which young agents can afford to rent and to buy a low dwelling, respectively. Likewise, |$i^{o}_{H}$| and |$i^{o}_{HL}$| are the thresholds above which agents can afford owning a low type dwelling, a high type dwelling or owning both a high and a low unit at the end of period 2 (landlords), respectively.23 Most of these thresholds are derived from credit constraints. Let us take threshold |$i^{y}_{L}$| as an example. This will be the threshold in the type distribution such that young households can barely afford a down-payment on an L unit (pL(1 − γ)). Hence, |$i_{L}^{y}=e_{1}^{-1}(P_{L}(1-\gamma ))$|⁠. The case of the marginal renters depends directly on having sufficient income to afford a rent, but is otherwise similar. Expressions for all thresholds can be found in Online Appendix B. In general, the relative position of all thresholds in steady state and, hence, the lifetime housing transitions, depend on model parameters. But we can use price bounds (5.1)–(5.3), price ordering R(1 − γ)−1 < pL < pH and assumptions (3.5)–(4.5) to show that steady state allocations will be similar to those represented in Figure 8, and display the following relationships between thresholds: Figure 8. View largeDownload slide Steady state allocation. End of period housing unit allocations by household type (horizontal lines) and age. Thresholds |$i^{age}_{j}$| determined endogenously indicated below each line. Allocations indicated previously the type-line for each age. ∅ corresponds to homeless agents, R to renters, L and H to owner occupiers of low and high type units, respectively, and HL to landlords owning both a low and a high type unit. Case covered in the proof of Proposition 1 in the text. Figure 8. View largeDownload slide Steady state allocation. End of period housing unit allocations by household type (horizontal lines) and age. Thresholds |$i^{age}_{j}$| determined endogenously indicated below each line. Allocations indicated previously the type-line for each age. ∅ corresponds to homeless agents, R to renters, L and H to owner occupiers of low and high type units, respectively, and HL to landlords owning both a low and a high type unit. Case covered in the proof of Proposition 1 in the text. \begin{equation} \begin{array}{l@{\quad}l} i_{R}^{y} < i_{L}^{y} < 1 < i_{H}^{y} & i_{H}^{o} < i_{L}^{y} \\ i_{R}^{o} < i_{L}^{o} < i_{H}^{o} < i_{HL}^{o} & i_{L}^{y} < i_{HL}^{o} < i_{H}^{y}\\ i_{h}^{o} < i_{h}^{y} \quad \text{for}\ h=\lbrace R,L,H\rbrace \end{array} \end{equation} (6) 5.3. Credit Constraints and the Composition of Housing Sales Using the affordability thresholds given previously, we can write demands for different types of units for young and old agents, as well as rental supply \begin{equation*} \begin{array}{l@{\quad}l@{\quad}l} D^{R}_{1} =i^{y}_{L}-i^{y}_{R} & D^{R}_{2} =i^{o}_{L} & S^{R} =1-i^{o}_{HL}\\ D^{L}_{1} =1-i^{y}_{L} & D^{L}_{2} =i^{o}_{H}-i^{o}_{L}&\\ & D^{H}_{2} =1-i^{o}_{H}&\end{array} \end{equation*} Rental demand by young agents, |$D^{R}_{1}$|⁠, is given by agents that can afford to rent but cannot afford a down-payment for an L unit. Demand for owner-occupation of low-type units will be given by the mass of agents who can afford the corresponding down-payment. Demands for old agents can be obtained analogously. Finally, supply of rental units is equal to the mass of landlords, which will be given by |$S_{R}=1-i^{o}_{HL}$|⁠. Now that we have all the expressions for demand and supply, we can rewrite the housing market equilibrium conditions for the two property markets and the rental market. We are left with \begin{equation} 1-i_{H}^{o}=S_{H}, \end{equation} (7.1) \begin{align} i^{y}_{L}-i^{y}_{R}+i^{o}_{L}&=1-i_{HL}^{o}, \end{align} (7.2) In addition to these equilibrium conditions we can also write down the expressions for transaction volumes as a result of the thresholds in i. Transactions of low units are equal to the mass of L units bought by young agents plus the mass of L units bought by old agents. These will be given by \begin{align} tr_{L} &= 1-i_{L}^{y}+i_{H}^{o}-i_{L}^{o}, \end{align} (8) \begin{equation} tr_{H} =1-i_{H}^{o}. \end{equation} (9) We can use the equilibrium conditions (7.1) and (7.2) to study how SS prices and allocations depend on γ and how a change in credit conditions affects the composition of housing transactions. This is the main result of this theoretical framework and is provided in Proposition 1. Proposition 1. Steady states with lower γ have (i) lower values of trL/trL + trH and (ii) higher values of SR if housing allocations can be described by (6). Proof. See Online Appendix B. The proof uses market clearing conditions to identify how endogenous property prices respond to changes in γ. Combined with the expressions for trL, trH, and SR, these show that SS with tighter credit have a lower fraction of L transactions and a larger fraction of renters. The proposition can be proved analogously for steady-state allocations different from those outlined in (6). Several of these alternative cases are covered in Online Appendix B.24 Tighter credit translates into lower SS prices in the L and H markets while leaving rents unaffected (given equation (5.3)). As a result, the number of old households able to keep their low type home when moving up the ladder increases with smaller γ. Because old agents are