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Oxford Economic Papers
, Volume Advance Article – Apr 12, 2018

19 pages

/lp/ou_press/how-free-admittance-affects-charged-visits-to-museums-an-analysis-of-7HENJI4OoI

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- Oxford University Press
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- © Oxford University Press 2018. All rights reserved.
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- 0030-7653
- eISSN
- 1464-3812
- D.O.I.
- 10.1093/oep/gpy011
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Abstract This study evaluates the effects of free visits to museums on charged visits. We take the Italian State museums and monuments as the case study, and we consider monthly data, aggregate at the national level, from January 1996 to December 2015. Within a multivariate analysis, which takes into account the seasonal structure of data, we document a positive influence of the number of free visits to museums and monuments on the subsequent charged visits. We also analyse the effect of a recent policy change (July 2014), consisting of an extension of free admittance. We show that the new rule has entailed an increase in both free and charged visits, as well as a stronger link between the patterns of free and charged visits. Our results can be informative in the ever-green debate on the museum attendance and its relations with individual choices and public policies regarding cultural consumption. 1. Introduction The BBC website, on 1 December 2011, the date marking the 10th anniversary of the government’s decision to end charges at England’s national museums, reported that: ‘Government-sponsored museums that have stopped charging since 2001 have seen combined visitor rates more than double in the past decade, figures show. […] Almost 18 million people visited the 13 attractions in 2010–11, compared with 7 million in 2000–01’ (BBC, 2011).1 In different recent interviews and statements, the Italian Minister for Culture and Tourism underlined the spectacular increase in numbers of museum attendance since 2014, also thanks to the fact that free admission was established for the first Sunday of every month in all Italian State museums and monuments, starting in July 2014.2 The official website of the Italian Ministry for Culture and Tourism (MIBACT) stresses that free visits have increased by 5%, and charged visits by 7% in the second semester 2014, with respect to the previous year. In 2015, the variation (on a year-to-year basis) is about +4% for free visits, +6% for charged visits, and +14% for revenues from entrance fee; whereas in 2016, the variation is +9% and +12% for charged visits and revenues, respectively (MIBACT, 2016, 2017a). Such data would suggest, according to the Italian Government, that the policy of promoting free admission to museums and monuments, among other reforms, has benefited charged visits too. Across countries, and across museums in any country, the rules regarding free vs charged admission to museums differ and have been changing over time, often according to the prevailing political view: roughly speaking, ‘market-orientated’ governments are more prone to consider museums as any other private cultural agencies that have to compete in the market choosing the optimal pricing strategy to maximize revenues; ‘welfare-orientated’ governments are more prone to favour free-of-charge admission rules, consistent with a social role of museums, useful to improve people’s cultural formation, to reinforce local identity of cities and regions, and to stimulate economic local development (Santagata, 2007). Nowadays, all possible combinations of rules seem to be present, in any country: there are cases in which the admission fee is required without exception; museums where charged admission is joint with strict or large policy regarding free or reduced tickets to certain sub-groups of people; museums where free admission is reserved to people subscribing a membership (Rushton, 2017); and museums with free admission for all, sometimes joint with a plea for voluntary contribution. This variety of admission rules holds also within a group of museums that are similar in nature or even managed by the same company. For instance, within the Smithsonian group in the US, some museums require an admission fee, whereas others are free (Smithsonian Institute, 2007). It is also possible that a museum offers free entry to permanent exhibition and charges for temporary exhibitions, or vice versa. Moreover, free entry, as a form of price discrimination, can be used in several circumstances as a marketing tool to promote regular charged visits (Kotler et al., 2008). A recent study of Chen et al. (2016) shows that free entry to public museums can also benefit private museums, increasing their paying visitors: Chen et al. (2016) examine the effects of the introduction of universal free admission to public museums in Taiwan, and they find that the new free-admission policy in public museums leads to a larger number of visits to both public and private museums. In other words, they document a positive externality from the free visits to public museums on the charged visits to private museums. In this article, we specifically revisit this point, aiming at assessing whether the dynamics of free visits affects current and future dynamics of charged visits. We take Italy as the case study and examine aggregate data on monthly visits to state museums and monuments between 1996 and 2015, with the final aim of detecting the relationship between free and charged visits to museums and monuments over time. The outline of the article is as follows. In Section 2, we briefly mention some relevant literature contributions. In Section 3, we present the data and discuss the statistic properties of the time series at hand: we show that the series of free and charged visits to museums and monuments show strong seasonal patterns, and the nature (stochastic or deterministic) of the seasonal pattern is debated. More importantly, we show that the shape of seasonal components differs between free and charged visits; this aspect, overlooked by available analyses, can provide some marketing and policy suggestions. In Section 4, we investigate the relationship between the dynamics of charged visits, free visits, and tourism flow series. We document that the new rule regarding free admission to state museums and monuments in Italy (dated July 2014) has entailed a structural break in the behaviour of both free and charged visits to these sites, and a new, stronger relationship has been established. Section 5 concludes with proposing some reflections on theoretical underpinnings and policy implications. 2. Free vs charged admission to museums: a brief review of literature The debate on the issue of free vs charged admission to museums is of interest for managers, policymakers, and academics (Bailey and Falconer, 1998; Cowell, 2007). The economic literature, based on theoretical and empirical research, mainly concerns the pros and cons of charging museum visits and the effect of entrance fee policies on museum attendance, considering the public and private nature of different outputs offered by museums (say, identification, preservation, and exhibition of the collection; see Fernandez-Blanco and Prieto-Rodriguez, 2011). The public good nature of the museums’ output and its educational content, and the merit good nature of cultural heritage, are theoretical reasons supporting the free attendance to public museums (Peacock and Godfrey, 1976; O’Hagan, 1995). However, pricing is not Pareto-efficient from a social-welfare perspective, as the marginal cost of an additional visitor is close to zero; moreover, if the admission fee is set equal to the average cost, all potential visitors, who are willing to pay more than the marginal cost but less than the average cost, will be excluded from the visit, thus entailing a violation of the equality opportunity principle (Santagata, 2007). On the other hand, free admission policy has regressive effects, as benefits go to individuals who are able to pay the entrance fee, and museums are subsidized by public