## Abstract

This study seeks to examine the consequences of “keeping up with the Joneses” on household fertility outcomes. “Envy” is introduced in a simple “quality-quantity” trade-off type of fertility model, where the trade-off is induced by the fact that being out of the labor market due to child-bearing is more expensive for people with higher human capital levels. The effect of introducing upward-looking “envy” in the model is that households, notably low-income ones, reduce fertility in an attempt to emulate consumption levels of their high-income neighbors. This effect is stronger the larger the reference consumption—that is, in areas with higher income inequality, which are characterized by longer right tails of income distributions. It follows that if households indeed tend to “keep up with the Joneses,” one should expect lower fertility rates in areas with higher income inequality compared to more equal areas. The empirical analysis using the American Community Survey confirms that indeed, households residing in more unequal metropolitan areas tend to have fewer children than households residing in more equal metropolitan areas.

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## Notes

The word “envy” is used as a shortcut (and a synonym) for the relative consumption/positional concerns; namely deriving utility not from the absolute level, but rather from the relative level of consumption. Such (utility) specification is referred to as “envy” in Alvarez-Cuadrado and El-Attar (2012) and Alvarez-Cuadrado and Long (2012); Varian (1974); Konrad (2004), “keeping up with the Joneses” in Gali (1994), “status” in Corneo and Jeanne (2001), “jealousy” in Dupor and Liu (2003), “consumption externalities” in Liu and Turnovsky (2005), “catching up with the Joneses” in Abel (1990), “status-seeking” in Ireland (1994), “relative consumption” in Samuelson (2004), “consumption externalities” in Turnovsky and Monteiro (2007), etc.

That is they try to match consumption of those whose income is higher than theirs. For discussion of importance of upward-looking comparisons see Alvarez-Cuadrado and Japaridze (2017).

If the sum of parameters

*τ*and*η*in Eq. (3) is less than 1 then, in the dynamic setting, there exists a steady state human capital level. If they sum to 1, then there are growth possibilities (if*μ*and*φ*are sufficiently large, there can be perpetual growth). Under that situation, there may be fertility convergence, but convergence in human capital.Note that I assume that the household will be always in the interior regime, that is it will dedicate positive amount of income to its children as \(w_th_t^i > \theta /\left( {\eta \varphi } \right)\).

The earlier version of the paper had Becker and Barro (1988) type of utility function. The problem was in a familiar form of \(V_t = u\left( {c_t - \widetilde c_t} \right) + n^\alpha V_{t + 1}\) where

*V*_{t}is the value function of the parent(s) consisting of the utility from consumption*u*(*c*_{t}) and the value of children discounted by the factor which is concave (0 <*α*< 1) in number of children*n*_{t}. In the numerical solutions for the steady states (when individual human capital is unchanged between generation of the same type of household: high- and low-income households) changes in local income inequality tend to reduce fertility and increase steady state level human capital of low-income households.If higher inequality was not associated with more right-skewed distribution then

*G*_{2}and Gini coefficient would coincide and we will have a 45 degree line.In fact the assumption on constant median income across metropolitan areas is not crucial. This is due to the fact that if variation in median income is caused by proportionally re-scaled income distribution and price level (from the ACS 2010 data, it follows that the correlation between median housing price, a proxy for the price level, and the median income is more than 0.6), the real income gap between the “top-earners” and the “rest” does not vary (constant inequality) so fertility should be the same. However if variation in median income is due to the variation in the shape of income distribution implying variation in the real income gap between the “top-earners” and the “rest” (affecting fertility decisions of households across metropolitan areas), it will be captured by variation in income inequality measures.

Although not present here due to arithmetical complexity, the less general model where parents have positional concerns in terms of the human capital of their children, described by a utility function \(ln\left( {c_t} \right) + \omega ln\left( {n_t\left( {h_{t + 1} - \phi \widetilde {h_t}} \right)} \right)\) where \(\widetilde {h_t}\) is the average human capital in the generation

*t*, qualitatively has the same implications, that is wider income gap between high and low-income households imply lower fertility for both high and low-income households.Note that from de la Croix and Doepke (2009) it follows that it is possible to have of lower average fertility in jurisdictions with higher inequality due to lower fertility of the richest who send their children to private schools, but this hypothesis also requires to have in cross-section that high-income households have fewer children than low-income households.

