Arindrajit Dube

 

Recent Posts by Arindrajit Dube

  • Guest Post: Dube on Growth, Debt and Past versus Future Windows

    Jun 1, 2013Arindrajit Dube

    Windows into the Past and the Future:  A Visual Elaboration

    Arindrajit Dube

    Recently, we have seen a number of explorations of the timing of growth around episodes of high debt as a way to discern the likely direction of causality in that relationship.  This is important, because we do observe that there is a negative correlation between contemporaneous debt and growth. For instance, this is true when using the corrected data from Reinhart and Rogoff, and equal weighting of country-year observations. Although there is no evidence of tipping points, a negative relationship remains.

    In a blog post in April, I showed that the timing of this negative relationship went against an interpretation where high debt caused low growth.  I showed that relationship between contemporaneous debt with future growth is much weaker than that with past growth—which is suggestive of reverse causality.  I used a 3-year window for this exercise. In other words, if we label current year as “0” I took the average growth rates in years 1,2 and 3.  In a more recent column at Quartz, Kimball and Wang’s follow-up analysis showed the relationship using a window between years 5-10.  In a working paper I that I wrote based on my blog post—but posted online after Kimball and Wang’s column—I followed the recent literature in taking a 5-year forward average growth rate, i.e., average growth taken over years 1-5.

    The general tenor of these findings is that the further into the future that the window stretches, the more attenuated the debt-growth relationship seems to be. However, the same does not appear to be true when considering windows stretching backwards in time: current debt is indeed strongly associated with past growth. 

    But how sensitive are these results to specific window lengths? More generally, as suggested by Evan Soltas, how do these results look when using windows of alternative lengths? That’s exactly what I’ll do here, by plotting the coefficients and confidence bounds for bivariate regressions of growth from alternative windows on contemporaneous debt. For example, the window labeled -2 uses average growth rates from dates -2 and -1. Similarly, the window labeled 3 uses growth rates from dates 1, 2 and 3.

    The results are stark, and confirm what we have already seen. The bivariate regression of current growth on current debt is around -0.018, meaning a 10 percentage point higher debt ratio (e.g., 110 versus 100) is associated with a lower growth by 0.18 percentage points.  This relationship is statistically significant at conventional levels using country-clustered standard errors. However, a 10 point higher debt ratio is associated with an even lower average growth 3, 5, or 10 years back, and this apparently spurious relationship appears stronger the further we roll back our window, clocking lower growths by 0.25 points or more in magnitude.

    In contrast, the further forward we roll our window, the weaker the relationship appears to be, falling roughly by 1/3 when we merely consider the growth rate in the next year. And it attenuates further when we take future rates: a 10 point higher debt ratio is associated with merely a 0.05 point lower growth in the next 10 years, which is statistically indistinguishable from zero.

    There is, however, a complication when doing this type of analysis. Namely, we should be mindful of the following possibility. Perhaps today’s high debt is not negatively correlated with the growth rate averaged over the next 10 years because the average debt level in the next 10 years is also not particularly high as compared to today.  (In statistical parlance, perhaps debt is strongly mean reverting.)  This can be checked: we can current debt on the average debt levels in the past and future windows in an analogous fashion as before.

    Reassuringly, a 10 point greater debt ratio today is associated with a 7 point or greater debt ratio over the next 10 years.  So this cannot be an explanation for the  near disappearance of the negative debt-growth relationship when taking forward averaged growth rates.  Similarly, there is a roughly symmetric relationship with past debt ratios which means that the highly asymmetric debt-growth relationship in the future versus past cannot be due to a similarly asymmetric relationship of current debt with future versus past debt.

    I mentioned the issues of serial correlation of debt and growth levels in passing in my original blog post, which is why I also showed the results with distributed lags, which explicitly controls for the past and future debt levels in the regression. While those fully account for the issues raised here, I think the analysis here showing the serial correlation in debt visually more informative about the patterns in the data.

    Of course, there are numerous ways to account for the reverse causality patterns, besides just considering forward-averaged growth rates. One strategy is to explicitly include past growth rates as a control. I did this in my blog post (see the last figure there), as well as in working paper.  This is also exactly what Kimball and Wang do in showing the “excess growth” over and beyond what is predicted by past growth.  However, I think their graphical approach in actually computing the predicted and excess growth rates based on past growth rates was a very nice way to make the point. At any rate, all these results all suggest effectively no relationship between debt and growth in the post-war sample of advanced industrialized countries that we analyzed.

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    Windows into the Past and the Future:  A Visual Elaboration

    Arindrajit Dube

    Recently, we have seen a number of explorations of the timing of growth around episodes of high debt as a way to discern the likely direction of causality in that relationship.  This is important, because we do observe that there is a negative correlation between contemporaneous debt and growth. For instance, this is true when using the corrected data from Reinhart and Rogoff, and equal weighting of country-year observations. Although there is no evidence of tipping points, a negative relationship remains.

    In a blog post in April, I showed that the timing of this negative relationship went against an interpretation where high debt caused low growth.  I showed that relationship between contemporaneous debt with future growth is much weaker than that with past growth—which is suggestive of reverse causality.  I used a 3-year window for this exercise. In other words, if we label current year as “0” I took the average growth rates in years 1,2 and 3.  In a more recent column at Quartz, Kimball and Wang’s follow-up analysis showed the relationship using a window between years 5-10.  In a working paper I that I wrote based on my blog post—but posted online after Kimball and Wang’s column—I followed the recent literature in taking a 5-year forward average growth rate, i.e., average growth taken over years 1-5.

