### Discussion Paper

No. 2018-41 | May 18, 2018
Wage inequality, labor income taxes, and the notion of social status
(Published in Special Issue The economics of social status)

## Abstract

The authors investigate the desirability of income taxes when the objective is to mitigate wasteful conspicuous consumption generated by people’s status-seeking behavior. They consider the joint role of pre-tax wage inequality and of social norms determining how social status is assigned. They find that if social status is ordinal (i.e., only one’s rank in the income distribution matters) then an income tax can decrease waste in conspicuous consumption only if the inequality of pre-tax wages (or earning potentials) is low enough – i.e., inequality and taxation are substitutes. Instead, if status is cardinal (i.e., also the shape of the income distribution matters) then the relationship between the inequality of pre-tax wages and the change in waste can be positive – i.e., inequality and taxation can be complements – although it is in general non-monotonic. This is because the value of social status is endogenous, potentially giving rise to a perverse self-reinforcing mechanism where more waste in conspicuous consumption induces a greater competition for status and vice versa.

D6, H3, J2

## Cite As

Ennio Bilancini and Leonardo Boncinelli (2018). Wage inequality, labor income taxes, and the notion of social status. Economics Discussion Papers, No 2018-41, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2018-41

Anonymous - Referee Report 1
September 24, 2018 - 08:24

This paper presents a carefully set up model of the effects of two types of status -- cardinal and ordinal (or, equivalently, based on amounts versus based on ranks) -- and pre-tax wage inequality on wasteful conspicuous consumption in an income tax system. The model is coherent, embeds both classic ...[more]

... and novel features, and yields interesting results. The paper should be published. I do raise several issues pertaining to aspects of the model, but these can be briefly noted and sustained scrutiny left to future work.

1. Income information as public or private. The model pertains to situations in which income information is private, so that signaling via conspicuous consumption become important in the status process. It should be made clear that in some economies or economic sectors income information is public -- consider CEOs, artists and entertainers, civil servants, and so on. A sentence or two is all that is needed to tell the reader that those sectors fall outside the model. In future work, you could provide information about the proportions in public- and private-information sectors across countries and over time.

2. What is consumed in conspicuous consumption, and why does it matter? The paper seems to assume that conspicuous consumption is "cost-free". But an important feature of the spending pertains to whether the purchases are for durables or nondurables. For example, when we buy a boat or a car, they remain assets that count toward our wealth. But when we buy dinners at three-star restaurants or expensive bottles of wine, the money's gone. This would not matter if only income generated status. But wealth also generates status -- as Veblen famously said. Thus, there might be a tradeoff between income-based status and wealth-based status. A future development of the model might address this matter.

3. Specification of status -- not only cardinal versus ordinal but also the sign of the second derivative. The paper correctly notes the fundamental importance of the particular specification of status, and attends to this by distinguishing between cardinal status and ordinal status. But it is equally important to distinguish between specifications in which status increases at an increasing rate, specifications in which status increases at a decreasing rate, and specifications in which status increases at a constant rate. Sociological work has long held that status increases at an increasing rate. Work by Bales, Mishler, Goode, Sorensen all embeds this insight. Sorensen proposed a specific functional form in which status increases at an increasing rate with the relative rank on the asset [ln(1/(1-relrank))], a function analyzed by Jasso and embedded in sociological basic theory.

4. Other basic processes generating utility. One could stop with status and analyze a model where the actors have only status concerns. But the paper also mentions comparison processes like relative deprivation and one of the formulas bears the signature of comparison processes, namely, the amount or rank is logged, so that the outcome has a negative second derivative. It would be useful to mention that combining the cardinal-ordinal dimension with the second derivative yields, potentially, six types of outcomes. In the sociological literature, Homans proposed that there are three big outcomes (of the sort that Rayo and Becker might call "carriers of happiness") -- comparison (Homans called it justice, which is one of the comparison processes), status, and power. Jasso embedded the Sorensen function (for status) and the justice evaluation function (aka comparison function) in which the outcome varies with the logarithm of the ratio of the actual holding to a reference holding, and increases at a decreasing rate with the actual holding. Because there is no literature on a functional form for power, and because power is not a synonym for either status or comparison, it is assigned a linear form. The setup constrains the input of the status function to be a relative rank, but the inputs for comparison and for power can appear as either amounts or ranks. Thus, in the current sociological conception, there are five types of societies (rather than the six possibilities -- with no cardinal status).

5. Why does the second derivative matter? In a few words, it matters because the results and implications may differ. For example, in the sociological setup, the Sorensen setup for status (increases at an increasing rate with relative rank) produces a negative exponential distribution of status, the Jasso setup for comparison (increases at a decreasing rate) in the ordinal case produces a positive exponential distribution for the comparison outcome, and in the cardinal case produces a negative exponential if the asset is Pareto distributed and a normal if the asset is lognormal. Thus, the two ordinal cases lead to distributions which are mirror images of each other (depending on the outcome and the associated second derivative), and a particular cardinal case leads to a distribution identical to the one in the ordinal status case. Moreover, as would be expected, all predictions differ. A brief footnote can indicate that incorporating the second derivative, as in the sociological literature, leads to six distinct possibilities, five of which appear in the Jasso setup, and future work might distinguish their predictions for wasteful conspicuous consumption.

