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Journal of Happiness Studies

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07-05-2018 | Research Paper

Growth, Inequality and Tunnel Effects: A Formal Mode

Author: Lewis Davis

Published in: Journal of Happiness Studies | Issue 4/2019

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Abstract

Hirschman and Rothschild’s (Q J Econ 87(4):544–566, 1973) tunnel effect refers to the propensity for individuals to be pleased by the success of others if they believe this signals an improvement in their own prospects. According to the current literature, tunnel effects may offset the utility losses from increases in peer income levels and income inequality. I develop a simple model of tunnel effects to evaluate these two channels of influence. The analysis confirms that tunnel effects create a positive link between happiness and economic growth. In contrast, rising income inequality generates a tunnel effect that increases the happiness of the rich but decreases happiness among the poor. The analysis confirms Hirschman and Rothschild’s informal analysis indicating that that tunnel effects may increase the happiness of the poor in the case of uneven development that involves both growth and rising income inequality. The model also highlights the differential impact of tunnel effects across age and income groups within the population. I close by discussing the model’s implications for empirical investigations of tunnel effects.

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Recent work has found evidence of a preference for status using a variety of comparison groups including co-workers (Brown et al. 2008; Clark and Oswald 1996), siblings (Kuegler 2009), those in the same neighborhood (Luttmer 2005), and others within one’s state of residence (Blanchflower and Oswald 2004). See Clark et al. (2008) for a review of the literature.

For example, on page 17, Ngamaba et al., appear to assume that “people in developing countries…[observe] other people’s increasingly rapid progression.” However, on average, low income countries grow no more rapidly than rich ones, and over the long run, they have grown more slowly, e.g. Pritchett (1997).

For the sake of symmetry, one could augment to the model to include retrospective utility, or the consumption of memories, for the old.

I am grateful to an anonymous referee for pointing out this relationship.

Inequality aversion is disutility from observed inequality and may arise from moral, ideological or psychological grounds. It differs from a taste for social status in that a rise in inequality increases the status and utility of the rich while decreasing the status and utility of the poor. In contrast, it reduces the utility of the inequality averse regardless of their position in the distribution of income. The model may be extended to incorporate pure inequality aversion, as was done in earlier versions of the paper. The current approach is preferred here as it facilitates the comparison with Hirschman and Rothschild.

Some papers take a macroeconomic perspective, treating status as a function of the log of average income, as measure of the national standard of living. The equation used here is more microeconomic in nature, and may be thought of as deriving from a set of pairwise comparisons between an individual and her peers, where the status is equal to the difference in log income levels: \(u_{t}^{i} (x_{t} ) = (1 - \psi )\ln y_{t}^{i} + \psi \frac{1}{{N_{j} }}\sum\nolimits_{j \in J} {\left( {\ln y_{t}^{i} - \ln y_{t}^{j} } \right)} = \ln y_{t}^{i} - \psi \overline{{\ln y_{t} }}\), where J is the set of an individual’s peers.

It may also be that mobility refers to the poor sector as a whole rather than its members. See Davis (2014) for a model along these lines.

Ravallion and Lokshin (2000) find differential tunnel effects for the rich and poor in transition Russia. Their analysis differs from most of the work cited here in that they are concerned with support for redistribution rather than with happiness.

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Title: Growth, Inequality and Tunnel Effects: A Formal Mode
Author: Lewis Davis
Publication date: 07-05-2018
Publisher: Springer Netherlands
Published in: Journal of Happiness Studies / Issue 4/2019
Print ISSN: 1389-4978
Electronic ISSN: 1573-7780
DOI: https://doi.org/10.1007/s10902-018-9991-1

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