Seppo Suominen Essays on cultural economics

5.3The method and sample

The ISSP 2007 survey was carried out between 18^th September and 11^th December 2007 by means of a mail questionnaire in Finland. The ISSP is a continuous programme of cross-national collaboration on social science surveys. The surveys are internationally integrated. In Finland the ISSP surveys are carried out together by three institutions: Finnish Social Science Data Archive, The Department of Social Research at the University of Tampere and the Interview and Survey Services of Statistics Finland²⁹. The other surveys mentioned in table 1 did not collect e.g. marital status, which has been shown to have an impact on the attendance of cultural events (Upright 2004, Frateschi & Lazzaro 2008).

Consider a logarithmic demand function:

(5-1)

where e_i is the total expenditure (x) elasticity and e_ik is the cross-price elasticity of the k^th price on the i^th demand. The Slutsky equation defines the cross-price elasticities: e_ik = e_ik^* - e_iw_i where e_ik^* is the compensated cross-price elasticity and w_k is the budget share. Substitution the Slutsky equation into the above demand function leads to:

(5-2)

The weighted price expression is the logarithm of the general index of prices and the above becomes

(5-3)

Then the demand is expressed in terms of real expenditure and compensated prices. However, if the goods can be grouped so that the preferences within groups can be described independently of the quantities in other groups (Deaton and Muellbauer 1983, 122). Then the utility function is separable. The consumption decisions are made in two stages: first the consumer considers how much of the composite commodity (cultural consumption) to consume as a function of price index of culture and incomes. Allocation of expenditures is made given the knowledge of total expenditure and appropriately defined group prices. At the second stage the consumer considers how much highbrow (opera, theatre) culture to consume given the prices of opera and theatre performance and cinema. Different culture events will be chosen to maximize a leisure subutility function subject to culture budget constraint while the overall utility function will determine the allocation to food, clothing, and leisure and so on. The utility function is written

(5-4) u[v₁(q₁) + v₂(q₂) + … + v_n(q_n)]

If two goods q_i and q_j are in different groups G and H and the subgroup or conditional demands are:

(5-5) q_i = g_Gi(x_G,p_G)

the substitution effect in the Slutsky equation can take the form
(5-6)

where µ_GH summarises the interrelation between groups G and H. This means that whole groups (Hicks aggregates) must be substitutes or complements for one other. By symmetry

(5-7)

It can be shown (Deaton and Muellbauer 1983, 138) that the expenditure elasticities are alone sufficient to determine all own- (e_ii) and cross-price (e_ij) elasticities if the utility function is additive.

(5-8) e_ii = -(µ/x)e_i – e_iw_i(1 - (µ/x)e_i)

(5-9) e_ij = – e_iw_j(1 - (µ/x)e_j)

However, using these separable utility function assumption or the conditional demand functions results into consequences that are hardly empirically verified since the goods cannot be complements, only substitutes with these separable utility functions. But if preferences are intertemporally separable, the budget shares should not be related to yearly incomes but to lifetime expected wealth W and this may explain differences across consumer groups. Consider an intertemporal utility function

(5-10 u[v₁(q₁, q₀₁), v₂(q₂, q₀₂), …, v(q_L, q_0L)]

subject to

(5-11)

where w_t is the wage rate in period t and full wealth W₁ is given by

(5-12)

where A₀ is the initial endowment of wealth, ρ is the discount factor (ρ_t = 1/(1+r_t)(1+r_t-1)…(1+r₂) and T is time in each period. The intertemporal schedule has two parts: a consumption plan and the labour supply function (l_t = T – q_ot).

The maximization problem results in standard consumption and labour supply equations

(5-13)

(5-14)

Consumption is linked to the future endowments, assets, wages and prices. Consumption and labour supply are positively related if leisure and consumption are substitutes. However, if leisure and consumption are complements, consumption is negatively related to labour supply (Deaton and Muellbauer 1983, 313). This model links labour supply and thus socioeconomic variables (like age, education, gender) to culture consumption decisions
The cultural participation questions in The ISSP survey were: “How many times in the last twelve months have you seen an art exhibition, opera or theatrical performance?” Or “How many times in the last twelve months have you been to the cinema?” Five alternatives were given: ‘ Every day’, ‘Several times a week’, ‘Several times a month’, ‘Less often’ or ‘Never in the last twelve months’. A conventional method to study this is to use some discrete choice model, like probit or logit. A Poisson model is more suitable to study count data, which is not the case here. The normal distribution for the binary choice (no = 0 / yes = 1) has been used frequently generating the probit model.

