In June 2017, a paper popped up by Jardim et. al at the National Bureau of Economic Research entitled Minimum Wage Increases, Wages, and Low-Wage Employment: Evidence From Seattle. This is the first of what will probably be many studies investigating the effects of the Seattle minimum wage changes, and generated a lot of press in a short amount of time, with headlines ranging in political charge from CNBC’s tame Seattle’s minimum wage hike may have cut wages and jobs: Study author to the LA Times’ more biting Seattle’s experience shows liberals are clueless about raising the minimum wage and everything in between. In this piece I will provide an in depth review of the article itself, try to explain the methodology that the researchers used, and summarize their findings.

What does economics say about minimum wages?

If you’ve taken an economics 101 course then you’re familiar with the 101 argument — if not, here’s a good video where Sal Kahn explains it. The story is simple. Employers buy labor from workers. When the price of labor goes up, employers can afford less of it. The implication is that a higher minimum wages lead to higher unemployment rates for low skilled workers.

It is important to understand however that the Econ 101 story is not the whole story. In Econ 101, you learn a very simple supply and demand model that relies on a lot of assumptions that might be unreasonable. It assumes that workers and employers have equal bargaining power, that the process of finding jobs and replacing workers is instantaneous, frictionless, and costless, that there are virtually infinite numbers of workers and employers at the ready to make employment agreements as soon as the price is right, it ignores human capital and different market sectors and segments and so on. Altering any of these assumptions can lead to drastically different outcomes, and it is not clear that the simple Econ 101 model most accurately describes reality. Importantly, there are models that are equal in their simplicity to the Econ 101 model, but which predict that minimum wage increases will increase employment for low skilled workers.

This is an important and oft-overlooked point. Many people have an understanding of the Econ 101 perfectly competitive labor market model and its predictions, but fewer understand that this is only one of many many possible models of the labor market, and that different models make different predictions. It is simply not possible to determine from a model alone what the outcomes of minimum wage changes will be, because we don’t know what the correct assumptions should be. The only way to determine that is to conduct empirical studies.

To the surprise of many economists, a majority of the quality empirical work done on minimum wages have found extremely modest or even zero disemployment effects associated with increased minimum wages. The most famous study in this field comes from is Card and Krueger (1992), which found no disemployment effects for fast-food workers during a large increase in the New Jersey minimum wage. Subsequent studies have found similarly small or non-existent effects.

Why is studying the effect of the minimum wage in Seattle hard?

We know when the minimum wage was increased. Why not just look at employment before and employment after and subtract? How come this isn’t easy?

Three possible outcomes of the Minimum Wage experiment. In the first, there is no change in employment due to the minimum wage increase. The second shows a positive change in employment due to the minimum wage increase, and the third shows a negative change in employment due to the minimum wage increase. Note that in all three cases the absolute level of employment increases, so looking at a simple before-and-after picture of the employment rates would be misleading.

What economists are interested in measuring in a case like this is the causal effect of the minimum wage change. This is defined to be the change in the employment rate relative to the counterfactual — that is, what would have happened if there were no minimum wage change. The figure sketches three possible outcomes of such a comparison. The orange line shows the actual employment rate, against the blue counterfactual line, which is what would have happened if everything else stayed exactly the same, but there was no minimum wage change. In the top panel, there is no effect: the the counterfactual world is more-or-less identical to the real world. The middle panel shows a positive effect on employment: employment in the real world is higher than employment in the counterfactual world at the end of the study period. Finally the bottom panel shows a negative effect, where employment in the real world is lower than it would have been otherwise. Comparing the real world to the counterfactual world allows us to make causal claims. We can say definitively that since nothing is different between the real and counterfactual worlds except for the occurrence of the minimum wage increase, that the minimum wage increase caused a change of employment of the measured effect size.

A crucial element of the sketches is that in each case, employment increases from the start to the end. Even in the world where the minimum wage causes a reduction in employment relative to the counterfactual, absolute employment still increases — in this case, due to the booming economy of Seattle.

