Monthly Archives: January 2014

Casual versus Causal Inference: Time series edition

In January 2014, a funny thing seems to have happened. Parts (though not all) of the econoblogosphere forgot why time series econometrics fell out of favor in the early 1990s when it comes to analyzing minimum wage policies.  Besides the fact that there is a lot more variation in minimum wages than just the federal (or average) minimum wage in the U.S., the timing of the minimum wage increases is very uneven. For example, U.S. minimum wage increases tend to occur more frequently during the late phases of the business cycle (see Figure 4).

Now this timing issue makes trouble even for state panel studies, but it really wreaks havoc on time series analysis. By not having a control group, time series evidence has to rely solely on changes in trends around the time of minimum wage increases, as this blog post by Kevin Erdmann most recently tries to do. In 6 out of the 7 episodes of minimum wages that he considers, employment trends slow down (or fall outright) following the minimum wage increases. In other words, the red post-MW trend lines have a smaller slope than the black pre-MW slopes.


It looks quite remarkable. Linking to this picture, Tyler Cowen quotes Erdmann: “Is there any other issue where the data conforms so strongly to basic economic intuition, and yet is widely written off as a coincidence?”

Well, here’s a reason why this evidence should be written off as a coincidence. Below, I overlay Erdmann’s graph with the NBER business cycle dates in light green. Why am I looking at this?  Because if the post-MW period includes a recession and the pre-MW period does not, that will misattribute the recessionary job losses to minimum wages.


I hand drew the recessions in, and I’m not known for my fine motor skills. But I think you get the gist from the picture above. In 5 of the 6 events, the “post periods” used to fit the post-MW red trend line appear to include a downturn. (In other words, the red trend lines and green shadings overlap.) Now, we know very well that teen employment falls during a downturn. This tends to make the red post-MW trends smaller, providing a very simple explanation for why in 5 out of the 6 cases, the teen employment trend slowed down. And the 6th increase (in September 1961)  happened right after the recession officially ended in February, so one could make an argument that the business cycle can help explain that one too.

Oh, and that 1 episode where the trend line actually rose after the minimum wage increase – which doesn’t fit the job loss explanation?  That would be the minimum wage increase in the late 1990s boom, where the post-MW period does not appear to include a recession. In other words, business cycles can explain the pattern of employment trend changes in at least 6 out of the 7 episodes, and maybe even partly in the 7th.

Look – whether minimum wages cause teen employment to fall remains controversial. I think the clearest U.S. evidence comes from comparing across border counties with different minimum wages, using regional controls, or using synthetic control groups. All of these suggest the impact on teen employment is fairly small for the kind of minimum wage increases we have seen in this country. But whatever your position is on this question, you should probably steer clear of simple time series evidence that economists on both sides of the debate have wisely moved away from.


The Poverty of Minimum Wage “Facts”

In a recent post, Tyler Cowen discusses my recent paper on minimum wages and poverty. Cowen acknowledges that “[my] paper, econometrically speaking, is a clear advance over [a 2010 paper by] Sabia and Burkhauser.”  However, he is more persuaded by “facts” such as simulation results from Sabia and Burkhuaser’s paper that claims “[o]nly 11.3% of workers who will gain from an increase in the federal minimum wage to $9.50 per hour live in poor households.”

Cowen concludes that my paper “pays little heed to integrating econometric results with common sense facts and observations about the economy.”

I’m pleased that Cowen thinks my paper represents a clear econometric advance. But I strongly disagree that the econometrics are at odds with common sense facts. Simulation studies are not facts, and when we interpret the relationship between wages and poverty properly, the econometric results appear eminently sensible.

Let’s start with the econometrics. First, both the weight of the existing studies, and my own econometric evidence that Cowen considers an advance, suggest that minimum wages have a modest impact on reducing poverty. I find minimum wage elasticities for the poverty rate ranging between -0.12 and -0.37.  This range of estimates is based on 16 different models, and the list includes just about every specification (or close to it) used in the literature. That includes specifications in Burkhauser and Sabia (2007), Sabia (2008), Sabia and Burkhauser (2010), and  Neumark and Wascher (2011)—except that I use more data.

Now, if this range does not include your preferred estimate, that’s fine. But, then you need to acknowledge that you also do not believe empirical results from regressions in the previous papers using one of the 16 models I do estimate. Another possibility is that you like one of the 16 models, but prefer earlier results that showed a weaker connection between the minimum wage and poverty. In that case, you need to explain why you believe a result from a smaller sample of data used to one that uses more data. This is especially important because many of the estimates in the literature are highly imprecise, in part due to use of small samples. You are not allowed to pick econometric results from a specification when you agree with the outcome, but dismiss results from the same specification when the results are not agreeable to you.