    The general tenor of these findings is that the further into the future that the window stretches, the more attenuated the debt-growth relationship seems to be. However, the same does not appear to be true when considering windows stretching backwards in time: current debt is indeed strongly associated with past growth. 

    But how sensitive are these results to specific window lengths? More generally, as suggested by Evan Soltas, how do these results look when using windows of alternative lengths? That’s exactly what I’ll do here, by plotting the coefficients and confidence bounds for bivariate regressions of growth from alternative windows on contemporaneous debt. For example, the window labeled -2 uses average growth rates from dates -2 and -1. Similarly, the window labeled 3 uses growth rates from dates 1, 2 and 3.

    The results are stark, and confirm what we have already seen. The bivariate regression of current growth on current debt is around -0.018, meaning a 10 percentage point higher debt ratio (e.g., 110 versus 100) is associated with a lower growth by 0.18 percentage points.  This relationship is statistically significant at conventional levels using country-clustered standard errors. However, a 10 point higher debt ratio is associated with an even lower average growth 3, 5, or 10 years back, and this apparently spurious relationship appears stronger the further we roll back our window, clocking lower growths by 0.25 points or more in magnitude.

    In contrast, the further forward we roll our window, the weaker the relationship appears to be, falling roughly by 1/3 when we merely consider the growth rate in the next year. And it attenuates further when we take future rates: a 10 point higher debt ratio is associated with merely a 0.05 point lower growth in the next 10 years, which is statistically indistinguishable from zero.

    There is, however, a complication when doing this type of analysis. Namely, we should be mindful of the following possibility. Perhaps today’s high debt is not negatively correlated with the growth rate averaged over the next 10 years because the average debt level in the next 10 years is also not particularly high as compared to today.  (In statistical parlance, perhaps debt is strongly mean reverting.)  This can be checked: we can current debt on the average debt levels in the past and future windows in an analogous fashion as before.

    Reassuringly, a 10 point greater debt ratio today is associated with a 7 point or greater debt ratio over the next 10 years.  So this cannot be an explanation for the  near disappearance of the negative debt-growth relationship when taking forward averaged growth rates.  Similarly, there is a roughly symmetric relationship with past debt ratios which means that the highly asymmetric debt-growth relationship in the future versus past cannot be due to a similarly asymmetric relationship of current debt with future versus past debt.

    I mentioned the issues of serial correlation of debt and growth levels in passing in my original blog post, which is why I also showed the results with distributed lags, which explicitly controls for the past and future debt levels in the regression. While those fully account for the issues raised here, I think the analysis here showing the serial correlation in debt visually more informative about the patterns in the data.

    Of course, there are numerous ways to account for the reverse causality patterns, besides just considering forward-averaged growth rates. One strategy is to explicitly include past growth rates as a control. I did this in my blog post (see the last figure there), as well as in working paper.  This is also exactly what Kimball and Wang do in showing the “excess growth” over and beyond what is predicted by past growth.  However, I think their graphical approach in actually computing the predicted and excess growth rates based on past growth rates was a very nice way to make the point. At any rate, all these results all suggest effectively no relationship between debt and growth in the post-war sample of advanced industrialized countries that we analyzed.

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  • Guest Post: Reinhart/Rogoff and Growth in a Time Before Debt

    Apr 17, 2013Arindrajit Dube

    [Mike Konczal here.  Yesterday I wrote about a paper by Thomas Herndon, Michael Ash and Robert Pollin of University of Massachusetts, Amherst. They replicated the influential Reinhart/Rogoff paper Growth in a Time of Debt. There were many responses on the internet, including Jared Bernstein, Matt YglesiasDean Baker, Paul Krugman, and many, many others. Reinhart and Rogoff have since responded with a statement. They believe that the findings do not "affects in any significant way the central message of the paper or that in our subsequent work." What is that message? That higher debt is associated with lower growth.

    From the beginning many economists (Krugman, Bivens and Irons) have argued that their paper probably has the causation backwards: slow growth causes higher debt. But now that Herndon, Ash and Pollin have made the data used public, perhaps a talented econometrician could actually answer this? Arindrajit Dube was up for the challenge. Dube is an assistant professor of economics at the University of Massachusetts, Amherst.]

    Growth in a Time Before Debt…

    Recent work by my colleagues at UMass Thomas Herndon, Michael Ash and Robert Pollin (2013)—hereafter HAP—has demonstrated that in contrast to the apparent results in Reinhart and Rogoff (2010), there is no real discontinuity or "tipping point" around 90 percent of debt-to-GDP ratio.

    In their response, Reinhart and Rogoff—hereafter RR—admit to the arithmetic mistakes, but argue that the negative correlation between debt-to-GDP ratio and growth in the corrected data still supports their original contention. Taking the Stata dataset that HAP generously made available as part of their replication exercise, I first reproduced the nonparametric graph in HAP (2013) using a lowess regression (slightly different than the specific method they used). The dotted lines are 95 percent bootstrapped confidence bands.