The obvious problem here is that we have no obvious way of measuring what happened in the counterfactual world, because we don’t live there. So the bulk of the work for economists studying minimum wage is to find clever ways of simulating the counterfactual which allow us to make comparisons between what is actually observed and what would have been observed in a counterfactual world.

Identification Strategy

So the trick of policy evaluation is to come up with clever ways of simulating the counterfactual, and comparing it to what actually happened. The authors come up with three candidate methods for doing this.

The first is the most straightforward. They compare what happens in Seattle to what happens in the surrounding regions where a minimum wage change did not take place. While this does yield statistically significant results showing a decline in employment due to the minimum wage change, the authors reject this method as being too prone to false results — essentially, the regions surrounding Seattle are not quite similar enough to Seattle to serve as a good proxy for the counterfactual case.

The remaining methods are more complicated. One is the Synthetic Controls (SC) approach, which works by creating a synthetic dummy Seattle as a weighted average of surrounding regions. Using data from before the minimum wage change, they find a combination from 40 other geographic units called Public Use Microdata Areas (PUMAs) which best approximates Seattle. So, quoting from Appendix 2 here, the trend in the number of jobs in Seattle is closely approximated as a mix of 21.9% Thurston County (Central), 21.9% Snohomish County (North), 13.3% Clark County (Southwest), and so on. Since these surrounding regions that contribute to the synthetic Seattle do not experience the change in minimum wage but appear to resemble Seattle otherwise, the authors justify comparing what happens in Seattle after the minimum wage to this same weighted average of surrounding regions.

The other method used by the authors is called the Interactive Fixed Effects (IFE) approach. This one is rather complex, but the idea is something like this. The changes in employment statistics in Seattle and the surrounding regions are the result of some complicated collection of factors, including the minimum wage, but also including trends and changes in the macroeconomy at the city, state, and federal level. While the SC approach attempts to use an average of the surrounding regions of Seattle as a proxy for these trends, the IFE approach tries to model them directly. IFE assumes that in each time period there is some set of “shocks” to the economy. As an example, you can imagine that these shocks are sectoral, so that in one time period the Finance sector is booming but the Energy sector is doing poorly, and the next period the Finance sector is down and Energy is up. The actual process is more general than this, and at no point are the individual shocks identified as belonging to one sector or another, but thinking about it this way helps to understand the idea. Different regions are assigned different sensitivities to the various shocks, so that maybe Seattle is very sensitive to Finance shocks but less so to Energy shocks, whereas Klickitat County (which has 400 MW of wind capacity) might have a higher sensitivity to Energy shocks. Again, this is a huge simplification (almost to the point of being a misrepresentation, honestly) of the IFE approach, but the motivating idea is the same. If the shocks and sensitivities are modeled correctly then all non-minimum-wage differences between Seattle and the surrounding regions are accounted for and the remaining differences can be attributed to the minimum wage change.

Data & Data Issues

The authors were able to take advantage of some of the most high quality employment data that has ever been made available for this purpose. The state of Washington collects quarterly payroll records for all workers covered by Unemployment Insurance. This means that any person who worked as an employee (no independent contractors or self-employed workers) in Washington over the study period is in the data. The data set includes both wages paid over the quarter and hours worked, which allows the authors to estimate effects on the hourly wage directly across all sectors and wage levels. This is very nice.

Multi-site Businesses

A problem with the data, and one of the central sources of criticism regarding the paper, is that the authors felt the need to exclude businesses with multiple sites. The reason for this is that apparently if a multi-site business has locations inside and outside of Seattle, it is not possible to distinguish between workers in Seattle (who would be subject to the minimum wage laws) and those outside (who would not). This exclusion makes up 11% of firms in Washington state — but 38% of the workforce. Personally, I wonder if there isn’t more the authors could have done to reduce the size of this exclusion. Could they have identified multi-site businesses whose multiple locations were all inside, or all outside, of Seattle and included those? I haven’t seen the data, so I don’t know what kind of undertaking that would have been, but it might have permitted for a more robust study. I imagine the authors thought of it though, and discovered that it would be prohibitively difficult or impossible.

