Wednesday, January 29, 2014

A Couple More Minimum Wage Regressions

I've done a couple more sets of regressions that take economic growth into account, and I have found very strong relationships.  The strongest relationship uses all three trends from each episode (pre-MW, MW, and post-MW).  It attributes a decrease of 3.6% in teen Employment-Population Ratio and 1.4% in total EPR to the implementation of the typical series of minimum wage increases.  Results below the fold:

Here is the graph of the Employment to Population Ratio.  In this version, I have added the trend of EPR for the 30 months after the MW episode.

Earlier Results from using only the MW periods

The earlier results were statistically significant for both teens and total EPR.  Those regressions just used 7 observations of the difference between the pre-MW slope and the MW period slope, cumulative over 30 months.

Coefficients were:

Teen EPR 0.62 -1.01
Total EPR 0.39 -0.57

In plain terms, for each 1% increase in the ratio of the Minimum Wage / Average Wage, teen EPR decreased 1% from the pre-MW trend and total EPR decreased 0.57% from the pre-MW trend over 30 months.  As can be seen in the graph above, there is a see-saw pattern, where EPR goes down in recessions and most MW episodes and goes up at other times, so this might be double counting, as the change in trend would reflect a change from a rebounding employment level to a declining employment level.

New Results from Using the change in trends for both the MW periods and Post-MW periods:

Dependent Variable:
Teen EPR, the difference in the slope of the trend, accumulated over 30 months.

Independent Variables:
MW/AW: The maximum change in the ratio of the minimum wage to the average wage from the beginning of the period.  For the post-MW periods, this will be zero.

RGDP: The 2 year change in real GDP for the period ending roughly 1 year after the beginning of the period defined by the dependent variable

Here are the results for Teen EPR:
Teen EPR Change in Trend

These are very similar to the results that only measured the change in EPR during the MW periods, with stronger significance for both the scale of the minimum wage hike and the F-stat for the complete regression.

And, remember, this is not just using a dummy variable for minimum wage hikes.  The scale of the MW hikes produces a more significant result.  Larger hikes are associated with deeper employment losses.

Here are the results for total EPR:
Total EPR Change in Trend

Again, this might be double counting, since we are measuring the change in trend between rebounding periods and declining periods.

Note, there are only 12 observations because I removed the 1976 episode, since the post-MW period was not free of new MW increases.

New Results from Using Trends from Pre-MW, MW, and Post-MW Periods

For this result, the dependent variable is just the slope for each period, not the change in slope.  Here we have 18 observations because we have 6 episodes, each with a pre-MW, MW, and post-MW period.  That should avoid the double counting.  The slopes of the non-MW periods will reflect some rebounding behavior in the EPR and the MW periods will reflect just the decline from the MW hikes.

Here are results:

Significance is very strong for both the variables and the complete regression.

For each 1% increase in the MW/AW ratio, teen EPR decreases by 0.42% and total EPR decreases by 0.16%, cumulative over 30 months.

If we use a dummy variable for the minimum wage increases, the average minimum wage episode is associated with a 3.6% decrease in teen EPR and a 1.4% decrease in total EPR, cumulative over 30 months.  (Note that since EPR is generally around 50% in these populations, the reduction in employment is roughly twice these levels.  Or, put another way, if all of the job losses were reflected in increased unemployment, the increase in the unemployment rate would be roughly double the decrease in EPR.)  As with the other regressions, incorporating the scale of the MW hikes increases the significance of the MW variable and the regression.

Here are graphs of actual EPR trends for each period, compared to the trends predicted by the model.  As can be seen in the graphs, the errors are generally balanced among the three groups of time periods.

Both variables, individually, have a significant correlation with employment over these 18 periods, but the significance is improved when combined.

A signal that the minimum wage is a strong factor here is that when the EPR slopes are regressed against the independent variables, individually, the errors from the RGDP regression are heteroskedastic.  They overestimate the EPR trend during the MW periods.  The MW regression, on the other hand, has errors that are not extremely different among the three periods.  A graph comparing the average errors within each subgroup for each variable is shown here. (This is for Teen EPR.  The pattern is similar for total EPR).

Thanks to everyone for the feedback on the original graph that led to all of this.  Please comment if you see any issues with the current post.

Since this is such a small data set, I am attaching it below.  This is the data for Teen EPR for the last regression:

  Teen Regression with all 3 periods
  Teen EPR Trend MW/AW%ch 2 yr RGDP
1956 2.77% 0 9.1%
1961 -1.03% 0 5.4%
1967 8.71% 0 11.0%
1990 1.87% 0 6.1%
1996 -0.47% 0 6.6%
2007 -0.16% 0 4.4%
1956 -5.15% 13.0% 6.2%
1961 -2.63% 7.5% 8.8%
1967 -0.21% 9.4% 6.6%
1990 -7.34% 7.5% 1.9%
1996 2.31% 5.8% 8.7%
2007 -7.53% 9.4% 2.0%
1956 1.34% 0 5.6%
1961 5.01% 0 11.4%
1967 -3.58% 0 3.4%
1990 3.25% 0 6.8%
1996 -1.18% 0 9.8%
2007 -0.42% 0 3.6%

This is the data for total EPR:
  Total Regression with all 3 periods
  EPR Trend MW/AW%ch 2 yr RGDP
1956 2.57% 0 9.1%
1961 -0.96% 0 5.4%
1967 1.87% 0 11.0%
1990 1.54% 0 6.1%
1996 0.25% 0 6.6%
2007 0.90% 0 4.4%
1956 -2.11% 13% 6.2%
1961 0.00% 7.50% 8.8%
1967 0.73% 9.40% 6.6%
1990 -2.16% 7.50% 1.9%
1996 0.91% 5.80% 8.7%
2007 -4.54% 9.40% 2.0%
1956 0.92% 0 5.6%
1961 1.31% 0 11.4%
1967 -2.14% 0 3.4%
1990 1.65% 0 6.8%
1996 -0.19% 0 9.8%
2007 -0.08% 0 3.6%

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