    There is a visible negative relationship between growth and debt-to-GDP, but as HAP point out, the strength of the relationship is actually much stronger at low ratios of debt-to-GDP.  This makes us worry about the causal mechanism. After all, while a nonlinearity may be expected at high ratios due to a tipping point, the stronger negative relationship at low ratios is difficult to rationalize using a tipping point dynamic.

    In their response, RR state that they were careful to distinguish between association and causality in their original research. Of course, we would only really care about this association if it likely reflects causality flowing from debt to growth (i.e. higher debt leading to lower growth, the lesson many take from RR's paper).

    While it is difficult to ascertain causality from plots like this, we can leverage the time pattern of changes to gain some insight. Here is a simple question: does a high debt-to-GDP ratio better predict future growth rates, or past ones?  If the former is true, it would be consistent with the argument that higher debt levels cause growth to fall. On the other hand, if higher debt "predicts" past growth, that is a signature of reverse causality.

    Below I have created similar plots by regressing current year's GDP on (1) the next 3 years' average GDP growth, and (2) last three years' average GDP growth. (My .do file is available here so anyone can make these graphs. After all, if I made an error, I'd rather know about it now.)

    Figure 2:  Future and Past Growth Rates and Current Debt-to-GDP Ratio

    As is evident, current period debt-to-GDP is a pretty poor predictor of future GDP growth at debt-to-GDP ratios of 30 or greater—the range where one might expect to find a tipping point dynamic.  But it does a great job predicting past growth.
     
    This pattern is a telltale sign of reverse causality.  Why would this happen? Why would a fall in growth increase the debt-to-GDP ratio? One reason is just algebraic. The ratio has a numerator (debt) and denominator (GDP): any fall in GDP will mechanically boost the ratio.  Even if GDP growth doesn’t become negative, continuous growth in debt coupled with a GDP growth slowdown will also lead to a rise in the debt-to-GDP ratio.
     
    Besides, there is also a less mechanical story. A recession leads to increased spending through automatic stabilizers such as unemployment insurance. And governments usually finance these using greater borrowing, as undergraduate macro-economics textbooks tell us governments should do. This is what happened in the U.S. during the past recession. For all of these reasons, we should expect reverse causality to be a problem here, and these bivariate plots are consistent with such a story.
     
    Of course, these are just bivariate plots. To get the econometrics right, when looking at correlations between current period debt-to-GDP ratio and past or future GDP growth, you should also account for past or future debt-to-GDP ratio.
     
    A standard way of doing this is using a "distributed lag" model - which just means regressing GDP growth on a set of leads and lags in debt to GDP ratio, and then forming an "impulse response" from, say, a hypothetical 10 point increase in the debt-to-GDP ratio (where 100 is when the debt level is equal to GDP).
     
    Figure 3 below reports these impulse responses. What we find is exactly the pattern consistent with reverse causality.
     
    The way to read this graph is to go from left to right. Here “-3” is 3 years before a 10 point increase in the debt-to-GDP ratio, “-2” is 2 years before the increase, etc.   The graph shows that GDP growth rates were unusually low and falling prior to the 10 point increase in the debt-to-GDP ratio.  If you average the growth differentials from the 3 years prior to the increase in debt, (i.e., the values associated with -3,-2,-1 on the X-axis), it is –0.6 (or 6/10 of a percent lower growth than usual) and statistically significant at the 5 percent level. In contrast, the average growth rates from years 1, 2 and 3+ after the 10 point increase in debt-to-GDP ratio is 0.2 (or 2/10 of one percent) higher than usual. 
     
    Figure 3: Impulse Response of GDP Growth from a 10-point increase in Debt-to-Income Ratio

    So what does this all show?  It shows that purely in terms of correlations, a 10 point increase in the debt-to-GDP ratio in the RR data is associated with a 6/10 of a percentage point lower growth in the 3 years prior to the increase, but actually a slightly larger than usual growth in the few years after the increase. During the year of the increase in debt-to-GDP ratio, GDP growth is really low, consistent with the algebraic effect of lower growth leading to a higher debt-to-GDP ratio.

    All in all, these simple exercises suggest that the raw correlation between debt-to-GDP ratio and GDP growth probably reflects a fair amount of reverse casualty. We can’t simply use correlations like those used by RR (or ones presented here) to identify causal estimates.

    [Aside:  For those who are more econometrically inclined, here is the picture with country and year fixed effects to soak up some of the heterogeneity.  Not much different. By the way, the standard errors in the panel regressions are clustered by country.]

    ----
    Addendum.
     
    Labor economists have long recognized that falling values of the outcome can sometimes precede the treatment. In the job training literature this is known as an "Ashenfelter dip." Those with a fall in earnings are more likely to enter training programs, creating a spurious negative correlation between training and wages. This has similarity to the problem of debt and growth studied here.
     
    One way in which economists control for such dips is by including the lagged outcome as a control.  In this case, we can control for a 1-year lagged GDP growth using a partial linear model. This still allows for a nonlinear relationship between GDP growth and debt-to-GDP ratio like in the bivariate case, but in addition controls for last period's growth.
     
    Here's the picture:
    Controlling for the previous year's GDP growth largely erases the negative relationship between debt-to-GDP ratio and GDP growth, especially for the range where debt is 30 percent or more of GDP.  This is because a fall in GDP precedes the rise in Debt-to-GDP ratio. This is yet another demonstration that the simple bivariate negative correlation is driven in substantial part by reverse causality.

