New Upjohn book on the minimum wage

I was wandering over to look at recent research published there by Morris Kleiner on occupational licensing (inspired by a new David Henderson post on the subject you should check out), and I noticed an announcement of a forthcoming meta-analysis on the minimum wage. It looks great. Here's the summary (it's just on the main page - doesn't even have an Upjohn Press page yet:

Institute to publish comprehensive study on the effects of the minimum wage

In his State of the Union address, President Obama called on Congress to act on a proposal to increase the minimum wage to $10.10 per hour. Raising wages, he said, is "Good for the economy; it's good for America."

To contribute to the discussion the Upjohn Institute is providing—prior to publication this spring—the findings of an exhaustive new study of the wage, employment, and poverty impacts of the minimum wage. Supported by the Upjohn Institute, Dale Belman and Paul Wolfson, authors of the forthcoming book titled What Does the Minimum Wage Do? (Upjohn Press), performed a meta-analysis on scores of published studies examining the effects of the minimum wage.  The studies were based on data mostly from the United States but also from other countries. The authors’ comprehensive analytical efforts allow them to conclude the following:

• Moderate increases in the minimum wage, characteristic of the United States over the last half of the twentieth century, have the effect that was intended by original supporters of the legislation; increasing the minimum wage substantially increases the earnings of those at the bottom of the income distribution and reduces wage inequality.
• Negative effects on employment resulting from increases in the minimum wage were too small to be statistically detectable in the meta-analsis. The authors conclude thatemployment effects are too modest to have meaningful consequences for public policy in the dynamically changing labor markets of the United States.
• Evidence of positive spillover effects on the wages of those earning slightly more than the new minimum wage is mixed, but generally supports their existence, particularly for women.
• The bottom line for Belman and Wolfson is that the minimum wage should be seen as one of a set of public policy tools aimed at improving the standard of living of the less well-off, and moderate increases in the minimum wage would likely aid low income individuals and families with acceptable costs to the nation.

What Does the Minimum Wage Do? is to be published in the spring of 2014. Click here to request an email letting you know as soon as the book is available, or pre-order your copy here.

Had a delicious McDonalds breakfast this morning...

No white kids behind the counter at all (and there were a surprising amount of people behind the counter... the minimum wage was definitely not driving this place to automation).

In fact there were no kids at all. No one under thirty except MAYBE the woman serving me right at the register, but she was certainly close if she was under thirty.

I know this varies by labor market and by shift and season, but just a datum I thought I'd share.

UPDATE: But Peter Schiff was absolutely right - none of them appeared to be starving either. And I sincerely agree with him that we can thank the market economy for that.

What is a "modest" increase in the minimum wage?

Bob Murphy asks me whether I think the proposed 39% nominal increase in the federal minimum wage counts as "modest". As readers know, I'm not a supporter of increases in the federal minimum wage. I don't think it spells disaster the way some people do, largely because of my read of the empirical literature. But I think it could hurt especially vulnerable labor markets and there are simply better policy options (and better ways of doing the minimum wage!) than raising the federal minimum wage.

Still, the question of what a "modest" minimum wage increase consists of is important.

We care about a couple things when answering this question, first and foremost being when the minimum wage is binding. If it's not binding it obviously doesn't matter.* The literature suggests that on average, past increases have not been large enough to be binding, at least in a disemployment sense (they are clearly binding on earnings, because we see increases in earnings as a result of the increases, again on average). There are at least two things to think about when it comes to whether the minimum wage is binding: erosion of the previous minimum wage level by inflation and productivity growth. Here's a very crude extension of an EPI chart to try to capture these things for the proposed increase:

I've done two things here. First I've crudely extended the erosion of the real value of the current minimum wage out to approximately 2016, which is when the $10.10 minimum wage is supposed to be set. Then I've added a horizontal red line indicating a crude estimate of the value of $10.10 in 2016, measured in 2011 dollars. We don't know what inflation will be going forward. I could be really fancy and use inflation expectations or TIPS spreads. Instead I just used an inflation calculator to see the 2008 dollar value of $10.10 in 2013 and I'm calling that the 2011 dollar value of $10.10 in 2016. So it's NOT perfect (2009 was a rough year), but it's ballpark. If you want to figure out something sturdier, please be my guest.

As it stands, without thinking about what is binding, this is certainly a huge jump relative to past increases.

I don't think that's the end of the story, though, because if you want to know whether the minimum wage is binding you really do have to think about trends in productivity, because that's what ought to determine labor demand. EPI has also done excellent work tracking what the minimum wage would look like if it had grown since the late sixties at the rate of productivity growth. Now productivity growth as it is measured is NOT the same thing as marginal productivity that we use in theory, but I think it's a fair proxy to consider when we're ballparking this sort of thing. And of course we don't have productivity information for minimum wage workers (although BLS now breaks it out by industry - perhaps someone should take a look at productivity growth in typical minimum wage industries). This is what EPI has on that:

Now we might not want to index the minimum wage today to the 1968 minimum wage. But even if you want to take the mid-nineties as your starting point - a period that a lot of research has covered and where the real value of the minimum wage was lower - productivity is outpacing real minimum wage growth by a substantial margin. Even if we halve the gap between the productivity line and the real minimum wage line, because we think that a 1968 baseline is too unrealistic a goal and minimum wage workers might not have as fast growing productivity anyway, and it still seems like the productivity-growth-consistent binding wage level is above $10.00 in 2011 dollars.

So Bob might not be satisfied because this is not a single clean answer, but I think I can narrow it down to four points!:

1. Yes, the jump in the real wage seems to be very big and in that sense is out-of-sample relative to the empirical tests we've been tossing around, but
2. The empirical tests don't tell us where the binding minimum wage is, and
3. When we look at productivity data - which should indicate something about where the binding point is, it seems like we still have a fair amount of running room before we hit this point, nevertheless,
4. Every labor market is different. DLR's average null effects have a distribution associated with them, so we can expect that many low wage labor markets (for example, in the South) would experience a negative effect from the minimum wage - even more so from an increase to $10.10.

So what is to be done? Well I think Bob Lerman (American University and the Urban Institute) has some good points to make in this interview:

"Lerman believes that wages will increase for low-income workers if you make them more skilled and valuable. “You can try to increase wages by mandate, but if you do that without doing anything on the productivity side, there will be fewer workers,” he says. To build a stronger labor force, Lerman has promoted apprenticeships and founded the American Institute for Innovative Apprenticeship. 

“You can get maybe six weeks of training to become a simple welder. Or you can have a serious apprenticeship program that gradually moves you into robotic welding and programmable stuff that makes people much more valuable,” he explains. “Just as you can be a cook at McDonald’s or move into a higher value-added culinary activity.”"

Acting on worker productivity, as Lerman suggests, will increase labor demand. Of course we can work on labor demand directly as well, through fiscal policy and direct employment measures (Jon Wisman, also of American Unviersity, talks about this later in the article). As this post suggests I don't know what to say about whether the minimum wage increase will be "modest" or not. But I really think that's the wrong question - at least it's the wrong policy question. If we have to ask that question maybe there are better ways to help low income workers than raising the minimum wage.

Point #4 about differences between local labor markets has bothered me a lot over the last year. I'd love to work more with this question, although I don't have the time now. State legislatures and local governments are in a much better position to assess what a modest minimum wage increase would be for their labor market, and if they make a mistake, the costs of the mistake will be less broadly distributed. So to the extent that there is action on the minimum wage I think it should happen at the state and local level. It just seems wiser than federal minimum wage increases.