So is this type of econometric evidence—of the sort that has become the hallmark of applied micro-economics in the past few decades—out of touch with the “real world?” Instead, should we turn to simulations like those in Sabia and Burkhauser to get closer to reality?  As a believer in the credibility revolution in economics, I’m going to go ahead and say, no. Actually, the type of estimates that I have found both in my own work, and generally from the literature, is what you would expect based on the pattern of wages and family incomes if you also account for the commonsensical—and empirically supported—propositions that: (1) workers above the minimum get some raise too (“spillover effects”), and (2) reported wages in survey data is measured with error which makes the relationship between low wages and low family incomes weaker than it is in reality.  The simulation results like Sabia and Burkhauser do not in fact account for these, and they understate the association between minimum wages and low family incomes.

So let us go through these points more carefully. As I report in my paper, poor workers are  disproportionately low-wage workers. In 2013, 63 percent of workers under the poverty line reported earning less than $10.10/hour, as compared to 22 percent of workers overall. This is broadly consistent with my econometric findings: that minimum wages raise family incomes relatively more at the bottom of the family income distribution.  At the same time, I also explicitly state that the relationship between low wages and low family incomes (e.g., poverty) is indeed imperfect. In 2013, around 18.9 percent of workers who reported earning under $10.10/hour were in families under the poverty line, and around 46.0 percent were below two times the poverty line. So yes, the minimum wage is a “blunt” tool if the only goal were to reduce poverty. (Curious why my estimate of 18.9 percent differs from Sabia and Burkhauser’s estimate of 11.3 percent? Jump to the Postscript at the end.)

But, I also point out in my paper that using the distribution of reported wages to make predictions about minimum wage impact on poverty—like Sabia and Burkhauser do—will almost certainly under-estimate the true effects. To see why, consider the assumptions made by Sabia and Burkhauser in their simulations:

  1. They assume that most workers reporting a wage under the old minimum will not get a raise when the minimum wage goes up.
  2. They also assume that no one above the new minimum will see a raise.

These assumptions are inconsistent with a large body of evidence. First, there is almost certainly some wage spillover or “ripple effects”, as shown most recently by Autor Manning and Smith (2010)—a paper Cowen says is of “highest academic pedigree.” A minimum wage increase ripples up to the 20th percentile of the wage, which would simply not happen if there were no spillovers. Interestingly, a recent study by the Hamilton Project uses spillover estimates from a paper by Neumark et al. (2004) to estimate that a total of 35 million workers would get a raise from increasing the minimum wage to $10.10/hour, many more than number of workers directly affected by the policy.

Second, many workers who report earning lower than the current minimum wage are in reality earning at or slightly higher than the minimum wage, and they will also see their wages rise. In general, the more measurement error there is in wages and other sources of incomes, the weaker the relationship between poverty and low wages will appear to be. Measurement errors don’t just “wash out”—they weaken correlations in what economists call an “attenuation bias.” The concern with measurement error in reported wages is also discussed in Autor, Manning and Smith 2010. And while measurement errors may lead to problems inferring exactly why we see spillover effects, they mean the kind of assumptions used by Sabia and Burkhauser will understate the true relationship between minimum wages and poverty.

Third, many of the workers who are truly being paid lower than the statutory minimum in the informal sector will see an increase, a phenomenon is sometimes called the “lighthouse effect.” There are different explanations for this, but consider the following analogy. There are people who drive at 70 miles an hour even when the speed limit is 65; now if the speed limit is lowered to 55, most people who were previously driving at 70 miles an hour will also lower their speed, while continuing to speed a bit. A similar logic applies to cases like the minimum wage where the probability of detection likely varies with the extent of violation.

So to take stock, if you consider the Sabia and Burkhauser simulation results  as “facts” you also are claiming that no worker reporting a wage below the old minimum will get a raise, and no one above the new minimum will get a raise. These are not very good assumptions, and they certainly are not facts.

Of course, you don’t have to make these assumptions. You could allow for spillovers. You could allow for wages to rise below the minimum. You could allow for measurement error in reported wages and other sources of income. But then you are not in a world where tabulating survey data gives you simple facts that are beyond reproach. You need to make additional assumptions to make causal claims. And we have not even begun to talk about behavioral effects—be they on labor demand side, or on labor supply side such worker search effort, etc. (And by the way those do not all go in the same direction.)  So you could add a lot more assumptions and continue with the simulation route, or you could use quasi-experimental approach used in almost all of applied micro-economics to empirically estimate the effect of minimum wages on poverty and other outcomes.  Of course, you would want to subject your identifying assumptions to specification checks and falsification tests to ensure you have reliable control groups; and you would account for possibly confounding policies such as state EITCs. And when you do all of that, and some more, you would probably end up with a paper like this one.