(5-15)

The function is the commonly used notation for the standard normal distribution (Greene 2008, 773) and x is a vector of explanatory variables and β is the corresponding vector of parameters. The logistic distribution which is mathematically convenient has been very popular.

(5-16)

The function is the logistic cumulative distribution function. If the responses are coded 0,1,2,3 or 4 (‘ Every day’, ‘Several times a week’, ‘Several times a month’, ‘Less often’ or ‘Never in the last twelve months’) the ordered probit or logit models have been very common. The models begin with y* = x’β + ε in which y* is unobserved and ε is random error. The discrete choices y are observed by the following way:

(5-17) y = 0, if y* ≤ 0

y = 1, if 0 < y* ≤ µ₁

y = 2, if µ₁ < y* ≤ µ₂

y = 3, if µ₂ < y* ≤ µ₃

y = 4, if µ₃ ≤ y*

The µ’s are unknown parameters to be estimated with β. If ε is normally distributed with zero mean and variance equal to one [ε~N(0,1)], the following probabilities ensue (Greene 2008, 831-832):

(5-18)

(5-19)

The cultural consumption y* thus depends on the following variables:

(5-20) y* = f(education, age, gender, marital status, province, incomes)

Since it has been shown that middle-aged are among the most active in highbrow cultural consumption, a suitable method is to classify age into age groups. The observation unit in the ISSP 2007 survey is a person 15-74 –years old and for the purpose of this study persons have been classified into 12 subsets: 15-19 –years old, 20-24 –years old, and so on with the last consisting persons of 70-74 –years old.

Descriptive statistics of the explanatory variables reveal that age (age group) and education are related. Most of the youngest in the sample were pupils or students (at a comprehensive, an upper secondary, a vocational school, of course, or at a college) and correspondingly the oldest had a rather low education (elementary or comprehensive school). A college level education was mainly replaced by bachelor’s degree education in the early 1990’s and, therefore, persons having a bachelor’s degree from a polytechnic (university of applied sciences) are somewhat younger than persons having a college diploma. Persons less than 50 –years old on average have a (better and) longer education than persons older than 50. Age and education are related with household or personal incomes. Middle-aged and high-educated seem to have the highest incomes (including all social security contributions, e.g. child benefit that may explain why the age group 30-34 has the highest incomes, see table 3). There are some differences in education between genders. Men are somewhat less educated than women.

Since the income variable in the sample includes all social security contributions (e.g. child benefit), the number of children is used as an explanatory variable. There are two different variables: the number of less than 6-year-old children and the number of 7-17-year-old children. This leads to the following relation explaining cultural consumption. Since the number of children is considered as explanatory variable, the marital status is also added.

(5-21) y* = f(education, age, gender, marital status, province, incomes, number of children)

Since the cultural participation variables are recoded conversely into binary variables: Art-consumption01234 (‘every day’ = 0, ’several times a week’ = 1, ‘several times a month’ = 2, ‘less often’ = 3, ‘never in the last 12 months’ = 4)  art1234_5 = art (‘no’ = 0, ‘yes’ = 1), some information is lost. However, the correlation of the original and the recoded variables is high: r = -0.937. Respectively the correlation of the original movie consumption variable and the recoded variable is also high: r = -0.844. The correlation of the recoded art participation and the movie consumption variables is positive: r = 0.397. Therefore, there are good arguments to study these sectors of culture jointly.

Figure 5: Nuts areas

Area1 = FI18 (Southern Finland), Area2 = FI19 (Western Finland), Area3 = FI13 (Eastern Finland), FI1A (Northern Finland) + FI20 (Ahvenanmaa –the South-Western archipelago) are considered as reference value.