* - You might still think there is an acceptable trade-off between wage increases and disemployment effects. This will be determined by your own policy preferences, labor demand elasticity, and what other policies you want to see acting in concert with the minimum wage. Let's put this prospect aside for the moment, and just say that when the minimum wage is binding in a disemployment sense we can legitimately start to worry about the immodesty of the increase.

Peter Schiff, The Daily Show, and the disemployment effects of the minimum wage

A lot of people are rightly chuckling at Peter Schiff after his performance on the Daily Show:

The Daily Show
Get More: Daily Show Full Episodes,The Daily Show on Facebook

Most of it is boilerplate arguments against the minimum wage. The worst thing with Schiff is how disconnected and unsympathetic he is.

Minimum wage workers aren't starving, after all!

They're just goofy rich teenagers, after all!

Socialism is bad, after all! (how the conversation went from the minimum wage to public ownership of the means of production is a complete mystery to me)

We're not all created equal, after all!

It was that last one that I think hit people the hardest, particularly because it was with reference to people with mental disabilities (he said maybe they should only get paid $2 and hour). But the funny thing is people with disabilities already can qualify for "special minimum wages".

This seems relevant to stronger claims about the disemployment effects of the minimum wage. If the minimum wage has no disemployment effects at all, what is the point of special minimum wages for disabled workers? Aren't you just denying those workers money? The reason we have special minimum wages (and why we don't have minimum wages of $20 an hour) is that everyone believes that at some point disemployment effects kick in.

I don't think this is a surprise to anyone. This is precisely why economists talk about "modest" minimum wage increases. But it is an interesting wrinkle to the law that is relevant to Schiff's interview.

Pete Seeger on gender economics and the engineering labor market

My daughter is a hummingbird

Paul Krugman on Mises and the Depression

Here. A very interesting post that links to another great post by LK on the subject. They tie Mises to the "soup kitchens caused the Depression" view, or more formally - that a variety of policy changes had major negative supply impacts.

While I'm on the subject of the longevity of Austrian Business Cycle Theory, I did not link to this post by Jonathan criticizing my claim in my recent Critical Review article that Hayek's BCT (although I'd throw in ABCT generally) was inconsequential for macro (after the 30s of course). Jonathan's argument doesn't really move me at all (in fact I cited some of the things that he mentions in the article), but it's worth looking at. I think he changes the question to "has any important macroeconomist ever cited Hayek or liked to read him", the answer to which is of course "yes", but not the question I'm interested in. The case that Hayek was essential to RBC is very weak. The connections are vague in the first place, they have nothing to do with the central features of Hayek's BCT, and none of the handful of what we consider foundational papers in that literature cite him or anyone having anything to do with his business cycle theory. It's true that Lucas cites him in another paper - not for his business cycle theory but for saying that a Walrasian general equilibrium view is important. Anyway, I could go on but there is really no case for this at all. But read Jonathan and see what you think.

Actually the best case for Hayek's influence on macro is that he helped move Keynes from the Treatise to the General Theory, but of course that has nothing to do with Hayek's own BCT.

Two quick observations on Don Boudreaux on the Super-rich

Here.

Well, three observations I guess because I want to preface this by saying that unlike many of Don's posts I think the vast majority of this is just fine, and it's really just Econ 101 - there's nothing especially libertarian or otherwise unsavory about it.

But there are two other points I'd like to make.

First, when Don says that Bill Gates got his wealth by being creative and giving people what they want and not by making people poorer, I think he is giving too short shrift to issues of bargaining over surplus. In undifferentiated markets perhaps that's OK. When you're dealing with people of Gates's caliber I think that's less appropriate. We as economists talk about distribution in a lot of ways. A popular way of explaining distribution is marginalism, which is appealing because marginalism is what two rational people would do if they had reasonable objectives they were pursuing. That's fine and dandy for a whole lot of things. But even without getting into any Marxian stuff at all, we also talk in terms of bargaining over surpluses. This is the framework that a lot of labor market and household models use, and I assume elsewhere in economics. If agents bargain over the surplus they create together some agent could have more bargaining power than another, and you can very reasonably think in terms of taking surplus from someone - making them poorer by virtue of the fact that you are capturing surplus that they had claim to as well but did not have the bargaining power to obtain.

We shouldn't be afraid to admit this may happen, and we shouldn't be afraid to put away silly phrases like "well nobody put a gun to his head so..." etc. You don't become some anti-market leftist if you admit that bargaining over surplus happens.

Second, towards the end of his post he makes a lot of assumptions about the relationship between distribution and growth. His claims are very dicey. There is obviously a lot of interest in questions of distribution, but most of this work as it relates to growth in mainstream economics comes on the supply side, typically as it relates to human capital. I understand there's an institutional literature too. But Don is thinking on the demand side and as far as I'm aware the only people to treat distribution and the demand-side of growth really seriously are Post Keynesian economists. And in Post Keynesian models and empirics, this relationship is a lot more ambiguous than Don imagines it to be. It all depends on the behavior of the investment function, its responsiveness to profits, expectations, leverage, and whether the super-rich are really entrepreneurial or serving in more of a rentier capacity. The consumption function is usually in the background in these models, which shouldn't be especially surprising. 

I would frame these points of departure from Don's main thrust as being a case of where he takes an Econ 101 sounding platitude and runs with it, but it doesn't quite work.

Douglass, Smith (and Malthus and Jefferson)

David Henderson has an interesting passage from Frederick Douglass on Adam Smith, generally zero-sum thinking. I find the bolded part (I've added it) especially interesting, though:

"The old doctrine that the slavery of the black, is essential to the freedom of the white race, can maintain itself only in the presence of slavery, where interest and prejudice are the controlling powers, but it stands condemned equally by reason and experience. The statesmanship of to-day condemns and repudiates it as a shallow pretext for oppression. It belongs with the commercial fallacies long ago exposed by Adam Smith. It stands on a level with the contemptible notion, that every crumb of bread that goes into another man's mouth, is just so much bread taken from mine. Whereas, the rule is in this country of abundant land, the more mouths you have, the more money you can put into your pocket, the more I can put into mine. As with political economy, so with civil and political rights."

This also echoes the views of both Thomas Malthus and Thomas Jefferson on population in the United States (notice the phrase "the more mouths you have"). Both (Malthus in later editions of his Essay on Population, and Jefferson in a letter to Jean Baptiste Say) were of the view that limitations on population in the form of subsistence wages were not in play in the United States in the same way that they were in Europe, and that this allowed for general opulence and growth. The key, of course, is abundant land. Data from the United States played an important role in proving Malthus's theory, demonstrating that the controlling factor in population was the capacity of a society to produce food.

I find the last sentence interesting from a rights theory perspective too.

Brad DeLong on the ACA and Massive Resistance

Brad DeLong makes an interesting analogy between state level resistance to the ACA and Massive Resistance here. It's interesting to see this (a couple days old, but I've got a backlog), considering I just started reading Harry Byrd and the Changing Face of Virginia Politics: 1945-1966 today. Of course the same issues of nullification or its equivalent are in play. Nullification is a funny thing. It's an extra-constitutional attempt to arbitrate constitutional questions that is usually invoked against another extra-constitutional attempt to arbitrate constitutional questions (i.e., judicial review). The only difference (and it's the critical difference), of course being that the people consider the latter entirely legitimate and the former illegitimate.

And the people here are quite relevant to how these things often play out.

Why did Massive Resistance end? What was it that kicked gravel in the gears of the Byrd machine?

The people, of course. Thousands of Virginians did not like having their schools held hostage to the ideology of these oligarchs (and perhaps "oligarchs" is not always appropriate today, but it certainly was in the 50s). People - regular Virginians - lost authority over their government when the General Assembly revoked the Arlington County School Board's status as a body of elected officials when it tried to integrate. in accordance with the Court's ruling.

