Tuesday, May 27, 2014

Revisiting Minimum Wage Workers as a Portion of the Labor Force

Here was my last post on this issue.  The post included this graph:


My point was that this historical relationship seemed pretty linear and stable, and for the number of workers at $10.10 or less without a binding minimum wage to be twice the number that there are with a binding minimum wage, there would have to be significant distortions in the labor force, probably including measurable disemployment.

Menzie Chinn, at www.econbrowser.com looked at the relationship here.  Using Durbin-Watson and other tests, he found that the correlation could be spurious because of a lack of stationarity.  There is a trend break at Minimum Wage levels below about 27% of the Average Wage (MW/AW), which I think is because the legal minimum begins to fall below the natural minimum wage in that range.  But, cutting the data off before 2001 doesn't seem to help much on the Durbin-Watson test.

So, clearly, there is a positive relationship between these ratios, but the coefficient (shown as .30 in the graph) may be suspect.  Because of Dr. Chinn's input, I also looked again at the EPI data that I had originally referenced, and realized that there was updated data as well as a couple of additional data points that I could add to the graph.

I looked at the same data from my original post, but as annual changes instead of as levels over time.  Residual autocorrelation and stationarity aren't issues in this data if we use yearly changes instead of levels.  Here are graphs of the annual changes over time and scatter plots of the annual change in the ratios.  The first scatter plot is of the entire period.  The second scatter plot is of the period 1981-2001.  This cuts out the period after 2001 during which the legal MW was too low to exert typical influence and 1980, which is an outlier.  Culling the data down to this period pulls the slope coefficient up to .378.

The final, large graph below compares historical MW employment with (1) the estimated level of MW employment using the coefficient from the yearly changes, (2) the estimated total number of MW workers plus workers not employed due to the MW (based on my estimate of a loss of 0.26% in total employment for each 1% increase in the MW/AW ratio), and (3) three EPI estimates of the number of workers at or below their proposed MW levels in 2014, 2015, and 2016.

EPI assumes no job loss (and, in fact, some job gains), so I would interpret the difference between the EPI estimates of MW workers and my estimate of the number of workers as a combination of:
(1) Job losers captured by my estimate.
(2) Job losers not captured by my estimate.
(3) Workers currently under the EPI proposed MW levels who would have new wage levels slightly above the MW after implementation.
(4) Job gains incorrectly assumed by EPI.

This is not an exhaustive list, but these seem like an obvious starting point.  Of course, there is a possibility that I have over-estimated the job losers, and there are other explanations for the gap.

If I understand him correctly, Dr. Chinn believes that there has been a shift in the distribution of low wage workers, so that, even though the coefficient of the slope of this relationship appears to have been below 0.5 in the past, it is currently much higher.  In other words, an increasing MW level will sweep up many more workers than it had in the past.  So, he sees the relationship implied from the EPI estimates of an increase of about 1% in the MW workers/Total Labor Force ratio as a reasonable possibility of the number of workers who would be working at a minimum wage for each 1% rise in the ratio of MW/AW.

It seems possible that this thesis could be tested now, if there is a set of data somewhere that compares the distribution of wages today with the distribution of wages in about 1989.  The minimum wage was in the same ballpark then as it is today, as a percentage of the average wage, so if there had been an exogenous shift in wage distribution, a comparison of those two sets would be informative.

But, what I think might be the most interesting aspect of this is how our priors feed into our interpretations of events in complex ways that prevent the data itself from creating an agreed upon measure.

To me, this graph is predictable.  I would expect MW legislation to create disemployment.  So, if we are measuring the number of workers earning less than 35% of the average wage, I would expect to see many more of them when the MW/AW ratio is only 25% than when the MW/AW ratio is 35%.  So, the EPI estimates seem fairly predictable to me, and the question comes down to how much will employment at the new MW level decrease as we raise the MW to that level - a question which this basic analysis might begin to crawl toward.

To someone who doesn't think that MW legislation creates disemployment, the number of workers earning 35% or less of the average wage should be relatively unchanged in any context where the MW/AW ratio is at or below 35%.  So, a large increase in low wage workers that just happened to coincide with a decreasing MW/AW level would appear to be an exogenous change to the labor market.  Since the decreasing MW level wouldn't seem like an explanation for increasing low wage employment, this increase in low wage employment would be bad news.  It would signal that wages are becoming more inequitable, divided between upper and lower classes.  It would signal an economy only creating low-wage, low-quality working opportunities.  These exogenous changes in the labor market would mean that many more workers would be affected by an increase in the minimum wage, and since the minimum wage would, on net, be beneficial to low wage workers, this would be a compassionate policy to implement, as a response to the shifting distribution of wages.

This seems like an issue that could finally be settled empirically, but previous federal increases in the minimum wage have, unfortunately, coincided with apparently exogenous labor crises.  This has happened with such regularity that we can't rule out the fact that Congress' motivation to increase the minimum wage is somehow correlated with some third variable that correlates both with Congress' motivation for raising MW and with labor crises.  After 60 years of this pattern, it seems unlikely to change, whether the minimum wage is the cause of job losses or not.  Of course, if I thought MW hikes were defensible, I would still recommend them as a policy prescription.  I would feel a duty to support positive policies, and Congress' knack for bad timing would be a problem for someone else to solve separately.

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