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Full-income and price elasticities of demand for German public theatre

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Abstract

This article provides estimates of price and income elasticities of demand for German public theatre, using a large and reliable data set for 178 theatres over 40 years (1965–2004). It is posited that the consumption of the performing arts is a time-intensive activity for which both a theatre ticket and leisure time are necessary. Thus, the impacts of ‘full-income’ (‘leisure time income’ added to disposable income) and the price of leisure time on theatre attendance are examined. The findings indicate that the demand for the performing arts is own-price inelastic. The disposable income elasticity is significant, positive and equals approximately one. In contrast, the full-income elasticity is well above one and greater than usual income elasticity indicating that the performing arts are a luxury good when leisure time income is included in the consumer’s budget. The positive full-income effect is, however, offset by the negative price of leisure effect indicating that leisure time is a complement for the performing arts. Additionally, three objective quality characteristics of theatrical productions which can positively influence theatre demand are examined.

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Notes

  1. Ekelund and Ritenour did not report the elasticities for price but only a normalised measure for income elasticity.

  2. Toma and Meads (2007) also found negative and significant price elasticity for symphony concerts but they did not use an income variable in their regression analysis.

  3. It should be noted that the approach implemented by Withers (1980) was also recognised as important by Moore (1966) and Throsby and Withers (1979).

  4. For a detailed overview of demand studies investigating the measurement of quality for the performing arts see Seaman (2006).

  5. These art genres can be produced by separate theatres or by just one theatre. There are also about 82 orchestras integrated in the theatres. These orchestras play mostly for musical theatre.

  6. The characteristics of the German public theatre sector are presented in Newman and Zieba (2007), where the production technology for the performing arts is examined.

  7. Except for the inclusion of about 70 theatres from East Germany, the number of German public theatres has been relatively stable over time. It should be noted that not all theatres were maintained in post-reunification East Germany as many of them were directly privatised, closed or merged with other theatres.

  8. In Germany there are also 230 large private (profit-oriented) theatres and about 2,000 very small private theatres which are called ‘free theatres’ and do not receive any subsidies. Private theatres are not the object of this empirical study due to the lack of detailed data for these theatres.

  9. The theatre reports (gathering data mostly for public theatres but also some data for public orchestras) have been prepared since 1945 for the German Stage Association and two other governmental institutions: German Association of Cities and Towns (Deutscher Städtetag) and Cultural Comission of Education Minister (Kunstausschuss der Kultusministerkonferenz). At the theatres’ requests to get regular access to the statistical data, theatre reports were published for the first time in 1965/66 in the form of the book called “Theaterstatistik”.

  10. Theatre Report usually gives reasons why some observations are not available for a theatre in a particular theatre season; only in a few cases there is no explanation. Furthermore, the layout of Theatre Report has not changed much during the last 40 years.

  11. The statistics in Figs. 1 and 2 are presented for the years 1965–1989 for West Germany only and for the years 1990–2004 for both West and East Germany.

  12. The consumer’s participation at an artistic event (including commuting to the theatrical venue) can take up to five hours. It also takes consumers time to select formal attire or relax before a long artistic performance.

  13. Toma and Meads (2007) applied jointly cross-sectional and time series data for 52 symphony orchestras over 3 years and examined attendance per capita using the population size of the county hosting the symphony.

  14. Withers (1980); Krebs and Pommerehne (1995); Ekelund and Ritenour (1999) used this approach in their time series models as it “accounts for population changes without including a population variable in the regression” (Ekelund and Ritenour, 1999). Gapinski (1984, 1986) also examined attendance per resident using jointly time series and cross-sectional data on 13 performing arts companies in London over 12 years. Forrest et al. (2000) used the visitor rate divided by the population of the relevant zone in their cross-sectional demand study. In the panel data model, Werck and Heyndels (2007), examined total attendance per theatre as the dependent variable and included the population size as an independent variable. This is a more standard approach. The demand models presented in this section are additionally estimated using total theatre attendance as the dependant variable to check for robustness of the empirical results (see Sect. 5).