Pretty soon people realized that their leaders were fighting for their own ideology and the people were losing their education and their votes in the process.

And I think it's likely that that is how this will end.

Federalism allows a diversity in how big a role government plays in our lives, and that's fine. People genuinely disagree on that and they try out different things. But what the people usually don't like is being held hostage so that politicians can have a talking point, particularly after multiple branches of government have spoken on the issue.

I could be wrong. Perhaps that's not how the people will view it in this case. But nullification is often an ideological last-ditch effort, and people generally don't like to get a raw deal for the sake of a last-ditch ideological effort.

Comment from Arin Dube on my Meer and West post

This one was worth pulling up to the main page. One of my big concerns with the state trends after reading Meer and West was whether it was genuinely a pre-period trend or whether it mixed in the post period. The bolded section below seems to deal with that nicely, which I find reassuring. I think Meer and West make a good point to keep in mind with these DID studies, but to reiterate what I said the last time (1.) even though it's a good point to keep in mind it does not seem to overthrow Dube's set of findings, and (2.) the really, really big difference is still in the county matching - what Meer and West call DID is really just a fixed effects model until you do the matching.

Here's Dube:

"Thanks for delving into this. Wanted to note a few things. Meer and West do not really offer a critique of the methodology of Dube Lester Reich (2010, 2012/3). That is because DLR's main specification does NOT rely on a county or state specific trends - the main methodology is to use compare only across counties within a pair (operationalized by using county-pair-specific time-period dummies that wash out variation between pairs.) So the primary border-discontinuity specification is not subject to any criticism from Meer and West. Indeed, Meer and West merely cite the Neumark Salas and Wascher study (I'd say more for support rather than illumination) as a critique of the border discontinuity methodology.  

Now, it is true that besides our preferred discontinuity specification, we *also* show results using "intermediate" specifications with state linear trends - as a way of showing that even less granular types of controls for spatial heterogeneity kills the disemployment estimate in the "canonical" place and time fixed effects. (And in Appendix Table A1 we additionally subject our discontinuity specification to state linear trends as a robustness check and show results are the same.) So in principle these specifications (but NOT our primary discontinuity specification) are subject to the issues with linear trends that Meer and West raise.

Even there, however, there are two important pieces of evidence that suggest Meer and West's critique is off base. First, we show dynamic specifications with 16 quarters of lags. This means that in models with state trends, those state trends are estimated WITHOUT using the first 16 quarters of post-intervention data - so they are largely PRE-existing trends; see the original Wolfers 2006 paper on this. (As Meer and West point out, most minimum wage differences last around 4 years).

Yet there is not an indication that the "long run elasticity" [associated with the t+16 value in Figure 4] in linear trend specification, that is largely estimated using PRE-existing state trends, is any more negative - as would be the case if Meer and West's explanation were correct. Moreover, during these 16 quarters, there is no indication of falling employment as suggested by Meer and West's simulation.

In general, if you estimate a set of flexible distributed lags (as we always do in DLR as well as Allegretto Dube and Reich), you should catch falling employment levels if there is a growth reduction. But we don't see that anywhere. Which raises serious doubts about the explanation Meer and West offer for the discrepancy between levels and growth as outcomes.

Finally, see this post by John Schmitt about the Meer and West paper's own findings regarding industries: http://www.cepr.net/index.php/blogs/cepr-blog/more-on-meer-and-wests-minimum-wage-study"

Interesting, but too cynical

Here.

My experience is that empirical economists care a whole lot about methods. They care about methods because they help us to understand problems we care about, of course. But what fires them up is neat modeling tricks that address tricky problems.

I can only speak from experience, but getting to know professionals in three different economics departments, a policy department, and professionally at the Urban Institute (both Urban economists and those I interacted with from elsewhere), they would get a lot more excited about their argument than about their answer.

This is not the case for, say, an advocacy organization in D.C., or activisty types I've come across at school and professionally. They care a lot more about the answer. And they'll cling onto the literature that gives them the answer that they want. But then again these guys don't write up analyses.

The minimum wage stuff is actually a good example of this. I don't really support the minimum wage as policy (although evidence for zero effects makes me OK with states trying things out - they have a better sense of appropriate levels - so I'm not a purist in that regard). Even at the state level I think it's an unnecessarily blunt instrument. And before I read the literature several years ago I personally thought that the minimum wage must have disemployment effects. At the time it fit my libertarianish ideological requirements, it fit what I thought I knew about economics, etc. I've really come around to the alternative view on the disemployment effects not because I was some huge energetic supporter of the minimum wage, and not because it was consistent with my ideology at the time, but despite those things - because the evidence was good. If there were disemployment effects in some cases (which I still expect there are), certainly there were enough positive employment effects elsewhere to get an averaged effect of zero.

Neumark, Salas, and Wascher Request

If anyone knows the Neumark, Salas, and Wascher critique of the contiguous counties approach as well as the Dube et al. response well and wants to write up a guest post, I'd be interested in hearing from you. I haven't gotten to these papers in my recent push to familiarize myself with the literature and am afraid I might not. But it's clearly important. As my last post suggests, I think the spatial heterogeneity point looms over all the other issues in this debate, so if it's poorly dealt with that matters.

I suspect it's not - I kind of got a sense of Dube et al.'s response to Neumark, Salas, and Wascher in one of their responses to Meer and West. But I'd be interested in hearing from someone that's done a closer reading.

Without dealing with that I really don't see where the model identification is. Without the county match you've really just got a fixed effects model that you're trying to pretend has the identification properties of a DID. Right?

Two different critiques of Dube, Lester, and Reich: Part 1 - Meer and West

Note: This post has changed a bit since I started it and I still feel like it's provisional (I'm maybe 76% sure of it now) in the sense that I'm still trying to get a grasp of how state-specific time trends have actually been operationalized across these studies. So, just a word of warning (and if you can clarify anything for me please do!).

*****

The other day I was writing about Bob Murphy's concern about including county specific time trends in DID estimate of the minimum wage (this post will assume your familiarity with that older post). I hope I made a persuasive case that generally speaking it makes good sense to include time trends in DIDs. County pair matches are great, but they aren't perfect and what they don't handle is county-specific time variant heterogeneity. And how do we deal with that?: County specific time trends.

However, at the time (as you'll see if you review my post linked above) I was thinking in terms of time-trends projected from the pre-treatment period. This is only sensible so I figured that's what was being done. If you include information from the post-period on universal time trends (or time fixed effects) that's fine of course because the variation explained by those sorts of time trends would have to be common to treatment and comparison cases alike. Not so for county-specific (or for the purposes of the Meer and West paper I'll be discussing here, state-specific) time trends. Now, maybe DLR did do time trends the way I assumed they would do them, in which case a lot of the Meer and West critiques are not substantial. But at this point I think Meer and West are right on this econometric point (whether it matters in the data is a different question, and a question for another post [or for your own googling... lots of people have talked about the results]).

OK, let's back up a little.

There are two potential critiques of including state or county-specific time trends, which I'll call the Meer and West Critique and the Murphy Critique (although clearly I'm putting them each in my own words). The Meer and West Critique comes from a working paper (Meer and West 2013, specifically Appendix A and B) that looks at the impact of minimum wages on employment growth. The Murphy Critique comes from Bob's post from about a year ago, with my own modification from the other day about the cases where his concerns will matter if county-specific time trends based on pre-period trends (it's only under specific conditions that it matters - see my old post). Both are important, but they are fundamentally different and pose fundamentally different burdens on the DLR specifications and results. The Murphy Critique poses many more problems econometrically and practically than the Meer and West Critique in the sense that it still has to be dealt with even if you use pre-period time trends. In my own words:

The Meer and West Critique: If the impact of the treatment is on growth rates rather than levels, then a DID with time trend controls and levels as the outcome "could lead to dramatically incorrect inference about the treatment effect" (Meer and West, 2013, pg. 38).