grants coming from general fiscal entrances. The private nature of the cultural services supplied by museums can justify the introduction of an entrance fee, both to avoid congestion (Maddison and Foster, 2003) and to get revenues to invest in increasing the quality of the services supplied (Peacock, 1969; Towse, 2005; Frei and Meier, 2006). However, it is well known that the museums’ competition for visitors cannot be based on the entry ticket (whose price is, in most cases, regulated, at least in public museums) but it is based on the quality of the collection and the related services that are useful to appreciate the collection. In any case, pricing is a relevant element of the marketing strategy, and it can prevent individuals from undervaluing free-of-charge cultural entertainment and postpone its consumption, while preferring other cultural activities that have a price and are offered for a limited period (Kotler et al., 2008). Museums’ managers are aware that the revenues from entrance fees cannot cover the high maintenance and management costs of museum: public grants are the main source of entrance, and the introduction of a pricing system could partially crowd out other financing sources, such as voluntary contributions (see Santagata and Signorello, 2000, on the case of Naples museums). Therefore, an optimal financing schedule of museums, consistent with an objective function that takes into account the utility of visitors and the goals of managers and stakeholders, usually combines the different sources of entrance: fees, public grants, and voluntary contributions (Prieto-Rodriguez and Fernandez-Blanco, 2006). In available economic literature, a large part of evidence regarding the effect of tickets on museum attendance is based on individual surveys, or research at specific museums, so that the conclusions are typically based on case studies (see the comprehensive review in Frateschi et al., 2009). Several contributions in literature have resorted to contingent valuation and stated preferences techniques to assess the willingness to pay for visiting specific museums (Santagata and Signorello, 2000; Bedate et al., 2009; Lampi and Orth, 2009; Baez-Montenegro et al., 2012, among others); only a few studies resort to aggregate data (e.g. Cowell, 2007, on visits to museums in the UK). Available empirical research generally suggests that price is not a serious barrier to visit museums, and the price elasticity of museum visits is low. Some researchers openly suggest that charged admission does not hurt attendance, and may have positive effects in terms of revenues, especially if the quality of the services increases (see O’Hagan, 1995; Luksetich and Partridge, 1997; Steiner, 1997). However, a side effect of price could be given by the composition of museum attendances, as price represents a perceived subjective barrier that is mainly related with the individual income, education, and occupational status (Kirchberg, 1998). On the other hand, the pieces of evidence collected in the UK case, after the 2001 reintroduction of universal free admission to government-sponsored museums, seem to suggest that the increase of attendance has concerned all segments of visitors, without a significant change in the profile of the typical visitor, especially as far as income and education levels are concerned (Martin, 2003; Cowell, 2007). Moreover, addiction is a relevant feature of cultural consumptions (Stigler and Becker, 1977), including museum attendance (Brida et al., 2016). This suggests that promoting the free admission of (young, but not only) people will enhance future demand (Brito and Barros, 2005, among others). From the standpoint of supply strategy, free admission in museums and monuments on specific days consists of a form of inter-temporal price discrimination, which may allow to increase revenues: from this perspective, our present analysis contributes to the literature vein on the aftermaths of price discrimination (see, e.g. Armstrong, 2006), providing empirical evidence on a specific case of price discrimination in the presence of consumers’ addiction. 3. Data and methods 3.1 Data We aim at analyzing the dynamics of free and charged visits to Italian State museums in aggregate terms. The data we consider are provided by MIBACT, and they are freely available from the www.statistica.beniculturali.it website (MIBACT, 2017c). In particular, we consider the monthly series of free and charged visits to all state museums and monuments, including historical parks and gardens and archaeological areas. The group of sites is very large (made by more than 400 spots) and heterogeneous: it includes not only superstar museums (like Uffizi in Firenze and the archaeological area of Pompei) but also minor heritage attractions, spread over Italy. Entrance prices are set by MIBACT. Only in some (minor) state sites entrance is always free for all people. In the other sites, only specific groups of people benefit from free entrance (people aged less than 18, students and professors of arts faculties, and other public officials). Discounted prices, usually 50% of the full price, apply to specific categories (e.g. people aged 18–25, people in organized groups, journalists, etc.). Average price, as computed as the ratio between entrance revenues and charged visits, was 4.46 euro in 1996 and 7.49 euro in 2015 (charged visits include both full- and reduced-price tickets); min-max full prices are 2–26 euro.3 It is very informative to take a preliminary look at the series under scrutiny regarding free and charged visits to museums and monuments. Figure 1 shows their patterns over time, whereas Table 1 gives some statistics. Both the free attendance and the charged attendance show strong seasonal pattern. The number of free visits is clearly larger than the amount of charged visits, especially due to attendance at peak seasons; the seasonal variation of free attendance is clearly larger than the seasonal variation of charged attendance; the peaks occur at different months, for free and charged attendance. Table 1 Descriptive statistics on time series FREEVIS PAYVIS Mean 1,468,755 1,300,212 Median 1,344,276 1,360,045 Maximum 3,981,811 2,511,003 Minimum 371,681 398,435 Std. Dev. 709,043.4 519,583.9 Month with min average Jan. (640,482) Jan. (620,815) Month with Max average Apr. (2,816,942) Aug. (2,0200,039) F test on seasonality F11,228 = 213.95** F11,228 = 371.24*** K test on seasonality K = 222.55** K = 214.83** F test on moving seasonality F19,209 = 2.47** F19,209 = 1.25n.s. SF (min-Max, 1996) 0.39–2.28 0.47–1.72 SF (min-Max, 2015) 0.54–1.59 0.54–1.46 Observations 240 240 FREEVIS PAYVIS Mean 1,468,755 1,300,212 Median 1,344,276 1,360,045 Maximum 3,981,811 2,511,003 Minimum 371,681 398,435 Std. Dev. 709,043.4 519,583.9 Month with min average Jan. (640,482) Jan. (620,815) Month with Max average Apr. (2,816,942) Aug. (2,0200,039) F test on seasonality F11,228 = 213.95** F11,228 = 371.24*** K test on seasonality K = 222.55** K = 214.83** F test on moving seasonality F19,209 = 2.47** F19,209 = 1.25n.s. SF (min-Max, 1996) 0.39–2.28 0.47–1.72 SF (min-Max, 2015) 0.54–1.59 0.54–1.46 Observations 240 240 Source: Authors’ calculations on data from MIBACT (2017c). Note: ***/**/* = significant at 0.1/1/5%; n.s.: not significant at the 5% level. FREEVIS denotes the free visits to museums and monuments; PAYVIS denotes the charged visits. Table 1 Descriptive statistics on time series FREEVIS PAYVIS Mean 1,468,755 1,300,212 Median 1,344,276 1,360,045 Maximum 3,981,811 2,511,003 Minimum 371,681 398,435 Std. Dev. 709,043.4 519,583.9 Month with min average Jan. (640,482) Jan. (620,815) Month with Max average Apr. (2,816,942) Aug. (2,0200,039) F test on seasonality F11,228 = 213.95** F11,228 = 371.24*** K test on seasonality K = 222.55** K = 214.83** F test on moving seasonality F19,209 = 2.47** F19,209 = 1.25n.s. SF (min-Max, 1996) 0.39–2.28 0.47–1.72 SF (min-Max, 2015) 0.54–1.59 0.54–1.46 Observations 240 240 FREEVIS PAYVIS Mean 1,468,755 1,300,212 Median 1,344,276 1,360,045 Maximum 3,981,811 2,511,003 Minimum 371,681 398,435 Std. Dev. 709,043.4 519,583.9 Month with min average Jan. (640,482) Jan. (620,815) Month