better able to price out young prospective buyers when credit is scarce, an increase in γ increases the stock of renters living in low type dwellings. Transaction volumes of these units decrease with tighter credit as less households retain their starter properties when trading up. An illustration of the effect of credit tightening on the allocation of units is presented in Figure 9. The same proof can be used to show the opposite happens with increased credit availability. Figure 9. View largeDownload slide Change in steady state for γ′ < γ. Figure displays the change in steady-state allocations resulting from a tightening of credit conditions. With tighter credit the fraction of agents retaining their L unit when moving up the ladder increases, as does the fraction of renters. Figure 9. View largeDownload slide Change in steady state for γ′ < γ. Figure displays the change in steady-state allocations resulting from a tightening of credit conditions. With tighter credit the fraction of agents retaining their L unit when moving up the ladder increases, as does the fraction of renters. 5.4. Transitions: Numerical Analysis The dynamic structure of the model links current wealth with prices in previous and subsequent periods. These, in turn, will be affected by credit conditions. As a result, it is unlikely that transitions between steady states will be instantaneous. In order to study these transitions, I now turn to a numerical analysis of the response of the key objects in Proposition 1 (i.e., fraction of renters, transaction volumes) to an unexpected and permanent increase in down-payment requirements. The code is set up to closely follow a discretized version of the recursive equilibrium definition that can be found in Online Appendix B. A discrete number N of agents are born each period, so that 2N agents demand housing at any point in time. Income distributions and parameters are chosen to satisfy assumptions (3.1)–(4.5), so that steady state allocations can be characterized by 6. The shock is modeled as an unexpected reduction in γ taking place in period 0. The transition path of prices pL and pH is selected so as to ensure markets clear throughout the transition period. Agents in the model are forward looking, so if future prices influence current decisions, the whole transition has to be solved for simultaneously. However, if vL, vH, and μ values are sufficiently large, agents’ decisions will continue to be solely determined by current credit conditions, as current utility flows strictly dominate the effect of future capital gains (or losses).25 The set of parameters used to illustrate transitions is provided in Table 5. Total housing stock is SL + SH = 1950 and N = 1000, so that only 2.5% agents will be priced out of the private housing market in equilibrium. Income distributions are uniform in all periods.26 Incomes for old agents are substantially larger than incomes for the young. Qualitatively, this is consistent with observed patterns and is required so that some old agents are able to price the young out of ownership at relatively high values of γ. The initial steady state is characterized by a maximum LTV of γ = 0.85. I separately study the transitions as a response of a drop to γf1 = 0.8 and a drop to γf2 = 0.75, both events representing a sudden tightening of credit. Table 5. Numerical analysis: parameter values. Parameters vL vH μ SL SH r γi γf1 γf2 Value 200 280 0.5 1100 900 0.01 0.85 0.8 0.75 Income Distributions Period 1 U[2, 4] Period 2 U[3, 20] Period 3 U[3, 20] No. of Households (born in t) 1000 Parameters vL vH μ SL SH r γi γf1 γf2 Value 200 280 0.5 1100 900 0.01 0.85 0.8 0.75 Income Distributions Period 1 U[2, 4] Period 2 U[3, 20] Period 3 U[3, 20] No. of Households (born in t) 1000 Notes: Parameters and income distributions for numerical analysis. Parameter γi represents initial maximum LTV ratios, γf1 indicates final γ after a 5 p.p. reduction, and γf2 indicates final γ after a 10 p.p. reduction. View Large Table 5. Numerical analysis: parameter values. Parameters vL vH μ SL SH r γi γf1 γf2 Value 200 280 0.5 1100 900 0.01 0.85 0.8 0.75 Income Distributions Period 1 U[2, 4] Period 2 U[3, 20] Period 3 U[3, 20] No. of Households (born in t) 1000 Parameters vL vH μ SL SH r γi γf1 γf2 Value 200 280 0.5 1100 900 0.01 0.85 0.8 0.75 Income Distributions Period 1 U[2, 4] Period 2 U[3, 20] Period 3 U[3, 20] No. of Households (born in t) 1000 Notes: Parameters and income distributions for numerical analysis. Parameter γi represents initial maximum LTV ratios, γf1 indicates final γ after a 5 p.p. reduction, and γf2 indicates final γ after a 10 p.p. reduction. View Large Transitions between steady states for LTV shocks of different magnitudes are reported in Figure 10. Shocks arrive in period 0. The left panel represents the evolution of transaction volumes for both L and H dwellings. Transactions of H dwellings are represented by the grey line. These are unaffected by credit tightening, as prices adjust to neutralize the shock and allocations do not change. The series for transaction volumes of L dwellings are represented in black lines. The solid and dashed lines represent the transition for a 10 p.p. and a 5 p.p. exogenous drop in LTV, respectively. In both cases we observe that sales of L units fall on impact, more so in the case of the