Testing separability of public consumption in household decisions

Abstract

In this paper we propose a sequential strategy, based on the microeconomic approach of the demand theory, in order to test for separability between private and public consumption. The aim of the present work is to verify, using a conditional almost ideal demand system, whether the different components of public consumption exert conditioning effects on the allocative structure of private spending. The empirical estimation of the model and the separability tests are developed for both a demand system in five functional categories of private spending, and for a demand system in six categories, where the private expenditures on those goods and services which can also be offered by the public sector are enclosed in a single functional category. The results of the separability tests, obtained using UK data for the 1974–2000 period, show that public individual consumption plays an important role in modifying consumer choices, while public collective consumption does not affect private consumption behaviours. The relationships between the different components of private spending and public individual consumption are both of substitutability and complementarity; in particular, we find that public individual consumption and the corresponding private expenditures on ‘Health, education, recreation and social protection’ are complements.

Keywords:

• Consumer demand
• government consumption
• non‐separability
• demand systems
• JEL Classification: D1, H3, H4

Acknowledgements

The authors are grateful to Carlo Andrea Bollino and Federico Perali for their useful suggestions and Matteo Ricciarelli for the research assistance. The authors would especially like to thank two anonymous referees for their comments. All errors are the authors own.

Notes

The derivation of the demand system from the conditional AI cost function is not presented here, but it is available from the authors upon request.

Precisely, private expenditure data are taken from ‘Household final consumption expenditure: classified by purpose’ (Blue Book, table 6.4 and 6.5), while the data concerning public consumption spending are taken from the annual series ‘General Government: analysis of total outlays by classification of function of government’ (Blue Book, table 11.2).

Many supporting arguments for this methodology can be found in the literature. A similar approach was adopted by Aschauer (1985) who, in a macroeconomic analysis of the effects of fiscal policy on private consumption, used consumer spending on non‐durables and services as a measure of private consumption in each period. Another justification for this methodology can be found in Marrinan (1998) who verifies that the proportion of durable to non‐durable spending is stable over time, so that the exclusion of non‐durable expenditures from total private consumption does not affect the results. On the contrary, some authors, such as Graham & Himarios (1991) and Ni (1995), show that the estimated relationship between private and public consumption depends on whether durable expenditures are omitted.

The definition is given in paragraph 9.72 of SNA93: ‘Household actual final consumption consists of the consumption goods or services acquired by individual households by expenditures or through social transfers in kind received from government units or non‐profit institutions serving households NPISHs’ (OECD, 1998).

In particular, two different tests are implemented. The first (ADF_(t)) is a univariate test for the null hypothesis of a unit root, with both an intercept and a time trend, in the data‐generating process of the variables of the model. The second (ADF_(F)) is a joint test to verify the simultaneous presence of a unit root and a deterministic time trend, with an intercept, in the variables.

The estimation of (10), imposing the diagonality restriction on Γ₀, implies that the OLS have the same statistical properties as those based on a two‐stage least squares (2SLS) estimation.

This statistic is asymptotically distributed as a χ ² with the number of degrees of freedom equal to the difference between the number of parameters of the restricted and unrestricted demand system. In the present analysis, the homogeneity constraint implies five degrees of freedom, while symmetry generates ten degrees of freedom. The joint imposition of both theoretical properties implies fifteen degrees of freedom.

The statistic is asymptotically distributed as a χ ² with the number of degrees of freedom equal to the number of non‐singular equations of the demand system. So, for the DAI5 and DAI6 models, there are four and five degrees of freedom, respectively.

The test was also carried out applying the small‐sample correction (11). However, since the adjusted test outcomes are close to the asymptotic results, they are not presented here.

The estimated parameters for the remaining conditional demand systems are not presented in the text, but are available upon request.