WHEN IS A GOOD TIME TO RAISE THE MINIMUM WAGE?

WHEN IS A GOOD TIME TO RAISE THE MINIMUM WAGE? SAMUEL M. LUNDSTROM I analyze changes in the target efficiency of the federal minimum wage over the past 25 years. Using static simulation methods I find that minimum wage target efficiency is currently close to its 25-year peak of the total monetary benefits generated by a 12% increase in the federal minimum wage, 16.8% would flow to workers in poverty. This exceeds the least target efficient year over this period by 4.7 percentage points and is only 0.6 percentage points below the peak. Furthermore, I find a very strong positive relationship between minimum wage target efficiency and the real federal minimum wage. The implication is that, from an efficiency standpoint, a good time to raise the minimum wage is when it is already high. This discovery raises the possibility that the minimum wage increases the employment of low-skilled poor individuals relative to the employment of low-skilled non-poor individuals. Moreover, this discovery may bolster the rationale for an indexed minimum wage whereby it is prevented from falling to less efficient levels. (JEL J21, J31, J38) I. INTRODUCTION The minimum wage is widely viewed by critics and advocates alike to be an inefficient form of income redistribution. 1 Regardless of whether or not the minimum wage is efficient, it is, nevertheless, an enduring policy at both the state and federal level. Given that it is almost certainly here to stay, it is important for policy makers to understand how to make the most effective use of minimum wage policy. Among the many questions faced by those who are tasked with minimum wage policy is the question of timing. Several economic and labor market changes have I am grateful to David Neumark, Marianne Bitler, Damon Clark, and Greg Duncan for helpful comments on this project. I am also grateful to two anonymous referees for their helpful comments and suggestions. Finally, I am grateful to the University of California, Irvine for supporting me in my research. Lundstrom: Department of Economics, University of California-Irvine, Irvine, CA 92697-5100. Phone 801-656-5421, Fax 949-824-2182, E-mail slundstr@uci.edu 1. Even Card and Krueger, whose work on the employment effects of the minimum wage is frequently cited by minimum wage advocates, acknowledge that the minimum wage is evidently a blunt instrument for redistributing income to the poorest families (Card and Krueger ). A primary reason for the inefficiency of the minimum wage is that the vast majority of low-wage workers are not poor, a fact first documented by Gramlich (1976) and confirmed in a number of later studies (e.g., Burkhauser and Sabia, ; Congressional Budget Office 2014). occurred in recent years which suggest from an efficiency standpoint, at least that now might be a good time to raise the minimum wage. First, since the late 1990s the teen employment rate has fallen precipitously. In, 42% of teens aged 16 19 were employed. By 2014, this figure had fallen to 26%. 2 Since teens make up a significant share of low-wage workers, and a larger share of non-poor low-wage workers, a reduction in teen employment could improve minimum wage target efficiency. 3 Second, since the poverty rate among low-skilled individuals has increased substantially. In, 19.1% of low-skilled individuals (individuals with less than a 12th grade education) lived in households with incomes below the poverty line. By 2014 this figure had risen to 23.1%. 4 If the household income of minimum wage workers near the 2. Estimated using data from the March Current Population Survey. 3. In, 28.6% of low-wage workers (those earning less than half the median wage) were teens aged 16 19. Only 8% of these workers were in households with income below the poverty line. Based on March CPS. 4. These calculations are derived from the March CPS for the respective years. ABBREVIATIONS CBO: Congressional Budget Office CPS: Current Population Survey Contemporary Economic Policy (ISSN 1465-7287) Vol. 35, No. 1, January 2017, 29 52 Online Early publication February 22, 2016 29 doi:10.1111/coep.12169 2016 Western Economic Association International