larger shock, as expected. Transactions trL continue to fall one period after the shock, before oscillating to convergence subsequently. The right panel represents the change in the fraction of renters in response to the shock. Again, the fraction of renters increases on impact and on the period after the shock, and later oscillates to convergence. The initial effect of credit tightening is partially muted because old potential landlords start period 0 with a substantial amount of debt acquired under the high LTV regime. After these have passed, transactions reach their trough. Oscillations also result from this initial difference. Figure 10. View largeDownload slide Transitions after credit shock. Left-panel represents the time series of transaction volumes for H and L type dwellings. The horizontal axis represents time, and the vertical axis represents number of sales. The grey line corresponds to trH, and black lines correspond to trL. Right-panel represents the time series for the fraction of renters, represented in the vertical axis. An unexpected, permanent shock to credit conditions takes place in period 0. Solid lines represent transitions for a 10 p.p. drop in γ. Dashed lines represent transitions for a 5 p.p. drop in γ. Figure 10. View largeDownload slide Transitions after credit shock. Left-panel represents the time series of transaction volumes for H and L type dwellings. The horizontal axis represents time, and the vertical axis represents number of sales. The grey line corresponds to trH, and black lines correspond to trL. Right-panel represents the time series for the fraction of renters, represented in the vertical axis. An unexpected, permanent shock to credit conditions takes place in period 0. Solid lines represent transitions for a 10 p.p. drop in γ. Dashed lines represent transitions for a 5 p.p. drop in γ. Figure 10 reveals that, for this set of parameters, the intuition obtained from the comparative statics carries when looking at the transition period. When credit tightens, transactions fall at the lower end of the market and the fraction of renters increases as more old agents become landlords by holding to their starter house. It is important to note that other sets of parameters may lead to similar transitions. Online Appendix B provides a sensitivity analysis by discussing three examples for other parameter choices, including the case of non-uniform income distributions. 5.5. Discussion Three comments are due regarding the model and its main results. The role of dual owners is critical to link transaction volumes with credit conditions, both in the short term and when comparing steady states. Note this differs from the mechanism in Ortalo-Magne and Rady (2006), in which trade-downs by older agents are used to link γ with transaction volumes. I do not include trade downs in this framework and certainly these do exist, but there is evidence that the scale of these housing market transitions is small (Yang 2009). The down-payment requirements are specified with the standard multiplicative form. However, it is necessary that collateralized borrowing is only available for one unit so that maximum borrowing in this context is pHγ, even if a household owns multiple units. Otherwise, borrowing scales with the number of units, new prices exactly offset changes in credit conditions and allocations are unaffected by credit tightening.27 The model provides a channel linking credit conditions to the composition of transactions. The presence of a rental market is necessary for this channel to exist. The crucial role of rental markets has the advantage of being an implication from the mechanism that can be tested at the microlevel. Intergenerational differences in the effects of credit tightening also play a crucial role in the model. Both aspects will be evaluated empirically in the next section. 6. Supporting Evidence The model indicates that credit tightening increases renting by the young at the lower end of the market. The change in rented stock needed to house those renters comes from a reduction of sales in those segments. In this section, I present different estimates showing this mechanism can explain the results in Sections 3 and 4. I show that the reduction in transaction volumes was stronger in LSOAs where renting increased. Therefore, the increase in rental supply was not provided by individual investors buying units to let. I also show that this correlation emerges exactly in 2008, as expected. Using individual data for a sample of English dwellings, I show that renting increased especially in relatively lower quality units after 2008. Finally, I also re-estimate equation 1 using the change in the fraction of renters as my outcome variable so as to directly test the effect of credit conditions on renting. Estimates show that changes in credit conditions had heterogeneous effects on the fraction of renters across qualities. I also show that there was an age pattern in the fall in transactions, with sales falling more in relatively young neighbourhoods. This is further evidence that it was houses typically bought by FTBs that experienced the strongest reduction in sales. Again, the correlation is observed after 2008, coinciding with the contraction in credit. 