Does the exclusion of multi-site businesses have the potential to bias the results? Maybe. If multi-site businesses respond on average exactly the same way that single-site businesses do to changes in the minimum wage, then excluding the multi-site businesses shouldn’t impact the quality of the study very much at all. However, if the multi-site businesses respond differently on average then the results of the study could be biased, and the direction of this bias would be determined by how the response differs. Maybe multi-site businesses, being larger, are better equipped to absorb the added labor costs of a higher minimum wage. Then the disemployment effects of a minimum wage would be exaggerated by this study. On the other hand, maybe multi-site businesses would respond to a change in the minimum wage in Seattle by shifting their workforce outside of Seattle — indeed this seems plausible intuitively (to me). In that case, exclusion of the multi-site firms could actually understate the disemployment effects.

One decision that the authors need to make is to determine which group of people to study. A naive approach might be to study minimum wage earners, but this would ignore cascading effects of the minimum wage on slightly higher earners. If I am paying you $11/hr while the minimum wage is $9.87/hr, you’re earning a slight premium on the minimum wage. When the minimum wage goes up to $11, if I leave your wage at $11, you’re now earning minimum wage. If my intention was to pay a premium, I’d better give you a raise too. For this reason, the authors reason, the question shouldn’t just be about what happens to minimum wage earners as a result of a minimum wage increase, but what happens to low wage workers in general. Determining that low-wage threshold is an empirical matter, and the authors solve it by looking for a wage level which does not appear to be affected by the minimum wage level in the data. The cut-off they settle on is $19.

Results

Wage effects

Since the authors focus on people earning less than $19 an hour, a natural question is: what is the impact of a minimum wage increase on the wage of low-wage earners? It isn’t simply (size of increase)/(old minimum wage) because of the aforementioned cascade effects. When the minimum wage goes from $9.47 to $11, people who used to earn $9.47 get a 14% raise (or they get fired), people who used to earn $10 get a 10% raise (or they get fired), and so on. Maybe people who used to earn $11 or $15 or $17 get raises too to keep their pay in line proportionally to the minimum wage.

Restricting our view to people making $19 or less before the increases, the authors find that the first minimum wage change to $11 is responsible for about a 1.7% wage increase, and the second to $13 is responsible for about another 3.1% wage increase.

These effects are small — maybe disappointingly so. Increasing the minimum wage by (13–11)/11 = 18% increased the wage of the average low-earner in Seattle by only about 3%. Of course, the workers at the very bottom end of that scale fared the best (unless they lost their jobs), but I would have hoped for a larger cascade effect.

Employment effects

Now we turn to the meat. The real question is what the effect of this measure is on overall employment for low-skilled or otherwise low-earning workers. It doesn’t look good.

The authors report that hours worked are around 9% lower under a $13 minimum wage than they would have been, and in terms of pure headcount, there are around 6% fewer jobs than there otherwise would have been. The disparity between the hours number and the jobs number also seems to suggest that employers responded to the minimum wage change by scaling back on hiring and cutting hours for existing workers.

Both models — the SC model and the IFE model — provide roughly the same estimates, and they are highly statistically significant in each quarter following the increase to $13.

The increase to $11 did not have such stark consequences, and in fact for the most part the authors did not find statistically significant evidence of any change to jobs or hours resulting from the increase to $11, except in the case of the IFE model, which finds significant job losses of around 3.2% in each quarter following the $11 increase (curiously the authors don’t mention this in the body of the paper). The estimates of the jobs and hours effects following the increase to $11 are without exception not positive in each quarter, ranging from 0.0% to 4.8%, but again these are mostly not statistically significant.