The Murphy Critique: If county specific time varying heterogeneity is correlated with treatment, then county-time trends will not identify the treatment effect, and the estimates of the treatment effect will be biased.

*****

To think about the Meer and West Critique, let's revisit those DID diagrams that I had before. Meer and West consider a case of "staggered treatment", where all cases ultimately get a treatment, but it occurs at different times. This is very common in actual empirical studies because policy changes don't all happen at once and usually many of the cases that are comparison cases at one point in time eventually get some form of the treatment. Consider the case of three periods, where group A is treated at the end of period 1 and group B is treated at the end of period 2. This would look something like this:

This makes the distinction between Treatment and Comparison "groups" a little more complicated because in one period group A will be the treatment group and in another period it will be the comparison group. But notice that this actually allows you to do two classic DIDs. You can do:

[(Period 2, A) - (Period 1, A)] - [(Period 2, B) - (Period 1, B)]

and you can do:

[(Period 3, B) - (Period 2, B)] - [(Period 3, A) - (Period 2, A)]

If you have thousands of counties all changing their minimum wage status multiple times, the number of DIDs you can do increases as well. This is the fixed effects model operating as a DID model that I referred to in my earlier post (you just need to be able to match treatment and comparison groups, like DLR do with contiguous county pairs, and the minimum wage variable and the county and time fixed effects do the rest).

This is the basic framework that Meer and West (2013) use, and which they illustrate using diagrams very similar to mine from the other day in their Appendix A. In their scenario (a), below, there is no treatment effect (no effect of the minimum wage) on either employment growth or levels. There is a time trend for each state, but you can see that it's common between the states so the time fixed effects should account for it. A DID estimator like the one I outlined above would find no effect of the minimum wage, regardless of whether the dependent variable was employment levels or growth in employment. (All three of the following figures come from Meer and West's paper.)

In scenario (b.), Meer and West assume a negative treatment effect on the employment levels, but not employment growth. Again, this is no problem in a standard DID. If the dependent variable is employment levels, the standard DID will find it because the time trends are common and controlled for. If the dependent variable is employment growth the standard DID will find the (correct) zero employment growth effect because the rate of change of employment doesn't change. Again, all is well with the standard DID.

Meer and West worry more about their scenario (c.), where the minimum wage reduces employment growth but has no effect on levels. In this case, a standard DID will identify a zero levels effect if employment levels are the dependent variable and a negative growth effect if growth rates are the dependent variable:

They call the zero levels effect result "counter-intuitive" - and it is at first. If you look at the first and second period (so the DID for state A), you clearly have employment levels getting closer in the post period (albeit as a function of the decline in the growth rate). So that should give you a negative levels effect in the DID. Same goes for the second period if you control for state specific trends, right? State B would have been closer than it is if the trend had continued, so if those state specific trends were controlled for you'd think the DID would pick up on a negative levels effect. But it doesn't.

This was what was difficult for me to grasp at first, because my assumption was that state-specific time trends were based only on the pre-period. At this point I don't think they are in DLR, because they specify the state specific time trend as:

 With Is being an indicator variable for a state. This makes no distinction between pre- and post-, so it seems to be the full study period state specific time trend. What seems to be going on here (although I find their explanation in Appendix A to be cryptic) is that using a time trend that covers the entire period makes the post-period employment performance look better than it should, because the contributions of the post-period to the time trend are absorbing the effect of the minimum wage.

This explanation of what's going on is confirmed in Appendix B, where Meer and West run simulations to demonstrate their point. They also present a figure where they draw the state specific time trends:

The state specific time trend for the treated state (the dashed line) is an under-estimate of the pre-period time trend, so when you adjust for time-invariant factors by including a state fixed effect (i.e. - when you shift the dashed line to have the same intercept or starting point as the solid line), then it doesn't look like the post period has decline from the trend the state was on! This is a problem because we know (from the way the data was constructed) that it declined from trend a lot in the post period. This is illustrated by plotting the results of the DID with and without this dotted line trend. The results on the right are near zero because the state specific trend absorbed much of the decline in the post period so that it was not attributed to the minimum wage:

Note that this should not be a problem if the time trend (the dotted line) was based only off of the pre-period time trend, as I had originally assumed was the case. Clearly the coding to get pre-period time trends when minimum wages are being implemented in many places at many different times would be difficult, but that's really the specification you want, IMO.

Meer and West have a different view. They think you're better off just omitting the state-specific trends, which they demonstrate bias the results if all the action is in growth rates rather than levels. This is a little dangerous, I think. It's all well and good for Meer and West to show us a simulation where there's not big spatial heterogeneity in time trends so that the only thing including time trends does is bias the results. But there is no particularly good reason to think this is true in practice. If spatial heterogeneity is substantial then you need those time trends (although it would be preferable to use pre-period time trends).

And actually Meer and West themselves give us a good reason NOT to drop time trends. They show that they do not bias estimates when the growth rate itself is the dependent variable. So it seems to me the ultimate moral of the story is more to look at a number of outcome variables than pulling the time trends out.

One last point I want to make here is that time trends aren't actually the huge difference between Meer and West on the one hand and DLR on the other. The big difference is that Meer and West do not use the contiguous county matches that DLR do. That means that all this talk of DIDs by Meer and West is a little bit of a stretch in the first place. What they have is a fixed effects model with no real matching of treatment and comparison counties at all (except, of course, in their simulation exercise).

It would be nice, then, to have a paper that does what Meer and West want (look at both employment growth and employment levels), and do it in the context of contiguous counties. There's a short Dube paper that does just that. He picks up the negative growth effects in the state level model that Meer and West prefer, but they go away when spatial heterogeneity is accounted for by the contiguous pairs.

So the bias that Meer and West seems to be more interesting in theory (and in simulation) than in practice. In practice, spatial heterogeneity seems to be the much, much bigger bias, and DLR still rule the roost on that count. And really, this makes sense I think. Why would the minimum wage have a greater impact on growth than on levels in the first place? The textbook theory everyone loves to allude to implies an impact on levels. If you think in terms of a search and matching model, you'd expect a minimum wage to introduce greater scrutiny of worker productivity on the front end and as a result lower separation rates on the back end, so that there are lower turnover rates overall (this is what Dube, Lester, and Reich find in another paper on the subject), but it's not immediately obvious why employment growth rates have changed after the level of employment has been reduced. I suppose if adjustments are made through attrition you might have some immediate declines in growth rates, but you'd think that would be temporary. I don't want to suggest it can't have an effect on growth rates - I'm just saying that it's very hard to imagine the situation that Meer and West are coming up with here in their simulation - where there is no effect on levels  but an effect on the growth rate.

So I chalk up the Meer and West Critique as an important reminder about time trends and maybe a reason in the future to think about grounding time trends in the pre-period only. But practically speaking it doesn't seem like it matters because when Dube does what Meer and West suggests (look at growth rates), there's no action.

The Murphy Critique is somewhat different. Hopefully I'll get to that in the next few days, but if not I think he should have something coming out on it at some point.

I'm very interested in your thoughts on this - let me know if I've missed something.

If you prefer analysis of the minimum wage that doesn't try to address identification problems to analysis that does, this is the post for you...

