Thursday, December 6, 2018

In-depth look at income and wealth data (pt. 3 of 3): Minimum wage policy and the income distribution

In this final part of this series of posts on income and wealth, I originally intended to discuss the data used to analyze income inequality but I will introduce a more specific topic within income inequality: minimum wage policy and its impact on the wage and income distributions. Given the ongoing public debate over stagnating real wages despite a strong labor market (see this piece by the Pew Research Center for a concise description of the trends and a few of the reasons given by economists for the wage stagnation for workers at the lower end of the earnings distribution), it is particularly relevant to revisit the evidence on minimum wage policy and its impact on income inequality.

In this post, I focus on two papers - Autor, Manning, and Smith (2016) and Dube (2018) both in American Economic Journal: Applied Economics - that discuss the distributional implications of minimum wage policy. These papers have significant differences in both methodology and level of analysis. While AMS (2016) focus on individual wage inequality, Dube (2018) focuses on household income inequality with two iterations on how income is defined. The first is the conventional definition of income that includes both earnings and cash transfers. The second is a broader definition that also includes tax credits and non-cash transfers that enables the author to assess the substitutability between minimum wage earnings and government benefits to derive results that are closer to general equilibrium. The choice and level of the outcome variables measured in these two papers - earnings versus income and at the individual versus household level - are important to treat as distinct and independently informative. As I discussed in an earlier post on household income inequality in the U.S. and Britain, the distributions of individual labor market outcomes and household incomes do not necessarily track one another closely.


In the U.S., minimum wage policy is determined at several levels of government: federal, state, and as of late even citywide minimum wages exist (in San Francisco, San Jose, Albuquerque, Santa Fe, and Washington, DC). This piece on minimum wage policy outlines the basics. In part because the U.S. federal minimum wage declined in real value almost continuously for thirty years between 1979 and 2007 (it was fixed in nominal terms between 1981-1990 and 1997-2007), more than thirty states enacted legislation over the same time period to raise their state minimum wages above the federally mandated level. The below graph tracks the real value of the federal minimum wage (in part indicating the motivation for state and city-level legislation on the issue):

Source: UC Davis Center for Poverty Research (2018)
The minimum wage has therefore seen significant state and time-based variation within the U.S. over the past several decades that continues to this day. This variation has been utilized by many empirical studies of the minimum wage including AMS (2016) and Dube (2018).  It should be noted that the ratio of real minimum wage to median wage provides some quick information about lower-tail inequality that will be discussed in greater detail below. For example, between 1950-1970 this ratio fluctuated between 45-55 percent but by 1989 it had fallen to 36 percent.

Estimation strategy

The challenge with estimates of the impact of minimum wage policy are that both minimum wage legislation and wage inequality levels are impacted by several other unobserved characteristics. For more details on these challenges and how research designs can overcome them, see Allegretto et al. (2013). These two papers take two very different approaches: while AMS (2016) employ an instrumental variables strategy, Dube (2018) employs a series of sensitivities and falsification tests to indicate the robustness of his results. The takeaway is that identification of the employment and inequality effects of the minimum wage is challenging and can result in complicated empirical strategies.

As Dube (2018) indicates of the initial fixed effects model that he presents: "A problem with the two-way fixed effects model [state and time fixed effects] is that there are many potential time varying confounders when it comes to the distribution of family incomes. As shown in Allegretto et al. (2013), high- versus low-minimum wage states over this period are highly spatially clustered, and tend to be differ in terms of growth in income inequality and job polarization, and the severity of business cycles." In other words, the legislation of minimum wage and wage inequality are both impacted by a number of factors that are not controlled for in an OLS or even two-way fixed effects model.

AMS (2016) also reference potential biases when they present their initial OLS model. They cite confounding evidence that the effective minimum wage is found to be equally significant on both the lower-tail and upper-tail inequality (where it is expected to only have a significant effect on lower-tail inequality since minimum wage policy is only binding for at most the 15th/20th percentile of the wage distribution). The initial OLS model that they present estimates the impact of the "bindingness" of the minimum wage at the state-year level (a variable initially employed in Lee (1999)) - the log difference between the effective minimum wage and the median wage - on the difference between the log real wage at a specific percentile and the log real wage at the median. The former variable on the "bindingness" of the minimum wage is included as a quadratic term because minimum wage is expected to have a larger effect on the part of the wage distribution where it is more binding (i.e. at the lower-tail of the wage distribution) rather than a linear effect. To address potential biases, they employ an instrumental variable strategy and instrument for the observed effective minimum wage.

Because they include the effective minimum wage as a non-linear term, AMS (2016) utilize a set of three instruments as opposed to just the first one: (1) log of the real statutory minimum wage; (2) square of the log of the real minimum wage; and (3) interaction between log minimum wage and average log median real wage for the state across all periods. While it is not discussed in great detail in the paper, this instrument (1) I would assume is the legislated federal minimum wage and it clearly impacts the state-level effective minimum wage (either the federal or state minimum whichever is higher) but does not impact wage inequality at the state-year level through any channel other than the state-level effective minimum wage.

