Abstract
This paper reexamines the Barro growth model in a context of interdependent preferences with consumption externality. Agents care about both consumption and social status, which is determined by their relative consumption in society. The results underline the individuals’ preferences for status as a key role in explaining long term growth and welfare. In particular, a higher growth rate may correspond to a lower social welfare if increment in growth is explained by status-seeking accompanied by the keeping up with the Joneses. Furthermore, we discuss two public financing systems from the viewpoint of growth and welfare. If lump-sum tax always implies a higher growth rate, income tax may perform better in terms of welfare when government size becomes sufficiently large.
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Notes
The government size is defined as the ratio of public spending to income.
In a model with endogenous leisure, Dupor and Liu (2003) introduced the notion of keeping up with (or running away from) the Joneses when the marginal rate of substitution between leisure and individual consumption increases (decreases) with respect to the average consumption level.
For example, Alvarez-Cuadrado et al. (2015) estimated the importance of the interdependence of preferences and habit persistence. The results suggest that households’ preferences derive almost 25% of their consumption services from comparison between their consumption and that of their neighbours, and around 35% from comparison between their current and past consumption. This implies that around 60% of individual satisfaction is from relative consumption.
Using German panel (GSOEP) spanning the years 1984–2001 and considering life satisfaction as a proxy of individual utility, Vendrik and Woltjer (2007) found the concavity of individual utility in relative income.
As the utility function is concave in c and the capital accumulation function is concave in k, then the first-order conditions of the Hamiltonian problem are also sufficient (Mangasarian 1966).
However, the social planner does not necessarily need to incorporate status concerns in her social objective. A non-welfarist social planner can calculate the optimal growth on the basis of another set of preferences, ignoring status concerns. In this case, individuals may attach a weight \(s > 0\) to social status while it is considered as null by the non-welfarist social planner. The optimal growth rate is that of the status externality free-centralized economy as shown in Rauscher (1997), Corneo and Jeanne (1997).
Combining (21) with (22), we can rewrite the optimal growth rate as \(\gamma ^{o} = \frac{\sigma }{1 - s + s \sigma } \left[ (1-\tau ) A^{\frac{1}{1- \alpha }}\tau ^{\frac{\alpha }{1- \alpha }} - \rho - \delta \right] \). The FOC for a maximum value of \(\gamma ^{o}\) is \(\frac{\partial \gamma ^{o}}{ \partial \tau } = \frac{\sigma A^{\frac{1}{1- \alpha }}}{1 - s + s \sigma } \left[ -\tau ^{\frac{\alpha }{1- \alpha }} + \frac{\alpha }{1-\alpha }(1-\tau ) \tau ^{\frac{\alpha }{1- \alpha }-1} \right] = 0\). It is satisfied when \({\hat{\tau }} = \alpha .\) Notice that the second derivative of \(\gamma ^{o}\) with respect to \(\tau \) is negative for \(\tau = {\hat{\tau }}\). This confirms that \({\hat{\tau }} = \alpha \) is the government size maximizing the optimal growth rate.
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I am thankful to the two anonymous referees of this journal and Cuong Le-Van for their useful comments. All remaining errors are mine.
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Pham, T.K.C. Keeping up with or running away from the Joneses: the Barro model revisited. J Econ 126, 179–192 (2019). https://doi.org/10.1007/s00712-018-0624-2
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DOI: https://doi.org/10.1007/s00712-018-0624-2
Keywords
- Income tax
- Lump-sum tax
- Keeping up with the Joneses
- Public spending
- Running away from the Joneses
- Status-seeking