In 2SLS estimation.

I use variable “CONSPUMA” to identify households at metropolitan area level.

Using the Gini coefficient, the least unequal city identified was Hampton, Virginia, where the

*GINI*_{c}was equal to 0.19, while the most unequal city identified was Los Angeles-Long Beach, California (followed by New York City, New York), where the*GINI*_{c}was equal to 0.46. Using the \(I_c^{90{\mathrm{/}}10}\) measure of inequality, the least unequal city identified was again Hampton, Virginia, where income at the 90th percentile was only 2.6 times that at the 10th percentile. The most unequal city identified was Springfield, Massachusetts (followed by New York City, New York), where the \(I_c^{90{\mathrm{/}}10}\) was equal to 15.96.The estimation is similar to the one found in Simon and Tamura (2009), but in addition to the controls used by them includes local income inequality measure and household income measure.

Note that by inclusion of metropolitan area-level median income and median housing price variables I control for the proportional shifts in income distributions, while the variation in the shape of income distributions is captured by inequality measures.

The area-level variables which are supposed to control for sorting on unobserved variables (affecting relative prices, quality and quantity preferences) across metropolitan are constructed after imposing sample demographic restrictions as it is reasonable to assume that they should be the relevant ones for the demographics of the sample. However one may argue that the housing market may not be segmented by the demographic characteristics of people within the metropolitan area. However the the correlation between median housing prices constructed before and after imposition of demographic restrictions is almost 0.99, so I abstain from presenting estimations with unrestricted housing prices.

By definition

*RICH*_{i,c}does not have a dollar value, so with*RICH*_{i,c}I do not have the problem of compatibility of incomes (e.g. a household with income of 60000 dollars in rural Vermont could be characterized as rich, while in New York City it could be characterized as poor). Using*RICH*_{i,c}, the Vermonter would probably be assigned a value of 1, while the New-Yorker would probably be assigned a value of 0.Note that I also did estimation of Eq. (18) dropping those in the top 10% of income distribution. In other words, those who are hypothesized to generate variation in benchmark consumption (and thus affect the fertility of the rest of population) are removed from the sample (so they can not pull down fertility in more unequal areas), but the effect of their income (and thus consumption setting benchmarks for lower income households) is preserved (captured by the income inequality measure). In that estimation I still observe negative inequality-fertility relationship, which in this case can not be explained by the “quality-quantity” trade-off among those who are in the top of income distribution in their respective metropolitan areas.

Note that it is not unheard of in the literature to have positive conditional correlation between fertility and income in cross-section for developed nations and the US in particular as evident from O’Malley Borg (1989); Jones et al. (2010); Rosenzweig and Schultz (1985) and Shields and Tracy (1986). It is common to find negative unconditional income-fertility relationship (which is true for the ACS 2010 1% sample used in this study too), however inclusion of other controls often flip the sigh. One may argue that if finding positive fertility-income relationship is not uncommon, observing

*β*> 0 may not be the best way of proving that it is my theory that explains the negative inequality-fertility relationship. However as indicated in the previous footnote, estimation where top earners are dropped, produces similar results.

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## Acknowledgements

I thank the following people for their advice, revisions and consultations: Francisco Alvarez-Cuadrado, Markus Poschke, Daniel Barzyck, Uma Kaplan, John Galbraith, Fabian Lange, Jean-François Mercier, Nagham Sayour. I thank also the anonymous referees of this journal whose help and guidance significantly improved this project.

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Japaridze, I. Envy, inequality and fertility.
*Rev Econ Household* **17**, 923–945 (2019). https://doi.org/10.1007/s11150-018-9427-z

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DOI: https://doi.org/10.1007/s11150-018-9427-z