6.1. Evidence from the Rental Market The fraction of people living as renters in England increased from 12.8% in 2008 to 16.4% in 2012.28 But where did this extra supply of rented housing come from? Building activity had stalled. In addition, the number of buy-to-let loans had dropped abruptly after 2007 so it is unlikely that buy-to-let could provide the units for this increase in renting. Moreover, a rush of investor buying would have increased transactions at the lower rungs of the housing ladder, which is the opposite of what I report in my stylized facts. The model may provide an answer: when credit tightens the extra supply of rental units comes from increases in let-to-buy. Disaggregated information on housing tenure is available at the LSOA level for the 2001 and 2011 census.29 I use this information to compute the increase in the fraction of private renters over this period. I expect the change in renting will be negatively correlated with the change in average yearly transactions between the boom and bust periods. The corresponding scatter plot is presented in the left panel of Figure 11. I also use my 2007–2009 LSOA panel to estimate regressions of the change in renting on the change in transactions after including different sets of controls and/or TTWA fixed effects. Results are reported in Table A.4 in Online Appendix A. In all specifications the correlation is negative and strongly significant. Figure 11. View largeDownload slide Rental markets and transaction volumes. Left-panel: Plots the drop in average yearly transactions between the boom (2000–2007) and bust (2009–2011) periods at the LSOA level in the vertical axis against the increase in the fraction of renters over total households between 2001 and 2011 in the horizontal axis. The slope of the fitted linear equation is −1.05 and is significant at conventional levels. Right-panel: Time-series of the cross-sectional correlations between the difference in the fraction of renters between 2001 and 2011, and the number of transactions for each semester between 2000 and 2013. Figure 11. View largeDownload slide Rental markets and transaction volumes. Left-panel: Plots the drop in average yearly transactions between the boom (2000–2007) and bust (2009–2011) periods at the LSOA level in the vertical axis against the increase in the fraction of renters over total households between 2001 and 2011 in the horizontal axis. The slope of the fitted linear equation is −1.05 and is significant at conventional levels. Right-panel: Time-series of the cross-sectional correlations between the difference in the fraction of renters between 2001 and 2011, and the number of transactions for each semester between 2000 and 2013. Although this correlation is suggestive, it is only consistent with the proposed explanation if it arises after 2008, when credit tightening took place. To test this, I calculate the cross-sectional correlations between the |$\Delta {Rent}_{j}$| and |$\textit{trans}_{j}$| for every semester between 2001 and 2011. The correlations are plotted in the right panel of Figure 11. A change in the sign of the correlation takes place during 2008, coinciding with credit tightening. I can also use individual property data to show that the increase in renting after 2008 was concentrated on the lower end of the market, consistently with the model predictions. For this purpose, I use the English Housing Survey (EHS), a yearly survey of the English housing stock.30 The EHS includes housing characteristics and prices that allow to estimate a hedonic model and obtain a proxy for housing quality using characteristics related to size (number of bedrooms, number of bathrooms, number of living rooms), building age and region of each unit. I then use this proxy to study how the quality composition of rented stock changed over time. A detailed account of this exercise is reported in Online Appendix A. The main result is that the quality composition of rented stock was stable between 2004 and 2007, before changing abruptly in 2008 and stabilizing thereafter. The increase in renting was concentrated in relatively low-quality segments. To directly test whether credit tightening caused these changes in rental markets, I re-estimate equation (1) using differences in the fraction of renters between 2001 and 2011 as my outcome variable. Estimates for variants of this specification are reported in Table 6. The main coefficient of interest is the effect of the interaction between ΔLTV and the standardized quality measure. We observe that it has the expected positive sign and is significant across all specifications. A tightening of credit conditions will lead to relatively higher renting in the lower end of the market. We also find a counter-intuitive positive effect of ΔLTV on renting in columns (1)–(3) and (5). This would indicate that credit tightening would lead to a reduction in renting on average. One potential explanation is that part of the change in renting may have happened before 2007 and could have been larger in markets with initially high LTV levels. To deal with this issue and other potential confounding factors, I also provide estimates including TTWA-fixed effects in columns (4) and (6). This yields positive coefficients on ΔLTV × Quality, as expected, indicating that a reduction in LTVs will have a positive effect on renting for units below average quality. The coefficient