  15. The choice of functional form is an empirical question. The log-linear (also called double-log) demand model was chosen over the simple linear model which will be discussed later.

  16. The parameter c j controls for unobservable characteristics of the theatre that are constant over time and λ t controls for unobservable characteristics that are common to all theatres but change over time. Hence, the possible large differences in theatre attendance per capita which occur across theatres at one point in time and which are induced by the relevant population size, are assumed as the theatre-fixed effects and are neutralised due to the within transform of the data (see also Sect. 5).

  17. It should be noted that full-income is interpreted as a single variable. Hence, the two components of full-income which are disposable income and leisure time income are not analysed separately. They are combined into a single overall constraint because of the assumption that time can be converted into goods through money income. Full-income constraint is also used in this model independently of the Becker’s (1965) activities analysis (see also Owen 1971).

  18. Nickell (1981) shows that because of the within transformation of the data, the lagged dependent variable is correlated with the error term and this correlation creates a bias that decreases only as the number of time periods approaches infinity.

  19. Most of the data in Theatre Report are available for yearly theatre seasons (which last from August/September until July/August of the following year). All other data reported for the fiscal year were transformed into theatre season equivalents following Tobias (2003).

  20. All city theatres and most of the regional theatres are located in the city districts. City districts are characterised by a rather small land area and they directly adjoin geographically larger districts. Most of the districts do not differ very much in the number of their inhabitants. The average district population was about 330 thousand in 2004/05 excluding Berlin with 3.4 million inhabitants and Hamburg with 1.8 million inhabitants.

  21. Due to the relatively small land size of German districts (especially city districts), the concept of including the border-sharing districts of neighbours is reasonable.

  22. The examination of the share of guest performances in total performances over 40 years revealed that in some cases city theatres had a greater percentage share of guest performances in total performances than regional theatres.

  23. The aggregate theatre attendance will be used as there is no possibility to classify theatre attendance by different art forms as many theatres are multi-branch theatres and separate ticket prices for different art forms are not possible to derive.

  24. The share of free tickets (also complimentary and staff tickets) in the total number of tickets sold is 5.4%. Preferential tickets are tickets highly reduced in price and they are offered to disabled or unemployed people, firms, trade unions, theatre members and other social groups. The share of these tickets in the total number of tickets is 6.2%.

  25. Operating revenues consist of box office receipts from: daily tickets, place rents, visitor organisations, tickets for guest performances of foreign ensembles and also tickets for guest performances at other locations, cloak room receipts and revenues from programme sales.

  26. Alternatively, employees may decide to accept a lower wage in return for a smaller cut in hours of work. See also Owen (1971).

  27. The full-price index includes both the consumer price index, CPI, and the leisure price index, LPI (see formula in Sect. 3). PLI = PL t /PL o where PL o is the price of leisure calculated for all of Germany for a base year and PL t is the price of leisure for the remaining years.

  28. T m is the time devoted to personal work (sleep, personal hygiene, etc.) and is fixed at 80 h per week (52 × 80 h a year). It is assumed that the time used for personal work cannot be avoided and thus it cannot influence the consumer’s leisure time.

  29. Thus, the total consumption time is measured as Tc jt  = (T − Tm − Tw jt ) ∙ k + (T − Tm) ∙ (1 − k) where k is the percentage share of all employed people in the total population.

  30. Thus, for the first matrix specification, PS jt is the average orchestra ticket price in the district in which theatre j is located. In the second specification, it is the average orchestra ticket price in the relevant districts. In the third matrix specification, for touring theatres, PS jt is calculated as the average price of all public orchestras in Germany.

  31. The theatre ensembles perform their guest performances often in studio theatre or open air, in class rooms, cultural/conference centres and even on an open lorry or on a bus. They play at festivals and cultural events supporting local tradition. Their repertoire includes as well classical performances as modern plays, cabarets and musicals.

  32. The expenses for décor and costumes include payments for costumes, stage design, props, musical instruments and other items but do not include costs for electricity, technicians and other variable costs. Thus, it assumed that they depend on the number of productions as they are not influenced by how often a particular production is staged.

