Higher inflation is modestly associated with higher income inequality

There is a fairly large literature looking at the relationship between inflation and income inequality. Some studies find that there is a positive correlation (more inflation is associated with more income inequality). Some studies find the opposite, a negative correlation (more inflation is associated with less income inequality). Still other studies find no relationship at all between (or, at least, no statistically significant relationship). So, what are we to make of this literature?

To the rescue comes this recent article by Andreas Sintos (University of Luxembourg), published in the journal Economic Systems (sorry, I don't see an ungated version online). Sintos presents a meta-analysis of 124 journal articles, containing 1767 estimates of the relationship between inflation and income inequality. Sintos distinguishes between two strands of the literature: (1) looks at how the level of inflation affects the level of income inequality (in other words, the variables are measured in levels); and (2) looks at how changes in inflation affect changes in income inequality (in other words, the variables are measured in differences). The difference is important. In my view, measuring the relationship in levels doesn't make a lot of sense. If you find that the relationship is positive, then that implies that, since inflation is generally positive, income inequality should be ever-increasing. That seems somewhat inconsistent with reality. In contrast, it seems to me that when the level of inflation changes, that might change inequality.

Anyway, Sintos finds that:

...once the correction for publication bias is made, we find that, on average, inflation has a (small-to-moderate) inequality increasing effect for both level and difference estimates...

In other words, inflation increases inequality (to the extent that we can attribute causality to these results - more on that later in this post). The bias-corrected average effect size ranges between 0.051 and 0.120 (which are interpreted as small and moderate effect sizes respectively). Sintos then goes on to investigate the study-level factors that are associated with the estimated relationship. For the result in differences (which I find more theoretically plausible):

...we find that ten regressors matter significantly for the underlying effect of inflation on income inequality in the primary studies... the BMA [Bayesian Model Averaging] results for difference estimates reveal a decisive effect for eight regressors: GDP deflator, Panel data, Time span, Log transformation, GDP growth, Financial development, Publication year, and Citations. Moreover, we find a strong effect for Trade openness and a weak effect for Education.

Specifically, studies that cover a longer time span, use log-transformed variables, and those that control for GDP growth, financial development, and trade openness find a more positive effect of inflation on inequality, as well as those studies that have attracted more citations. Studies that use the GDP deflator (rather than the change in the Consumer Price Index) as a measure of inflation, use panel data, and those that were published most recently, find a more negative effect (or a smaller positive effect) of inflation on inequality. A couple of things jump out from that. First, the fact that more recent studies, which we would expect to use more sophisticated methods and better-quality data, find smaller effects, should lead us to believe that the 'true' effect is somewhat smaller (less positive) than what Sintos finds on average. However, when Sintos goes on to simulate the effect that would be obtained from the theoretical 'best study', they find that:

The associated prediction, which represents the model average across the models estimated using BMA, is 0.275, with a standard error of 0.115 (95% CI 0.051–0.500), for level estimates, and 0.540, with a standard error of 0.236 (95% CI 0.077–1.002), for difference estimates.

This is somewhat larger than the bias-corrected average effects reported in the paper. That makes me wonder whether the assumption that studies are improving in quality over time actually holds. Could it be that more lower-quality studies, or perhaps studies with lower-quality data, are increasingly being published? We don't have a direct answer to that question, but the correlation matrix reported in Figure 2 in the paper suggests that more recent publications are less likely to use OLS regression, and more likely to control for the variables that have important effects (as noted above). So, I remain somewhat at a loss to explain why the 'best study' estimates are larger than the bias-corrected average effects.

Second, the fact that studies that report more positive results have attracted more citations should be a bit of a concern. The literature had a diversity of results, and while the bias-corrected average effect is positive, that in itself shouldn't lead researchers to cite papers with positive effects more than those with the opposite, or with null effects. There is clearly a bit of cherry picking going on in terms of what results are cited in the literature.

Finally, the results don't establish causality definitively. Many of the studies deal with endogeneity problems, but not all of the studies do. So, while we can tell a plausible causal story here, we can't be sure about it. Nevertheless, this paper is another model of reporting meta-analytic results, the second such paper that I've read this year (see here for my post about the other paper). Given the importance of meta-analysis for estimating the average effect across a literature as a whole, the trend towards clearer exposition and interpretation of the results of meta-analyses is very welcome.

What we can take away from this paper is that higher inflation is modestly associated with higher income inequality. Given the sheer number of things that appear to be correlated with inequality, it would be expecting too much for inflation to have a large effect. But nevertheless, when we consider income inequality, inflation (or change in the inflation rate) appears to be an important consideration.