is strongly significant for column (6), indicating that, for units with quality 1 s.d. below the mean, a 1 percentage point drop in LTVs increases renting by 0.353%. Note that the coefficient in column (4) is also positive, but not significant (p-value: 18%). With this caveat in mind, I interpret this as evidence that credit tightening leads to more renting at the lower end of the housing market. Table 6. Change in loan-to-value and fraction of private renting (OLS and IV). OLS IV (⁠|$\textit{ltv}_{t-1}$|⁠) IV (⁠|$\textit{ltv}_{1999}$|⁠) Δ LTV × Quality 0.153** 0.111** 0.165*** 0.0995 0.475*** 0.353*** (0.08) (0.05) (0.06) (0.07) (0.09) (0.08) Δ LTV 0.118** 0.0965*** 0.146*** 0.676*** (0.05) (0.04) (0.05) (0.22) Quality 0.590 0.770 1.106* −0.116 3.167*** 1.840*** (0.94) (0.62) (0.57) (0.69) (0.63) (0.59) Controls No Yes Yes Yes Yes Yes TTWA Effects No No No Yes No Yes Observations 34309 34308 34308 34308 34291 34291 OLS IV (⁠|$\textit{ltv}_{t-1}$|⁠) IV (⁠|$\textit{ltv}_{1999}$|⁠) Δ LTV × Quality 0.153** 0.111** 0.165*** 0.0995 0.475*** 0.353*** (0.08) (0.05) (0.06) (0.07) (0.09) (0.08) Δ LTV 0.118** 0.0965*** 0.146*** 0.676*** (0.05) (0.04) (0.05) (0.22) Quality 0.590 0.770 1.106* −0.116 3.167*** 1.840*** (0.94) (0.62) (0.57) (0.69) (0.63) (0.59) Controls No Yes Yes Yes Yes Yes TTWA Effects No No No Yes No Yes Observations 34309 34308 34308 34308 34291 34291 Notes: LSOA level regressions. Dependent variable in all specifications is the change in the fraction of households living in private renting accommodation taken between the 2001 and 2011 census. Columns (1) and (2) correspond to OLS estimates whereas the remaining columns correspond to IV estimates, with instruments indicated in the table header. Standard errors clustered at the TTWA level. *Significant at 10%; **significant at 5%; ***significant at 1% View Large Table 6. Change in loan-to-value and fraction of private renting (OLS and IV). OLS IV (⁠|$\textit{ltv}_{t-1}$|⁠) IV (⁠|$\textit{ltv}_{1999}$|⁠) Δ LTV × Quality 0.153** 0.111** 0.165*** 0.0995 0.475*** 0.353*** (0.08) (0.05) (0.06) (0.07) (0.09) (0.08) Δ LTV 0.118** 0.0965*** 0.146*** 0.676*** (0.05) (0.04) (0.05) (0.22) Quality 0.590 0.770 1.106* −0.116 3.167*** 1.840*** (0.94) (0.62) (0.57) (0.69) (0.63) (0.59) Controls No Yes Yes Yes Yes Yes TTWA Effects No No No Yes No Yes Observations 34309 34308 34308 34308 34291 34291 OLS IV (⁠|$\textit{ltv}_{t-1}$|⁠) IV (⁠|$\textit{ltv}_{1999}$|⁠) Δ LTV × Quality 0.153** 0.111** 0.165*** 0.0995 0.475*** 0.353*** (0.08) (0.05) (0.06) (0.07) (0.09) (0.08) Δ LTV 0.118** 0.0965*** 0.146*** 0.676*** (0.05) (0.04) (0.05) (0.22) Quality 0.590 0.770 1.106* −0.116 3.167*** 1.840*** (0.94) (0.62) (0.57) (0.69) (0.63) (0.59) Controls No Yes Yes Yes Yes Yes TTWA Effects No No No Yes No Yes Observations 34309 34308 34308 34308 34291 34291 Notes: LSOA level regressions. Dependent variable in all specifications is the change in the fraction of households living in private renting accommodation taken between the 2001 and 2011 census. Columns (1) and (2) correspond to OLS estimates whereas the remaining columns correspond to IV estimates, with instruments indicated in the table header. Standard errors clustered at the TTWA level. *Significant at 10%; **significant at 5%; ***significant at 1% View Large 6.2. Transactions and Household Age Young households move to neighbourhoods where other young people live in search for lower prices, but also adequate local amenities, quality schooling, and so on.31 Although the model in Section 5 does not explicitly distinguish between young and old neighbourhoods, it does predict less transactions by the young. I can test whether this is consistent with observed patterns. For this purpose I use population and age structure data from the ONS disaggregated at the LSOA level for 2007. This allows me to know the fraction of population by age group for all the LSOAs in England and Wales. I combine this information with my transactions data set to check if the drop in transactions and prices had an age profile. The results are illustrated in Figure 12. I plot the change in average yearly transactions between the pre-crisis (2000–2007) and crisis (2009–2011) periods against the mean adult (over 25) population for each LSOA. The upward sloping pattern is clear: transactions dropped less in areas populated by older households, with a correlation of 0.4. Figure 12. View largeDownload slide Difference in transactions by LSOA mean age. The figure plots the average change in yearly transactions between benchmark (1995–2007) and crisis periods (2008–2013) in the vertical axis and the mean adult age at the Lower Super Output Area level. Adults are defined as individuals of age above 25. The slope of the fitted linear equation is 1.27 and statistically significant at conventional levels. Figure 12. View largeDownload slide Difference in transactions by LSOA mean age. The figure plots the average change in yearly transactions between benchmark (1995–2007) and crisis periods (2008–2013) in the vertical axis and the mean adult age at the Lower Super Output Area level. Adults are defined as individuals of age above 25. The slope of the fitted linear equation is 1.27 and statistically significant at conventional levels. Again, I test the robustness of this relationship by running a regression of the change in transactions between 2007 and 2009 on the mean adult age an LSOA. The resulting estimates are presented in Table A.6 in Online Appendix A. Across specifications we observe that the coefficient on |$\overline{Age}$| is positive and significant. These coefficients confirm the robustness of the correlation reported in Figure 12. 