So where does this leave us?   As I said in my paper, policies like cash transfers, food stamps, and EITC are better targeted to help the poor, although even there minimum wages are better thought of as complements and not substitutes. More generally, however, motivations behind minimum wage policies go beyond reducing poverty. The popular support for minimum wages is in part fueled by a desire to raise earnings of low and moderate income families more broadly, and by fairness concerns that seek to limit the extent of wage inequality, or employers’ exercise of market power.  And the evidence suggests is that attaining such goals through increasing minimum wages is also consistent with a modest reduction in poverty, and moderate increases in family incomes at the bottom.  

Postscript. If you were paying close attention, you would have noticed a potential discrepancy. Sabia and Burkhauser argue that 11.3 percent of workers who will gain from an increase in the federal minimum wage to $9.50 per hour live in poor households, and 36.8 percent are under twice the poverty line.  I find that 18.9 percent of workers who will gain from an increase to $10.10 an hour are in families below the poverty line, and 46.0 percent under twice the poverty line. So what is going on here? Two things. First, Sabia and Burkhauser use the “household” as the unit to calculate poverty status, while I use “family.” While neither is clearly superior to the other, you should know that official Census definition of poverty uses the family as the unit. And for whatever reason, Sabia and Burkhuaser use a family based poverty measure when they run regressions, but use households when the do simulations. Second, low wage workers actually appear to be somewhat poorer today than they were in 2008, which is the period Sabia and Burkhauser were analyzing. I will have more to say on this in a future post, but the upshot is that even on this narrow count, it is more accurate to say the 19 (and not 11) percent of workers who report wages below the proposed $10.10/hour are in families that would be officially designated as being poor. And as I explained above, this number is almost certainly too small due to measurement error in both wages and other incomes. Return to the post.

Separating signal from noise: a review of 12 major studies on minimum wages and poverty

Excerpted from Section 2 of my paper:  Minimum Wages and the Distribution of Family Incomes. Key sections are in bold. Alterations (but not deletions) from the paper are marked in square brackets [ ].

In this [post], I review the key papers on the topic of minimum wages and [poverty] based on U.S. data, and discuss their findings and limitations. My primary goal here is to provide a quantitative summary of the existing evidence, focusing on the [official] poverty rate elasticity as the most commonly estimated distributional statistic. [A poverty rate elasticity with respect to the minimum wage of, say, -0.2 means that a 10 percent increase in the minimum wage reduces the poverty rate by 2 percent. Note that this is different from a 2 percentage point reduction in the poverty rate.]

I begin by describing the process of selecting studies for this review. First, I only consider peer-reviewed publications since the early 1990s, i.e., the beginning of the “new economics of the minimum wage” literature. Second, I only include studies that report estimates for some statistic based on family incomes (such as poverty, quantiles, etc), and not other outcomes such as utilization of public assistance. Third, studies are included only when they empirically estimate the effect of minimum wages, as opposed to simulate such effects. This selection process yields 13 studies, 12 of which are used in my quantitative summary.

As a way to quantify the existing evidence, Table 1 reports the key estimates from the 12 studies for which I could construct an elasticity of the poverty rate with respect to the minimum wage. When the original estimates are not reported as poverty rate elasticities, I use information in the paper to convert them (and standard errors) to that format for comparability. To minimize the impact of subjective judgment, I have used the following guidelines for selecting estimates. (1.) I report estimates for all of the demographic groups studied in each paper; the sole exception is for workers, since minimum wages can affect who is in that group and lead to sample selection problems. (2.) When a study uses multiple econometric specifications, I include all of them in Table 1, except: (a.) the handful of estimates that did not include state and time fixed effects (or equivalent) as controls; (b.) estimates from sub-periods reported in a few of the papers, and (c.) specifications with lagged minimum wages reported in a few of the papers. Overall, these guidelines lead me to report 54 elasticities in Table 1, which represent either all or nearly all of the estimates of minimum wage impact on the poverty rate available in each of the papers.