with Max average Apr. (2,816,942) Aug. (2,0200,039) F test on seasonality F11,228 = 213.95** F11,228 = 371.24*** K test on seasonality K = 222.55** K = 214.83** F test on moving seasonality F19,209 = 2.47** F19,209 = 1.25n.s. SF (min-Max, 1996) 0.39–2.28 0.47–1.72 SF (min-Max, 2015) 0.54–1.59 0.54–1.46 Observations 240 240 Source: Authors’ calculations on data from MIBACT (2017c). Note: ***/**/* = significant at 0.1/1/5%; n.s.: not significant at the 5% level. FREEVIS denotes the free visits to museums and monuments; PAYVIS denotes the charged visits. Fig. 1 View largeDownload slide Patterns over time of free and charged visits to museums and monuments. Source: Authors’ elaboration on data from MIBACT (2017c). Fig. 1 View largeDownload slide Patterns over time of free and charged visits to museums and monuments. Source: Authors’ elaboration on data from MIBACT (2017c). These simple pieces of evidence, perhaps overlooked by available analyses in literature, provide valuable elements for reflection and policy implications. First, the peak months for free visits are the spring months (April and, in the second place, May), due to the visits of school students in organized tours, which typically take place in spring. Second, the peak months for charged visits are in summer (August and, in the second place, July): this clearly suggests that tourist flows (whose peaks are in August and July) have an effect on the size of visits to museums and monuments. The fact that tourist arrivals drive visits to museum and monuments is widely documented (see Cellini and Cuccia, 2013, for a specific analysis of the Italian case). Third, descriptive statistics regarding the measure of seasonality confirm what is already clear from the graphical inspection: if we rely on standard analysis of seasonal components, the usual tests in Table 1 (based on the X12-Arima seasonal adjustment program, assuming a multiplicative datum structure) drive to the conclusion that the presence of significant seasonal components cannot be rejected; however, seasonality appears to be more limited and more stable over years for the charged attendance as compared with the free attendance. More formally, the appropriate F-test on moving seasonality detects moving seasonal factors for free visits with a clear tendency to reduce over time (as shown by the change of seasonal factors), whereas it rejects the presence of moving seasonality for charged visits. 3.2 The nature of seasonality Seasonality may have a stochastic or a deterministic nature; that is, the time series can be characterized by the presence of seasonal unit roots or by the presence of deterministic seasonal components. Several tests have been proposed to detect the presence of seasonal unit roots. In particular, Dickey et al. (1984) provide an extension of Dickey–Fuller test (originally proposed for evaluating the unit root in yearly data) to the case of seasonal series. Beaulieu and Miron (1993) and Hylleberg (1995) offer contributions for additional test procedures, still following a regression-based approach, focusing on quarterly and monthly data, respectively. Tests along these lines have been largely employed to analyse monthly time series in the field of tourism (see, e.g. the recent application in Cellini and Cuccia, 2013, referred to in Italy).4 However, both Smith and Taylor (1998), analyzing quarterly data, and Taylor (1998), dealing with monthly data, observe that the Dickey–Hasza–Fuller procedure does not allow for different time trends across the seasons, and they show that the null hypothesis of the presence of the seasonal unit root is easily rejected, if one allows for different trends across seasons. In simpler words, Smith and Taylor (1998) and Taylor (1998) point out that seasonal unit roots disappear from the data generation process, if one accounts for different time trends for seasons across years. In more formal terms,5 let Yt denote a monthly time series, and let Yt=a+ρYt−12+vt be the representation of the data-generating process. The series possesses a seasonal unit root if the null hypothesis ρ=1 cannot be rejected. Operationally, this amounts to considering the regression equation Δ12Yt=a+αYt−12+vt, and to evaluating the null hypothesis α=ρ−1=0 (the symbol Δ12 denotes the 12th difference, that is Δ12Yt≡Yt−Yt−12). However, more complex deterministic components of the data generation process of Yt should be taken into account. Specifically, 12 different constant terms (one for each season) instead of one constant term should be taken into account; in such a case, a has to be interpreted as a 12-component vector, a={ai}i=112.6 Second, a number of autoregressive terms of Δ12Yt should be considered to have white noise regression residuals; in most cases, the 1st, 2nd, and 12th lags of the dependent variable are statistically significant and sufficient to make white noise residuals. Third and most important, a deterministic trend (T) should be appropriately considered as well, even if the inclusion of a trend makes the test for seasonal unit roots less powerful. Accordingly, a procedure should be used, in which the following regression equation is considered: Δ12Yt=∑i=112ai+τT+αYt−12+∑jβjΔ12Yt−j+εt [1] and specifically, the significance of the coefficient α is evaluated, to test for the presence of the seasonal unit root. To this end, the distribution of the Student-t statistics is non-standard, and specific tabulations of critical values are provided by Dickey et al. (1984). If the null of the seasonal unit root is not rejected (i.e. α=0), the series is seasonally integrated. Seasonally integrated series possess s unit root processes, specifically one unit root for each of the s seasons. Taylor (1998) observes that the appropriate inclusion of 12 different trend terms (one for each season) leads to rejecting the null of the seasonal unit root, whereas the same null hypothesis cannot be rejected in the presence of only one trend, which is common to all seasons. He also shows that the evaluation of the presence of a seasonal unit root in the presence of 12 time trends corresponds with evaluating the auxiliary regression: Δ12Yt=∑i=112ai+∑i=112biYt−i+∑i=112ciTi+εt [2] (where Ti is a deterministic trend that is specific for month i) and with testing the null b1 = b2 = … b12 = 0. Table 2 reports the results of both the standard Dickey–Hasza–Fuller procedure and the procedure suggested by Taylor (1998), as applied to the series under consideration in the present analysis. Both procedures lead to rejecting the presence of seasonal unit roots for both the series of free attendance and the charged attendance.7 In the cases of both charged visits and free visits, some components of the vector {ci} i=112 are statistically significant, whereas others are not, so that the consideration of different time trends across seasons appears appropriate, and the conclusion is that seasonal unit roots are absent, in the presence of different seasonal trends. Table 2 Test on seasonal unit roots FREEVIS PAYVIS Hasza-Dickey-Fueller test (critical value Student-t 5%: −6.13) −0.665 (−8.19)*** −0.55 (−8.68)*** Taylor F1,2,…12 test (critical value 5%: 7.240) 12.916 (p = 0.000)*** 12.090 (p = 0.000)*** FREEVIS PAYVIS Hasza-Dickey-Fueller test (critical value Student-t 5%: −6.13) −0.665 (−8.19)*** −0.55 (−8.68)*** Taylor F1,2,…12 test (critical value 5%: 7.240) 12.916 (p = 0.000)*** 12.090 (p = 0.000)*** Source: Authors’ calculations. Note: Hasza-Dickey-Fuller test reports the estimate of the alpha coefficient (and its Student-t) in [1]; only significant lag terms of Δ12Yt are considered. Taylor F1,2,....12 test considers eq. [2] and provides the result of the F- test on the null b1 = b2 = ...b12 = 0. In both cases, the null is the presence of a seasonal unit root. Table 2 Test on seasonal unit roots FREEVIS PAYVIS Hasza-Dickey-Fueller test (critical value Student-t 5%: −6.13) −0.665 (−8.19)*** −0.55 (−8.68)*** Taylor F1,2,…12 test (critical value 5%: 7.240) 12.916 (p = 0.000)*** 12.090 (p = 0.000)*** FREEVIS PAYVIS Hasza-Dickey-Fueller test (critical value Student-t 5%: −6.13) −0.665 (−8.19)*** −0.55 (−8.68)*** Taylor F1,2,…12 test (critical value 5%: 7.240) 