7. Alternative Explanations We know changing credit conditions are by no means the only possible driver of variation in housing turnover or tenure choice. The stylized facts documented in Section 3 can also be the result of changes in the labour market, internal migration, and other forces affecting demand and supply in housing markets. I investigate several of these alternative explanations empirically and describe the main results of those analyses here. Outputs from of these exercises can be found in Online Appendix A. First, I consider internal migration (within and between regions) as an alternative source of changes in composition. Housing transactions may be driven by geographical moves between or within a region, which may be horizontal (space) rather than vertical (quality). These moves were surely affected by the 2008 shock to labour markets that led to a generalized drop in internal migration.32 Less moves between districts with lower prices could generate heterogeneous changes in volume across qualities. To test whether this was the case, I use origin–destination data on moves at the district level from the ONS. I find no evidence that the reduction of between-district moves in 2008/2009 was concentrated in cheaper districts. In fact, these results suggest that internal moves fell more between relatively high-quality areas. A change in composition could be induced by a change in prices, coupled with either nominal loss aversion or the increase in households underwater (i.e., with negative housing equity). I provide evidence that these are unlikely to explain away the stylized fact for housing volumes. Because the 2007 drop in housing prices was preceded by a long expansion, most of the households affected by these constraints had purchased between 2005 and 2007.33 In Figure A.6 of Online Appendix A, I show that excluding from the sample houses sold in this period does not remove the heterogeneous change in transaction volumes. Finally, I analyse the potential impact of changes in unemployment and youth unemployment on the composition of sales. For this purpose, I exploit variation induced by a shift-share type instrument. Although my instrumental variable estimates do confirm an effect of unemployment on transaction volumes, they do not support the hypothesis that unemployment shocks explain the composition of sales. Results and a description of this exercise are provided in the Online Appendix. Increases in unemployment appear to disproportionately reduce transactions at the upper end of the market, so cannot explain a reduction in volumes at the other end. These results are informative, but do not constitute a complete study of either of these mechanisms, which continue to be interesting objects for further analysis. Yet the tests referred to previous do suggest that none of these drivers played an important role in explaining the stylized facts reported in this paper. 8. Conclusions This paper presents evidence on the change in the composition of traded dwellings that occurred during the 2008/2009 downturn in the UK housing market. Using different methods to identify housing types, I arrive at the same conclusion: the fraction of transactions corresponding to cheaper housing units decreased markedly during the crisis, breaking a pattern of relative stability that had endured during the boom. I show that the large change in maximum Loan-to-Value ratios offered by British banks is a likely explanation for this change in composition. I link these two facts using a theoretical framework in which tighter credit constraints imply that younger, poorer households are priced out of the ownership market by richer households that retain their starter homes when trading up. The framework’s predictions are consistent with recent observed changes in the rental market and changes in transactions by age of neighbourhood residents. These results are novel in several aspects. In the first place, they show that the distribution of transactions may change over the housing cycle and provide a new stylized fact that could be used in other attempts to model how different market segments perform over time. Second, I provide a rationale for these changes in composition by incorporating changes in rental supply into the analysis. Finally, the empirical analysis confirms that deposit requirements can affect housing tenure. In this regard, my model suggests that initiatives seeking to reduce deposit requirements can be effective in increasing home-ownership rates. Although the analysis here does not take into account the cost associated to these policies, it clarifies the mechanism through which credit conditions can simultaneously affect the ability of young households to get on the housing ladder and the supply of units for rent. This paper opens several directions for further research. First, the change in the composition of transactions may be a general feature of housing cycles (such as the price-volume correlation) or something