Monday, November 4, 2013

Deeper into the Minimum Wage

I've worked some more at digging into the numbers.  First, here is an excellent breakdown at Political Calculations.  Also, Tyler Cowen linked to a study which suggested that the negative employment effects of minimum wages were not all felt immediately, but over time through slower hiring.

So, I kind of kicked around the data a little bit, and it looked to me like the strongest correlation was at about 6 to 12 months after minimum wage legislation took effect.  However, many of the instances where minimum wages have been increased have been in serial yearly steps, so the timing effect could just be a reflection of the fact that many episodes where the minimum was raised would have seen another boost 12 months later.  In fact, several problems with finding any trends in the data include:
  • Many cases of serial implementation on an annual schedule.
  • The 1970s, where high inflation led to a series of minimum wage increases that were merely reflections of a higher cost of living.
  • Employment volatility is very high in teens and declines as age increases, apart from minimum wage effects.
  • Minimum wage, even if the effect is significant, only accounts for a very small percentage of changes in employment over time.
I have tried to work around these issues by looking specifically at the 19 instances of federal minimum wage hikes, and the behavior of employment around them.  The period of time after an initial minimum wage hike experiences falling employment more than twice as often as in normal times.  Either Congress has had exceedingly bad luck in the timing of MW hikes, or they are causing real damage to labor markets.  In trying to answer that question, I find, (1) a distinctive pattern of employment decline among teen workers associated with MW hikes and (2) a pattern of employment loss that appears to scale with the size of the MW increase, with the caveat that we are necessarily looking at very few separate instances.

More below the fold.

I will use the following methods to try to parse out the employment effects of the MW increases:

1) I measure MW changes as a proportion of the average wage (AHETPI after 1963 and a substitute measure before then) to neutralize inflation and labor market fluctuations.

2) In the 1970's, there were a series of nominal MW hikes which did not collectively raise the MW in real terms.  I removed this period from the data in order to retain a data set with a clear divide between periods with a rising real wage floor and a falling real wage floor.

3) I detrend changes in employment.  This simple method doesn't rid us of generational fluctuations, but gets rid of most of the bias from long term trends, which appear to be fairly stationary.

4) I will group each month from 1954 to 2013 into 3 categories:
  1. Months that are not within 2 years after a MW hike.
  2. Months within 2 years after any MW hike that occurs at least 2 years after any previous hikes.
  3. Months within 2 years after any MW hike that occurs within 2 years of a previous hike.
The serial nature of the MW hikes, and their character in the 1970's as merely inflation adjustments, are visible in the following chart:

After removing the 1970's data, the number of months in each category, and the % of months with negative trailing 6 month employment growth are:

% Negative No. of Months Period
Group 1     28.60% 371   no MW
Group 2     63.10% 168 <2yr after 1st hike
Group 3     33.70% 83  <2yr after followup hikes

I think we can get an idea of the effect of MW increases on changes in employment by looking at the following effects:
  1. I will compare the behavior of teen employment to total employment for each group.  Since MW is a supply shock to low wage labor, it is mostly felt by teenage workers, and this should show up in Groups 2 and 3.
  2. I will compare the detrended employment trends for each group.
  3. I will measure the effect of the scale of the MW increase on employment levels.  If the effect on employment correlates well with the scale of the increase, and if coherent behavior between the month groups correlates to the scale of the MW increases, this will suggest that MW is effecting employment levels.
  4. I will review the employment change over time during the individual MW hike episodes.

1) Effect on Teen Employment
The graph below compares the behavior of the three groups of months.  Changes in employment have been detrended, so for the set of all months, the linear trendline would intersect the origin, with the high positive slopes shown here, since teen employment (on the y axis) is more volatile.  The periods have been increased to 6 months in the second graph in order to see the trends better.
The red months are after initial MW hikes.  When total employment is at trend, Teen Employment activity is below trend after MW hikes and above trend when there have not been hikes.  Since MW laborers are heavily teen, we can measure part of the effect of MW hikes as a shock to teen employment, relative to total employment.  (After the most recent series of hikes, 25% of teen hourly workers were working at or below MW, compared to 6% of hourly workers in total.)

The data does show a strong negative correlation between MW hikes and teen employment.  The measured scale of the relative growth in teen employment is:
  • Group 1: +.093% (+.54% over 6 months (rolling))
  • Group 2: -.142% (-.71% over 6 months (rolling))
  • Group 3: -.095% (-.51% over 6 months (rolling))
Adjusted standard errors for the alphas are about .07% for the monthly data and between .25-.3% for the 6 month data.  So in the 6 month data, even based on this broad categorization of 2 year periods, a negative relative correlation of teen employment to changes in MW has p<.025 for Group 1 and p<.05 for Group 3.  And p<.025 for Group 2 for both 1 month and rolling 6 month data.

The placement and slope of the trend lines make intuitive sense.  Group 2 should have the most relative effect on teen employment.  Since group 3 includes many smaller hikes and would include expectations of returning to a group 1 context, it has a negative effect, but smaller.  Group 1 has a positive effect, because, as seen in the chart above, when the MW is level in nominal terms, it is decreasing in real terms, so there would be a slow positive supply effect.

In months where total employment is declining excessively, business cycle effects would overwhelm MW effects in a Group 2 environment, but in a growing labor context, MW effects would dominate, so we see a slightly lower slope in the Group 2 trend.  In the Group 3 context, a bullish labor environment would allow teen employment to recover more rapidly, so the slope there is slightly steeper.

So, as a first estimate, we should be able to say that initial MW increases of an average scale in a typical labor market, are responsible for a swing of -5.6% in teen employment, compared to total employment ((.093%-(-.142%))*24 months).  There is a significant shock to teen employment coincident with MW increases.

In other words, even if all the negative effects on total employment were a result of unlucky timing, this would suggest that MW hikes would at least create a demand shock for teen employment of this amount.

If we divide Group 1 into Group 1A (periods completely unrelated to MW hikes) and Group 1B (Periods 2-4 years after a final MW hike), the intuition remains intact.  The Purple line represents Group 1A, which roughly intersects at the origin, and where for each percentage gain or loss in total employment, there is about a 1.6% gain or loss in 16-19 year old employment.  After a MW hike, 16-19 year olds suffer relative job losses across economic outcomes (red line).  In subsequent MW hikes, if the economy begins to recover before the 2 year period ends, 16-19 year olds can see some catch-up employment recovery, coming out of the MW hike shock, but in a poor economy, they continue to fair much worse.  As time passes beyond 2 years from the last MW hike, this teen labor sensitivity to economic conditions continues, but to a lesser degree, as inflation pulls the de facto MW back down, and employment behavior settles back into long term trends.

Separating the Group 1 months into these two subgroups illuminates a couple of points.  The graph here illustrates the basic question for MW policy.  In a perfect market, laborers to the left of the red line would be unemployed and laborers to the right of the red line would be employed.  MW proponents must argue that labor markets are inefficient, so that in practice, the maximum market clearing price for low wage workers tends to be much higher than the paid wage.  As the red line moves to the right, wages for almost all workers would rise with the price floor.

(1) My data suggests that after the MW becomes elevated (the red line moves to the right), many MW workers cease to be employed.  After the MW hikes stop, inflation causes the red line to move slowly back to the left.  Group 1B represents this period of time, where MW workers would be priced back into the labor force.  Group 1A represents a labor context where inflation has had enough time to move the red line far enough to the left that very few workers would voluntarily labor for a lower wage (the portion of the graph where the blue line is nearly horizontal), so the MW price floor not a large factor during these periods.

2) During the Group 1A (non-MW) period, r-squared is .24.  During and after MW hikes, r-squared spikes to the .4-.49 range.  During these times, MW becomes a significantly more important factor in employment growth.

Both of these findings, together with the statistically significant decrease in teen employment after MW hikes, suggest that low wage labor markets are efficient enough to see measurable negative shocks in teen employment as a result of the MW price floor.

2) Compare Trends among groups
Here is a table showing the detrended average monthly change in employment for each group:
Here are the numbers for rolling 6 month periods:
If we make the conservative assumption that MW hikes only effect teen unemployment, the previous step suggested that we can attribute about half of the change in teen employment shown here to MW hikes.  Over two years, that amounts to a swing from Group 1 to Group 2 of -5.6%.
In the next step, I will review the behavior of employment through different episodes to estimate how much of the employment effects in the other age groups and the remaining effect in the teen age group might also be attributed to MW hikes.
As an aside, we can see here the same effect that popped up in my previous post on MW, where the effect of MW appears to diminish in the older age groups, except that it is slightly weaker in the 20-24 age group, which I had speculated might be the result of a substitutional relationship between the 16-19 age group and the 20-24 age group, with out-of-work young adults picking up jobs where teens have been priced out of the labor force.

Again, if we add an additional 2 year period after the last in each series of MW hikes, we see some age-related employment behaviors: 
For total employment, there has been an average decline in employment of about -.67% for the 2 years after a MW hike (for a total decline of -2.68% over 2 years), relative to periods with no MW changes.  The labor demand shock slowly declines until it returns to the previous growth rates.  For 16-19 year olds, there is a very large initial shock of -2.12% every 6 months for 2 years, totaling a drop from trend of 8.5%.
For 20-24 year olds, the trends over the time after a MW hike follow a similar path to 16-19 year olds, but at higher levels.  In fact, relative to periods not associated with MW changes, 20-24 year olds see net growth in employment after MW hikes.  Two likely causes are:
1) A substitution effect between 16-19 year olds and 20-24 year olds.  Some employers, forced to raise wages, might be able to salvage their business models by substituting more productive older workers.  A weaker effect may be at work for 55+ workers.  This is easily imagined in, say, low end retail, where a business with an equilibrium labor pool that consisted of low-productivity teens, when forced to increase wages, would mitigate those costs by hiring 20-24 year olds or retirees who are more dependable and productive.
2) A substitution effect between higher education and work.  There could be a tendency for more 20-24 year olds to enter college during times when wages are low and more entry level jobs are claimed by 16-19 year olds; and 20-24 year olds might tend to remain out of college during high MW episodes, when they might see higher wages and less competition from teens.
If this is the case, then I was wrong in my earlier post, where I speculated that a higher minimum wage could send unemployed young workers to more schooling in an effort to raise their wage demands.  This analysis suggests that a higher minimum wage might actually reduce enrollment in higher education by drawing 20-24 year olds into the labor force.  This would be one aspect of the minimum wage that would be a net benefit.  As Bryan Caplan has argued, much higher education is probably an unproductive arms race of signaling.  It is also possible that laborers willing to take minimum wage jobs would have been more likely to fail to complete a degree program.  (Their acceptance of such employment could be a reflection of their expectations in this regard.)

Or, considering the high proportion of MW jobs that are part time, students may simply be substituting work for other forms of school financing, or they may be reducing their class load in order to defray school expenses with new employment opportunities.
3) Effect of the scale of MW Increases
I used the trailing 2 year change in MW/AE as the minimum wage measure, and trailing 6 month detrended changes in employment as the employment measure.  I confirmed that the MW/AE measure that I used does not smuggle in a business cycle effect.
I correlated the 6 month change in employment with the 2 year change in MW/AE.  If MW had no effect on employment and the historical numbers from step 1 above were purely an artifact of bad timing from Congress, we would see flat trend lines for all three groups.  Groups 2 & 3 would show below trend employment growth and Group 1 would show above trend employment growth.  If there was no "poor timing" effect, and all of the measured decline in employment during periods of MW hikes could be statistically attributed to the MW, then we would still see a flat trendline for Group 1.  Group 3 reflects a number of factors, so its trendline would be less predictable.  The trendline for Group 2 would have a negative slope, with the worst employment declines coming during large changes in MW/AE.  It would intersect the origin, and if the relationship was fairly linear, the extended trendline would intersect the mean value point of Group 1.  This would reflect a context where employment recovered as the the real MW decreased through inflation and suffered proportionately to changes in MW.
Surprisingly, this appears to be just what we find, suggesting that all of the negative consequences of MW hikes described above can be attributed to MW.  This is a little bit shocking, since it would mean that the typical initial MW hike has decreased total employment by about 2 1/2% compared to trend and has decreased teen employment by nearly 10% compared to trend over the 2 year period following the MW increase.  These correlations are surprisingly similar to the total employment effects in Step 2 above that didn't take scale into account.  Here is the graph of Total Employment to MW/AE:

The trendline for Group 2 reflects a decrease of 1% in employment over 6 months for every 10% increase in MW/AE.  The trend line intersects very near the origin.  The mean values for Group 1 are a change of -2.87% in MW/AE and a gain of .18% in employment above trend.  The Group 2 trendline would predict a gain of approx. .3% in employment given a change of -2.87% in MW/AE.
I have left the Group 3 data points from the 1970's in this graph, to show the two distinct periods - months in the late 1970's when minimum wage increases should have had little effect because they were not even adjusting for inflation are to the left of the y-axis, and true follow-up serial MW hikes from other periods are to the right of the y-axis.  A coherent trendline is less clear here, but as the polynomial trend line demonstrates, the months on the right tend to correlate with Group 2 and that correlation breaks down as data points drift to the left.  This is what we would expect if MW was the driving force here.
Believe it or not, this analysis probably understates the effect. First, there appears to be a slightly negative relationship between two year changes in AE and 6 month changes in employment.  This is evident in the above graph in the slightly upward sloping trend for the Group 1 months (because AE is in the denominator of the independent variable).  Possibly, the MW hike itself could be causing a statistical rise in average wages.  So, there might be a naturally upward slope to the trendlines before factoring in MW employment effects.  Also, as can be seen in the individual data points, there is a clear serial pattern during each MW hike episode.  I will show later that this represents a nadir around 6 to 12 months after the MW hike.  So, my broad measure here of just averaging the effects over 24 periods (which actually reflects some of the period just before the MW hike, since I am using rolling 6 month employment data) will tend to include some periods slightly before the hikes and some periods nearly 2 years after the hikes with less negative employment results.  Adjusting for the first effect would lower the trendline slope and adjusting for the second effect would lower the trendline level.
Here are the results, by age group.  I will only show the mean value for Group 1, the data points for Group 3, and the data points and trendlines for Group 2.
The apparent substitution effect between the 16-19 and 20-24 age groups shows up here.  It looks like this effect is strong enough to boost 20-24 employment in both Group 2 & Group 3 at smaller MW hikes, but as the scale of a MW hike increases, it appears to effect both age groups similarly.  When the two age groups are merged, they appear similar to the others, but with a steeper relationship between changes in employment and MW increases:
So, we have behavior across age groups that is remarkably consistent with our expectations if all of this unemployment was the result of MW increases.  A strong effect among the young that becomes less important as age increases except for a slight reversal at 55+. 
4) Change in Employment Over Time During MW Hikes
Of the 19 MW hikes since 1956, there are three distinct categories, as mentioned previously.
There are 6 MW hikes from 1975 to 1981 of 7% to 15% that roughly match the high level of inflation at the time.  There is no systematic correlation between employment and MW hikes during these episodes.
There are 7 MW hikes (1956, 1961, 1967, 1974, 1990, 1996, 2007) of 12% to 33% that introduce a higher MW alone or as the first in a series.  These are the Group 2 episodes from above.
There are 6 MW hikes of 8% to 14%, 5 of which end a pair or series of hikes (1963, 1968, 1991, 1997, 2009) , and one (2008) that is in the middle of a series.
 The average employment behavior, by age group, of the 7 Group 2 (initial MW hikes) episodes is shown here:
In these graphs, the employment behavior is broken into 6 month periods.  The MW hike is implemented at the beginning of the 6m+1 period.  For the 7 distinct MW hike episodes, the fall in total employment, coincident with the MW hike is evident, peaking in the 6 to 24 months after the hike.  Also, the graph shows the initial steep shock in the 16-24 age group, which begins to swing positive after 18 months.  The red and green lines show the separate 16-19 and 20-24 age group behaviors, with most of the employment shock hitting the 16-19 year olds.
The next graph shows the continued employment behavior during the period of the final MW hike during the episodes where more than one serial hike was implemented.  The graph shows the drop in employment coming out of the initial MW hikes, in periods 6m-2 and 6m-1.  Then, after the final MW hike (between 6m-1 and 6m+1), we see total employment recovering back toward normal growth levels.  This comes at first from old and young workers, as they continue to substitute for teen workers.  Then, as that effect subsides, teen employment starts to recapture its losses as employers prepare for a new period where inflation pulls the MW levels back down over time.  During this time, employment of middle aged workers continues to fall slightly, relative to trend.  In the following months, middle-aged employment growth rates will slowly recover to normal levels.

The cumulative loss in employment, relative to trend, over 4 years after a typical MW hike, has been about 3%.  Rough regressions against unemployment versus employment data suggest that about 1/3 of this loss registers as unemployment and about 2/3 registers as exits from the labor force.  This is plausible, since most MW jobs are part time or marginal.
It seems possible to me that if half of the initial shock to teen employment could be attributed uniquely to the MW hike, that the effect on complementary jobs, consumption, and other feedback could contribute to the negative shocks that show up across age groups, associated with MW hikes.  Some of the subsequent job losses among the older age groups could, therefore, be from higher wage jobs.
In the recent crisis, the number of workers at MW rose from 2% to 6% over 4 years, resulting from an increase in the real MW of about 35%.  If 3% of workers were lifted from the new MW level over those four years by performance raises unrelated to MW and if 3% of workers left the employment rolls due to the MW hike, then a total of 12% of workers would have been affected by the MW hikes over that time.  That would mean that only 1/4 of them would have lost their jobs as a result of the MW hike, and only 1/3 of those might be categorized as unemployed.  In other words, only 1/12 of affected workers would become officially unemployed, but the MW hikes would have had a significant impact on the production and total employment levels of the economy.
These numbers seem plausible to me, and they also could plausibly lead to some macroeconomic labor market shocks, as outlined above.  On the other hand, these are only 7 episodes and there are many factors that influence the labor market.  All in all, though, theory and experience should call for a significant bearish shift among investors the next time a significant minimum wage hike is planned.

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