Local government allocation of cultural services

Abstract

In the present paper, we analyse the allocation process for cultural services in Norwegian municipalities. The cultural sector at this administrative level is decomposed into the following eight subcategories: children’s and youth activities, libraries, cinemas, museums, arts dissemination, cultural heritage, cultural schools, and other cultural services. By means of budget shares for these eight cultural services and a residual sector consisting of all other municipal services, we estimate a system of demand relations which are interdependently linked to each other by a budget restriction. Our analyses are based on data from 409 out of 429 Norwegian municipalities during the period 2002–2010. In the empirical analyses, we mainly focus on the effects of income variation for the cultural services. We estimate effects of free income, matching grants to each sector, and user fees and other sector-specific income for each sector. We also estimate crowding-out effects for the cultural sectors of demographic variables indicating higher demand for services such as education, childcare, and health services. Our results confirm previous results. There are interesting differences within the group of cultural services, and these are partly related to different levels of national standardisation and regulation among the cultural services.

Appendices

Appendix 1: Result tables for the regression models

See Table 11.

Table 11 Estimated coefficients for the Tobit models

Appendix 2: Elasticities with respect to free income, matching grants and fee income

Derivation of (1) with respect to I yields $\frac{{\partial S_{i} }}{\partial I} = \beta_{i} .$ From the definition of S _i , it follows that

$$\frac{{\partial S_{i} }}{\partial I} = \frac{{\partial \left( {\frac{{p_{i} x_{i} }}{Y}} \right)}}{\partial I} = \frac{{p_{i} \frac{{\partial x_{i} }}{\partial I} - A_{i} }}{Y}.$$

(7)

Combining ∂S _i /∂I = β _i and (7) it follows that

$$\beta_{i} = \frac{{p_{i} \frac{{\partial x_{i} }}{\partial I} - S_{i} }}{Y}.$$

(8)

Rearranging into an elasticity, we find that

$$\varepsilon_{iI} \equiv \frac{{\partial x_{i} }}{\partial I}\frac{I}{{x_{i} }} = \beta_{i} \frac{I}{{S_{i} }} + \frac{I}{Y}.$$

(9)

The same steps as above also yield the corresponding elasticities with respect to matching grants to sector j (G _j ) and user fees/box office income to sector j (U F _j ):

$$\varepsilon_{{i,G_{j} }} \equiv \frac{{\partial x_{i} }}{{\partial G_{j} }}\frac{{G_{j} }}{{x_{i} }} = \eta_{ij} \frac{{G_{j} }}{{S_{i} }} + \frac{{G_{j} }}{Y}$$

(10)

$$\varepsilon_{{i,UF_{j} }} \equiv \frac{{\partial x_{i} }}{{\partial UF_{j} }}\frac{{UF_{j} }}{{x_{i} }} = \varphi_{ij} \frac{{UF_{j} }}{{S_{i} }} + \frac{{UF_{j} }}{Y}$$

(11)

Instead of presenting elasticities for the effects of matching grants and user fees/box office income per sector, Tables 6 and 7 in the paper show the increase in expenditures per sector following an increase in grants and user fees to the same sector. These tables only show own effects per sector, omitting the cross effects. The interpretation becomes the number of NOK in extra expenditures on each sector if the same sector receives an extra NOK in grants or user fees. The marginal increase in expenditures on each sector (expend _i ) arising from an increase in matching grants to that sector (G _i ) or user fees (UF _i ) is defined from the regression parameters in (1) as follows:

$$\frac{{\partial {\text{expend}}_{i} }}{{\partial G_{i} }} = \eta_{ii} Y + S_{i} ,$$

(12)

$$\frac{{\partial {\text{expend}}_{i} }}{{\partial UF_{i} }} = \varphi_{ii} Y + S_{i} .$$

(13)

However, these derivatives apply only when there are no corner solution outcomes. With corner solution outcomes, the Tobit coefficients in the derivatives must be scaled by the predicted probability of having strictly positive outcomes.