    Follow or contact the Rortybomb blog:

      

     

    [Mike Konczal here.  Yesterday I wrote about a paper by Thomas Herndon, Michael Ash and Robert Pollin of University of Massachusetts, Amherst. They replicated the influential Reinhart/Rogoff paper Growth in a Time of Debt. There were many responses on the internet, including Jared Bernstein, Matt YglesiasDean Baker, Paul Krugman, and many, many others. Reinhart and Rogoff have since responded with a statement. They believe that the findings do not "affects in any significant way the central message of the paper or that in our subsequent work." What is that message? That higher debt is associated with lower growth.

    From the beginning many economists (Krugman, Bivens and Irons) have argued that their paper probably has the causation backwards: slow growth causes higher debt. But now that Herndon, Ash and Pollin have made the data used public, perhaps a talented econometrician could actually answer this? Arindrajit Dube was up for the challenge. Dube is an assistant professor of economics at the University of Massachusetts, Amherst.]

    Growth in a Time Before Debt…

    Recent work by my colleagues at UMass Thomas Herndon, Michael Ash and Robert Pollin (2013)—hereafter HAP—has demonstrated that in contrast to the apparent results in Reinhart and Rogoff (2010), there is no real discontinuity or "tipping point" around 90 percent of debt-to-GDP ratio.

    In their response, Reinhart and Rogoff—hereafter RR—admit to the arithmetic mistakes, but argue that the negative correlation between debt-to-GDP ratio and growth in the corrected data still supports their original contention. Taking the Stata dataset that HAP generously made available as part of their replication exercise, I first reproduced the nonparametric graph in HAP (2013) using a lowess regression (slightly different than the specific method they used). The dotted lines are 95 percent bootstrapped confidence bands.

    There is a visible negative relationship between growth and debt-to-GDP, but as HAP point out, the strength of the relationship is actually much stronger at low ratios of debt-to-GDP.  This makes us worry about the causal mechanism. After all, while a nonlinearity may be expected at high ratios due to a tipping point, the stronger negative relationship at low ratios is difficult to rationalize using a tipping point dynamic.

    In their response, RR state that they were careful to distinguish between association and causality in their original research. Of course, we would only really care about this association if it likely reflects causality flowing from debt to growth (i.e. higher debt leading to lower growth, the lesson many take from RR's paper).

    While it is difficult to ascertain causality from plots like this, we can leverage the time pattern of changes to gain some insight. Here is a simple question: does a high debt-to-GDP ratio better predict future growth rates, or past ones?  If the former is true, it would be consistent with the argument that higher debt levels cause growth to fall. On the other hand, if higher debt "predicts" past growth, that is a signature of reverse causality.

    Below I have created similar plots by regressing current year's GDP on (1) the next 3 years' average GDP growth, and (2) last three years' average GDP growth. (My .do file is available here so anyone can make these graphs. After all, if I made an error, I'd rather know about it now.)

    Figure 2:  Future and Past Growth Rates and Current Debt-to-GDP Ratio

    As is evident, current period debt-to-GDP is a pretty poor predictor of future GDP growth at debt-to-GDP ratios of 30 or greater—the range where one might expect to find a tipping point dynamic.  But it does a great job predicting past growth.
     
    This pattern is a telltale sign of reverse causality.  Why would this happen? Why would a fall in growth increase the debt-to-GDP ratio? One reason is just algebraic. The ratio has a numerator (debt) and denominator (GDP): any fall in GDP will mechanically boost the ratio.  Even if GDP growth doesn’t become negative, continuous growth in debt coupled with a GDP growth slowdown will also lead to a rise in the debt-to-GDP ratio.
     
    Besides, there is also a less mechanical story. A recession leads to increased spending through automatic stabilizers such as unemployment insurance. And governments usually finance these using greater borrowing, as undergraduate macro-economics textbooks tell us governments should do. This is what happened in the U.S. during the past recession. For all of these reasons, we should expect reverse causality to be a problem here, and these bivariate plots are consistent with such a story.
     
    Of course, these are just bivariate plots. To get the econometrics right, when looking at correlations between current period debt-to-GDP ratio and past or future GDP growth, you should also account for past or future debt-to-GDP ratio.
     
    A standard way of doing this is using a "distributed lag" model - which just means regressing GDP growth on a set of leads and lags in debt to GDP ratio, and then forming an "impulse response" from, say, a hypothetical 10 point increase in the debt-to-GDP ratio (where 100 is when the debt level is equal to GDP).
     
    Figure 3 below reports these impulse responses. What we find is exactly the pattern consistent with reverse causality.
     
    The way to read this graph is to go from left to right. Here “-3” is 3 years before a 10 point increase in the debt-to-GDP ratio, “-2” is 2 years before the increase, etc.   The graph shows that GDP growth rates were unusually low and falling prior to the 10 point increase in the debt-to-GDP ratio.  If you average the growth differentials from the 3 years prior to the increase in debt, (i.e., the values associated with -3,-2,-1 on the X-axis), it is –0.6 (or 6/10 of a percent lower growth than usual) and statistically significant at the 5 percent level. In contrast, the average growth rates from years 1, 2 and 3+ after the 10 point increase in debt-to-GDP ratio is 0.2 (or 2/10 of one percent) higher than usual. 
     