Here (HT - Tyler Cowen).

Here's the featured graphic:



So my title is admittedly snarkier than a lot of the other minimum wage posts, but it's because I'm truly dumbfounded as to how this has taken off. I gather the author is a finance guy and that may explain some things. Not that I'm an expert on that, but it seems to me if you're in finance, identifying trends in data and forecasting from them can serve you well as long as nothing major changes structurally. That's the sort of situation where Friedman's brand of positivism that is so embattled actually makes sense.

But you just can't do that to understand the underlying causal mechanisms.

I've got a more detailed comment in Cowen's post to this effect, but if you eyeball his red lines (and as far as I know eyeballing is our only option at this point - I don't see the data anywhere), five of the seven red lines coincide with a recession. Teen employment goes down during a recession?!? Incredible! The two that don't occur in a recession both have increasing red lines, and the one red line that's increasing and during a recession is during a relatively mild recession in the otherwise high-growth 1960s.

So even looking casually at this we have a big, big problem.

Why is this so popular???

Arin Dube on poverty and the minimum wage

This is related to the Sabia and Burkhauser post I had up yesterday. Dube has a new post up summarizing his contributions, which Tyler Cowen did not seem to be as impressed with as Sabia and Burkhauser (well... he thought the econometrics were fine but the results didn't conform to what Cowen considered common sense [if you found that odd you're not alone]).

A lot of the post is summarizing the differences between the two papers, including two big ones: Sabia and Burkhauser assume that workers under the old minimum wage will not get a raise, and they assume that those earning above the new minimum wage will not see a raise.

Obviously both are problematic and they make a big difference. When you deal with that, some measurement error issues in survey data (always be careful about survey data at the tails of the distribution especially - very high or very low income), and the quasi-experimental approach of Dube (rather than the simulation approach of Sabia and Burkhauser), their estimates for the impact on poverty are higher (18.9 percent of beneficiaries are poor rather than 11.3). Obviously this doesn't change the underlying conclusion that this is not a policy just targeted at the poor. As I tried to summarize in the last post, it's not clear why anyone would think it was in the first place. Just do a few calculations with a hypothetical wage earner and you'll see that most (just over 80% in Dube's case and just under 90% in Sabia and Burkhauser's case) shouldn't be living in poor families. This was the key insight of the post, in my opinion (bolding is mine):

"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 wage 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."  

The minimum wage is not well-targeted on poor families but it does seem to be targeted on low-income families

...which isn't to say it only affects low-income families of course. Lots of teenagers not from low-income families get their first work experience in a minimum wage job too.

But back to the question of poverty - this is somewhat of a cheat post because I am just reproducing a comment on David Henderson's recent post on the subject (see links to his NCPA paper for more details and his post for more links).

*****

I have been writing a lot about the state time trends that Bob Murphy has been musing on lately, but I feel like I need to get to Meer and West and the flows, as well as Sabia-Burkhauser.

As a general reaction to the poverty reduction question, it sounds reasonable to me but I'm not sure poverty is the right lens to look through. I think a few basic calculations show in the first place that it's going to be more relevant for a broader category of low income families than poor families per se.

$7.25 x 35 hours x 50 weeks for someone that actually takes some time off but maybe doesn't have paid vacation and has a generous amount of hours on the cusp of full and part time (OR two part time jobs) gives you $12,687. That already exceeds the poverty line for a single person, and is just a few thousand short of a family of two. If you add minimum wage workers to the family, family income grows faster than the poverty line.

So this is not a poor person's policy from the beginning and certainly not if we're talking about the people making as high as $9.50. You don't even need to go to the data you just need to do a few thought experiments.

Whether it's well-targeted or not is a different question. A lot of these families are still low-income. We seriously consider expanding SCHIP to them, for example, even if not all benefits. I'm not sure how marginal these households are but as we've seen, one minimum wage earner in a household can account for a difference of up to 100% of the FPL, so losing that second or third person could make the family at 300% suddenly at 200%, or the family that's at 200% suddenly 100%. So it's not like these families are in a position where they're marginal workers - their income really matters even if they're not below the poverty line.

So all the commentary so far - from you [David Henderson], Cowen, etc - seems fine as far as it goes but I think it's still clearly a policy targeted at lower income families.

I promise the next post is going to be about the minimum wage (in all likelihood) or something else substantive about economics

Fool me once...

So I got fooled once by David Henderson's post where I thought he was going to say that everybody agrees that the question is about the role of labor supply incentives in the ultimate impact of UI on unemployment.

Shame on him, so the saying goes... but I'm not sure that's entirely fair - so let's say maybe shame on me for expecting that.

Now I see a post from Russ Roberts titled simply "Paul Krugman is not a hypocrite".

FANTASTIC!, I honestly thought.

We are making progress!

We are not making outrageous personal attacks and we're going to talk about economics, even if we disagree very strongly about the scientific reasonableness of a claim!

Well this is fool me twice, so it's definitely "shame on me" at this point.

If we are going to make personal commentaries rather than talk about economics in the economic blogosphere, you should tell me how ridiculously cute my almost-four-month-old daughter is.

Krugman on UI... and another great big sigh of disappointment for the economics blogosphere

Krugman derangement system can be pretty impressive sometimes, but the recent spat has to win some sort of prize. I've commented in a few places on it, but I thought this blog might need a little break from the more serious minimum wage wage posting I've been doing.

Russ Roberts recently accused Krugman of lacking intellectual credibility because he mentions a micro labor supply effect of unemployment insurance in his textbook but in a recent blog post he criticizes Robert Barro for inferring that because of these micro incentives, the idea that UI can reduce unemployment is (to quote Krugman's paraphrase) "self-evidently absurd".

Of course it's not "self-evidently absurd" at all. You can have negative incentive effects and a reduction in unemployment quite plausibly if the unemployment rate is high because of demand problems. There is no contradiction whatsoever. And Russ Roberts, with a PhD from the University of Chicago, should be able to understand this point.

Then David Henderson jumped in and I thought things would get a little more sane when I read: "The issue--and everyone on both sides agrees that this is the issue--"... and I was SURE the next line would say "is whether or not you can acknowledge negative incentive effects and still argue that UI reduces unemployment".

Because THAT is what the issue is, and David is usually mild-mannered and to the point and I honestly expected that's what I would read next. But no, it continues: "is whether Krugman is being hypocritical in his discussion of unemployment insurance."

A good alternative to this is Chris Dillow's post. He starts by referencing Bob and Russ, but he doesn't say anything like "The issue--and everyone on both sides agrees that this is the issue--is whether Bob and Russ are being jackasses to Krugman"

Because there's a point where the Krugman derangement syndrome gets old and we need to focus on the economics if we really want to be an economics blogosphere.

For what it's worth Barro clearly understands there's nothing even passingly hypocritical in Krugman's case. Barro writes:

"Yet Keynesian economics argues that incentives and other forces in regular economics are overwhelmed, at least in recessions, by effects involving "aggregate demand." Recipients of food stamps use their transfers to consume more. Compared to this urge, the negative effects on consumption and investment by taxpayers are viewed as weaker in magnitude, particularly when the transfers are deficit-financed. Thus, the aggregate demand for goods rises, and businesses respond by selling more goods and then by raising production and employment. The additional wage and profit income leads to further expansions of demand and, hence, to more production and employment. As per Mr. Vilsack, the administration believes that the cumulative effect is a multiplier around two."

Of course, he goes on to dispute the argument, and that's fine. As I said above - THAT should be the real question here: who is right about the effect of UI. But despite disagreeing, Barro knows full well that nobody says that the incentive effects aren't there, they say that they are overwhelmed by other effects when the economy is demand-constrained.