Dube (2018) does not employ an IV strategy in his paper on household income distribution but he includes several sensitivities and falsification tests of his original model to indicate the robustness of his results. His original model is the two-way fixed effects model that he critiques in the section above. In his "most saturated" specification he includes in addition to his original controls, division-specific year effects (to capture the effects of regional shocks on minimum wage legislation that may be driving some of the spatial heterogeneity that we see in minimum wage levels), state-specific recession-year dummies (to address the concern that minimum wage legislation is correlated with state business cycle fluctuations), and state-specific linear trends (to capture long-run trend differences across states). It is challenging to assess the effectiveness of these sensitivities and tests at obtaining causal estimates in comparison to quasi-experimental methods (seminal example is Card and Krueger (1993) in their study of the employment effects of minimum wage).


Based on their instrumental variables empirical strategy, AMS (2016) find that a 10 log points increase in the effective minimum wage leads to a reduction in the 50/10 inequality (inequality between the 50th percentile and 10th percentile in the wage distribution) by 2 log points for women, 0.5 log points for men, and 1.5 log points for the pooled sample. For a better understanding of why this paper uses log points as opposed to percentages, see this post on the topic. Women see a larger effect because a greater share of women work at minimum wage (6 percent of women in 2012 compared to 3 percent of men).

Source: Bureau of Labor Statistics (2013)
They are also able to state that the decline in the real minimum wage explains less than 50 percent of the rise in 50/10 inequality between 1979 and 2012 indicating that the majority of the rise in inequality over this period is due to changes in underlying wage structure (contradicting earlier findings that the decline in the real minimum wage contributed to around 60 percent of the rise in wage inequality over this period). This study indicates that erosion of the real minimum wage played a significant role in the growth of wage inequality over the past several decades but other factors, including skill-biased technological change and increased import competition from low-income countries which compose the "changes in underlying wage structure" that AMS (2016) reference, played a larger role than the decline in the real minimum wage.

What then of the related outcome of household income inequality? Dube (2018) finds that the poverty rate elasticity with respect to the minimum wage is between -.220 and -.552 indicating that a ten percent increase in the minimum wage yields between a 2.2 and 5.5 percent decrease in the poverty rate. He finds a first order effect of the minimum wage on the family income distribution of a ten percent increase in the minimum wage yielding between 1.5 and 4.9 percent increase in the pretax cash incomes of the 10th and 15th quantiles. This finding is indicated in the graphic below with the green line for cash income. The more interesting finding in my opinion is how much these minimum wage gains are offset by reductions in other government benefits due to ineligibility based on the higher income. He finds that for the bottom fifth of the income distribution, 30 percent of the gains to income resulting from minimum wage are offset by reductions in non-cash transfers and tax credits indicating that the relationship between wage and income (in its broader definition) is not nearly 1:1 for the poorest Americans. This is indicated in the graphic below with the orange line for cash income, tax credits, and non-cash transfers.

Source: Washington Center for Equitable Growth (2017)
  • These two papers' findings are consistent with one another though they measure different outcomes - individual wage inequality versus household income inequality. They both indicate that minimum wage has a significant impact on inequality (as well as absolute indicators such as the share of Americans living below the poverty line measured in Dube). 
  • It should be noted that the policy debate over minimum wage consists not only of discussion on the benefits of minimum wage policy on inequality, poverty, and other outcomes of interest but the costs in terms of the employment effects (i.e. hiring and firing decisions of firms, indicators of the quality of work, etc...). Economists are far from agreement on the employment effects of minimum wage (not discussed in this post). The extent to which minimum wage gains are offset by public assistance is also an important consideration and Dube's contributions to this question form part of a broader literature on the linkages between minimum wage and the existing social safety net. 
  • An important note about both of these papers is that by construction they reflect not only the mechanical effect of minimum wage (in increasing wages for individuals working at or below minimum wage) but may also reflect spillover effects on those who already work above it. This is an area for future research, however, since AMS (2016) attribute these additional effects not as spillovers but as measurement error of wages for low-wage workers. Specifically, they find that these spillovers do not "represent a true wage effect for workers initially earning above the minimum" rather accepting the null hypothesis that "all of the apparent effect of the minimum wage on percentiles above the minimum is the consequence of measurement error."
  • Increased trade and automation have yielded dramatic changes to the underlying wage structure of the economy. These changes may not be reflected in the share of workers who work at federal minimum wage (this share declined prior to 2000 and has remained roughly constant between 2000 and 2018 excepting a significant increase at the recession) but perhaps it has increased the share of those in the lower percentiles of the wage distribution. 
    • While these jobs in the lower percentiles may not be "minimum wage" jobs they are certainly part of a broader pattern of low-paying jobs in the U.S. These jobs - and the people who hold them - are illustrated in this article in the New York Times. The article indicates that nearly one-third of workers in the U.S. earn at or below $12/hour with 7.6 million Americans designated as "working poor" meaning they spent at least half of the year in question working or searching for work and were below the poverty line. 
  • Minimum wage policy will not - in a mechanical sense - impact these other low-paying jobs nor will it address factors that impact the underlying wage structure of the economy. However, in an environment in which trade and automation have changed the wage structure dramatically, it has been evidenced to address both wage and household income inequality. 
  1. Autor, D., Manning, A., Smith, C.L. (2016). The Contribution of the Minimum Wage to US Wage Inequality over Three Decades: A Reassessment. American Economic Journal: Applied Economics. 
  2. Dube, A. (2018). Minimum wages and the distribution of family incomes in the United States. Forthcoming in American Economic Journal: Applied Economics
  3. Allegretto, S., Dube, A., Reich, M., Zipperer, B. (2013). Credible Research Designs for Minimum Wage Studies. IRLE Working Paper #148-13. 
  4. Card, D., Krueger, A. (1993). Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania. American Economic Review

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