30 CONTEMPORARY ECONOMIC POLICY poverty line falls, these workers might be pushed into poverty, thereby improving target efficiency. In this study, my objectives are to: (1) determine how the target efficiency of the federal minimum wage has changed during this period of declining teen employment and increasing poverty and (2) determine whether, in general, the teen employment rate or the poverty rate are good predictors of minimum wage target efficiency. This is done by examining how closely changes in target efficiency correlate with changes in teen employment or with changes in the poverty rate. I then consider other possible correlates of minimum wage target efficiency. Using data from the March Current Population Survey (CPS) for the years 1990 through 2014, I find that the target efficiency of the federal minimum wage is currently near a 25-year high. Evidence from a static simulation implies that of the total monetary benefits generated by a 12% increase in the real federal minimum wage, 16.8% would flow to workers in poverty. This exceeds the least target efficient year over this period by 4.7 percentage points and is only 0.6 percentage points below the peak. I find fairly weak relationships between the teen employment rate and minimum wage target efficiency and between the poverty rate and minimum wage target efficiency. However, I find a very strong positive relationship between minimum wage target efficiency and the level of the real federal minimum wage. This is surprising because, given the positive relationship between the skill and income distributions, we expect the minimum wage to better target poor workers when it is low. The implication is that a good time to raise the minimum wage from an efficiency standpoint, at least is when it is already high. This discovery raises the possibility that the minimum wage increases the employment of low-skilled poor individuals relative to the employment of low-skilled non-poor individuals. Furthermore, this finding could bolster the rationale for indexing the minimum wage, whereby it is prevented from falling to less efficient levels. II. LITERATURE REVIEW Neumark and Wascher () provide a thorough review of the literature concerned with minimum wage target efficiency. The first of these was conducted by Gramlich (1976). Gramlich simulated an increase in the 1973 federal minimum wage, assuming no behavioral or general equilibrium effects. He found that only about half of the total benefits would flow to workers with family incomes below the median. Since the Gramlich (1976) study, a number of other papers have conducted similar simulation-type analyses of the target efficiency of the minimum wage (e.g., Burkhauser and Sabia, ; Congressional Budget Office 2014; Horrigan and Mincy ; Johnson and Browning 1983). Many of these newer studies attempt to improve upon the Gramlich approach by accounting for employment effects and other relevant parameters in their simulation models. However, in general, these studies do not allow model parameters to vary across the income distribution. As an analysis of minimum wage target efficiency relies on identifying differential impacts across the income distribution, it is not clear that these more complicated models provide additional insight on target efficiency. A notable exception is the recent report issued by the Congressional Budget Office (CBO 2014). They include a disemployment effect in their model that varies by worker age, and they account for changes in prices and business profits, all of which have distributional consequences. However, in many cases the parameter values imposed on their model are crudely approximated, due largely to the lack of reliable estimates in the literature. 5 In the simulation conducted here, I opt to follow the more simple Gramlich approach, ignoring any behavioral or general equilibrium effects. I do this for two reasons. First, since there is no consensus with regards to the employment effects of the minimum wage, it is not clear how the model should be adjusted to account for behavioral responses. 6 Second, while more complex simulations, as in the CBO study, are extremely valuable, there is also value in a static analysis as it provides a type of best-case scenario for minimum wage changes. III. SIMULATION METHODS The simulation methodology employed here loosely follows Burkhauser and Sabia 5. An example is the imposition of a minimum wage employment elasticity for adults that is one-third the size of the teen elasticity. Since there are few estimates of the minimum wage employment elasticity for low-skilled adults, the chosen value appears to largely be based on a theoretical prediction rather than an empirical estimate. 6. To see the current state of the minimum wage debate see, for example, Dube, Lester, and Reich (), and Neumark, Salas, and Wascher (2014).

LUNDSTROM: WHEN TO RAISE THE MINIMUM WAGE? 31 (, ; hereafter BS). Instances where my approach differs from BS s approach are made explicit throughout this section (in the footnotes). These differences are also summarized in the Appendix Table A1. In addition, in the Appendix Table A2, I replicate BS s results, then illustrate how the simulation results are changed using my approach. For the simulations, I postulate that in each year from 1990 through 2014 the federal minimum wage was higher by a fixed percent than it actually was. The sizes of the minimum wage increases used in these simulations are based on historical means. Since 1990, the federal minimum wage has increased seven times. The mean increase was 11.7% and the range of increases was 8.4% 13.6%. With this in mind, the static calculations are based on simulated increases in the federal minimum wage of 8%, 12%, and 16% in each year from 1990 to 2014, thereby covering a range that exceeds somewhat the historical norms. 7 Furthermore, the 12% increase roughly matches the first phase of a proposal by House Democrats to raise the federal minimum wage from its current level of $7.25 to $10.10. The Fair Minimum Wage Act (H.R. 1010) proposes that this increase take place in three steps of $0.95 each (the first $0.95 increase represents a 13.1% increase in the federal minimum wage from its 2014 level). 8 The simulation conducted here is static, assuming no behavioral or general equilibrium effects. Furthermore, it is assumed that the simulated minimum wage increase only affects the wages of workers who are directly affected by the increase. A directly affected worker is defined as one whose hourly wage falls between $0.05 less than the prevailing minimum wage (i.e., the higher of the state or federal minimum wage) and the new federal minimum wage. 9 In 7. Burkhauser and Sabia do not simulate the same percentage increase in each year. Rather, they simulate minimum wage increases that match proposed increases. In they simulate an increase from $4.25 to $5.15 (21%); in they simulate an increase from $5.15 to $7.25 (41%); and in they simulate an increase from $7.25 to $9.50 (31%). While there is merit in simulating minimum wage hikes that match proposed increases, it makes cross-year comparisons difficult since efficiency calculations are sensitive to the size of the simulated increase. 8. The full text of H.R. 1010 can be accessed at the following website: http://democrats.edworkforce.house.gov/ sites/democrats.edworkforce.house.gov/files/documents/ FairMinimumWageAct-BillText.pdf. 9. Burkhauser and Sabia define a directly affected worker as a worker whose wage falls between some amount (the amount varies from simulation to simulation) less than the other words, if the prevailing minimum wage is $7.25 and the new federal minimum wage is $8.20, only those workers earning between $7.20 and $8.20 are assumed to experience a wage increase. During the time period covered in this study, many states adopted minimum wages that exceeded the contemporaneous federal level. Observations from those states where the prevailing minimum wage exceeds the federal level will experience a simulated increase in the minimum wage that is less than the simulated federal increase. In some instances the prevailing state minimum wage exceeds even the simulated federal level, meaning that no observations from those states will be included in the sample for those time periods. I test whether my conclusions are sensitive to this restriction by performing the analysis again using observations only from states that are fully bound by the federal minimum wage over this time period. The advantage of this latter approach is that the same set of states is represented in each year. The disadvantage is that it fails to accurately represent the set of states that would be impacted by an increase in the federal minimum wage in each year. The simulation is performed in two steps. First, the annual benefit received by each directly affected worker is calculated as the product of his wage increase (due to the simulated minimum wage hike), his usual weekly hours, and his annual weeks worked. Second, minimum wage target efficiency is determined by identifying the total share of annual benefits that flows to poor workers. A worker is defined as poor if his income-to-needs ratio the ratio of total household income to the household size adjusted poverty level is less than one. IV. DATA Data are drawn from the March CPS, outgoing rotation group files for the years 1990 2014. These data are ideally suited to the present study since they provide detailed information on individual wages and household income. Observations are included for individuals aged 16 64 from all 50 states plus the District of Columbia who are determined to be directly affected by an increase in the federal minimum federal minimum wage and the simulated federal minimum wage. This approach does not account for the fact that in many cases the state minimum wage is binding.