Krugman is obviously not a hypocrite. That is NOT the question at hand. Krugman does not lack intellectual credibility. Krugman is not the embodiment of Orwellianism (a comment on Russ's blog). Let's get back to economics, people.

Brief, and entirely unsatisfying post on Ozimek and the minimum wage

Commenters "Lord" and Bob Murphy both suggest I look at Ozimek's post on DLR here. It's very good, although I don't know how much it resolves. It goes over a lot of the time-trend issues we've been over here. Wolfer's identification of bias, for example, is similar to what identified as the case that Bob was talking about, which could be a possibility (although one I doubt).

The flows may help to solve these sorts of questions - there are papers on that from Dube and from Meer and West. I'd have to read them. But I can't see how that definitively resolves anything. There can be no rate-of-change change without a change in the flows so the same ambiguities in the changes or lack of changes in the levels is going to be there in the flows too. The difficult task isn't identifying a trend change (which requires a flow change and results in a level change), the difficulty is identifying the right counterfactual trend.

It ultimately boils down to whether we think the time-trends are appropriate or not and if there's an obvious econometric test for it I'm not sure what it is. Time-tends may be wrong, but Occam's razor seems to suggest we should include them (as in DLR). Spatially heterogeneous time trends seem more reasonable than just the right circumstances that would actually introduce bias by including time trends.

Neumark and Wascher suggest we might want non-linear time trends instead of linear ones. One reasonable way to test this is to do an out of sample specification test using the comparison cases. So use a couple specifications of the time trend for periods -12, -11, -10,..., -2, -1, 0, and then figure out which specification best predicts the trend in 1, 2, 3, 4,...,10, 11, 12. Since these cases don't have any dynamic effects of the minimum wage, it should give you a better sense of the non-linearity of time trends. Now, you have to argue that that specification of the time-trend (linear, non-linear, etc.) is also true in the treatment case. But since we're not using the same slopes or parameters itself that seems defensible.

Really I'd need to read Meer and West and the responses but I feel like many of the same points are made here that I made the other day, namely: (1.) time trends should help to reduce bias in most cases, but (2.) you can imagine specific scenarios where the opposite would be the case.

Entirely unsatisfying, eh?

I still think DLR offers the most sensible default - just at first appearances. That doesn't mean there isn't something else going on, but I think it needs to be demonstrated.

Ryan Long on the econometrics of the minimum wage: a big picture explanation

I've been a little concerned that my last couple posts have been confusing for some people based on some comments from Ryan Long about all the variables DLR are putting in, so I want to zoom out to the big picture a little. First Ryan expressed concern that we're adding too many variables in a fixed effects model and that that is losing us significance*. Recently he expressed concern that we were just adding variables to reduce bias on the idea that adding more variables reduces bias.

This one concerns me a lot more and now I'm worried more people have missed the whole point of these posts. We are not just chucking things in the model and waiting to lose the significance. We have a treatment effect we're trying to estimate but we have non-experimental data so we need to figure out a way to mimic an experiment and get at least a good sense of what the treatment effect is. DLR have chosen to do that with what is at its core a DID set-up.

But once you do that, the comparison group you have can still run into certain problems that can bias the result. We've worked a lot with these models, though, so we know ways around those problems and usually that involves adding other variables. We're not just adding them for the hell of it - we're adding them because when you add a variable it changes which bit of variance in the data you are using to estimate the effect.

That bolded sentence is the key here.

And that's been the point of my last several posts. Bob Murphy raised concerns (not Ryan's concerns - I think Bob understands the big picture about non-experimental estimation I'm laying out here) about certain variables that were added. My view is that all of these were essential to get unbiased results and represent an improvement on earlier estimates.

So that has been the point. I've been trying to explain why changing the model in X way gets you a better estimate than refraining from changing it in X way. It's not just a matter of adding any ol' variable.

* Don't worry - it's not the case - there's a tremendous amount of degrees of freedom so there is no concern about that. In fact DLR's models should have (I'd have to double-check) many orders of magnitude more degrees of freedom than Neumark and Wascher's, which was a state study. Moreover, only the significance of the minimum wage variable in the employment model dropped, not in the others. If it were a df problem they'd all be mush - there'd be no reason for one model to be unaffected and one to lose significance if that were the problem. Finally, Ryan can easily look at the standard errors - they haven't exploded or anything like that. It's just a regular old insignificant effect - no funny business. That would not have gotten past the editors and the referees of RESTAT.

More thoughtful than you might think at first on the minimum wage...

I saw this on facebook the other day.

It sounds like your usual Bill Maher complaint that some of you may be quick to dismiss, and ultimately I don't know if I entirely agree with it either. But there's more to it than first meets the eye, and it hinges on questions of wage bargaining, monopsony, etc. in a lot of ways.

So what is the economic science behind intuition like this? What's your take on it?

Thinking about the specifications of the Dube, Lester, and Reich minimum wage study: Part 2 - controlling for county level trends

Q: When is a fixed effects model not a fixed effects model?
A: When it's a difference-in-differences model.

The most important question in any impact analysis is "how do they identify their model"? Sometimes its buried in the math, but there are a few canonical forms of how to identify a model (often very closely related) that in my opinion at least help to think about model specification and exactly what kind of assumptions and variation the authors are relying on.

I'm sure a lot of you know that a fixed effects model is just a model you run on panel data with dummy variables for each cross-sectional unit to soak up all the time-invariant non-observed characteristics, and dummy variables for each time period to soak up all the common time trends. The big thing you don't get automatically in a fixed effects model is control of time-variant variables that are cross-sectional unit specific.

Turning a fixed effects model into what is essentially a difference-in-differences (DID) model is pretty straightforward. In fact we discussed it in the last post on Dube, Lester, and Reich (DLR): you just include county-pair fixed effects in their case. These fixed effects capture any variation across pairs, so the only variation left to estimate the minimum wage coefficient on is variation within a pair, between the counties in that pair over time. DLR have intermediate versions of this, restricting the estimation of the effect to pairs within regions, states, and metropolitan areas. But what they're narrowing in on is essentially the DID. The logic of the DID is straightforward and I want to walk through it before getting to more of Bob Murphy's thoughts.

You have panel data so you've got data before and after a treatment. You also have two cases: a treatment case (on the left, below), and the comparison case (on the right). The treatment case may be changing over time anyway without the treatment, so to isolate the treatment effect any changes in your comparison case (the paired county in DLR), is subtracted out of the treatment effect. Why? The changes in the comparison cannot (or should not... there's a different literature on that issue) be affected by the treatment because it didn't get the treatment. So that small gap on the right is the counterfactual of what would have changed in the absence of treatment, and therefore cannot be attributed to the treatment effect on the left. Notice also that it doesn't matter if the comparison case is a little different from the treatment case (see how I've drawn it a little lower?). What matters is the differential response to treatment, because the DID estimator is:

[(Post-Treatment) - (Pre-Treatment)] - [(Post-Comparison) - (Pre-Comparison)]

[UPDATE: I had the terms switched above before - this version is correct. You take the raw change in the treatment case, but then you want to subtract out the change in the comparison case from that]

So if there's something about the comparison group that's time-invariant that makes it a little different from the treatment group, that's OK. That's why we have county dummy variables. What's more problematic is differences in the counties over time (which I'll discuss below).

