To begrudge or not to begrudge: consumption and leisure externalities revisited

Abstract

This article employs a dynamic general equilibrium model to study the implications of a nonstandard preference structure for the short-run dynamics of the economy. Preferences in this model are assumed to contain comparison elements for consumption and leisure, i.e. agents care about how their own consumption and leisure compares to a certain reference stock that is determined by the economy's average level of consumption and leisure. This specification inevitably creates externalities. We then estimate the model and find that these externalities are both positive and statistically significant.

Acknowledgements

The author is grateful to Thomas Hintermaier, Juraj Katriak and a anonymous referee for very helpful discussions and suggestions.

Notes

¹ On the other hand, ‘inward-looking’ preferences, also known as habit formation, assume that the reference stock is composed of an individual's own consumption history. The relevance of this specification is underlined by a growing body of theoretical and applied work. For instance Karagiannis and Velentzas (2004) show by decomposing total changes in Marshallian demand that a large part of these changes can be explained by habit formation. Further examples are Hamori and Tokunaga (1999) who analyse stock market behaviour allowing for inward-looking agents and Alvarcz-Cuadrado et al . (2004) who study the implications of habit formation for economic growth.

² Since the utility function is continuously differentiable, strictly concave and defined on a compact set, the first-order conditions are also sufficient for maximum.

³ A detailed description of these steps can be found in the Appendix.

⁴ See the Appendix for the detailed exposition.

⁵ Note that since the resource constraint y_t = c_t + s_t holds, (11) reduces to a 3D system, where and .

⁶ 0 _{n × m} and İ_{n × n} denote, respectively, a matrix of zeros and the identity matrix where the subscripts indicate their dimension.

⁷ The covariance matrix Ξ is symmetric by definition since the errors across the same series are equal.

⁸ To repeat, β ∈ (0, 1), α ∈ (0, 1), γ > 0, η ∈ (0, 1), δ ∈ (0, 1), φ ∈ (−1, 1). Moreover, the eigenvalues of the matrix V are restricted to lie inside the unit circle to ensure asymptotic stability of f_t . For convenience we have shifted the precise description of the Kalman filter-maximum likelihood setup to the Appendix.

⁹ The added VAR errors and the corresponding covariance Matrix are given by 

The SE were obtained by computing the Hessian matrix of the likelihood function evaluated at its maximum. The SE are equal to the square root of its diagonal elements.

¹⁰ w_t and v_t represent random disturbances, and the time invariant matrices A and B relate the past to the current state and the state in period t to the measurement x_t respectively.

¹¹ Recall that T = E _t−1(U_t ) and the product of two independent random variables is zero, hence E _t−1 U_t