    Figure 3: Impulse Response of GDP Growth from a 10-point increase in Debt-to-Income Ratio

    So what does this all show?  It shows that purely in terms of correlations, a 10 point increase in the debt-to-GDP ratio in the RR data is associated with a 6/10 of a percentage point lower growth in the 3 years prior to the increase, but actually a slightly larger than usual growth in the few years after the increase. During the year of the increase in debt-to-GDP ratio, GDP growth is really low, consistent with the algebraic effect of lower growth leading to a higher debt-to-GDP ratio.

    All in all, these simple exercises suggest that the raw correlation between debt-to-GDP ratio and GDP growth probably reflects a fair amount of reverse casualty. We can’t simply use correlations like those used by RR (or ones presented here) to identify causal estimates.

    [Aside:  For those who are more econometrically inclined, here is the picture with country and year fixed effects to soak up some of the heterogeneity.  Not much different. By the way, the standard errors in the panel regressions are clustered by country.]

    ----
    Addendum.
     
    Labor economists have long recognized that falling values of the outcome can sometimes precede the treatment. In the job training literature this is known as an "Ashenfelter dip." Those with a fall in earnings are more likely to enter training programs, creating a spurious negative correlation between training and wages. This has similarity to the problem of debt and growth studied here.
     
    One way in which economists control for such dips is by including the lagged outcome as a control.  In this case, we can control for a 1-year lagged GDP growth using a partial linear model. This still allows for a nonlinear relationship between GDP growth and debt-to-GDP ratio like in the bivariate case, but in addition controls for last period's growth.
     
    Here's the picture:
    Controlling for the previous year's GDP growth largely erases the negative relationship between debt-to-GDP ratio and GDP growth, especially for the range where debt is 30 percent or more of GDP.  This is because a fall in GDP precedes the rise in Debt-to-GDP ratio. This is yet another demonstration that the simple bivariate negative correlation is driven in substantial part by reverse causality.

    Follow or contact the Rortybomb blog:

      

     

    Share This

  • Minimum Wage Laws and the Labor Market: What Have We Learned Since Card and Krueger's Book Myth and Measurement?

    Sep 1, 2011Arindrajit Dube

    alan-kruegerAlan Krueger's work with David Card was seminal when it first came out, but it has also stood the test of time.

    alan-kruegerAlan Krueger's work with David Card was seminal when it first came out, but it has also stood the test of time.

    Alan Krueger's recent appointment to head the Council of Economic Advisers has led to renewed interest in his book on minimum wages, coauthored with David Card, called Myth and Measurement. In that book, published in 1995, the authors forcefully argued that the evidence showing minimum wage increases killed jobs was fragile. Their own case study comparing fast food restaurants in New Jersey and Pennsylvania after a minimum wage increase in New Jersey showed that if anything, employment rose in New Jersey following the legislated hike.

    Myth and Measurement went on to argue that the totality of evidence pointed towards the inadequacy of the simple supply-and-demand model for understanding the labor market for low-wage workers. Instead, they argued employers have some power to choose wage polices: paying a little bit more would attract more workers to a company and reduce the number leaving the company because of a better offer, but would mean higher labor costs due to paying more to those who would have stayed at the firm anyway -- the "inframarginal" workers. Card and Krueger called this the "dynamic monopsony" model, and they argued that it accorded with the data much better than the canonical supply and demand model.

    The reaction to the book was unforgettable, even for those of us who were mere undergraduates at the time. Mixed in with praise for the authors' clear-headed (if brave) analysis was scathing commentary from established labor economists who considered Myth and Measurement nothing short of heresy. In his 1995 review of the book in Industrial and Labor Relations Review, Daniel Hammermesh scolded the authors that "[a] wonderful world of reduced inequality through higher wage minima with no loss of jobs is regrettably not an option." It has been an eventful 16 years since the publication of that book, so it seems a good time to take stock of how the authors' central theses have stood the test of time. Writing a retrospective review of Myth and Measurement is particularly tempting, since I just finished a review of the more recently published book Minimum Wages by David Neumark and William Wascher for the Journal of Economic Literature, which should be coming out in September. (For the uninitiated, Neumark and Wascher have staked out a position in the minimum wage debate arguing that minimum wages reduce jobs and increase poverty, and therefore implementing them is generally an undesirable policy.)

    So what have we learned from -- and since -- Myth and Measurement? Let me highlight three things. First, it is useful to understand the methodological contribution of Card and Krueger's work. The idea of using "natural experiments" -- where there is a sudden change in policy -- was a hallmark of their work and since then has become a standard device in the empirical economist's toolkit. Additionally, the idea that geographical proximity is a good way to construct a control group has been strongly vindicated by many studies, including ones looking at minimum wage impacts. Indeed, today there is a plethora of studies using border discontinuity designs. While there were problems with their case study when it came to properly accounting for statistical power (something that I take up below), overall Card and Krueger's work has made a lasting (and positive) methodological contribution.

    Second, Card and Krueger's own follow-up work (Card and Krueger 2000), as well as subsequent studies, largely validated the claim that fast food employment does not drop in any meaningful way in response to the kind of minimum wage increases that we have seen in this country. While critics typically focused on the fact that they found sizeable positive effects on jobs in some cases, the more policy relevant point of the book was that minimum wages do not seem to "kill jobs" while they raise wages at the bottom. This point has been firmly borne out by careful follow up research.