The profile over time in the diagram above is flat, but we could easily imagine a common time trend (imagine the slopes in the figure below are the same!). This doesn't matter for the simple DID case at all for two reasons. First, if the portion of these time trends common to all counties is already absorbed by the time period dummy variables I mentioned above. Any other time trend that is common between the paired counties will be subtracted out of the treatment effect by the exact same logic of the case without the time trend: we are removing the change in the comparison group from the

As I alluded to above, the big trouble comes in when you have time trends in the treatment and comparison group that are different. That would look something like this:

If you implement the DID estimator here it will make the treatment effect a lot smaller because there was a big change in the comparison group over time relative to the treatment group (in other words, the match might have been good, but it wasn't perfect). Looking at what's actually going on, though, you can tell that the true treatment effect should be exactly the same - we're just conflating the rate of change that has nothing to do with the treatment effect with the treatment effect itself.

What you want to do in this case is control for the trend rate of change by county so that any increase in the comparison group in the post period that follows that rate of change is not used to penalize the treatment effect. You could just as easily imagine a scenario where you'd want to do this because it would over-estimate the treatment effect. I draw it this way because this is what DLR came across. Once you control for that time trend, you're back to the situation of the first picture (common time trends will be swept up in the county-specific time trends, which is just fine - we don't care about common trends), and you've got an unbiased DID again.

So as best as I can tell, Bob Murphy has two related concerns. First, he's concerned that we're including other controls when we were supposed to be dealing with all that by matching counties. That, I hope, is clear from both this post and the last post: even good comparison groups can be improved upon. You never have a perfect comparison group until you have random assignment.

But there's another issue he has with this. About a year ago, Bob wrote:

"What Dube, Lester, and Reich are really saying here, is that maybe for some reason minimum wage hikes happen to be concentrated in regions that have lower than average employment growth. Hence, just because we find that teenage employment grows more slowly in regions with higher minimum wages, doesn’t mean we can blame it on the relatively higher minimum wage. But hang on a second. Minimum wage hikes aren’t randomly distributed around the country, such that we might happen to get an outcome where they tend to be concentrated in slow-growth regions. On the contrary, minimum wage hikes are implemented by “progressive” legislatures, who also (given my economic worldview) implement other laws that retard adult employment growth.

For example, suppose that if a state legislature jacks up the minimum wage, then it is also likely to pass “pro-labor” stuff like laws giving unions more organizing power, laws allowing unfairly terminated employees to receive years of back pay, and laws granting extra perks for maternity leave. Now, these last three items I listed: Would they reduce the employers’ incentives to hire teenagers or adults, more? On the margin, they would make it costlier to hire adults, because if penalties are expressed in years of back pay, or have to do with paid leave, or strengthen unions who traditionally are going to organize adults…You get the picture. Adults make more than teenagers, and so these rules will penalize adult employment more than teenage employment.

Thus, if my model here is correct, it would produce the pattern we actually see: Looking narrowly at minimum wage laws, they seem to retard teenage employment. But then when you ask if states with high minimum wage laws have a bigger slowdown in teen employment versus adult employment, the signal becomes much weaker. It looks like, by dumb luck, for some reason all the minimum wage hikes happen in states that also have slower-than-average employment growth among adults."

So Bob's issue is bigger than the easily dispatched with concern that we matched on counties and then decided that wasn't good enough (I didn't quote that part). The concern is that somehow we are absorbing the effect of the minimum wage.

This may happen under very special circumstances, but generally it's not a problem. Bob is - I think - forgetting the panel element to the data. We are subtracting out the pre-period from the post-period for both the treatment and the comparison, and then comparing those two differences. We know the post period minus the pre period for the comparison group should have no effect at all of the minimum wage so that is the appropriate counterfactual. When we are controlling for a county specific trend we are saying "those secular trends that were going on before anyone adopted a minimum wage would have gone on if the minimum wage hadn't been adopted, so we want to clean that out of the treatment effect". If they are common between counties, my diagram two shows why that's not a concern. If they're different between counties (maybe because one has a progressive legislature), it needs to be accounted for. You are not weakening the signal you are making the signal more accurate because the only impact attributable to the minimum wage is what changes after its implementation. A time trend that continues on the same after as it did before does not change after the implementation of the minimum wage.

What special circumstances might justify Bob's fear? Time trends that are not the same before and after the minimum wage and that are not related to the minimum wage. That might look something like the following:

Let's say the true impact of the minimum wage does not increase the rate of growth of Y in the post period. In other words, let's say the slopes in both these cases would have happened without the minimum wage. If we control for county time trends using pre-period data in this case, we would find that the minimum wage had the effect of:

#1. A one time, persistent, positive shock to Y, and
#2. An increase in the rate of growth of Y

Why? Because we're differencing out the county trend in the comparison case, but we're only differencing out part of the county trend in the treatment case. The rest of the county trend in the treatment case is going to be attributed to the treatment. The #2 effect is false and introduces bias into the estimate of the treatment.

So, in order for Bob's fear to be a problem you can't just have county or state specific differences in trend between treatment and control cases. You'd need to have trends that change at the implementation of the minimum wage, and in a way that biases (rather than just adds noise) to the estimate.

It's not a completely crazy fear. You could have, for instance, a very liberal state legislature that implements a bunch of stuff at once, including a minimum wage law. That's possible, but the effect isn't clear to me. If Bob thinks the liberal legislature will tend to make employment for teens worse, and all these reforms were clustered, that would understate the effect of the minimum wage. Of course the opposite could also be true if a bevy of liberal reforms were to help. If it hurt adults more than it hurt youth that only seems like it would impact the minimum wage estimate if the effect of the minimum wage were estimated relative to the impact on all adults, and I don't think it is. I'm not really sure where those concerns about adult employment relative to youth employment come from.

So I will concede that because lots of different changes may happen together in a state legislature, it would be nice to account for that (of course if the increase is coming from a federal increase, whatever is going on in the state legislature shouldn't matter). These could certainly improve the estimate further. But I don't see any clear evidence that controlling for county time trends doesn't improve the estimate. Remember, the trends as calculated vary across counties, not the difference between the pre- and post- trends. And as my last figure illustrates you'd need the difference between pre- and post- trends for this to mess up the DID estimator.

There may be a Part 3 to this series. DLR also include placebo effects as a sensitivity analysis on these time trends. But I don't have a good sense yet of how all that works right now. If I have time to figure that out and put that together I will.

The minimum wage and turnover

I've been spending a little time poking through Arin Dube's publications and working papers today, and one interesting working paper I found was some research on the impact of the minimum wage on employment flows (also with Lester and Reich). Aside from being interesting in its own right, I'm sharing it here because it speaks to another suggestion that Bob Murphy had in his recent post. Bob writes:

"Again, even taking the new generation of studies at face value, they overlook a major drawback to the progressive goal: The studies look at the absolute growth in employment, rather than the unemployment rate, among low-skill workers. So even if it’s true that, say, a Burger King franchise will hire roughly the same number of teenagers between now and 2020 as it otherwise would have, it might not be the same group of teenagers getting jobs. Rather, at the $7.25 level there will be lower-skilled applicants cycling through, with a high turnover rate as the store manager tries to find the few decent workers in the bunch. At the higher rate of $10.10 per hour, higher-skilled kids (perhaps those from affluent families who are home from college) will enter the mix in greater numbers. The manager will be pickier on the front end in giving somebody a bite at the apple, and there will be less turnover. (Note that this isn’t merely hypothetical; the studies finding “no effect” often cite “lower job turnover” as an explanation for how the firm responds.) Thus, even taking the studies at face value, it is entirely possible that there are a bunch of people with low skills who now can’t get a job, who otherwise would have been able to. They are merely being displaced by higher skilled workers who otherwise would not have been interested in a position paying so little."