12.916 (p = 0.000)*** 12.090 (p = 0.000)*** Source: Authors’ calculations. Note: Hasza-Dickey-Fuller test reports the estimate of the alpha coefficient (and its Student-t) in [1]; only significant lag terms of Δ12Yt are considered. Taylor F1,2,....12 test considers eq. [2] and provides the result of the F- test on the null b1 = b2 = ...b12 = 0. In both cases, the null is the presence of a seasonal unit root. As underlined by Taylor (1998), the interpretation of a time series as a seasonally integrated series (and hence the consideration of seasonally differentiated series for inference and regression analysis), in the face of a true data-generating process, which includes different seasonal deterministic time trends and no seasonal unit root, leads to errors due to the over-differentiation of the series at hand. For the reasons mentioned earlier, we consider the time series of free and charged attendance to Italian State museums and monuments as seasonally stationary in the presence of different seasonal constant and time-trend components. The same conclusion—that is, the rejection of the seasonal unit root, in the presence of different seasonal constant and time-trend terms—is reached for the series of tourist arrivals and overstays. The F1,2....12 Taylor tests provide, in any case, values well above the critical value (which is 7.24 at the 0.05 significance level): the test statistics are 17.701 for arrivals and 9.469 for overstays. 3.3 Research design The aim of this study is to evaluate the effect of free visits to museums and monuments on (contemporary and subsequent) charged visits. Taking into account the seasonal nature of the series at hand, largely discussed in the previous section, we opt for considering the following general specification: Yt=∑i=112ai+∑i=112ciTi+βXt+γZt+∑i=112λiYt−i+∑i=112φiXt−i+εt. [3] Variable Y denotes the charged visits to museums and monuments, variable X denotes the free visits, and variable Z is a control variable corresponding to the tourist arrivals (or tourist overstays, depending on the specification). The ai coefficients correspond to the seasonal dummy variables; the terms ciTi represent the seasonal trend terms; and polynomial terms ∑i=112λiYt−i and ∑i=112φiXt−i represent the lags of the dependent variable Y and independent variable X, respectively. Noteworthy, we proceed from the general to the particular specification, and we maintain only the significant terms in the regression specification. Thus, only a sub-set of the 12 seasonal dummy variables and only a subset of seasonal trends are statistically significant (at the 10% level), and are kept in the final specification. Similarly, only the significant lags of variables X and Y are kept in final specification: usually, the lags of 1st, 2nd, and 12th order. It is also worth underlying that we provide the results with all variables in level (not in log): this is consistent with the suggestion of Taylor (1998) and other subsequent works that document that econometric inference in the presence of deterministic seasonal components (seasonal dummies and seasonal deterministic trends) is more reliable when variables are in level, instead of logged; however, in all regressions we are going to show, the substantial results (sign and statistical significant of all regressors) remain unchanged if variables are logged (results are available on request). 4. The dynamic effects of free attendance on charged visits to museums and monuments 4.1 Main results This section provides the core findings of this study. The results of regression eq. (3) are reported in Table 3, Column 1. Table 3 Regression results Dependent variable: PAYVIS [Column 1] [Column 2] [Column 3] (OLS) (OLS) (IV) Constant ( ×1,000) 110.3 162.2 141.8 (1.66)* (2.50)*** (2.23)** Seasonal constant dummy ( ×1,000) [month number in brackets] [1] −224.8 [1] −257.2 [1] −216.1 (−4.78)*** (−4.59)*** (−4.54)*** [6] 19,291 [4] 152.5 [4] 102.5 (1.75)* (3.21)*** (2.68)*** [7] 42,356 [7] −105.9 [11] −313.7 (3.49)*** (−1.99)*** (−5.79)*** [8] 53,320 [8] 23,065 (4.29)*** (1.88)* [11] −242.2 [11] −317.9 (−4.49)*** (−5.10)*** Seasonal deterministic trends [month number in brackets] [2] −111.8 [2] −122.3 [2] −99.8 (−4.93)*** (−4.60)*** (−4.22)*** [6] −9772.7 [8] −11,486 [9] −56.3 (−1.78)* (−1.88)* (−2.77)*** [7] −21,304.5 [9] −59.0 [12] −101.6 (−3.50)*** (−2.93)*** (−4.44)*** [8] −26,756.6 [12] −117.3 (−4.30)*** (−4.50)*** [9] −155.3 (−5.52)*** [12] −84.1 (−3.61)*** TOURARRIVALS 0.115 0.043 0.021 (6.39)*** (4.11)*** (3.00)*** FREEVIS −0.203 −0.03 (−5.87)*** (−0.98)n.s. FREEVIS(-1) 0.084 (3.10)*** FREEVIS(-2) −0.084 (−2.50)** FREEVIS(-12) 0.136 (3.74)*** CUM_FREEVIS 0.112 0.100 (2.29)** (2.46)** PAYVIS(-1) 0.269 0.249 0.253 (5.81)*** (5.54)*** (5.93)*** PAYVIS(-12) 0.216 0.368 0.485 (3.70)*** (5.94)*** (7.98)*** R2 0.96 0.94 0.93 F 248.3*** 231.3*** 305.1*** Durbin h 2.84*** −1.12 −1.11 Observations 228 228 228 Dependent variable: PAYVIS [Column 1] [Column 2] [Column 3] (OLS) (OLS) (IV) Constant ( ×1,000) 110.3 162.2 141.8 (1.66)* (2.50)*** (2.23)** Seasonal constant dummy ( ×1,000) [month number in brackets] [1] −224.8 [1] −257.2 [1] −216.1 (−4.78)*** (−4.59)*** (−4.54)*** [6] 19,291 [4] 152.5 [4] 102.5 (1.75)* (3.21)*** (2.68)*** [7] 42,356 [7] −105.9 [11] −313.7 (3.49)*** (−1.99)*** (−5.79)*** [8] 53,320 [8] 23,065 (4.29)*** (1.88)* [11] −242.2 [11] −317.9 (−4.49)*** (−5.10)*** Seasonal deterministic trends [month number in brackets] [2] −111.8 [2] −122.3 [2] −99.8 (−4.93)*** (−4.60)*** (−4.22)*** [6] −9772.7 [8] −11,486 [9] −56.3 (−1.78)* (−1.88)* (−2.77)*** [7] −21,304.5 [9] −59.0 [12] −101.6 (−3.50)*** (−2.93)*** (−4.44)*** [8] −26,756.6 [12] −117.3 (−4.30)*** (−4.50)*** [9] −155.3 (−5.52)*** [12] −84.1 (−3.61)*** TOURARRIVALS 0.115 0.043 0.021 (6.39)*** (4.11)*** (3.00)*** FREEVIS −0.203 −0.03 (−5.87)*** (−0.98)n.s. FREEVIS(-1) 0.084 (3.10)*** FREEVIS(-2) −0.084 (−2.50)** FREEVIS(-12) 0.136 (3.74)*** CUM_FREEVIS 0.112 0.100 (2.29)** (2.46)** PAYVIS(-1) 0.269 0.249 0.253 (5.81)*** (5.54)*** (5.93)*** PAYVIS(-12) 0.216 0.368 0.485 (3.70)*** (5.94)*** (7.98)*** R2 0.96 0.94 0.93 F 248.3*** 231.3*** 305.1*** Durbin h 2.84*** −1.12 −1.11 Observations 228 228 228 Source: Authors’ calculations. Note:t-stat (Column 1 and 2) or z-stat (Column 3) in parenthesis; ***, **, * denote significance at the 1%, 5%, 10% level, respectively; n.s. stays for not-significant at the 10% level. TOURARRIVALS denotes the tourist arrivals. CUM_FREEVIS is the monthly average of free visits, computed over the previous 12 months. Table 3 Regression results Dependent variable: PAYVIS [Column 1] [Column 2] [Column 3] (OLS) (OLS) (IV) Constant ( ×1,000) 110.3 162.2 141.8 (1.66)* (2.50)*** (2.23)** Seasonal constant dummy ( ×1,000) [month number in brackets] [1] −224.8 [1] −257.2 [1] −216.1 (−4.78)*** (−4.59)*** (−4.54)*** [6] 19,291 [4] 152.5 [4] 102.5 (1.75)* (3.21)*** (2.68)*** [7] 42,356 [7] −105.9 [11] −313.7 (3.49)*** (−1.99)*** (−5.79)*** [8] 53,320 [8] 23,065 (4.29)*** (1.88)* [11] −242.2 [11] −317.9 (−4.49)*** (−5.10)*** Seasonal deterministic trends [month number in brackets] [2] −111.8 [2] −122.3 [2] −99.8 (−4.93)*** (−4.60)*** (−4.22)*** [6] −9772.7 [8] −11,486 [9] −56.3 (−1.78)* (−1.88)* (−2.77)*** [7] −21,304.5 [9] −59.0 [12] −101.6 (−3.50)*** (−2.93)*** (−4.44)*** [8] −26,756.6 [12] −117.3 (−4.30)*** (−4.50)*** [9] −155.3 (−5.52)*** [12] −84.1 (−3.61)*** TOURARRIVALS 0.115 0.043 0.021 (6.39)*** (4.11)*** (3.00)*** FREEVIS −0.203 −0.03 (−5.87)*** (−0.98)n.s. FREEVIS(-1) 0.084 (3.10)*** FREEVIS(-2) −0.084 (−2.50)** FREEVIS(-12) 0.136 (3.74)*** CUM_FREEVIS 0.112 0.100 (2.29)** (2.46)** PAYVIS(-1) 0.269 0.249 0.253 (5.81)*** (5.54)*** (5.93)*** PAYVIS(-12) 0.216 0.368 0.485 (3.70)*** (5.94)*** (7.98)*** R2 0.96 0.94 0.93 F 248.3*** 231.3*** 305.1*** Durbin h 2.84*** −1.12 −1.11 Observations 228 228 228 Dependent variable: PAYVIS [Column 1] [Column 2] [Column 3] (OLS) (OLS) (IV) Constant ( ×1,000) 110.3 162.2 141.8 (1.66)* (2.50)*** (2.23)** Seasonal constant dummy ( ×1,000) [month number in brackets] [1] −224.8 [1] −257.2 [1] −216.1 (−4.78)*** (−4.59)*** (−4.54)*** [6] 19,291 [4] 152.5 [4] 102.5 (1.75)* (3.21)*** (2.68)*** [7] 42,356 [7] −105.9 [11] −313.7 (3.49)*** (−1.99)*** (−5.79)*** [8] 53,320 [8] 23,065 (4.29)*** (1.88)* [11] −242.2 [11] −317.9 (−4.49)*** (−5.10)*** Seasonal deterministic trends [month number in brackets] [2] −111.8 [2] −122.3 [2] −99.8 (−4.93)*** (−4.60)*** (−4.22)*** [6] −9772.7 [8] −11,486 [9] −56.3 (−1.78)* (−1.88)* (−2.77)*** [7] −21,304.5 [9] −59.0 [12] −101.6 (−3.50)*** (−2.93)*** (−4.44)*** [8] −26,756.6 [12] −117.3 (−4.30)*** (−4.50)*** [9] −155.3 (−5.52)*** [12] −84.1 (−3.61)*** TOURARRIVALS 0.115 0.043 0.021 (6.39)*** (4.11)*** (3.00)*** FREEVIS −0.203 −0.03 (−5.87)*** (−0.98)n.s. FREEVIS(-1) 0.084 (3.10)*** FREEVIS(-2) −0.084 (−2.50)** FREEVIS(-12) 0.136 (3.74)*** CUM_FREEVIS 0.112 0.100 (2.29)** (2.46)** PAYVIS(-1) 0.269 0.249 0.253 (5.81)*** (5.54)*** (5.93)*** PAYVIS(-12) 0.216 0.368 0.485 (3.70)*** (5.94)*** (7.98)*** R2 0.96 0.94 0.93 F 248.3*** 231.3*** 305.1*** Durbin h 2.84*** −1.12 −1.11 Observations 228 228 228 Source: Authors’ calculations. Note:t-stat (Column 1 and 2) or z-stat (Column 3) in parenthesis; ***, **, * denote significance at the 1%, 5%, 10% level, respectively; n.s. stays for not-significant at the 10% level. TOURARRIVALS denotes the tourist arrivals. CUM_FREEVIS is the monthly average of free visits, computed over the previous 12 months. Some comments are in order. First, the amount of tourist arrivals is significant and, hence, its inclusion is appropriate. This piece of evidence confirms what is intuitive and already known: the amount of tourist arrivals affects attendance at museums and monuments. It is important to report that the deterministic trend is not significant, if tourist arrivals are considered in the specification, whereas the time trend would be significant in the absence of tourist arrivals among regressors (this clearly means that the time trend would capture the increase of tourism flows, if inserted). Second, the contemporary free entrance emerges to exert a negative impact on charged visits. So, there is a certain degree of crowding out between free and charged entrance (the coefficient is equal to −0.20, and it is statistically significant); in other words, contemporary free and charged visits appear to behave as substitute goods, at this stage of analysis. Third, the most important piece of evidence, in our reading of results, is the positive and significant effect of the 12th lag of free entrance (the slope-coefficient is +0.14, statistically significant): the number of free visits affects charged visits, with a lag of one year. Verbally, an increase in the number of free visitors may have a negative effect on the contemporary number of charged visits, but it has a counterbalancing positive effect, with a 1-year lag. Free visits and 1-year-later charged visits behave as complement goods. As to the meaning of the reported coefficients, we have to remember that variables are considered in level; thus, the coefficient of, e.g. 0.14 attached to FREEVIS (-12) means that for each additional free visit at time t−12, we have 0.14 additional charged visit in the current time t. The fact that only the 1st, 2nd, and 12th lag of free visits appear in the regression is not arbitrary, but it is consistent with the choice of keeping in regression only the statistically significant lags within 12 lags (in fact, we also tested for the 13th lag, which is insignificant). However, it can be interesting to evaluate the effect of cumulative past free visits, instead of evaluating specific lags. Thus, Column 2 of Table 3 considers the effect of the number of past free visits, as measured by the cumulated (or monthly average) datum over the previous 12 months;8 the result is clear: the free visits during the previous 12 months have a positive and significant effect on the number of current charged visits, and the contemporary free visits become no longer significant. In other words, contemporary free and charged visits appear to behave as substitute goods if the relation is conditioned on selected lagged values of free visits, whereas this links disappears, in the relation conditioned on the average free visits over the 12 previous months. There is no doubt about the fact that the average past free visits are complement with current charged visits, that is, a positive externality is at work between free and subsequent charged visits. Further improvements of the econometric estimation reported in Column 2 of Table 3 can be proposed: we observe that the contemporary free visits can be omitted from the specification, as insignificant; moreover, tourist arrivals can be endogenous (as also suggested by the outcome of a recent analysis of Campaniello and Richiardi, 2017). Indeed, the Hausman exogeneity test as applied to this explanatory variable in the estimation under scrutiny rejects the null of exogeneity (Chì-sq = 33.17, p = 0.000). This result is interesting per se, as it is a signal for an influence of museum attendance on tourism arrivals. Hence, we have also run the regression with the Instrumental Variable (IV) method, with the tourist arrival variable instrumented by its own 1st and 12th lags;9 however, the IV estimatates are substantially similar with the Ordinary Least Squares (OLS) estimates (see Column 3 of Table 3): Maintaining only the significant dummy variables in the specification, no changes occur in the statistical significance of the economic variables under scrutiny; simply, tourist arrivals and past cumulated free visits show slightly smaller coefficients. It is easy to compute some elasticity coefficients, based on the estimates at hand; in particular, the elasticity of the charged visits with respect to the average past free visits (over the earlier 12 months) turns out to be 0.13 or 0.11 (according to the OLS or IV estimates, respectively).10 Apart from the specific numerical value, the meaning is that the increase of free visits make a small but statistically significant contribution to the increase of subsequent charged visits, ceteris paribus. The substantive results remain unchanged if we substitute tourist arrivals with tourist overstays in the specifications of Table 3: this outcome is unsurprising, as the correlation between the time series of tourist arrivals and overstays is 0.924. Moreover, we have made two further robustness (or refinement) checks. First, inspired by the outcome from the analysis of Borowiecki and Castiglione (2014)—who resort to data on Italian provinces observed in 2006 and 2007 and find that foreign tourism flows are related with museum attendance, whereas domestic flows are mainly related with consumption of performing arts—we have checked whether domestic and foreign tourist arrivals exert a different effect in our regression exercises. The answer is positive: if we split tourist arrivals between domestic and foreign, the positive and significant effect is specifically exerted by the foreign flow, which is perfectly in line with the findings of Borowiecki and Castiglione (2014).11 Second, one could wonder whether our results are led by superstar attractions or they are still valid also for minor sites. Of course, it is difficult to select ‘superstars’, also because the attendance to specific cultural sites varies across the years under consideration. Only two attractions are always among the first three most visited sites (namely, the museum Galleria degli Uffizi in Firenze and the archaeological area of Pompei). If we delete these two sites from our sample, all substantial results remain unchanged. Moreover, if we focus on museums only (whose average size, as measured by charged and free visits, is lower than the average size of all sites, including monuments, archaeological areas, and historical garden), the substantial results still remain unchanged (results are available on request). These pieces of evidence lead us to exclude that our aggregate results are led by superstar attractions; however, we are ready to admit that more accurate analysis would be necessary to draw a final result on this aspect. 