    And finally, the idea that search frictions may mediate minimum wage impacts has been taken up by numerous papers since Myth and Measurement -- and has become much less controversial than at the time it was proposed. All in all, I would consider that a pretty good track record for any book in economics.

    Findings on Employment

    Let's begin with the book's core empirical findings about the impact of minimum wages on jobs in the fast food industry. What most stirred up the profession was that in some of Card and Krueger's specifications, employment in New Jersey actually rose in response to the mandated wage increase in a statistically significant fashion. The positive effect was inconsistent with the competitive model, but was consistent with a monopsonistic model where employers have some wage setting power.

    However, the authors pointed out that in other specifications (especially those that were not weighted by firm size), the estimates were much less precise. They argued that "at a minimum, we believe that our estimates call into question the prediction that an increase in the minimum wage will lead to significant employment losses at affected firms. In particular, even our least precise estimates reject the hypothesis that the elasticity of demand for labor by fast-food employers is greater than 0.3 in absolute value."

    Subsequent research that built on Myth and Measurement has found that while the sizeable positive effects in some of their specifications were likely due to chance, the lack of job loss was very much a robust finding. Card and Krueger's own subsequent analysis in 2000 using Unemployment Insurance filings by firms (which was closer to the universe of firms in the two states than their original sample) over a longer period already moved towards this view, as the employment elasticities, while still positive, were smaller in magnitude and not statistically distinguishable from zero.(1) My own work with William Lester and Michael Reich (2010) demonstrated this point by comparing contiguous counties across state borders and pooling over 64 different border segments with minimum wage differences over a 17-year period (1990-2006). It's like doing 64 different NJ-PA "experiments" and pooling them together. In the figure below, the dark line shows the distribution of the measured employment elasticity across the 64 "experiments." The four vertical lines are four different published estimates from individual case studies in the literature.

    card-and-krueger-graph

    Local areas are buffeted by all kinds of economic shocks, and even if these are not correlated with minimum wage increases on average, they lead to clustering in the data, leaving us with less statistical variation than may be apparent at first glance. Such clustering was not accounted for in Card and Krueger's work or virtually in any work during that time, which explains why a sizeable positive effect could be found by chance alone. Since then, we have learned that computing standard errors without accounting for such clustering can lead to false precision. At the end of the day, however, our key conclusions were similar to Card and Krueger's, as the implied labor demand elasticity was effectively zero, and "statistical bounds (at the 95% confidence level) around our contiguous county estimates of the labor demand elasticity as identified from a change in the minimum wage rule out anything above 0.48 in magnitude." (The labor demand elasticitity measures the proportional change in employment for a group of workers in response to a proportional change in their wages.) Importantly, although one of the common criticisms of Myth and Measurement was that it only considered short-run responses, we also showed that was not a fatal flaw. Even when we considered long-term effects using a 17-year panel, the finding of no disemployment effect remained.

    What about other research since Myth and Measurement that has looked at the effect of minimum wages on jobs in the U.S.? The most common since the 1990s has been the "state panel" approach pioneered by David Neumark and William Wascher. Like the individual case study, it uses only differences in minimum wages across states to form inference. However, instead of comparing two areas that may be similar based on, say, proximity, the "state panel" studies effectively compare all states to all states, while accounting for possible differences by including statistical controls. The state panel approach has tended to find negative effects, especially when considering a high impact demographic group such as teenagers.(2) For example, in their 2008 book titled Minimum Wages, Neumark and Wascher review 10 state panel studies following up on the initial controversy; nine out of 10 of these studies find evidence for jobs loss.

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    There are some obvious virtues for the state panel approach, since it uses a lot more variation than an individual case study. However, it also assumes that we can find enough control variables to include in our regression that will make Texas look like Massachusetts. As it turns out, this is a heroic assumption that badly biases the results.

    In a series of papers (Allegretto Dube Reich 2009, 2010; Dube Lester and Reich 2010, 2011) we show the nature of bias in the state panel studies. The kind of states that have tended to have higher minimum wage in the past 20 years have been quite different from those who have tended to have lower minimum wages. As an example, today 11 states plus DC have a local minimum wage of at least $0.25 above the federally mandated minimum of $0.25/hour. Eight of these 11 states are either in New England or on the West Coast. (The remaining three are Illinois, New Mexico, and Nevada.)

    In other words, there is a very strong regional component to the minimum wage variation. This can lead to very misleading inference if we compare teen employment growth in, say, Texas and Massachusetts. Given factors such as climate, proximity to Mexico, and others that are usually not fully accounted for in state panel approaches, we might expect very different trends in employment in those states quite apart from minimum wages. Similarly, the growth rate in low-wage jobs has been quite different in states like Texas, North Dakota, and Indiana even thought these states have had the same binding minimum wage (i.e., the federal) over the past two decades. Unless one controls for the "unobserved" (or more accurately "not directly observed") sources of heterogeneity in the growth prospects across areas, conclusions may be badly flawed. A telltale sign of this flaw that our studies revealed is that in the state panel model, the job losses occur substantially prior to the actual change in policy.

    So what are some ways of correcting the deficiencies of the state panel approach? One fruitful way is to recognize the core insight of Card and Krueger's research design that compared areas across the NJ-PA border. When comparing places directly across a border, many other (potentially unobservable) confounding factors are roughly similar. We implemented this strategy in numerous papers using a variety of data sets (QCEW, QWI, CPS, Census). The results were unambiguous: whatever group we considered -- restaurant workers, teenagers, teenagers of disadvantaged backgrounds -- the state panel approach always produced an erroneous negative estimate when it came to employment. Once we accounted for the regional heterogeneity, there was no employment loss to speak of. Other authors who have accounted for such heterogeneity largely confirm that employment effects from minimum wage increases in the US have been close to zero or even positive (e.g., Addison et al., 2009, 2011).

    Inadequacy of the Simple Supply and Demand Model of the Labor Market

    Another important part of Myth and Measurement argued for the inadequacy of the simple supply-and-demand model in thinking about the low-wage labor market. Card and Krueger's primary evidence for this view was that employment didn't fall, and may have risen, in response to a minimum wage increase. A simple model of "monopsony" is a firm that has some wage setting power due to search frictions. Employees say to themselves, "If my employer doesn't give me the raise I was promised I might look for other jobs, but there is no guarantee I'll find one to my liking immediately." Conversely, raising the wages a little won't immediately lead to a crush of workers outside the office, since only a fraction of potential workers may find out about it.

    In Card and Krueger's dynamic monospony model, separation and recruitment rates are functions of the wage rate and so the model allows positive firm-level labor supply elasticities. They argue that empirically plausible magnitudes of the labor supply elasticities facing a firm are consistent with small positive or zero effects of a minimum wage increase on employment levels. Why? Because firms do not fully internalize the gains from paying a slightly higher wage. A higher wage reduces quits and increases recruitment among "marginal workers," thereby increasing employment. But a higher wage also means paying more to those who would have stuck around anyway -- the "inframarginal workers." This logic means firms don't raise wages as high as is "efficient" from a societal, as opposed to a profit maximization, perspective. When a minimum wage hike raises the bottom wage, it leads to fewer quits and more recruitment, and hence greater employment. Of course eventually, if the wage is raised enough, the firm may simply go out of business. But over a range, the effect of increasing jobs at some firms may dominate the reduction of jobs from firms not producing at all.

    So how has subsequent research spoken to the issue of "dynamic monopsony" or "search friction"? One piece of evidence comes from this year's Nobel Prize in Economics to Professors Peter Diamond, Dale Mortensen and Christopher Pissarides "for their analysis of markets with search frictions." In other words, thinking about the labor market in terms of search frictions has become eminently respectable. Indeed, Dale Mortensen's paper (with Kenneth Burdett) in 1998 formalized the dynamic monopsony model in an equilibrium context with search frictions and competition. Such a model can help us understand a variety of facts about the low wage labor market: why similar workers are paid differently, why there is so much job-to-job mobility, and -- wait for it -- why minimum wage policies could have little in the way of disemployment effects. Indeed, in some cases, by compressing the wage distribution, minimum wage increases may actually improve the functioning of the labor market.

    In recent work with Michael Reich and William Lester (2011), we estimated the effect of minimum wages on separations and new hires, along with the effects on employment and wages. We find a striking pattern when we consider either a high-impact demographic group (teens) or a high-impact sector (restaurants): while the effect of minimum wages on employment is close to zero, both separations and new hires fall sharply in response to a minimum wage hike. As we then go on to show, this "trifecta" of results -- strong positive wage effect, close to zero employment effect, and strong negative turnover effect -- are a signature of a Burdett-Mortensen type model with a sizeable amount of search frictions. We estimate that the "labor supply elasticity" facing the firm falls in the 4 to 10 range, suggesting wages are about 10-20 percent lower due to employers' market power. While quantitatively our estimates of labor market power are in the lower range of Card and Krueger's suggestions, the qualitative importance of search frictions is borne out in the data with more careful work. And more recent firm-level studies, such as those surveyed by Ashenfelter, Farber and Ransom (2010) in an entire volume of the Journal of Labor Economics devoted to the issue of monopsony, have indeed found labor supply elasticities consistent with substantial wage setting power.

    Today, thankfully, we do not need a large positive minimum wage effect on employment to motivate the use of more realistic models of the labor market. The importance of frictions is borne out through many other types of empirical evidence -- including the extent of wage dispersion, especially for similar workers, or how turnover responds to minimum wage policies, to name a few. Many papers (e.g., Flinn 2006, Giuliano 2007 ) have looked at how minimum wage effects may vary when the labor market is characterized by search or information frictions. The fourth volume of Handbook of Labor Economics has an entire chapter by Alan Manning on "Imperfect Competition in the Labor Market." In that sense, Myth and Measurement was a harbinger of things to come.

    Standing the test of time is a challenge for any work, but especially so for a book that has elicited such vitriol from some corners of our profession. In another review of the book in Industrial and Labor Relations Review, labor economist Finish Welch had this to say: "I question David Card and Alan Krueger's models and how they do empirical research. Although the notoriety surrounding Myth suggests important conclusions that challenge economists' fundamental assumptions, I am convinced that the book's long-run impact will instead be to spur, by negative example, a much-needed consideration of standards we should institute for the collection, analysis, and release of primary data." Sixteen years later, it is safe to say that the book's long-run impact has not been on standards for collection, analysis and release of primary data. Instead, what has happened is that today, writing a paper arguing that moderate increases in minimum wage do not have any appreciable effect on jobs because the labor market exhibits search friction is not a conversation stopper or a career ender. On that count alone, Myth and Measurement should be considered a success.

    (1) Neumark and Wascher (2000) evaluated payroll records from restaurants from a sample that was in large part collected by the restaurant industry-funded organization Employment Policies Institute and found that the policy clearly reduced employment. However, as shown in Card and Krueger (2000) who used administrative UI records, this was likely driven by the selective nature of that payroll data.

    (2) The reason labor economists studying minimum wages have focused so much on teens is not because we think that the impact on teens is especially important from a policy perspective. Rather, the reason is because such a high fraction of teens (around a quarter) earn the minimum wage, making them the canary in the coalmine when it comes to detecting minimum wage effects. A similar logic applies to studying restaurant workers.

    Arindrajit Dube is an Assistant Professor in the Department of Economics at the University of Massachusetts Amherst.

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  • Zeroing in on Unemployment?

    Jan 17, 2011Arindrajit Dube

    jobless-man-150Debunking some recent explanations for the sky-high unemployment rate.

    Zero is so in these days. At least in the macro-economics blogosphere. So we now have a renewed discussion of "Zero Marginal Product" (ZMP) of labor as an explanation for the persistently high unemployment rate.

    jobless-man-150Debunking some recent explanations for the sky-high unemployment rate.

    Zero is so in these days. At least in the macro-economics blogosphere. So we now have a renewed discussion of "Zero Marginal Product" (ZMP) of labor as an explanation for the persistently high unemployment rate.

    Most flippantly, this is probably a macro-economic version of Godwin's Law.  If you talk about unemployment long enough, someone will eventually bring up marginal product being lower than the wage. Usually, it takes the form of blaming the minimum wage for unemployment: if wages could fall enough, employment would reach equilibrium, but the minimum wage prevents equilibration. (As it turns out, careful research on the minimum wage does not find a disemployment effect, even during high unemployment spells in the United States -- see forthcoming Industrial Relations, and for evidence on minimum wage more generally see here.)

    Somewhat surprisingly, then, the most recent discussion about ZMP seems to have bypassed the minimum wage and gone straight for the zero. Less importantly, I think there is a little bit of "zero envy" going on here -- wanting to promote ZMP as an alternative to the "zero lower bound" on interest rates as an explanation of our economic malaise. More importantly, I think the ZMP argument (as it has been made) is fraught with numerous logical difficulties. First, it has been suggested by Tyler Cowen that we can understand ZMP as labor hoarding -- in a world where firms don't actually hoard labor. I think this argument really gets it wrong.  Fundamentally, it confuses firm-level and market-level notions of marginal product.

    Labor hoarding occurs when a firm chooses to pay a wage above marginal productivity for a period of time because there are adjustment costs in hiring.  So a worker's marginal product at a particular firm may be lower than the wage, and yes, in some cases may be zero, though that's an extreme case. But the operative phrase is at a particular firm. It doesn't mean that the person's maximal marginal product (across all possible jobs) is suddenly really small. It just means that (say) Ford might keep a worker around even if production is at 50% of the usual rate because it's costly for them to let him go and then rehire someone else. If they were to let the new worker go, it's not the case that her marginal product at her next best alternative job is suddenly zero or really small.

    The second -- and more fundamental -- point is this. The marginal product of labor is not well defined in the presence of aggregate demand externalities. This is almost a tautology, and is true in any New (or old or Post) Keynesian model that I am aware of. The reasons are simple to explain.  Let's say I'm a restaurateur. I don't want to hire additional waiters because their marginal product is less than the wage I would have to pay them (whatever it may be -- including zero!). However, if other firms (say other restaurants,  grocery stores, department stores, etc.) all hired more people as well, then suddenly the marginal product of that server I was thinking of hiring just rose. And I might just hire her. This is the fundamental point in any model with aggregate demand externalities.

    I wrote a short paper 14 years ago (with Ethan Kaplan) on how such externalities may shape labor supply decisions and worker discouragement in the presence of heterogeneous labor. We showed how, in the presence of demand externalities, a wage subsidy (such as the Earned Income Tax Credit) financed by a tax on profits can be Pareto improving by encouraging the employment of workers who otherwise might (inefficiently) stay out of the labor market. In light of the healthy profits earned by US corporations these days, it is particularly useful to think about employment-friendly policies financed by profits. And the reason for that is not limited to "populist" sensibilities. There are "hard headed" rationales based on the desire to make our economy work better.

    But don't take my word for it -- the entire two-volume set of New Keynesian Economics is full of papers that imply that the marginal product of labor is a function of aggregate demand. Take as an example "Imperfect Competition and the Keynesian Cross" by N. Gregory Mankiw. Or "Monopolistic Competition and the Effects of Aggregate Demand" by Olivier Jean Blanchard and Nobuhiro Kiyotaki. So that makes me wonder -- what's the real explanatory power of the ZMP argument, when well-argued explanations show that the marginal product depends on fiscal and monetary policies?

    I think the question of why we are seeing high and persistent unemployment is terribly important. And we should welcome explanations of all sorts as we try to figure out the answers. However, I don't see an appeal to zero marginal product of labor a particularly enlightening explanation for our troubles.

    Arindrajit Dube is an Assistant Professor of Economics at UMass Amherst.

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