Welfare Outcomes for Low Wage Earners

So raising the minimum wage had a positive effect on wages and a negative effect on hours. Which effect wins? What’s the overall effect of the policy? Are we better off or worse off than we were without it?

One way to answer comes from comparing the size of the wage effect to the size of the employment effect. Since the effect on hours and jobs was much larger than the effect on wages, the overall effect of the policy ends up not being good for low wage earners. For folks earning less than $19/hr, the number of hours worked fell by 9% while the average wage went up by only 3%. A nice way to summarize this change is to express it as an elasticity, which is simply the ratio of those percentages: the wage elasticity of demand for low-wage labor in Seattle is estimated at a whopping -3.

The implication here is that increasing the minimum wage hurts low-wage earners more than it helps them. While some low-wage earners do end up making more money, that is offset drastically by the large cuts in hours and jobs that result.

The results are significant — and I don’t mean in the sense of p-values. These are big meaningful numbers that the authors come up with. The job loss estimate implies that the minimum wage increase to $14 eliminated 6,317 jobs paying less than $19/hr among single-site businesses, and reduced the hours worked by those who kept their jobs by 9% on average. This adds up overall to a reduction in income paid to low-wage workers in Seattle of about $120 million per year.

Some criticisms that I think are misplaced

The Economic Policy Institute has published a blog post with some criticisms of this paper which I believe are mostly misplaced.

The measured effect is too big

Firstly, they argue that the effect size, expressed as an elasticity of -3, is considerably larger than the effect sizes measured elsewhere. Now, for me this criticism is prima facie silly — the authors are simply reporting the results, and so long as that’s being done in earnest, there is nothing inherently wrong with having found a large effect — but the authors at EPI also fail to note that the they aren’t comparing apples to apples. Previous work has estimated elasticities as the ratio of the change in employment to the change in the minimum wage. This is not what this paper does. Here, the authors have estimated the change in the wage as a result of the change in the minimum wage, and used that estimate in the calculation of elasticity. Hence it is not correct to compare this estimate to previous estimates as they are measuring qualitatively different things — one is the labor elasticity of demand with respect to the minimum wage, while here we are truly estimating the labor elasticity of demand with respect to the actual wages of low wage workers. Jardim et. al do provide elasticities computed the traditional way in Table 9, where they find point estimates ranging from -0.08 to -0.27 — high, but well within the ranges found in previous works.

40% of businesses are excluded

EPI and others have complained about the exclusion of multi-site businesses from the study population. It would have been really nice to keep them. However, I believe that the exclusion of multi-site businesses is not necessarily an indictment of the study. In the end, the study finds that employment for low wage earners decreased due to the change in minimum wage. The only way that this result would be invalidated by the inclusion of multi-site businesses is if the multi-site businesses would have increased hiring in response to the minimum wage hike so much that it offset the decrease in employment in single-site businesses. I think this seems unlikely. The exclusion of multi-site businesses affects the precision with which the authors can measure the employment effects of the minimum wage, but I don’t believe that it is necessarily a reason to question the basic results.

Another study found the opposite result

EPI and others have also complained that there was another study at Berkeley that found an opposite result. They can’t both be right so let’s go back to the drawing board. The other study focuses on the restaurant sector and, using a similar methodology (the synthetic control method), they find that there is no detectable effect on employment in the restaurant industry. They can’t both be right, so we’re back to the drawing board. What these critics miss is that the Jardim study actually did this too, and found the same result. In section 6.5 they restrict their sample to restaurant workers and find that the effect on employment in that industry is approximately zero. The conclusion for them is not that the minimum wage does not have an effect, but rather, that the traditional focus on the food services industry as representative of low-skilled or low-wage workers is misguided. Skilled restaurant workers make well above the minimum wage, and so they aren’t the correct group to study. Jardim et al. are able to focus their work directly on low-skilled workers rather than settling for a single industry, which actually makes this result stronger.