4.2 The 2014 policy intervention A point worth investigating, also for the political debate in Italy, consists of evaluating whether the July 2014 governmental decision of permitting universal free admission to state museums and monuments on every first Sunday of any month entails a significant structural break in the relationship between free and charged visits. The answer is positive: taking July 2014 as the breakpoint, the Chow breakpoint test provides the statistics: F15,228 = 2.09 (p = 0.01), LR = 33.57 (p = 0.003), which mean that the absence of structural break has to be rejected. To establish which specific coefficient(s) show structural instability, we investigate possible breaks in July 2014 involving the constant term and the slope coefficients of contemporary and past free visits, as well as the control variable related to tourism flow. The results (see Table 4, Column 1) show that a significant structural break affects the impact of contemporary free visit on charged visits: this coefficient turns out to be positive and significant after the breakpoint, whereas it was not significant earlier. The same result—that is, the structural break occurs in the relationship between contemporary free and charged visits—is obtained, if we start by considering a segmented slope coefficient for each regressor (i.e. a pair of coefficients applied to each variable, as considered before and after the breakpoint), and then we test for the equality of the pair coefficients for each regressor before and after the breakpoint. The coefficient equality is rejected only in the case of the contemporary free visits, which are not significant before the breakpoint and become significant in the sub-period after July 2014. Table 4 The effects of governmental decision in July 2014 Dependent variable: PAYVIS [Column 1] [Column 2] [Column 3] (OLS) (OLS) (IV) Constant ( ×1,000) 260.0 18,125.9 17,926.7 (3.85)*** (1.97)* (1.92)* Trend (year) −9042.3 −8936.2 (−1.93)* (−1.90)* Seasonal constant dummy ( ×1,000) [month number in brackets] [1] −283.2 [1] −249.8 [1] −245.3 (−5.19)*** (−4.41)*** (−4.88)*** [4] 147.9 [4] 141.4 [4] 103.2 (3.23)*** (3.07)*** (2.78)*** [7] −104.9 [7] −125.2 [11] −302.6 (−2.03)** (−2.43)** (5.59)*** [8] 30,660.0. [8] 2754 (2.50)** (2.32)** [11] −326.5 [11] −289.4 (−5.40)*** (−4.66)*** Seasonal deterministic trends [month number in brackets] [2] −135.46 [2] −121.2 [2] −116.1 (−5.21)*** (−4.53)*** (−4.71)*** [8] −15,268.7 [8] −13,730 [8] −59.3 (−2.50)** (−2.31)** (−2.70)* [9] −54.94 [9] −54.1 [12] −116.4 (.2.82)*** (−2.79)*** (−4.93)*** [12] −128.9 [12] −117.2 (−5.06)*** (−4.52)*** TOURARRIVALS 0.045 0.048 0.019 (4.36)*** (4.74)*** (2.56)** FREEVIS −0.029 −0.027 (−1.10)n.s. (−1.02) n.s. CUM_FREEVIS 0.081 0.226 0.252 (1.63)n.s. (2.42)** (2.66)*** PAYVIS(-1) 0.238 0.209 0.197 (5.42)*** (4.75)*** (5.29)*** PAYVIS(-12) 0.324 0.377 0.470 (5.34)*** (6.02)*** (7.53)*** DU(Since07-2014) −898,498 (−0.41)n.s. DU(Since07-2014)* TOURIST_ ARRIVALS −0.003 (−0.24)n.s. DU(Since07-2014)* FREEVIS 0.200 0.086 0.081 (2.40)** (4.48)*** (4.17)*** DU(Since07-2014)* CUM_FREEVIS 0.376 (032)n.s. R2 0.94 0.94 0.94 F 195.3*** 222.1*** 276.1*** Durbin h −2.57** −1.90 −1.30 Observations 228 228 228 Dependent variable: PAYVIS [Column 1] [Column 2] [Column 3] (OLS) (OLS) (IV) Constant ( ×1,000) 260.0 18,125.9 17,926.7 (3.85)*** (1.97)* (1.92)* Trend (year) −9042.3 −8936.2 (−1.93)* (−1.90)* Seasonal constant dummy ( ×1,000) [month number in brackets] [1] −283.2 [1] −249.8 [1] −245.3 (−5.19)*** (−4.41)*** (−4.88)*** [4] 147.9 [4] 141.4 [4] 103.2 (3.23)*** (3.07)*** (2.78)*** [7] −104.9 [7] −125.2 [11] −302.6 (−2.03)** (−2.43)** (5.59)*** [8] 30,660.0. [8] 2754 (2.50)** (2.32)** [11] −326.5 [11] −289.4 (−5.40)*** (−4.66)*** Seasonal deterministic trends [month number in brackets] [2] −135.46 [2] −121.2 [2] −116.1 (−5.21)*** (−4.53)*** (−4.71)*** [8] −15,268.7 [8] −13,730 [8] −59.3 (−2.50)** (−2.31)** (−2.70)* [9] −54.94 [9] −54.1 [12] −116.4 (.2.82)*** (−2.79)*** (−4.93)*** [12] −128.9 [12] −117.2 (−5.06)*** (−4.52)*** TOURARRIVALS 0.045 0.048 0.019 (4.36)*** (4.74)*** (2.56)** FREEVIS −0.029 −0.027 (−1.10)n.s. (−1.02) n.s. CUM_FREEVIS 0.081 0.226 0.252 (1.63)n.s. (2.42)** (2.66)*** PAYVIS(-1) 0.238 0.209 0.197 (5.42)*** (4.75)*** (5.29)*** PAYVIS(-12) 0.324 0.377 0.470 (5.34)*** (6.02)*** (7.53)*** DU(Since07-2014) −898,498 (−0.41)n.s. DU(Since07-2014)* TOURIST_ ARRIVALS −0.003 (−0.24)n.s. DU(Since07-2014)* FREEVIS 0.200 0.086 0.081 (2.40)** (4.48)*** (4.17)*** DU(Since07-2014)* CUM_FREEVIS 0.376 (032)n.s. R2 0.94 0.94 0.94 F 195.3*** 222.1*** 276.1*** Durbin h −2.57** −1.90 −1.30 Observations 228 228 228 Source: Authors’ calculations. Note:t-stat (Column 1 and 2) or z-stat (Column 3) in parenthesis; ***, **, * denote significance at the 1%, 5%, 10% level, respectively; n.s. stays for not-significant at the 10% level. Table 4 The effects of governmental decision in July 2014 Dependent variable: PAYVIS [Column 1] [Column 2] [Column 3] (OLS) (OLS) (IV) Constant ( ×1,000) 260.0 18,125.9 17,926.7 (3.85)*** (1.97)* (1.92)* Trend (year) −9042.3 −8936.2 (−1.93)* (−1.90)* Seasonal constant dummy ( ×1,000) [month number in brackets] [1] −283.2 [1] −249.8 [1] −245.3 (−5.19)*** (−4.41)*** (−4.88)*** [4] 147.9 [4] 141.4 [4] 103.2 (3.23)*** (3.07)*** (2.78)*** [7] −104.9 [7] −125.2 [11] −302.6 (−2.03)** (−2.43)** (5.59)*** [8] 30,660.0. [8] 2754 (2.50)** (2.32)** [11] −326.5 [11] −289.4 (−5.40)*** (−4.66)*** Seasonal deterministic trends [month number in brackets] [2] −135.46 [2] −121.2 [2] −116.1 (−5.21)*** (−4.53)*** (−4.71)*** [8] −15,268.7 [8] −13,730 [8] −59.3 (−2.50)** (−2.31)** (−2.70)* [9] −54.94 [9] −54.1 [12] −116.4 (.2.82)*** (−2.79)*** (−4.93)*** [12] −128.9 [12] −117.2 (−5.06)*** (−4.52)*** TOURARRIVALS 0.045 0.048 0.019 (4.36)*** (4.74)*** (2.56)** FREEVIS −0.029 −0.027 (−1.10)n.s. (−1.02) n.s. CUM_FREEVIS 0.081 0.226 0.252 (1.63)n.s. (2.42)** (2.66)*** PAYVIS(-1) 0.238 0.209 0.197 (5.42)*** (4.75)*** (5.29)*** PAYVIS(-12) 0.324 0.377 0.470 (5.34)*** (6.02)*** (7.53)*** DU(Since07-2014) −898,498 (−0.41)n.s. DU(Since07-2014)* TOURIST_ ARRIVALS −0.003 (−0.24)n.s. DU(Since07-2014)* FREEVIS 0.200 0.086 0.081 (2.40)** (4.48)*** (4.17)*** DU(Since07-2014)* CUM_FREEVIS 0.376 (032)n.s. R2 0.94 0.94 0.94 F 195.3*** 222.1*** 276.1*** Durbin h −2.57** −1.90 −1.30 Observations 228 228 228 Dependent variable: PAYVIS [Column 1] [Column 2] [Column 3] (OLS) (OLS) (IV) Constant ( ×1,000) 260.0 18,125.9 17,926.7 (3.85)*** (1.97)* (1.92)* Trend (year) −9042.3 −8936.2 (−1.93)* (−1.90)* Seasonal constant dummy ( ×1,000) [month number in brackets] [1] −283.2 [1] −249.8 [1] −245.3 (−5.19)*** (−4.41)*** (−4.88)*** [4] 147.9 [4] 141.4 [4] 103.2 (3.23)*** (3.07)*** (2.78)*** [7] −104.9 [7] −125.2 [11] −302.6 (−2.03)** (−2.43)** (5.59)*** [8] 30,660.0. [8] 2754 (2.50)** (2.32)** [11] −326.5 [11] −289.4 (−5.40)*** (−4.66)*** Seasonal deterministic trends [month number in brackets] [2] −135.46 [2] −121.2 [2] −116.1 (−5.21)*** (−4.53)*** (−4.71)*** [8] −15,268.7 [8] −13,730 [8] −59.3 (−2.50)** (−2.31)** (−2.70)* [9] −54.94 [9] −54.1 [12] −116.4 (.2.82)*** (−2.79)*** (−4.93)*** [12] −128.9 [12] −117.2 (−5.06)*** (−4.52)*** TOURARRIVALS 0.045 0.048 0.019 (4.36)*** (4.74)*** (2.56)** FREEVIS −0.029 −0.027 (−1.10)n.s. (−1.02) n.s. CUM_FREEVIS 0.081 0.226 0.252 (1.63)n.s. (2.42)** (2.66)*** PAYVIS(-1) 0.238 0.209 0.197 (5.42)*** (4.75)*** (5.29)*** PAYVIS(-12) 0.324 0.377 0.470 (5.34)*** (6.02)*** (7.53)*** DU(Since07-2014) −898,498 (−0.41)n.s. DU(Since07-2014)* TOURIST_ ARRIVALS −0.003 (−0.24)n.s. DU(Since07-2014)* FREEVIS 0.200 0.086 0.081 (2.40)** (4.48)*** (4.17)*** DU(Since07-2014)* CUM_FREEVIS 0.376 (032)n.s. R2 0.94 0.94 0.94 F 195.3*** 222.1*** 276.1*** Durbin h −2.57** −1.90 −1.30 Observations 228 228 228 Source: Authors’ calculations. Note:t-stat (Column 1 and 2) or z-stat (Column 3) in parenthesis; ***, **, * denote significance at the 1%, 5%, 10% level, respectively; n.s. stays for not-significant at the 10% level. Elaborating on the regression analysis in the presence of the structural break specifically regarding the effect of contemporary free visits on charged visits, we come to the conclusion that the inclusion of a general deterministic trend is appropriate in this specification (Table 4, Column 2), even in the presence of tourist arrivals. Moreover, all results are robust to the consideration of tourist overstays instead