32 CONTEMPORARY ECONOMIC POLICY FIGURE 1 Time-Series Plots of the Share of Benefits Accruing to Poor Directly Affected Workers 8% simulation 12% simulation 16% simulation 0.250 0.050 1990 2014 Share of benefits accruing to poor workers Notes: Share of annual benefits accruing to poor workers who are directly affected by the respective simulated increases in the federal minimum wage. Directly affected workers are defined as those workers earning between $0.05 less than the prevailing minimum wage (the higher of the state or federal minimum wage) and the simulated federal minimum wage. Poor workers are defined as those workers with household income below the poverty line. Data are drawn from the outgoing rotation group March CPS files. Observations are weighted using the CPS earnings weight. The table of values used to construct this figure is shown in the Appendix Table A3. wage. Observations are weighted using the CPS earnings weights. 10 As described in the previous section, an annual benefit is simulated for each directly affected worker by computing the product of his wage increase, his usual weekly hours, and the weeks worked per year. For hourly workers the CPS reports the hourly wage; for non-hourly workers, hourly wages are estimated from usual weekly earnings and usual weekly hours worked. The CPS reports the number of weeks worked for the previous year and it is assumed that this number does not change in the current year. In constructing a worker s income-to-needs ratio, total annual household income is divided by a household-size adjusted poverty threshold that is published by the U.S. Census Bureau. V. SIMULATION RESULTS Estimates from the 8%, 12%, and 16% simulations are shown in Figure 1. This figure displays a time-series plot of the share of benefits 10. Burkhauser and Sabia use workers aged 16 64 in one study and 17 64 in a second study. Burkhauser and Sabia are, apparently, inconsistent in their use of sample weights a point that is made clear in the replication that is included in the Appendix. Moreover, Burkhauser and Sabia restrict the sample to only include individuals who work at least 15 hours/week and who worked at least 14 weeks in the past year. I do not include these hours and weeks restrictions since doing so would likely be particularly restrictive for teen workers who are, on average, less attached to the labor force. accruing to poor workers for each simulation. As presented here, the results are quite noisy. In order to reduce noise in the estimates, the results are shown again in Figure 2, but this time using 5- year moving averages. All remaining results are presented using 5-year moving averages. (Note: the x-axis on figures using 5-year moving averages only shows the midpoint year for each 5-year span.) Several things stand out when looking at Figure 2. First, for each simulation, target efficiency peaked near the time period (labeled on Figure 2), and target efficiency remains close to the peak in 2014 (labeled on Figure 2). This suggests that, from an efficiency standpoint, now is probably a good time to increase the federal minimum wage (although it would have been slightly better a few years ago). Second, target efficiency, in general, is better when the minimum wage hike is smaller. A. What Is Driving Changes in Target Efficiency over this Time Period? The share of total minimum wage benefits accruing to poor workers will increase for two reasons: (1) the mean annual benefit received by poor workers increases relative to the mean annual benefit received by non-poor workers, and/or (2) the fraction of directly affected workers in poverty increases. The objective in this section is to determine which of these factors is most closely associated with changes in target

LUNDSTROM: WHEN TO RAISE THE MINIMUM WAGE? 33 FIGURE 2 Time-Series Plots of the Share of Benefits Accruing to Poor Directly Affected Workers, Based on 5-Year Moving Averages Share of benefits accruing to poor workers 8% simulation 12% simulation 16% simulation Notes: Results are computed using 5-year moving averages where the listed year represents the midpoint of the 5-year average. Directly affected workers are defined as those workers earning between $0.05 less than the prevailing minimum wage (the higher of the state or federal minimum wage) and the simulated federal minimum wage. Poor workers are defined as those workers with household income below the poverty line. Observations are weighted using the CPS earnings weight. The table of values used to construct this figure is shown in the Appendix Table A4. efficiency over this time period. In this portion of the analysis I focus exclusively on the 12% minimum wage hike simulation. I do this in order to simplify the discussion and because the conclusion that is drawn is the same regardless of which simulation is used. Mean Benefit Received by Poor Workers Relative to Non-Poor Workers. A time-series of the ratio of the mean annual benefit for poor workers to the mean annual benefit for non-poor workers (using the 12% simulation) is shown in Figure 3. This time-series is then overlaid on a time-series of the simulated benefits accruing to poor workers. This plot allows us to visualize whether changes in this ratio are potentially driving changes in the share of benefits accruing to poor workers over this time period. Looking at Figure 3, the relationship appears quite weak (correlation coefficient of 0.179). Fraction of Directly Affected Workers in Poverty. A time-series plot of the fraction of directly affected workers in poverty overlaid on a timeseries plot of the simulated benefits accruing to poor workers (using the 12% simulation) is shown in Figure 4. As before, this plot allows us to visualize the strength of this relationship. Looking at Figure 4, it is clear that changes in the fraction of directly affected workers in poverty are driving changes in target efficiency (correlation coefficient of 0.952). VI. WHAT IS DRIVING CHANGES IN THE FRACTION OF DIRECTLY AFFECTED WORKERS IN POVERTY? Having established that changes in minimum wage target efficiency from 1990 through 2014 were driven by changes in the fraction of directly affected workers in poverty, I now try to identify the variables that are most highly correlated with the fraction of directly affected workers in poverty. In general, the fraction of directly affected workers in poverty will increase for three reasons: (1) the mean household income of directly affected workers falls, (2) the wages of non-poor directly affected workers rise relative to the wages of poor directly affected workers (thereby pushing relatively more non-poor workers beyond the directly affected wage range than poor workers), or (3) the employment of low-skilled poor individuals rises relative to the employment of low-skilled non-poor individuals (the decline in teen employment is an instance of this). In this section my objective is to identify which of these factors is most closely associated with changes in the fraction of directly affected workers in poverty. A. Examining the Relationship between Household Income and the Fraction of Directly Affected Workers in Poverty Changes in household income among lowskilled individuals might drive changes in the fraction of directly affected workers in poverty.