All in all, an interesting and important paper.

References

Jasso, G. 2008. “A New Unified Theory of Sociobehavioral Forces.” European Sociological Review 24:411-434.

Jasso, G. 2015. “Societies, Types of.” Pp. 878-886 in J. D. Wright (ed.), The International Encyclopedia of the Social and Behavioral Sciences, Second Edition, Volume 22. London, UK: Elsevier.

Ennio Bilancini and Leonardo Boncinelli - Reply to Referee Report 1
March 19, 2019 - 22:04

We thank the Referee for raising important issues, which we have briefly discussed in the revised version of the paper (and which have motivated us to further reflection).

Here we summarize the revisions made in response to Referee 1's comments.

1) We have added footnote 11 to warn ...[more]

... the reader that our analysis only applies to cases where individual income is not public information.

2 & 5) We have added a final paragraph to the conclusions, containing future research directions (a few of these come from suggestions by Referee 2). In this paragraph we mention that future research may investigate the role of conspicuous durable consumption, and the possibility that going into the details of cardinal status, by following the insights from the sociological literature, may allow to obtain sharper predictions.

3 & 4) In the new footnote 3 we recognize the importance, when status is cardinal, of the second derivative. We also give credit to the important work in this respect by Homans, Sorensen and Jasso.

Anonymous - Referee Report 2
November 19, 2018 - 08:47

see attached file

Ennio Bilancini and Leonardo Boncinelli - Reply to Referee Report 2
March 19, 2019 - 22:12

We thank the Referee for the many useful suggestions, which we have tried to accommodate into the paper to the best of our possibilities.

Here we summarize the revisions made in response to Referee 2's comments.

Main Points 1 & 3) We have added a paragraph at the ...[more]

... end of the conclusions where we accommodate her/his suggestions (and also a few suggestions coming from Referee 1).

Main Point2) We have have changed "the amount of income earned plays the twofold role of generating social status and granting the purchasing power required for the signal” into "the amount of income earned plays the twofold role of granting the purchasing power required for the signal and, in a separating equilibrium where the signal allows to perfectly infer the income, generating social status". Indeed, as the Referee points out, an increase in income has an effect on social status if the signal perfectly reveals the income (which happens in fully separating equilibria only).

We made use of the suggestions listed in Minor Issues to correct inaccuracies and improve the clarity of the exposition.

Anonymous - Referee Report 3
December 04, 2018 - 10:42

This paper investigates the nexus between wasteful conspicuous consumption and income taxation in a signalling model. The main result is that the kind of motivations for status competition together with the degree of inequality in society change the impact of the introduction of an income tax on wellbeing. The authors ...[more]

... compare the use of ordinal vs. cardinal status competition showing that many cases can happen. Interestingly, when status competition is based on cardinal differences, the introduction of a linear income tax can even increase the competition for status inducing an increase in the conspicuous consumption.

I have very few observations on the manuscript:

1) The authors introduce income taxation as a linear tax where government revenues are redistributed as a lump sum transfer without changing average income. One different hypothesis could be to tax only conspicuous consumption instead of income, or using different remedies (see Pagano and Vatiero, 2017). I would suggest the author to better discuss their assumption since the starting point of the paper is the effect of income taxation when its objective is to mitigate wasteful consumption.

2) Although graphical representations in Section 5 are clear, it would be useful to add a complete taxonomy of the cases which helps the comparison between the ordinal and the cardinal case.

3) An intuitive explanation of the thresholds (\sigma_h, \sigma_x, etc.) could strongly increase the interest in the paper. For instance, consider \sigma_h (eq. 18), ceteris paribus, as long as the relative importance of leisure time (a) increases, the threshold increases. This would induce an increase in the likely of the “positive” effect of income tax introduction, why?

4) Following previous comment, wages are given in the model and do not depend on the share of high and low skilled workers. Do the results hold even when the wage ratio depends on labour supply composition?

Ennio Bilancini and Leonardo Boncinelli - Reply to Referee Report 3
March 19, 2019 - 22:18

We thank the Referee for pointing out passages where our exposition was not particularly easy to read, allowing us to improve the readalibility of the paper in this revised version.

Here we summarize the revisions made in response to Referee 3's comments.

1) we now briefly mention taxation ...[more]

... on conspicuous consumption at the beginning of the Introduction, and in footnote 1, where we also refer to Pagano and Vatiero (2017).

2) We have restated Proposition 3, in the attempt to make it clear which is the taxonomy of cases arising under cardinal status.

3) We commented in footnote 17 the effect of an increase in $a$ on $\sigma_x$. We did not do the same for $\sigma_l$ and $\sigma_h$ because the same increase in $a$ has not a clear impact in the latter cases.

4) In our analysis we treat the wage ratio $w_h/w_l$ as exogenous, but of course it may well depend on, for instance, the share of high- and low-skilled workers. Since this share is also exogenously fixed, our results are not affected by these considerations, which only point to focus attention on the specific ratio determined by the existing distribution of skills among workers.

Ennio Bilancini and Leonardo Boncinelli - Revised Version
March 21, 2019 - 07:58

see attached file