of arrivals. In sum, even if caution is necessary, in front of the limited number of observations available for the period in which the new governmental policy is operative, it seems to be correct, affirming that the decision of promoting free visits to state museums and monuments emerges to have a structural effect, which strengthens the positive relationship between free and charged visits. More specifically, our analysis suggests that a stronger link is established between contemporary free and charged visits, which start to behave as complementary goods under the new, larger, free admission policy. In other words, the positive externality from free to charged visits to museums and monuments appears to emerge even without time lag, after the governmental decision of promoting free visits to state museums and monuments through free admission on the first Sunday of each month has come into place. At the same time, the effect of past free visits on current charged visits remains positive and significant. Also in this case, the substantial evidence does not change if one takes into account that tourist arrivals are not exogenous: the IV estimates (taking the 1st and 12th lags as the instrumental variables for the tourist arrivals) are reported in Column 3 of Table 4.12 From these specifications, we obtain that, under the new free admission policy, the elasticity coefficient of monthly charged visits with respect to contemporary free visits is equal to 0.07 (irrespective of OLS or IV estimator), and the elasticity of monthly charged visits with respect to the average monthly free visits over the previous twelve months is equal to 0.25 or 0.28 (according to OLS or IV, respectively). The quantitative dimension of these effects, though limited, is statistically significant. 5. Theoretical underpinnings, policy implications and concluding remarks The fact that the opportunity cost of cultural consumption is decreasing in the stock of consumed cultural services and commodities, and cultural consumption is characterized by addiction are milestones in cultural economics, since the Becker and Murphy (1988) analysis, not to mention Stigler and Becker (1977) and even the intuition in Principles (Marshall, 1890, Bk 3, Ch. 3). These arguments provide support for the point that enhancing free visits to museums and monuments today drives toward increasing demand tomorrow. This theoretical prediction is supported by our present analysis. More interestingly, our analysis provides a further piece of evidence: a new free admittance policy for Italian State museums and monuments, consisting of enlarging the opportunity of free visits, has led to a higher positive effect of free visits on both subsequent and contemporary charged visits. We would like to underline that our findings are fully in line with the results recently presented by Chen et al. (2016), in the case of Taiwan, even if our present research design and method (and data, of course) differ from theirs. Chen et al. (2016) show that the introduction of the free admittance to public museums has entailed a significant difference in both free visits to public museums and charged visits to private museums, in Taiwan. They employ a difference-in-difference specification approach, which is appropriate in the analysis of panel data. Here, we have analysed aggregate time series data, with no panel structure, limiting our attention to public museums and monuments. We have documented a structural break over time, due to the enlargement of free-admission policy. In both cases, Italy and Taiwan, the substantial evidence is the same—although the institutional differences between the cases, and the methodological differences in the analysis designs: the enlargement of museum free-admission policy leads to an increase of charged visits. We can suggest that these pieces of evidence are in line not only with the addiction-in-cultural-consumption argument but also with the points of the consumption framing theory (Tversky and Kahneman, 1981; Thaler, 1985). Substantially, the framing theory states that consumers make their choice on the basis of a mental accounting system: they first allocate income to specific expenditure categories (for instance: food, clothes, culture, and so on), and in a second stage they make the choice within each expenditure category. If the museum entrance is free instead of charged (on a given day, or in a given place), consumers who use this opportunity remain with a higher disposable income to spend for other goods and services within the expenditure category to which museum visits belong. Possibly, this expenditure category includes not only museum visits but also other cultural (and perhaps recreational and tourist) goods and services. This may explain why the increase in the demand for museum entrance does occur, when a larger free-admission policy is introduced, but with a pretty low sensitivity (the elasticity of charged visits with respect to free visits is less than one). The possibility of free visits to a museum entails a saved sum of money, which will be devoted by consumers to other museum visits or to other goods or services within the same expenditure category. The expenditure category can be more or less wide, depending on the mental structure of specific consumers. Consumers who are usual museum visitors, and have a specific mental accounting expenditure area for museum visits, simply use the saved money derived from free admittance, to visit other museums. Other consumers may re-allocate expenditures within the same expenditure category: the wide area of cultural, recreational, and tourism expenditures is perhaps the relevant mental accounting area for people who are not usually museum visitors. From a policymaking perspective, we could suggest that the free-admission policy to public museums has beneficial effects not only on subsequent charged visits to public (and private) museums but also on the whole cultural and entertainment industry, as well as on tourism and hospitality markets. From these perspectives, it would be interesting to analyse how strong is the effect of the museum free entrance policy enlargement on the demand for related goods. This is left to our future research. Of course, the fact that full and discounted entrance tickets, along with free entry for certain people groups, already existed before the new rule of July 2014, and still continue to exist, means that third-degree price discrimination was, and it is, operative. Likely, price determinants respond to social considerations rather than purely profit maximization. In any case, the universal free entrance on the first Sunday of each month can be interpreted as a further form of price discrimination. The profitability of such form of inter-temporal price discrimination for state museums and monuments clearly comes from the addiction phenomena that characterize consumers’ behaviour: free attendance today increases future willingness to pay and reduces future demand elasticity, entailing larger future revenues. The evidence that revenues of Italian State museums and monuments have increased in 2015 (and 2016) in nominal and real terms is consistent with such a guess, even if detailed data are not available to obtain a specific measure of the gain from price discrimination.13 Further, it has to be noticed that our aggregate data do not permit to distinguish additional visits of usual visitors from new visitors; nor are we able to distinguish between different types of visitors and different motivations for visit.14 Thus, we are not able to assess whether or not the new policy rule regarding free admission has entailed a change in the characteristics of population attending museums, as, e.g. the levels of income and education are concerned. Moreover, aggregate data cannot say anything about the ‘quality’ of a visit, which could be affected by crowded attendance. From these viewpoints, the effects of free-admission policy in modifying the socioeconomic characteristics of museum visitors and the quality of their fruition can be questionable. Again, the period under consideration coincides with an important challenge faced by museums (and even monuments): digitalization—which may affect the way in which heritage and collections are proposed by cultural institutions and brought to fruition (inside and outside the museum) by consumers; hence, new technologies may affect the visitor numbers and the museum pricing policies (Borowiecki and Navarrete, 2016, 2017). Clearly, our data set does not permit us to evaluate which part of the change in museum visitors’ number is attributable (with positive or negative sign) to digitalization. However, our theoretical considerations may suggest that museums could use digital tools to induce addiction and enhance future visits. Lastly, we have not dealt with the territorial distribution of museums and monuments, their attendance and tourism flows: this is the issue of a large body of literature, even with specific reference to the Italian case (Massidda and Etzo, 2012; Patuelli et al., 2013; Borowiecki and Castiglione, 2014; Borowiecki, 2015; Campaniello and Richiardi, 2017). Admittedly, significant differences across Italian regions and provinces exist as far as cultural endowment, visits to museums and monuments, and tourist flows are concerned. However, it is hard to exploit the cross-section differences, if one is interested in studying the dynamic relations between free and charged visits to museums and monuments: consider that not all Italian regions, not to mention provinces, have state museums and monuments; monthly data are not available for provinces; and updated monthly data on tourist flows are only partially available for regions and provinces. In the present analysis, we have preferred to focus on the time dynamics of variables, resorting to available national aggregate data. We have taken into account monthly time series. From a methodological point of view, our analysis has shown that the monthly series of tourist arrivals and free and charged visits to museums and monuments can be considered stationary around deterministic seasonal trends (rather than seasonally integrated), provided that different deterministic monthly constants and monthly trends are accounted for. The theoretical and political investigation on the reasons why different months show markedly different trends, in Italy over the period under scrutiny, is left to future analysis. Surely, there is still a need for public policies aimed at reducing the seasonality of both tourism flows and museum and monument attendance. However, the consideration of monthly time series has permitted us to highlight the inter-temporal links between free and charged visits to museums and monuments, which can have important implications for economic and cultural policy as well as for the management of cultural sites. Supplementary material Supplementary material is available online at the OUP website. This material consists of data and instruction for replication. Acknowledgments We thank Trine Bille, Chiara Dalle Nogare, Luis Cesar Herrero Prieto, Elisabetta Lazzaro, Isidoro Mazza, Ilde Rizzo and David Throsby, along with the participants to the 2016 ACEI Congress, 2017 IATE, EWACE, SIEP, and SIE Conferences, and other University seminars, for helpful comments. Our thanks also go to the editor and three referees. The responsibility for the content remains on the authors only. Footnotes 1 Some effects of the 2001 reintroduction of universal free admission to the government-sponsored museums in the UK are analysed by Cowell (2007); see also the previous analysis by Martin (2003). They show that the number of visits to free-admission museums in the UK has been increasing since 2001, but it is less clear whether the number of visitors has increased, or the same people go more often to museums. Eidelman and Céroux (2009) provide an analysis of the case of France, where completely free entry to a number of museums and monuments was introduced in 2008. 2 See, among many others, the statement of Minister Dario Franceschini published in the official website of the Ministry (MIBACT, 2017b). 3 Total annual revenues from entrance tickets moved from 52.7 (in 1996) to 155.5 million euro (in 2015). Over the same period, the revenues from complementary goods and services increased from about 25 to 49 million euro. These data on prices and revenues show an increase in both nominal and real terms (the Consumption Price Index increased by about 43% in the 20-year period under consideration). The state museums and monuments do not have an autonomous budget, and it is impossible to provide consistent data on costs. From a recent exploratory study commissioned by MIBACT to Association Civicum, only few museums appear to be able to cover operative costs with revenues from entrance tickets, additional services, and private transfers; in most cases, revenues from tickets cover a part between 5% and 16% of estimated costs. However, these pieces of evidence are based on a very small number of museums (only 26)—see Civicum (2017). 4 Comprehensive reviews of theoretical aspects and applied investigations of seasonal integration and co-integration are offered by Fransen (1996) and Ghysels and Osborn (2001). 5 This methodological paragraph follows Cellini and Cuccia (2013, Section 4). 6 Operationally, one can evaluate 11 additional seasonal dummy variables beyond the constant term, and evaluate whether the additional seasonal dummy variables are significant (Fransen and Kunst, 1999). 7 It is worth reporting that Cellini and Cuccia (2013) find the opposite result, that is, the presence of the seasonal unit root cannot be rejected, with reference to the series of total visits (the sum of free and charged visits) over the shorter time span 1996–2011. Clearly, these results cannot be seen as inconsistent, since the series and the time spans under consideration are different; here, we can rely on longer time series. 8 The variable under consideration is CUM_FREEVISt=∑i=112(FREEVISt−i)/12, indifferently labelled as ‘cumulated’ or ‘average’ free visits over the past 12 months: note that the cumulated value is divided by 12, so that the average number of monthly free visits over the past 12 months is obtained. Of course, the cumulated value or the monthly average value over the 12 past months has the same statistical properties in the regression analysis, as they differ for a constant multiplying factor. 9 These instruments are correctly correlated with the endogenous variable; these are also strong (F2,213 = 414.8, p = 0.000) and appropriate according to the Sargan test (LM = 0.007, p = 0.930). 10 If we resort to a log-log specification, the estimate of the same elasticity coefficient emerges to be 0.18 (with standard deviation equal to 0.06; Student-t = 3.03); the slight differences are also due to the fact that the set of seasonal dummies do vary across the different specifications, under the criterion to keep only significant regressors. 11 We have preferred to report the results with total tourist arrivals in Table 3, since informative criteria lead to prefer this specification. In any case, the consideration of separate regressors for domestic and foreign tourist arrivals does not change the conclusions regarding the effects of the other control variables and, in particular, the effect of cumulated past free visits on current charged visits (results are available on request). 12 In this case, the Hausman exogeneity test rejects the null (Chì-sq = 25.9; p = 0.000) and the considered instrumental variables are strong and appropriate according to the Sargan test (LM = 0.70, p = 0.400). 13 It is also worth mentioning that starting from 2009 different administrative acts have been adopted to provide state museums with a larger degree of managerial and technical-scientific autonomy (though not autonomous budget); these reforms have contributed toward promoting innovation and enhancing attractiveness, apart from the price effects. 14 Brida et al. (2016) and Lattarulo et al. (2017) are examples of studies regarding the motivation of visitors to Italian museums. 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Oxford Economic Papers – Oxford University Press

**Published: ** Apr 12, 2018

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