34 CONTEMPORARY ECONOMIC POLICY FIGURE 3 Time-Series of the Mean Annual Benefit Received by Poor Workers Relative to the Mean Annual Benefit Received by Non-Poor Workers, Overlaid on a Time-Series of the Share of Total Benefits Accruing to Poor Workers. Based on 12% Simulation Share of benefits to poor workers Share of benefits to poor workers Poor/non-poor annual benefits r = -0.179 1.060 1.010 0.960 0.910 0.860 Ratio of poor annual benefits to non poor annual benefits Notes: Results are computed using 5-year moving averages where the listed year represents the midpoint of the 5-year average. Poor workers are defined as those workers with household income below the poverty line. Observations are weighted using the CPS earnings weight. The values used to create this figure are shown in the Appendix Table A5. FIGURE 4 Time-Series of the Fraction of Directly Affected Workers in Poverty, Overlaid on a Time-Series of the Share of Total Benefits Accruing to Poor Workers. Based on 12% Simulation Share of benefits to poor workers Share of benefits to poor workers r = 0.952 Fraction of directly affected workers in poverty Notes: Results are computed using 5-year moving averages where the listed year represents the midpoint of the 5-year average. Directly affected workers are defined as those workers earning between $0.05 less than the prevailing minimum wage (the higher of the state or federal minimum wage) and the simulated federal minimum wage. Poor workers are defined as those workers with household income below the poverty line. Observations are weighted using the CPS earnings weight. The values used to create this figure are shown in the Appendix Table A6. In order to explore this relationship, a time-series plot of the poverty rate of low-skilled individuals is overlaid on a time-series plot of the fraction of directly affected workers in poverty (where an individual is considered low-skilled if he has less than a 12th grade education). A separate plot is created for each simulation and shown in Figure 5. As expected, the correlations are all positive, but they are not particularly strong (the correlation coefficients are 0.381, 0.442, and 0.372 for the 8%, 12%, and 16% simulations, respectively). This finding suggests that while changes in household income likely explain some of the variation in the fraction of directly affected workers in poverty over this time period, it is probably not the whole story.

LUNDSTROM: WHEN TO RAISE THE MINIMUM WAGE? 35 FIGURE 5 Time-Series of the Poverty Rate of Low-Skilled Individuals Overlaid on a Time-Series of the Fraction of Directly Affected Workers in Poverty. (a) 8% Simulation, (b) 12% Simulation, (c) 16% Simulation (a) (b) Fraction of directly affected workers in poverty Poverty rate of low-skilled individuals r = 0.381 0.275 0.250 0.225 Poverty rate of low-skilled individuals (c) Fraction of directly affected workers in poverty Poverty rate of low-skilled individuals r = 0.442 0.275 0.250 0.225 Poverty rate of low-skilled individuals Fraction of directly affected workers in poverty r = 0.372 0.275 0.250 0.225 Poverty rate of low-skilled individuals Poverty rate of low-skilled individuals Notes: Observations are limited to states where the simulated federal minimum wage is binding. An individual is lowskilled if they have education <12 years. Results are computed using 5-year moving averages where the listed year represents the midpoint of the 5-year average. Directly affected workers are defined as those workers earning between $0.05 less than the prevailing minimum wage (the higher of the state or federal minimum wage) and the simulated federal minimum wage. A worker in poverty is defined as one whose household income falls below the poverty line. When constructing the 5-year moving averages, annual poverty rates are weighted by the annual population of working age individuals. The values used to create these figures are shown in the Appendix Table A7.

36 CONTEMPORARY ECONOMIC POLICY B. Examining the Relationship between the Wages of Non-Poor Workers Relative to the Wages of Poor Workers, and the Fraction of Directly Affected Workers in Poverty If the wages of non-poor directly affected workers rise relative to the wages of poor directly affected workers, then relatively more non-poor workers will be pushed beyond the directly affected wage range than poor workers. This will lead to an increase in the fraction of directly affected workers in poverty. To explore this relationship, a time-series plot of the ratio of the mean wage of non-poor directly affected workers to the mean wage of poor directly affected workers is overlaid on a time-series plot of the fraction of directly affected workers in poverty. As before, a separate plot is produced for each simulation. These plots are shown in Figure 6. The correlations are all positive as expected but they are also quite weak (correlation coefficients of 0.159, 0.083, and 0.096 for the 8%, 12%, and 16% simulations, respectively). The implication is that an increase in the wages of non-poor workers relative to the wages of poor workers does a bad job of predicting changes in the fraction of directly affected workers in poverty over this time period. C. Examining the Relationship between the Employment of Non-Poor Individuals Relative to the Employment of Poor Individuals, and the Fraction of Directly Affected Workers in Poverty If the employment of low-skilled poor individuals rises relative to the employment of low-skilled non-poor individuals, the fraction of directly affected workers in poverty may rise. As discussed in the Introduction, the large reduction in teen employment since the late 1990s could lead to such an outcome. To explore the relationship between teen employment and the fraction of directly affected workers in poverty, a time-series plot of teen employment is overlaid on a time-series plot of the fraction of directly affected workers in poverty. A separate plot is created for each simulation and shown in Figure 7. (Note: the right-hand-side y-axis for teen employment is reversed in order to make the relationship between the two variables more apparent.) The correlation is quite weak for each simulation (correlation coefficients of 0.174, 0.311, and 0.323 for the 8%, 12%, and 16% simulations, respectively). This suggests that, while changes in teen employment may play some role in changes in target efficiency over this time period, the role is probably minor. Of course, the relationship between teen employment and target efficiency is just one of many that could be explored in this section. More generally, I would like to create a time-series showing the employment of poor, low-skilled individuals relative to the employment of similarly-skilled non-poor individuals. This time-series could then be compared to a timeseries of the fraction of directly affected workers in poverty. Unfortunately, the CPS does not contain a skill variable that can be used to identify similarly-skilled individuals across the income distribution. 11 However, it might be possible to detect this relationship in another way. Recall that one of the assumptions underlying the static simulation methodology employed here is that changes in the level of the federal minimum wage do not affect employment (or, if they do, the effects are similar across the income distribution). If this is not true if, for example, as the real minimum wage falls more poor workers are priced back into the labor market than non-poor workers the level of the federal minimum wage might itself be strongly correlated with changes in target efficiency. In order to explore this possibility, a timeseries plot of the real federal minimum wage (in 2014 dollars) is overlaid on a time-series plot of the fraction of directly affected workers in poverty for each simulation. These plots are shown in Figure 8. The correlations are all very strong (correlation coefficients of 0.828, 0.892, and 0.865 for the 8%, 12%, and 16% simulations, respectively). Surprisingly, the correlations are all positive. If the relationship is causal, this implies that as the real federal minimum wage increases, the employment of poor minimum wage workers rises relative to the employment of non-poor minimum wage workers. And, conversely, as the real minimum wage falls the employment of poor minimum wage workers falls relative to the employment of non-poor minimum wage workers. Whether the relationship is causal or not, these results clearly show that over the last 25 years, 11. I attempted to use low-education as a proxy for lowskill, but this is very imperfect. The wages of poor highschool dropouts are, on average, $9.79 (in 2014 dollars) over this time period. The wages of non-poor high-school dropouts are $12.19 (in 2014 dollars) over this same time period. This wage discrepancy indicates that the non-poor high-school dropouts are likely higher skilled than poor highschool dropouts.

LUNDSTROM: WHEN TO RAISE THE MINIMUM WAGE? 37 FIGURE 6 Time-Series of the Mean Wage of Non-Poor Directly Affected Workers Relative to the Mean Wage of Poor Directly Affected Workers Overlaid on a Time-Series of the Fraction of Directly Affected Workers in Poverty. (a) 8% Simulation, (b) 12% Simulation, (c) 16% Simulation (a) Fraction of directly affected workers in poverty (b) Fraction of directly affected workers in poverty Ratio of non-poor wages to poor wages Ratio of non-poor wages to poor wages r = 0.159 r = 0.083 1.02 1.01 1.00 0.99 1.03 1.02 1.01 1.00 0.99 Ratio of non-poor wages to poor wages Ratio of non-poor wages to poor wages (c) Fraction of directly affected workers in poverty r =0.096 1.03 1.02 1.01 1.00 0.99 Ratio of non-poor wages to poor wages Ratio of non-poor wages to poor wages Notes: A time-series plot of the ratio of wages for non-poor directly affected workers to the wages of poor directly affected workers is overlaid on a time-series plot of the fraction of directly affected workers in poverty for each figure. Results are computed using 5-year moving averages where the listed year represents the midpoint of the 5-year average. Directly affected workers are defined as those workers earning between $0.05 less than the prevailing minimum wage (the higher of the state or federal minimum wage) and the simulated federal minimum wage. Poor workers are defined as those workers with household income below the poverty line. The values used to create these figures are shown in the Appendix Table A8. at least the real level of the federal minimum wage is a very strong predictor of minimum wage target efficiency. VII. SENSITIVITY ANALYSIS It is possible that the results of the preceding analysis are sensitive to certain restrictions placed on the sample. In particular, in any given year the sample consists of observations from all states that are bound by the simulated federal minimum wage. Many observations in each year come from states where the state minimum wage rate exceeds the contemporaneous federal level, meaning that the simulated wage hike is somewhat less than intended (e.g., if the state

38 CONTEMPORARY ECONOMIC POLICY FIGURE 7 Time-Series of Teen Employment to Population Ratio Overlaid on a Time-Series of the Fraction of Directly Affected Workers in Poverty. (a) 8% Simulation, (b) 12% Simulation, (c) 16% Simulation (a) Fraction of directly affected workers in poverty (b) Teen Employment to Population Ratio r = -0.174 0.240 0.290 0.340 0.390 Teen employment to population ratio Fraction of directly affected workers in poverty Teen Employment to Population Ratio r = -0.311 0.240 0.290 0.340 0.390 Teen employment to population ratio (c) Fraction of directly affected workers in poverty Teen Employment to Population Ratio r = -0.323 0.240 0.290 0.340 0.390 Teen employment to population ratio Notes: Observations are limited to states where the simulated federal minimum wage is binding. Results are computed using 5-year moving averages where the listed year represents the midpoint of the 5-year average. Directly affected workers are defined as those workers earning between $0.05 less than the prevailing minimum wage (the higher of the state or federal minimum wage) and the simulated federal minimum wage. Poor workers are defined as those workers with household income below the poverty line. When constructing 5-year moving averages the annual teen employment rates are weighted by teen population. The values used to create these figures are shown in the Appendix Table A9.

LUNDSTROM: WHEN TO RAISE THE MINIMUM WAGE? 39 FIGURE 8 Time-Series of Real Federal Minimum Wage Rate (in 2014 Dollars) Overlaid on a Time-Series of the Fraction of Directly Affected Workers in Poverty. (a) 8% Simulation, (b) 12% Simulation, (c) 16% Simulation (a) Fraction of directly affected workers in poverty (b) Fraction of directly affected workers in poverty (c) Fraction of directly affected workers in poverty 0.180 0.160 0.140 0.120 Real federal minimum wage Real federal minimum wage Real federal minimum wage r = 0.828 r = 0.892 r =0.865 7.750 7.250 6.750 6.250 5.750 7.75 7.25 6.75 6.25 5.75 7.750 7.250 6.750 6.250 5.750 Notes: Results are computed using 5-year moving averages where the listed year represents the midpoint of the 5-year average. Directly affected workers are defined as those workers earning between $0.05 less than the prevailing minimum wage (the higher of the state or federal minimum wage) and the simulated federal minimum wage. A worker in poverty is defined as one whose household income falls below the poverty line. The real federal minimum wage may vary somewhat across simulations since different states are included in each year for the different simulations (because of the constraint that observations are only drawn from states where the simulated federal minimum wage binds) this affects the population in a given year and moving averages are population weighted. The values used to create these figures are shown in the Appendix Table A10. Real federal minimum wage Real federal minimum wage Real federal minimum wage minimum wage rate is $8.00 and the federal minimum wage rate is $7.25, a 12% simulated increase in the federal minimum wage will effectively raise the minimum wage in that state by only 1.5%). In other cases, the state minimum wage rate exceeds the simulated federal minimum wage rate, meaning that no observations are drawn from that state in those years. It is unclear how these year-to-year changes in both the size of the effective simulated minimum wage change, as well as which states are represented, may be influencing the results. In this section I redo the analysis, but this time the sample is restricted to only include

40 CONTEMPORARY ECONOMIC POLICY observations from states that are fully bound by the federal minimum wage in all sample years (i.e., the sample is restricted to states that never increase the minimum wage beyond the federal level). There are 17 states that meet this criteria. 12 The results from this sensitivity analysis are shown in Figure 9. For the sake of brevity, only results from the 12% simulation are presented, though the conclusions are the same for all simulations. In Figure 9(a), a time-series plot of the share of benefits accruing to poor workers using the restricted sample is overlaid on a time-series plot of the share of benefits accruing to poor workers using the original sample. The general pattern of changes in target efficiency is the same for both samples over this time period, though the estimates are generally somewhat higher for the restricted sample. Nevertheless, using the restricted sample, we would still conclude that from an efficiency standpoint now is a good time to increase the minimum wage: 18.8% of the total annual benefits would accrue to workers in the 2014 time period (labeled on Figure 9(a)), 1.8 percentage points below the peak, and 5.3 percentage points above the trough over this time period. In Figure 9(b), a time-series plot of the fraction of directly affected workers in poverty is overlaid on a time-series plot of the share of benefits accruing to poor workers using the restricted sample. As with the original sample, the correlation is very strong (correlation coefficient of 0.882). The relationship between the share of benefits accruing to poor workers and the mean annual benefit for poor workers relative to the mean annual benefit for non-poor workers is comparatively weak the correlation coefficient is 0.589 (for the sake of brevity this figure is not displayed). As with the original sample, the implication is that changes in target efficiency are primarily driven by changes in the fraction of directly affected workers in poverty. In Figure 9(c), a time-series plot of the real federal minimum wage is overlaid on a timeseries plot of the fraction of directly affected workers in poverty. As with the original sample, the relationship is quite strong the correlation coefficient is 0.714. For the sake of brevity, the other plots are not displayed, but the relationships are all comparatively weak (the 12. The 17 states that are fully bound by the federal minimum wage in every year from 1990 to 2014 are: Alabama, Georgia, Idaho, Indiana, Kansas, Kentucky, Louisiana, Mississippi, Nebraska, Oklahoma, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, and Wyoming. correlation coefficient for the fraction of directly affected workers in poverty and teen employment is 0.094; the correlation coefficient for the fraction of directly affected workers in poverty and the poverty rate of low-skilled individuals is 0.485). In summary, the conclusions reached using the restricted sample are identical to the conclusions that are reached using the original sample. VIII. DISCUSSION OF RESULTS The preceding analysis reveals three things. First that the target efficiency of the federal minimum wage is currently near a 25-year high. Second, that changes in target efficiency over the past 25 years are overwhelmingly a function of changes in the fraction of directly affected workers in poverty, rather than changes in the mean annual benefit received by poor workers relative to non-poor workers. And third, while the decline in teen employment and the general increase in poverty may have contributed to the increase in minimum wage target efficiency over the past decade, of the factors considered here, the real level of the federal minimum wage is the strongest predictor of minimum wage target efficiency. The discovery of a positive relationship between the real federal minimum wage and minimum wage target efficiency is surprising. Given the positive relationship between the skill and income distributions, we would expect this relationship to be negative. That is, if the real minimum wage level falls, we expect individuals to be priced into the market who are, on average, lower skilled than the lowest skilled workers in the existing labor pool. Furthermore, given the positive relationship between skill and income, we would expect that these individuals are, on average, poorer than are workers in the existing labor pool. These findings suggest that the opposite might be taking place. Though a positive relationship between the real minimum wage and target efficiency is counterintuitive, this result can easily be explained if the supply of poor low-skilled labor is more elastic than is the supply of non-poor low skilled labor. A high labor supply elasticity for poor low-skilled labor might occur, for example, if these individuals are on the margin of eligibility for means-tested income support or welfare programs. While the techniques employed in this study provide a weak basis for causal inference, the fact that such a strong positive relationship

LUNDSTROM: WHEN TO RAISE THE MINIMUM WAGE? 41 FIGURE 9 Sensitivity Analysis: The Sample Is Restricted to States That Are Fully Bound by the Federal Minimum Wage in All Years. (a) Time-Series of the Share of Benefits Accruing to Poor Workers Using the Restricted Sample Overlaid on a Time-Series of the Share of Benefits Accruing to Poor Worker Using the Original Sample. (b) Time-Series of the Share of Benefits Accruing to Poor Workers Overlaid on a Time-Series of the Fraction of Directly Affected Workers in Poverty (Restricted Sample). (c) Time-Series of the Real Federal Minimum Wage Rate (in 2014 Dollars) Overlaid on a Time-Series of the Fraction of Directly Affected Workers in Poverty (Restricted Sample) (a) Share of benefits accruing to poor workers (b) 0.220 0.190 0.160 0.130 Full sample Restricted sample r = 0.789 Share of benefits accruing to poor workers (c) 0.240 0.210 0.180 0.120 Share of benefits to poor workers r = 0.882 0.240 0.210 0.180 0.120 Fraction of directly affected workers in poverty Fraction of directly affected workers in poverty 0.240 0.210 0.180 0.120 r =0.714 7.75 7.25 6.75 6.25 5.75 Real federal minimum wage (2014 dollars) Real federal minimum wage Notes: Results are computed using 5-year moving averages where the listed year represents the midpoint of the 5-year average. Directly affected workers are defined as those workers earning between $0.05 less than the federal minimum wage and the simulated federal minimum wage. Poor workers are defined as those workers with household income below the poverty line. The values used to create these figures are shown in the Appendix Table A11. between the minimum wage and target efficiency exists at least raises the possibility that a binding minimum wage causes the employment of low-skilled poor individuals to increase relative to the employment of low-skilled non-poor individuals. If future research reveals that this is the case, there are several important implications. First, this implies that a static simulation of the sort employed in this study tends to understate target efficiency since it fails to account for the increased employment of poor individuals relative to non-poor individuals that is caused by a minimum wage hike. Indeed, such a discovery would raise questions concerning the finding

42 CONTEMPORARY ECONOMIC POLICY presented in Section IV that target efficiency, in general, is better when the minimum wage hike is smaller since this finding is derived from a static simulation. If a higher minimum wage level is more efficient than a lower minimum wage level, then it might also be the case that a larger minimum wage change is no less efficient than a smaller one. Of course, it may still be the case that the optimal path to a higher, more efficient minimum wage is through a series of small changes. This is a subject for future research. A second, and related, implication of a positive relationship between the minimum wage and target efficiency is the potential desirability of indexing the minimum wage, whereby it is prevented from falling to less efficient levels. This is especially true in light of the possibility that large minimum wage changes are less efficient than small ones. Indexing the minimum wage ensures that changes to the minimum wage occur in small, incremental steps. Finally, there are a number of cautions that must be exercised in interpreting these results. First, it might be tempting for minimum wage advocates to use these results as a justification for dramatic increases in the minimum wage, on the grounds of improved efficiency. But it must be remembered that over the 25-year span considered in this study, the federal minimum wage stayed within a narrow range of $6.23 and $7.55 (in 2014 dollars, based on 5-year moving averages). It is not at all certain that the positive relationship between the minimum wage and target efficiency would persist at levels outside of this range. Second and at the risk of being repetitive it must be remembered that the methods employed in this study provide a weak basis for causal inference. While the strong relationship between the real federal minimum wage and target efficiency is compelling, it is possible that this relationship is being driven by factors that have not been considered. Lastly, the policy objective of optimal target efficiency cannot, in the end, be entirely divorced from considerations of employment and general equilibrium effects. If efficiency gains come at the expense of an overall reduction in employment or an increase in the price of goods, then these costs must be weighed in the balance. IX. CONCLUSION In this study I use static simulation techniques to analyze changes in the target efficiency of the federal minimum wage over the past 25 years. In so doing I discover that the target efficiency of the federal minimum wage is currently near its 25-year peak. In particular, I find that of the total monetary benefits generated by a 12% increase in the federal minimum wage, 16.8% would accrue to poor households. This exceeds the least target efficient year over this time period by 4.7 percentage points and is only 0.6 percentage points below the peak. Furthermore, I find a very strong positive relationship between the level of the federal minimum wage (in 2014 dollars) and minimum wage target efficiency. The implication is that a good time to raise the minimum wage from an efficiency standpoint, at least is when it is already high. This discovery raises the possibility that the minimum wage increases the employment of low-skilled poor individuals relative to the employment of lowskilled non-poor individuals. Those who favor the minimum wage as a means to combat poverty might view the results of this study as an indication that the minimum wage is better positioned now than at most years in the past few decades to do so (from an efficiency standpoint, at least). They might also view the results of this study as being supportive of an indexed federal minimum wage, whereby the minimum wage would be prevented from falling to less efficient levels. At the same time, minimum wage critics might argue that, even with so many forces working in favor of improved target efficiency including decreased teen employment, and a high poverty rate the minimum wage continues to do a bad job of targeting the poor. And both groups would be correct. The minimum wage is a blunt instrument for addressing poverty, and there is no evidence suggesting that it will cease to be so in the foreseeable future. Nevertheless, so long as policy makers continue to rely on the minimum wage, the results of this study may be useful as they consider ways to make the most efficient use of an imperfect tool. APPENDIX BURKHAUSER AND SABIA REPLICATION Burkhauser and Sabia (, ; hereafter, BS) perform simulations for the years,, and. The approach taken by BS is similar to mine, with a few differences: (1) they restrict the sample to workers who work at least 15 hours/week and 14 weeks in the past year; (2) they include workers aged 17 64 in the study, and 16 64 in study; (3) they are (apparently) inconsistent in the use of weights I can replicate the and results if I do not weight the observations, but I must use weights to replicate the

LUNDSTROM: WHEN TO RAISE THE MINIMUM WAGE? 43 result; (4) they define directly affected workers as having wages between the contemporaneous federal minimum wage and the simulated minimum wage (versus the prevailing minimum wage i.e., higher of state or federal and simulated minimum wage); (5) they do not use the same percentage increase in the minimum wage in each year they simulate minimum wage changes that are consistent with proposed or actual increases for the given years. While there is certainly merit in simulating proposed minimum wage increases, it makes cross-year comparisons difficult since target efficiency calculations are sensitive to the size of the simulated increase. In this Appendix I replicate BS s results, then show how the results are changed as my approach is implemented, step by step. All results are shown in Table A2. Column 1 shows BS s published results for the share of benefits accruing to poor (i.e., ITN < 1) workers. Column 2 shows the results from my replication. I am able to replicate BS s results almost perfectly. Column 3 shows results from a simulation where one change is made to the BS approach: all observations are weighted (using the CPS earnings weight). The estimate is reduced somewhat, and the estimate increases slightly, though the changes are not significant. Column 4 shows results from a simulation that includes the column 3 change, plus two additional changes: workers aged 16 64 are included in all years and the work requirement of at least 15 hours/week and 14 weeks/year is dropped. I am concerned that the hours and weeks restriction might be particularly restrictive for teens given their low attachment to the labor market. In fact, these changes have very little impact on the estimates. Column 5 shows results from a simulation TABLE A1 Differences in Simulation Methodologies Between Burkhauser and Sabia (, ) and Lundstrom (this article) Burkhauser and Sabia Lundstrom (1) (2) (1) Use of sample weights: Sample weights appear to be used in the paper, but not the paper. (2) Working-age population Workers ages 16 64 in the paper, definition: and 17 64 in the paper (3) Other sample restrictions: To be included a worker must work at least 15 hours/week and must have worked 14 weeks in the past year. (4) Directly affected worker A worker whose wage is between the definition: federal minimum wage and the simulated federal minimum wage. (5) Size of the simulated minimum wage change: Varies from one simulation to the next. Sample weights are used for all simulations. Workers ages 16 64 are used for all simulations. No additional sample restrictions other than the age restriction. A worker whose wage is between the prevailing minimum wage (i.e., the higher of the state or federal level) and the simulated minimum wage. The same percent increase for each year. TABLE A2 Replication of Burkhauser and Sabia Burkhauser and Sabia Results Replication Step No. 1 Step No. 2 Step No. 3 Step No. 4 (1) (2) (3) (4) (5) (6) Share of benefits accruing to workers in poor households: Year: 0.142 0.141 0.131 0.134 0.127 0.136 Standard error: (0.019) (0.019) (0.018) (0.019) (0.029) Sample size: 689 689 900 832 363 Year: 0.127 0.122 0.128 0.129 0.124 0.101 Standard error: (0.012) (0.015) (0.014) (0.014) (0.028) Sample size: 1,351 1,351 1,737 1,559 300 Year: 0.109 0.106 0.106 0.106 0.109 0.158 Standard error: (0.011) (0.011) (0.011) (0.011) (0.049) Sample size: 1,733 1,733 1,994 1,783 123 The share of minimum wage benefits accruing to poor workers. Standard errors are presented in parentheses. Burkhauser and Sabia results (column 1): the and results are from Burkhauser and Sabia (), Table 10. The result is from Burkhauser and Sabia (), Table 7. Replication (column 2): these estimates are based on a replication following the Burkhauser and Sabia approach exactly. Step no. 1 (column 3): one change from the Burkhauser and Sabia approach: all observations are weighted (versus just weighting the observations). Step no. 2 (column 4): all changes from column 3 are included plus the sample is restricted to workers ages 16 64 (as opposed to 17 64 for and ), and the sample restriction requiring 15 hours of work/week and 14 weeks of work/year is dropped. Step no. 3 (column 5): all changes from column 4 are included, plus directly affected workers are defined as having wages between the prevailing minimum wage (i.e., higher of state or federal) and new minimum wage, as opposed to workers with wages between the federal minimum wage and new minimum wage. Step no. 4 (column 6): all changes from column 5 are included, plus the same 12% increase in the minimum wage is implemented in each year (12% is roughly the historical average increase).