  33. Among these changes are the inclusion of about 70 theatres from former East Germany in 1990/1991, and many other structural changes such as theatre mergers, privatisation and establishing or closing of theatres.

  34. The Hausman test confirmed that the fixed-effects estimator is consistent but the random effects estimator is not. The F-test of the null hypothesis that the constant term is equal across individual theatres was rejected at the 1% level indicating that there exist significant theatre-specific effects. Such effects can be, for example, the relevant population size which does not change over time, the capacity of theatrical venue or a number of other theatres located in the relevant market.

  35. Serial correlation (of order 1 but not higher) could be confirmed by Wooldridge’s (2002) test for panel data. Stock and Watson (2008) show that in the presence of serially correlated errors only the clustered variance estimator is consistent and it should be applied to the fixed-effects estimator. Thus, the standard errors are clustered over the individual theatres and they allow for correlation within the panel (individual theatre) over time. The cluster-robust standard errors are also valid in the presence of cross-sectional heteroskedasticity. Clustering on the panel variable affects only the standard errors and does not affect the estimated coefficients.

  36. The linear model was tested against the log-linear model using the MacKinnon, White and Davidson (1983) test. The differences between the predicted values were calculated and included in both artificially nested models. The results indicate that the log-linear model encompasses the linear model.

  37. For example, in Table 3, column (1), the adjusted R-squared are 36%, 41% and 44%, for the three matrix specifications, respectively. In column (2) of Table 3, the adjusted R-squared values are 33%, 42% and 45%, for the three specifications, respectively.

  38. The individual theatre dummies are excluded from estimation due to the within transformation of the data in the fixed-effects model.

  39. It should be noted that the guest performances index has also the expected and positive sign and is highly significant when the 23 regional (touring) theatres are excluded from the regressions.

  40. In this additional specification, the estimates of the ticket price equal 0.28 for both demand models given by Eqs. 1 and 2, and for the whole period. The disposable income elasticity (I jt ) equals 0.64, whereas the elasticities of full-income (FI jt ) and the price of leisure (PL jt ) equal 4.14 and −3.04, respectively. The estimated orchestra ticket price varies between 0.02 and 0.05. As for the quality variables, guest performances (G jt ) and décor and costumes (D jt ) equal 0.5 and 0.7, respectively. The elasticity of artistic wages (A jt ) varies from 0.3 to 0.5. The estimated demand functions have slightly lower adjusted R-squared, ranging from 0.29 to 0.30.

  41. The slightly higher significance level of the population variable coefficient for the whole period may be connected with the fact that the market of theatres located on the former West–East German border as well as the market for theatres located in and around West/East Berlin has increased after the German reunification in 1990/1991.

  42. The findings with regard to own-price elasticity are compatible with those obtained in the study by Gapinski (1986) with own-price elasticities ranging between −0.07 and −0.30, Moore (1966) with elasticities between −0.63 and −0.33 and also the study by Werck and Heyndels (2007) with elasticities between −0.16 and −0.14. The estimates found by Withers (1980) are slightly higher and range between −0.62 and −1.19. The short-run price elasticity estimated by Krebs and Pommerehne (1995), using the aggregate time series data for German public theatres for the period 1965/1966–1991/1992 also equals −0.16.

  43. The income estimates are higher than those obtained in the studies by Moore (1966) and Gapinski (1986) but are lower than those found in the study by Werck and Heyndels (2007) or Gapinski (1984). The nearest estimates to this study are found by Withers (1980) with elasticities ranging between 0.64 and 1.08.

  44. Gapinski (1986) also found cross-price elasticity for theatre ranging from 0.9 to 0.18.

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  1. Economics Department, Trinity College Dublin, College Green, Dublin 2, Ireland

    Marta Zieba

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  1. Marta Zieba
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Correspondence to Marta Zieba.

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This article was the winner of the President's Prize for the best paper by a graduate student at the 2008 meetings of the Association for Cultural Economics International, held in Boston.

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Zieba, M. Full-income and price elasticities of demand for German public theatre. J Cult Econ 33, 85–108 (2009). https://doi.org/10.1007/s10824-009-9094-2

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