Dube's work suggests that at least part of this story is right - the lower turnover part. Their work doesn't seem to speak to the second half of Bob's point about low skill workers.

[I had initially misunderstood this point from Bob - for some reason I read "at the $7.25 level there will be lower-skilled applicants cycling through, with a high turnover rate", and I thought he was referring to the last increase. My comment on this point was therefore a little confused, but I share the skepticism about increased turnover - we apparently agree on more than I thought! You could imagine arguments either way -I don't think it makes sense to increase turnover, but you could imagine ex post learning about productivity at least counter-acting any decline in turnover from more careful screening. However, Dube's research seems to suggest that the forces that act to reduce turnover are stronger.]

Minimum wage theory: a commenter's question

I am not a very good theorist. To some extent I think I probably grasp macro theory better than micro theory, but the point is I'm not a theorist in any case. Day in and day out I am an empirical economist with varying degrees of sophistication depending on the project I'm working on. Out of personal interest I sometimes moonlight as a third-rate dealer in second-hand theories of first-order importance (in other words, I like to do a little history of economic thought).

I don't pretend to be a theorist, though, and in the interest of not pretending to be one I wanted to just share commenter YouNotSneaky!'s questions and thoughts about the theory behind the nil effect of the minimum wage in the data:

"Can you give a link to a paper that makes the monopsony argument? It's been awhile since I looked at it. I did look up the Burdette & Mortensen matching model recently which I gather is what this argument is based on. However, in that model (or ye basic search model, like say in Romer's Adv Macro) minimum wage still decreases employment. In B&M a minimum wage *can* increase social welfare but that's different (the increase in utility of those who retain higher paying jobs is greater than those who experience longer unemployment spells). You can use the B&M monopsony model to argue for minimum wage, but you can't use it to explain why the empirical work does not detect employment effects.

Personally I'm pretty sure something else is going on (probably the data just isn't good enough, not enough variation, close to equilibrium min wages, adjustments in hours rather than persons etc)

This is one version of the B&M http://econ.tau.ac.il/papers/macro/postmatch.pdf"

I don't know Burdette and Mortensen specifically although it is this sort of model that Manning uses and refers to when he talks about monopsony and the minimum wage. I've read a little of him, and I've read some of Pissarides on equilibrium unemployment. I rely on much simpler expositions of fixed costs and turnover to motivate my understanding of the connection to the minimum wage - namely, the Oi paper on quasi-fixed factors. And I agree (and have stated here) that this flavor of models is not entirely reassuring on the employment effects, however that should be more apparent in the long run than in the short run I think. I don't know - let me know what you think about that argument.

I think the data is getting better and the identification strategies are getting better and the result is not going away, so I would not blame the data.

I do think the other two issues raised are relevant: that these are often "modest" increases, not departing far from the equilibrium wage, and that there are adjustments on other margins potentially. Dube, Lester, and Reich do provide an upper bound on the hours adjustment. It's not immediately obvious to me why it would make sense to make your adjustment on hours rather than employment (in the pre-Obamacare era at least!). The only reason to do that, it seems to me, is to deliberately fool economists.

Thinking about the specifications of the Dube, Lester, and Reich minimum wage study: Part 1

Bob Murphy recently probed some important questions about the Dube, Lester, and Reich paper on the minimum wage (hereafter DLR). Ultimately I think Bob's concerns are misplaced, but these are exactly the issues we should be thinking about and arguing about with the minimum wage literature - not petty assertions that the other side doesn't understand the law of demand. So let's jump right in - Bob writes:

"I admit that I have not studied them in depth, but if you look at the discussion in the survey article I mentioned above, here’s what it sounds like: You can take all of the adjacent counties in the country for which you have continuous data over a long period (such as 16 years), where the applicable minimum wage is occasionally different in each county (because they fall in different states). If you “naively” run a regression on this dataset, then the classical consensus emerges: It does indeed seem that a higher minimum wage is associated with a slowdown in the growth of employment."

I think this is an entirely fair read of DLR. Their paper has two samples - a full county sample and a contiguous county sample that is a collection of county-pairs (with some counties repeated if they are paired with multiple border counties). They find this classical result in both samples if they just run a regression akin to Neumark and Wascher. This is a good thing - we want confirmation of results across datasets (Neumark and Wascher use states). Bob continues:

"However, this could be a spurious result, because states with high population growth might just so happen to also match the federal minimum wage, rather than setting a higher state level. To correct for this, the newer studies introduced a regional dummy variable into the regression analysis, at which point the negative effect of the minimum wage almost disappears.

If indeed what I just described is what’s going on, then that seems ludicrous. The point of matching contiguous counties is to isolate all other relevant variables, except for the applicable minimum wage. You can’t use the weather (one of the explanations given in the survey article to explain the flaw in the original studies, which did not correct for geography) to explain why people would flock to one county versus the adjacent one."

This is where I think Bob starts to get things wrong. In the first place I don't think he's understanding what DLR are doing. The regional dummies and the matching are not being done together. See DLR's description here (specification 1 is the naïve regression described above):

Remember that even when you use the second sample of contiguous counties they aren't automatically matched yet. It's just a whole bunch of counties thrown in together that happened to be on state borders. When you start introducing geographic controls into the fully county sample (specifications 1 through 4), you very quickly lose the negative correlation. In other words, spatial heterogeneity matters crucially for these results. The finding that even regional time specific dummies in the full sample will lose you the negative effect is the whole reason why they are justified in going further and "matching" (as Bob phrases it) the counties. But there is no matching until specification 6. Specification 5 runs the naïve regression on the raw contiguous counties file, and specification 6 finally introduces county-pair dummies that "match" the counties (it would be more accurate to say that they eliminate the between-pair variation and only rely on the within-pair variation to identify the minimum wage effect). You might have to go to table 2 in the paper to see it clearly enough, but only the regressions where the red outlined contiguous county dummies are included are "matched":

Now Bob also raises concerns about why they're tossing other stuff in when they've already got a county match. I hope it's clear that they are not "matching" counties until the sixth specification, but this point is still worth addressing because it is relevant for other issues that Bob raised with the paper almost a year ago. Finding a good comparison group is the principal task of the microeconometrician. It's identical to the issue of "identifying your model". But when you find a good comparison group it doesn't mean there's no room left for improvement. So you'll often include other controls or matching procedures after finding a good comparison group (in this case, contiguous counties).

When I was at the Urban Institute, one project I was on was to evaluate a job training program for high-growth industries (often advanced manufacturing and ironically now, construction). We had individual level data, but we paired cases that showed up in contiguous localities (in this case a WIA designated area, not necessarily a county). One county's workforce investment board would direct people to the program we were looking at, the other would just have the training options that were generally available. That was a big step forward compared to what we're calling here the "naive" approach of comparing our treatment cases to anyone in the country that ever sought out job training. By focusing on contiguous localities we got a much better comparison sample. But there was still a lot to be improved on. So after that, we used propensity score matching to further match the characteristics of the group, and then on top of that we included other control variables in the ultimate model specification.

The point being that you never have a perfect comparison group. Using contiguous counties in DLR is a big improvement on Neumark and Wascher but that hardly means that everything is controlled for.

This gets us into the controls they add - specifically, time trends. I'll get that up in Part 2, hopefully soon. that deals with the concerns raised by Bob about a year ago. I wanted to get it in here, but I realized there's a lot to say to clarify the basic specification issues raised in his more recent post.

To sum up - even very simple controls for spatial heterogeneity like regional dummies strongly imply that you need to control for geography, motivating DLR to introduce their contiguous counties strategy.