exclusive of the recent British experience. Understanding whether this is the case can help to provide a new fact around which to construct our housing models and motivate the standard composition adjustments that have characterized the construction of house price indices for decades. Second, other factors such as income shocks or changes in expectations could also affect the composition of sales. Although some of these elements are discussed in Section 7, they may warrant specific analyses of their own. Finally, ladder models such as the one presented here may be used to answer questions about housing affordability for the young, an ongoing problem in several cities that is increasingly attracting the attention of policy-makers and academics. Acknowledgments I would like to thank Manuel Arellano, Philippe Bracke, Carlos Garriga, Christian Hilber, Boqian Jiang, Dirk Krueger, Rocío Madera, Claudio Michelacci, Pedro Mira, Josep Pijoan, Diego Puga, Luca Repetto and Olmo Silva as well as seminar participants at Bank of Italy, Banco Central del Uruguay, CEMFI, Hebrew University of Jerusalem, LSE, NHH, Universidad de Barcelona, Uppsala University and Zicklin School of Business together with participants at the III Workshop on Urban Economics at IEB, the SERC 2014 conference, the EEA-ESEM 2014 annual congress and the 2016 UEA Meetings as well as three anonymous referees for useful comments and suggestions. Funding from the European Commissions Seventh Research Framework Programme through the European Research Council Advanced Grant “Spatial Spikes” (contract 269868) is gratefully acknowledged. Notes The editor in charge of this paper was Dirk Krueger. Footnotes 1. Evidence of time series correlation between sale volumes and prices is presented in Berkovec and Goodman (1996), Lamont and Stein (1999) for the United States and Andrew and Meen (2003), Ortalo-Magne and Rady (2004), Benito (2006) for the United Kingdom. 2. There are some exceptions. Smith and Tesarek (1991) study the evolution of housing prices across qualities during a Houston boom-bust episode in the 1980s. Case and Mayer (1996) study cross-sectional differences in the evolution of prices over time and relate them to changes in supply and demand factors. 3. Chambers et al. (2009) propose a quantitative model with heterogeneous housing types and renting to understand the effect of mortgage markets innovations on US home-ownership rates. Their analysis does not focus on studying the composition of sales or the dynamics of transactions. 4. The Price Paid data set excludes properties that are likely to be sold at a discount either because they are transfers or conveyances (e.g., transfers under court order, sale of shares of a property), leases under 7 years of their expiry date, transfers of more than one property as part of a portfolio or right-to buy properties. These transactions amount to roughly an 80% of the total transactions reported by HM Revenue & Customs. 5. Information on labour markets is usually available at the local authority level. In the small minority of cases in which local authority data is not available I impute the corresponding regional figure (20/300 cases for unemployment). 6. On average a postcode sector contains 2,995 households housing 7,272 people. There are 8,464 PS with at least one transaction in the Land Registry data set. Postcode districts are aggregations of postcode sectors. There are roughly 2,900 postcode districts in the United Kingdom and 2,345 postcode districts with positive sales in my Land Registry data set. 7. The previous housing downturn in the United Kingdom had taken place in the late 1980s when rising mortgage rates and a worsening of labour market conditions affected affordability in UK housing markets (Jowsey 2011). 8. The period used in the estimation of quality does not affect the qualitative results. 9. For example, detached houses in postcode sector E1 4, semi-detached houses in postcode sector WC2A 2 or detached houses in postcode sector CV4 7. 10. In order to further explore this, I have divided houses into high and low quality by splitting them with respect to the TTWA-specific median and estimate price indexes for each of these groups. After their peak in late 2007, prices fell for both groups to their lowest level in 2009. The fall was not quite symmetric, the index for low units fell by 18% whereas the one for high units fell by 16%. Still, the difference is rather modest and masks substantial heterogeneity between cities. 11. Very similar patterns are observed using data from the Council of Mortgage Lenders on all mortgage providers. See Figure A.8 in Online Appendix A. 12. Evidence from the Wealth and Assets Survey and the Survey of Building Society Mortgages show that first-time-buyers are the group taking up the largest LTV mortgages. This is the case because they have lower accumulated wealth and hence are less capable of paying large deposits. 