Card and Krueger (1995) consider the short run impact of the 1990 federal minimum wage increase on the poverty rate for those 16 years or older, and regress the change in the state-level poverty rate between 1989 and 1991 on the the proportion earning below the new federal wage in 1989 (“fraction affected”).  Their bivariate specification has an implied minimum wage elasticity for the poverty rate of -0.39, but controls for employment and regional trends reduce the overall elasticity in magnitude to the range (-0.36, -0.08), and the estimates are not statistically significant at the conventional levels. They also find that the 10th percentile of the (unadjusted) family earnings distribution responds positively to the minimum wage increase, with an implied elasticity between 0.28 (bivariate) and 0.20 (with controls); these are statistically significant at conventional levels. A major problem with this analysis is that the estimates are imprecise. This is mainly due to the very short panel structure. For example, the 95 percent confidence interval associated with the poverty rate elasticity in their most saturated model is quite wide: (-0.65, 0.49).

Addison and Blackburn (1999) consider teens, young adults, and junior high dropouts between 1983-1996. Using state-year aggregated data and two-way fixed effects, they find sizable poverty rate elasticities for teens and junior high dropouts in the range of (-0.61, -0.17), with an average of -0.43. They find more modest sized estimates for young adults (an average elasticity of -0.24). Morgan and Kickham (2001) study child poverty using a two-way fixed effects model with data between 1987 and 1996, and find a poverty rate elasticity of -0.39. Stevans and Sessions (2001) consider the overall poverty rate in the 1984-1998 period; their most comparable estimate is from a two-way fixed effects model, and appears to yield an elasticity of -0.28. Gunderson and Ziliak (2004) consider the impact of a variety of social policies on the poverty rate and the squared poverty gap using both post and pre-tax income data between 1981 and 2000. For the population overall, they find a small overall poverty rate elasticity of -0.03, with a range of -0.02 to -0.06 across demographic groups. However, they specifically control for the wage distribution, including the ratio of 80th-to-20th percentile wages. This inclusion of the inequality measures is problematic, as it could block the key channel through which minimum wages would actually reduce poverty, namely raising wages at the lower end of the wage distribution. DeFina (2008) uses state-aggregated data from 1991-2002 and finds that minimum wages reduce child poverty in female-headed families, including those headed by someone without a college degree. The estimated poverty rate elasticities are -0.42 and -0.35, respectively.

Burkhauser and Sabia (2007) examine the effects on state-level poverty rates for 16-64 year olds and single mothers during the 1988-2003 period using specifications with two-way fixed effects. Depending on controls, their estimates of the poverty rate elasticity range between -0.08 and -0.19 for the population overall, and between -0.07 and -0.16 for single mothers. While none of the estimates are statistically significant, the point estimates are all negative, and the confidence intervals are consistent with sizable effects. In a follow-up study, Sabia and Burkhauser (2010) consider the 2003-2007 period and find little effect [of minimum wages on poverty]. This study is limited by a rather short sample period. Since it is an update of their previous paper, it is unfortunate that they do not also report estimates using the full sample (1988-2007) instead of just considering a five year period. While their point estimate is small (-0.05), the 95 percent confidence interval is fairly wide (-0.34, 0.24).

Sabia (2008) uses individual level CPS data from 1992-2005, and a two-way fixed effects specification augmented with state-specific quadratic trends to study the effect on single mothers. He finds statistically insignificant but again mostly negative and often sizable estimates, with a poverty rate elasticity of -0.22 from his main specification; for single mothers without a high school degree, the estimate is larger in magnitude (-0.28) while still not statistically significant. Sabia and Nielsen (2013) use the SIPP between 1996-2007 and find an overall point estimate of -0.31 (without state-specific linear trends) or -0.03 (with trends). However, these are imprecise estimates, as the 95 percent confidence intervals are (-0.93, 0.30) and (-0.27, 0.22), respectively—the former set is consistent with nearly all other estimates in the literature. Their estimates also appear to be sensitive to the inclusion of state-specific trends, but again, the imprecision of the estimates makes it difficult to draw any firm conclusion. Overall, two of the four papers coauthored by Burkhauser and/or Sabia suggest small to modest negative effects, while the other two produce fairly imprecise or fragile estimates. However, the overall evidence from their papers does not actually rule out moderate sized poverty rate elasticities.

Neumark and Wascher have coauthored three papers that are of particular relevance. Neumark and Wascher (2002) consider movements in and out of poverty by forming two-year panels of families with matched March CPS data between 1986 and 1995. Because they do not directly estimate the effect of the policy on poverty rates, Table 1 does not include estimates from this paper. [However, in a related paper], Neumark, Schweitzer and Wascher (2005) also use [the same data] between 1986 and 1995. They estimate the effect of discrete minimum wage [changes] on the distribution of the income-to-needs ratio, and their estimates suggest that an increase in the minimum wage actually increases the fraction of the population in poverty: they report a poverty rate elasticity of +0.39.

This is the only paper in the literature that I am aware of which finds such a [clear] poverty-increasing impact of the policy for the overall population. [H]owever, there are numerous non-standard aspects of their research design. Their method does not properly account for state and year fixed effects. They “mimic” state and year fixed effects by shrinking all families’ incomes by the proportionate change in the median income in that state (pooled over years) and also by analogously shrinking the median change in that year (pooled over states).  This constitutes an assumption that state and year effects are scale shifts that proportionately shrink the entire family income distribution. In other words, they impose the assumption that various counterfactual quantiles in states are moving proportionately to the median, which is an unattractive assumption, and much more restrictive than the inclusion of state and year dummies in a regression of the poverty rate on minimum wages [which is the standard approach]. Additionally, they use an ad hoc adjustment in the change in densities to account for the fact that some observations have both contemporaneous and lagged increases. These non-standard techniques raise serious questions about the study, especially since it stands out in terms of producing a sizable positive poverty rate elasticity. To my knowledge, no one, including any of the authors, has used this methodology in any previous or subsequent paper.

In contrast, Neumark and Wascher (2011) uses a more conventional approach to study the interactive effects of EITC with minimum wages over the 1997-2006 period. Although their focus is mostly on wage and employment effects, they do provide some evidence of minimum wage effects on the share of 21-44 year olds with incomes below the poverty line and one-half the poverty line.  Like most of the literature, they include state and year fixed effects; they also include demographic and state-level controls similar to this paper. Unfortunately, the authors do not report an overall minimum wage effect, and instead focus on their interaction effects with EITC. However, we can use the regression coefficients along with other information provided in that paper to back out a poverty rate elasticity with respect to the minimum wage using straightforward calculations. For the broadest group that they considered—21-44 year old family heads or individuals—their results suggest a minimum wage elasticity of -0.29 for the proportion with an income under the poverty line, and -0.45 for the proportion with an income less than half the poverty line (“extreme poverty”).  For a group constituting the majority of non-elderly adults (and representing many children as well), the evidence from Neumark and Wascher (2011) suggests that minimum wages have a moderate-sized impact in reducing poverty and extreme poverty. These results seem to be qualitatively different from the findings in Neumark et al. (2005), and much more similar to rest of the literature.

To take stock, the results in this literature are varied and sometimes appear to be inconsistent with each other. But is it possible to filter out some of the noise and actually obtain a signal? First, I note that across these 12 studies, nearly all (48) of the 54 estimates of the poverty rate elasticity are negative in sign. Indeed, only one study by Neumark et al. (2005) suggests that minimum wages actually increase the overall poverty rate. Moreover, this study uses an unconventional methodology that is both different from all other studies, and is also problematic.

Second, if we take an “average of averages” of the poverty rate elasticities for the overall population across the seven studies that provide such an estimate so that (1) each study is weighted equally, and (2) within each study, all specifications reported in Table 2 are weighted equally as well, we obtain an average poverty rate elasticity of -0.07. However, excluding Neumark et al. (2005) [which uses a problematic and unconventional methodology], the “average of averages” of the poverty rate elasticities is -0.15. [Overall] the existing evidence points towards a modest impact on the overall poverty rate.

Besides these seven studies, five additional studies reviewed here provide estimates for subsets of the population. If we take an “average of averages” of the poverty rate elasticities across all 12 studies, while (1) weighting each study equally, and (2) weighting each specification and group within study equally as well, we also obtain an elasticity of -0.15. If we exclude Neumark et al. (2005), the “average of averages” across the 11 studies is -0.20. There are, of course, other ways of aggregating estimates across studies. However, when I consider the set of nearly all available estimates of the effect of minimum wages on poverty, the weight of the evidence suggests that minimum wages tend to have a small to moderate sized impact in reducing poverty. [Below, I also plot histograms of all 54 elasticities—both unweighted, as well as weighted by the inverse of the number of estimates in each of the 12 studies, so that each study is weighted equally.]


While there is a signal in the literature that minimum wages tend to reduce poverty, it is also true that the existing evidence is clouded by serious limitations. These include (1) inadequate assessment of time-varying state-level heterogeneity [i.e., states with high and low minimum wages have very different trajectories on a host of dimensions unrelated to the policy]; (2) limited sample length and/or exclusion of more recent years that have experienced substantially more variation in minimum wages; (3) insufficient attention to serial correlation [which means many of the tests of statistical significance may be incorrect]; (4) use of questionable estimators; and (5) frequent omission of demographic and other covariates. In [my own analysis], I use more and better data along with more robust forms of controls to address these limitations in the existing literature.