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07-04-2023

Intratemporal elasticity of substitution between private and public consumption: new evidence and implications

Authors: John Nana Francois, Andrew Keinsley

Published in: Empirical Economics | Issue 4/2023

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Abstract

This paper estimates the intratemporal elasticity of substitution (IES) between private and public consumption in private utility. Using panel data for 17 European countries over 1970-2018, we estimate the IES to lie between 0.6 and 0.74. When combined with the relevant intertemporal elasticity of substitution, our estimated IES implies that private and public consumption are Edgeworth complements. The panel estimate, however, conceals a large heterogeneity where the IES ranges from as low as 0.3 in Italy to 1.3 in Ireland. This suggests that the crowding-in (out) effect of fiscal policies involving change in government consumption will differ across countries. This cross-country variation in the IES is positively correlated the share of health spending in public expenditure but negatively correlated with the share of public order and safety in government expenditures. We also find a U-shape relationship between the size of IES and government size.

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I illustrate the relevance of intratemporal elasticity of substitution in a simple RBC model in section 2.

Unlike Fiorito and Kollintzas (2004) where no temporal utility function is specified, we specify a CES aggregator function for effective consumption. The study, however, shares the same underlying assumption of permanent income hypothesis. Additionally, while Fiorito and Kollintzas (2004) focuses on the sub-categories of government consumption (i.e., merit and public goods), we concentrate on aggregate public consumption, which is often focused on in both empirical and theoretical work. We, however, employ the decomposition of public consumption into merit and public goods to attempt to explain the relationship between private and government consumption studied in the paper.

See for instance, https://www.aicgs.org/2020/01/fiscal-stimulus-for-the-european-economy-the-right-thing/ for further discussions.

Boehm (2019) shows that the government investment multiplier is near zero whereas the government consumption multiplier is approximately 0.8.

The section also allows for a partial review of the literature.

I employ the Stata program developed by Abrigo and Love (2016) for this simple exercise. As stressed by the authors, the GMM estimator suffers from weak instrument problems when the endogenous variables have a unit root. we run unit-root tests on the differenced data and find no unit roots in the variables we employ for the exercise.

There is, however, a number of studies that do not find a positive response of private consumption following an increase in government consumption. See for instance, Ramey and Shapiro (1998) and Ramey (2011). Other studies instead find mixed response of private consumption following an increase in government consumption (see Hur et al. 2010, for the case of developing Asia)

In standard New Keynesian models with zero lower bound of interest rates, a rise in public consumption induces fiscal multipliers greater than unity (Christiano et al. 2011)

In a far from an exhaustive list, other existing studies such as Coenen and Straub (2005), Forni et al. (2009), and Hagedorn et al. (2019) extend Galí et al. (2007) to include other mechanisms to generate a positive consumption multiplier. The fraction of non-Ricardian household in these studies has been set between 0.2\(-\)0.5. Recently, however, Havranek and Sokolova (2020) find that the fraction of non-Ricardian household in the data is small (i.e., 0.11) and therefore, implies little evidence of deviations from consumption smoothing. Other studies such as Davig and Leeper (2011) and Zubairy (2014) explore other channels (i.e., regime-dependent multipliers and deep habits, respectively) away from the one proposed by Galí et al. (2007) to generate a positive multiplier. Other studies such as Canova and Pappa (2011) investigate the theoretical conditions for effectiveness of government consumption expenditure expansions.

It is important to mention that the presence of this channel does not discount the other channels discussed in the literature such as the presence in incomplete markets (Hagedorn et al. 2019), heterogeneous agents (e.g., Achdou et al. 2017; Galí et al. 2007; Hagedorn et al. 2019), deep habits (e.g., Zubairy 2014), and regim e-switching policy (e.g., Davig and Leeper 2011). The marginal utility channel complements these other channels in expanding our understanding on the size and sign of the government consumption multiplier.

The model in this paper is similar to Bouakez and Rebei (2007); however, we leave the presence of habits out as we are not after the hump-shaped response of private consumption. Habits are explored in Bouakez and Rebei (2007).

The first-order conditions for private and public consumption from the optimization problem are \(\partial U_{t}/\partial C_{t} = \epsilon _{t}\lambda C_{t}^{-1/\theta } C_{e}^{1/\theta }u' \) and \(\partial U_{t}/\partial G_{t} = \nu _{t}(1-\lambda ) G_{t}^{-1/\theta } C_{e}^{1/\theta }u' \), respectively.

Alternatively, one can identify \(\theta \) if one has access to a valid and informative set of instruments, which is naturally challenging to come by. Specifically, it is challenging, and in some cases difficult, to find adequate and appropriate instruments using macroeconomic data is challenging because of complicated interrelationships (Temple 1999)

It is also worth noting that studies such as Amano and Wirjanto (1998), Kwan (2009) and Dawood and Francois (2018) do not account for possible change in estimation results depending on which variable is selected as the regressand.

I use the ‘xtwest’ command by Persyn and Westerlund (2008) in Stata for this exercise.

See Holly et al. (2010) for details.

Note that a small RMSE generally implies our model is good at predicting the observed data, whereas if RMSE is large, this generally means our model is relatively fails to account for important features underlying our data.

See also Eberhardt and Presbitero (2015) for additional discussion on the selection of the lag length for the cross-sectional averages.

For the case where the price ratio is used as the regressand, the IES is given by \(\theta = \frac{1}{\beta }\), where \(\beta \) is the coefficient estimate.

We use the Stata command xtmg to implement the Common Correlated Effects Mean Group estimator (see, Eberhardt 2012).

We are grateful to one of our anonymous referees for this suggestion.

The panel group-mean estimator (\(\theta ^{M}\)) is computed as \({\hat{\theta }}^{M} = \frac{1}{N} \sum _{i = 1}^{N} \theta _{i}\), where \(\theta ^{i}\) is the country-specific estimate for the ith country in the panel and \(N= 17\) is the number of countries in the panel.

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Title: Intratemporal elasticity of substitution between private and public consumption: new evidence and implications
Authors: John Nana Francois
Andrew Keinsley
Publication date: 07-04-2023
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 4/2023
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-023-02387-w

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