13. The Bank of England’s Credit Conditions Survey records lending availability and borrowing conditions as reported by British banks. Survey responses indicates (i) there was a substantial reduction in credit availability for secured lending between the last quarter of 2007 and the first of 2009; (ii) maximum loan-to-value mortgages offered by British banks also decreased during this period; (iii) there was a substantial tightening of the criteria used to approve borrowers for secured lending, coupled with a substantial reduction in the percentage loan requests being approved; and (iv) the reduction in credit availability was almost entirely concentrated on high LTV mortgages (over 75%). Figures in support of each of these points are presented in Figure A.9 in Online Appendix A. 14. We can see this specification as a differenced version of the equation in levels: \begin{eqnarray*} &&\log (\textit{trans})_{it}= \alpha _{i}+\beta _{1}LTV_{jt}+\beta _{2}LTV_{jt} \times \textit{Quality}_{i}+\beta _{3} \textit{Quality}_{i} \times d_{2009}+\delta d_{2009}+\phi X_{it}+\epsilon _{it}. \end{eqnarray*} Note that d2009 is a fixed effect for observations recorded in 2009. Given that we are using a two period panel, the within-groups and first-difference estimator coincide. 15. I use data at the most disaggregated level available. Descriptive Statistics for the city level variables are presented in Table A.2 in Online Appendix A. 16. This would be the case especially if there was a substantial expansion of credit in the United Kingdom in the 2000–2007 period. Although this is certainly the case in the United States—and did affect subsequent market outcomes (Mian and Sufi 2009)—lending conditions had been relatively lax in England and Wales for some time. See left panel of Figure 7. 17. The over-identification test in this specification does not reject the null of valid instruments with a p-value of 0.58. 18. The term let-to-buy is used in the United Kingdom to refer to transitions in which a household trades up the ladder and rents out the unit where they resided when young. Not to be confused with buy-to-let, which is associated to expressly buying a unit to rent it out. 19. The fact that some agents do not have access to property via the private market is a necessary consequence of the assumption that |$\bar{S} < 2$|⁠. Agents are assumed to pay off their income as social rent (or transfer to parents) to ensure next period wealth is still monotonous in i. 20. The fact that rental utility is invariant with housing type explains why there is only one rental price Rt. 21. This will mean that nothing guarantees |$r \, p_{L,t} \ne R$| in equilibrium. Although the absence of institutional investors in the model may seem puzzling, recent reports on the matter indicate the UK market for private rented dwellings is dominated by small investors (see Montague and collaborators 2012). 22. A simple example of housing stock, credit constraints, and interest that would satisfy these conditions would be SH = 0.85, 2 − SH − SL = 0.05, r = 0.01, γ = 0.8 for uniform income distributions e1(i) ∼ U[2, 4] and e2(i) ∼ U[2.5, 15]. 23. Subindices for each threshold are as follows. Subindex R corresponds to thresholds for rental affordability (agents to the right of the threshold can rent), L corresponds to owner-occupation of a low type unit, H corresponds to occupation of an H unit, and HL to ownership of both an H and an L unit (agents residing in H and renting out the other property). 24. For example, Proposition 1 can also be proved for the case in which some young agents own H units. 25. In order to determine transition prices, I first find the price vector that clears housing markets with myopic agents and then verify that this transition also clears the market when agents are forward looking. For sufficiently low values of vL and vH, or a sufficiently large change in γ the price paths for myopic and forward looking agents may not coincide. This is not the case for the parameters in Table 5. 26. Uniform distributions are chosen for income because they allow to easily verify assumptions (3.5)–(4.5) are met. Examples of transitions for other distributions are provided in Online Appendix B. 27. The fact that borrowing does not scale with housing wealth is broadly consistent with observed patterns in the Wealth and Assets Survey. That being said, this is a consequence of agent’s decisions and not a constraint imposed by lenders. So we can interpret the nonscalability assumption as a reduced-form alternative to a full characterization of households’ borrowing decisions. 28. The evolution of the fraction of renters is reported in the left panel of Figure A.10 in Online Appendix A. The right panel shows the evolution of aggregate buy-to-let lending. 29. Unfortunately, disaggregated data on renting is not available at the yearly frequency. Most of the increase in renting over the 2001–2011 period took place after 2008. Moreover, the increase in renting between 2002 and 2008 was mainly fuelled by purchases by buy-to-let investors that should have a positive effect on transactions. 30. I use the waves between 2004 and 2011 and restrict my sample to owner-occupied and private rental dwellings. 31. The striking persistence of average age the LSOA level is evidence of this. 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TI - Credit Constraints and the Composition of Housing Sales. Farewell to First-Time Buyers?
JF - Journal of the European Economic Association
DO - 10.1093/jeea/jvz017
DA - 2020-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/credit-constraints-and-the-composition-of-housing-sales-farewell-to-jqi9l4F9S1
SP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -