ABSTRACT CAN MINIMUM WAGE HELP FORECAST UNEMPLOYMENT? by John Michael Tyliszczak

ABSTRACT CAN MINIMUM WAGE HELP FORECAST UNEMPLOYMENT? by John Michael Tyliszczak Using federal and state-level monthly minimum wage and seasonally adjusted unemployment data, I compare Autoregressive and Distributed Lag models to determine if minimum wage can improve forecasts of unemployment. I also employ Granger- Causality tests in the Distributed Lag models to determine if lagged values of minimum wage have a statistically significant impact on current values of unemployment. Utilizing the metric mean absolute squared prediction error (MASPE), I find inconclusive results that Distributed Lag models generate better forecasts than Autoregressive models, indicating that minimum wage may not be a uniformly useful addition to the out-ofsample forecast of unemployment. Additionally, through Granger-Causality testing, I do not find consistent statistically significant effects of lagged minimum wage on unemployment. However, when evaluating the long-run propensity of minimum wage from the Distributed Lag models, I find statistically significant results across a subset of states with average wages that rank in the bottom half of all states. This indicates that states with low average wages may have a labor market comprised of more minimum wage jobs, thus leading to a significant relationship between minimum wage and unemployment.

CAN MINIMUM WAGE HELP FORECAST UNEMPLOYMENT? A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Arts by John Michael Tyliszczak Miami University Oxford, Ohio 2017 Advisor: Dr. Jing Li Reader: Dr. Bill Even Reader: Dr. George Davis 2017 John Michael Tyliszczak

This Thesis titled CAN MINIMUM WAGE HELP FORECAST UNEMPLOYMENT? by John Michael Tyliszczak has been approved for publication by The Farmer School of Business and Department of Economics Dr. Jing Li Dr. Bill Even Dr. George Davis

Table of Contents 1 Introduction 1 2 Literature Review 2 3 Data 5 4 Econometric Models 7 5 Results 10 6 Conclusion 13 References 15 A Tables 16 B Figures 36 iii

List of Tables 1 State Minimum Wage Descriptives. 16 2 State Unemployment Descriptives (Total Population) 18 2a State Unemployment Descriptives (Persons Ages16-24).. 20 3 Summary of Forecast MASPE (Total Population).. 22 3a Summary of Forecast MASPE (Persons Ages 16-24)... 24 4 Summary of Granger-Causality Test (Total Population)... 26 4a Summary of Granger-Causality Test (Persons Ages 16-24).. 28 5 Summary of Long-Run Propensity (Persons Ages 16-24)... 30 6 Summary of Forecast Models vs. Random Walk (Persons Ages 16-24).. 32 7 2016 State Total Wage Descriptives. 34 iv

List of Figures 1 State of Ohio Minimum Wage vs Unemployment.. 36 2 State of Ohio Forecast Error... 37 3 State of New York Minimum Wage vs Unemployment...... 38 4 State of New York Forecast Error.... 39 v

1. Introduction The first minimum wage set in the United States, of $0.25 per hour, was established as part of the 1938 Fair Labor Standards Act (FLSA, 1938). Stigler (1946) suggested that the objective of minimum wage legislation was to eliminate extreme poverty. Since its inception, both the intended effect as well as the unintended consequences of minimum wage legislation has been the focus of extensive research. Over time, more data has become available and more regional variation in minimum wage occurs through state wage floors that exceed federal, enabling a variety of analyses to be performed in order to determine the policy effects of this legislation. From the onset, many economists viewed the labor market as one that would act like a competitive market, much like that of a commodity. In this model firms will determine the amount of labor to enlist based on the cost. As pointed out by the Minimum Wage Study Commission, which was created by Congress in 1977, the establishment of a minimum wage and subsequent increases to that wage will negatively affect employment in two ways: If the cost of low-skilled labor (which minimum wage employees tend to be) increases, then firms will look to utilize other inputs such as machinery or higher-skilled workers. Additionally, the higher labor costs will also cause firms to raise the price of the goods they produce, which will lower demand for the goods, and with fewer goods being demanded fewer workers are needed to produce them (Minimum Wage Study Commission, vol. 1, p. 32). The merits of this model with respect to labor have been greatly debated and subsequent research has found contradicting evidence which attempts to discredit this view. However, there are more nuances of the theory which are not always highlighted but relevant to the assessment of the model suitability. As noted by the Minimum Wage Study Commission, When one says that the minimum wage will reduce employment, the basis for comparison is the level of employment that would otherwise occur if everything else except the level of the minimum wage were the same (p. 32). The Commission goes on to point out that reduced employment may not only be seen through actual layoffs, but can materialize through slowed hiring or not replacing workers who leave voluntarily. Cases where employment increases after an increase in the minimum wage does not contradict the theory, as the theory would imply that increases in employment would have been greater if the minimum wage had not been increased. 1

Neumark and Wascher (2006) note a second point that has often been ignored in interpreting the evidence of case studies of a specific industry is that the neoclassical model of the labor market does not predict that employment in a particular sub-sector of the economy will decline in response to a general minimum wage increase (p.33). A significant portion of the new minimum wage research, particularly those which find zero or positive effects from increases in minimum wage, focus on case studies within particular industries or sub-sectors and the fact that employment rises in one sub-sector does not imply that it rises in all sectors with significant minimum wage coverage. Unlike most research in the space, the goal of this paper is to determine if the minimum wage can be used to better forecast changes in unemployment. Significant debate exists regarding the appropriate model form and variables to include in an analysis aimed at finding and quantifying a causal relationship between minimum wage and unemployment. As noted by Neumark and Wascher (2006), results of minimum wage studies are by no means always statistically significant, regardless of the directional impact. If there is conclusive evidence that minimum wage improves forecasting of unemployment, then the focus of the research can continue to be on the directional impact and resulting policy implications that stem from such results. The intent of this paper is not to determine the positive or negative impact or quantify the effect. It will be up to alternative specifications of models which focus on more specific worker demographics and more fully control for other facts which may also have an effect on unemployment. 2. Literature Review There has been extensive research into the effect of minimum wage dating back to not long after the 1938 Fair Labor Standards Act set the initial floor of $0.25 per hour. The implications supposed and/or uncovered from the analyses can be generalized into two camps: 1) the existence of wage floors (and subsequent increases in the floor) will have a negative effect on employment through the demand for labor and 2) wage floors have no impact or a positive impact on employment. Since the implementation of the minimum wage legislation, a significant amount of data has become available to empirically test the effect of wage floors. Additionally, new research design and econometric approaches have also aided in the robustness 2

of the findings but have done little to settle the debate regarding the true impact of minimum wage on employment. In the nearly 70 year history of research regarding this topic, there have been numerous research designs employed on a wide array of data. The differing model specifications, measurement of data and which groups within the labor pool are most appropriate to study have been a significant source in the varying impacts found in the new line of research. The previously well accepted theory driving the hypothesis of the first camp is that the labor market is competitive and firms will determine the amount of labor to enlist based on the cost. These two fundamental theories are the basis for the argument against minimum wage legislation. However, even in the early period of research into this topic, some economists have questioned the appropriateness of a competitive market model for labor. The varying empirical findings related to this topic seem to be driven as much by model design as true behavior of the labor markets. Studies can be grouped into two camps: 1) those utilizing panel data (and some early and recent research utilizing time-series data) and 2) those which focus on case studies, utilizing treatment and control data for the purposes of analysis. Similarly, studies also have varying findings depending on the variable choice of the model. The majority of studies which find negative effects from raising minimum wage tend to account for both contemporaneous and lagged effects of the minimum wage. Allowing for a lagged impact in the models is argued for on one aspect as the need to substitute capital for workers, which is a substitution that may take a longer time than adjusting labor levels alone. Interestingly, some of the well-known literature finding an absence of the disemployment effect only model contemporaneous effects of changes in the minimum wage. However, more recent examinations into the effects of minimum wage on employment have found either no disemployment effects or positive impacts on employment within examined demographics. Card and Krueger (1994) run a case study on fast food restaurants in New Jersey and Pennsylvania following a 1992 increase in New Jersey s minimum wage. They conducted telephone surveys and analyzed the data of these restaurants in both states, using New Jersey as a treatment and Pennsylvania as a control (as the restaurants in Pennsylvania were close in proximity to NJ but did not endure an increase in the minimum wage). The authors found positive and significant employment growth post-increase in the New Jersey stores which exceeded that of the stores in the control market. Even within the New Jersey, they found faster 3

employment growth from restaurants that were initially paying lower wages, and thus incurred an even larger impact from the increase in minimum wage. One perceived short coming of the Card-Krueger analysis is potential measurement error in their data. Neumark and Wascher (2000) replicated the study using payroll records from fastfood restaurants in the same universe as the Card-Krueger sample. The authors point out that restaurant managers were asked about the number of part and full time employees, but those answers may have been subjective and ambiguous as to the period of time to which they refer. The payroll data utilized by Neumark-Wascher eliminates this ambiguity as the data always pertain to the payroll period. Utilizing the same model with different data, Neumark-Wascher find a decline in full-time employment in New Jersey relative to the restaurants in Pennsylvania. Card-Krueger (2000) provided subsequent analyses utilizing the payroll data but was unable to replicate their original positive and significant employment effects. Neumark and Wascher were not the only critics of the Card-Krueger analysis or of case studies of this type all together. Hamermesh (1995) points out three conditions relevant to interpreting Card-Krueger s work (but can be applied to all case studies): 1) the pre-period should be sufficient that the treatment does not adjust before the event, 2) the post-period must be sufficiently long to feel the full effects, and 3) that no other factors are in play to drive differences between the test and control. Hamermesh concludes that conditions 1 and 2 were not satisfied in this specific Card-Krueger analysis, but goes on further to say that they were not satisfied in other case studies undertaken by Card and/or Krueger (Card and Krueger, 1992 & Katz and Krueger, 1992). Additionally, Hamermesh also notes a failure of Card-Krueger to meet condition 3, indicating it was unlikely to expect restaurants in both New Jersey and Pennsylvania to behave identically in the absence of the wage increase. While his argument may be valid, the ability to meet this specific criterion seems onerous and would likely find all test-control analyses evaluating different regions of the country as insufficient. Even with the relatively recent literature showing positive effects of minimum wage on employment, the vast majority of analysis into this topic has found some level of disemployment effects. Based on a review of 102 studies on this topic, Neumark and Wascher (2006) find that the majority of studies in this space find negative employments effects from minimum wages. by our reckoning nearly two-thirds give a relatively consistent (although by no means always statistically significant) indication of negative employment effects of minimum wages, while 4

only eight give a relatively consistent indication of positive employment effects (p.121). The authors go on to call for longer panel studies including both federal and state variation, point out concern over some problematic issues with case studies, and point out that substitution within low-wage workers certainly appears evident even if most analyses are based on total teenage employment. 3. Data The data used for this analysis came from two separate sources. The first set of data is unemployment and comes from the Bureau of Labor Statistics 1. I extracted monthly, state-level, seasonally adjusted unemployment data from the Local Area Unemployment Statistics (LAUS) database. These data covered the time period of January 1983 through December 2014, and are based on the Current Population Survey (CPS) which is the source of the national unemployment rate. Two measures of unemployment are evaluated in the analysis: Total unemployment and unemployment for individuals ages 16-24. Total unemployment is based on the official definition of people who are jobless, actively seeking work, and available to take a job as defined by the CPS. Meanwhile the 16-24 year old group is a combination of two sub-groups: individuals 16-19 years old and individuals 20-24 years old. This more narrowly defined group of workers, teenagers and young adults, are more heavily employed in industries and jobs that pay the minimum wage. Therefore any relationship that exists between minimum wage and unemployment should be more pronounced within this group. The second set of data is state and federal minimum wage levels obtained from the Tax Policy Center website 2. The data available are annual minimum wage rates, by state and federal from 1983-2014. While the minimum wage rates reported are annual, detailed notes are provided for each state regarding when new rates took effect mid-year. This allowed for rates to change mid-year, or for states to have multiple rates within a given year providing more variation in the data. An example of multiple changes to minimum wage in a calendar year can be found in Idaho in 1997. The minimum wage at the beginning of the year was $4.25 which increased to $4.75 on 4/1/97. On 9/1/97, the minimum wage increased again to $5.15. 1 https://www.bls.gov/data/#unemployment 2 http://www.taxpolicycenter.org/statistics/state-minimum-wage-rates-1983-2014 5

An additional set of data, the Consumer Price Index (CPI), was also collected from the BLS website. The CPI is a representation of retail and service establishment prices from 87 urban areas throughout the country and is used as a measure of inflation. This set of national, monthly indices will be used to adjust the nominal minimum wage values to create a real minimum wage which accounts for inflation over the duration of the analysis period. Lastly, I calculate a real effective minimum wage for each state/month observation. The real effective minimum wage is defined as the greater wage between the state minimum wage 3 and federal minimum wage 4 in a given month. Since minimum wages across states vary compared to the federal minimum wage, an effective minimum wage represents the wage employees (covered by the FLSA) in a given state are likely to earn in a given month. All employees covered by the FLSA are required to be paid at least the federal minimum wage. If a particular state s minimum wage is greater than the federal wage, then covered employees in that state are entitled to the higher wage. It is important to note that the higher state minimum wages do not always cover the same worker base as the federal minimum wage as governed by the FLSA. In these cases, some workers will be exempt from the higher state minimum wage and as a result will be paid the federal minimum wage. Summaries of the minimum wage data are provided in table 1. The mean minimum wage, standard deviation, minimum and maximum values are provided for each state. The highest minimum wage was found in Washington state which increased $9.32 in 2014 (up from $9.19 in 2013). Washington also has the highest standard deviation in minimum wages across the defined period. Summaries of the total unemployment data are provided in table 2. The mean monthly unemployment, the standard deviation, minimum and maximum values are reported for each state. The average total unemployment rate ranges from a low of 3.6% in Nebraska to a high of 8.3% in West Virginia. In addition to having the highest average total unemployment rate, West Virginia also contains the highest standard deviation for the series (3.1). Similarly, Michigan boasts a high total unemployment average (8.1%) and high volatility in the series (std. dev = 2.7). 3 Adjusted for inflation by dividing monthly state minimum wage by the respective CPI value for that month. 4 Adjusted for inflation by dividing monthly federal minimum wage by the respective CPI value for that month. 6

Summaries of the unemployment data for 16-24 year olds are provided in table 2a. As seen with total unemployment, Nebraska has the lowest average unemployment for 16-24 year olds at 7.8%. Meanwhile, Mississippi has the highest average rate for this cohort at 18.3%. West Virginia also contains the highest standard deviation for this series (5.5). Figure 1 displays the monthly trends of real minimum wage and unemployment for 16-24 year olds in the state of Ohio. The minimum wage data display discrete increases for when the nominal wage is increased then a steady decline as the CPI increases over time. Unemployment on the other hand displays more of a stationary trend with peaks and valleys throughout the designated time period. Figure 3 displays the same data for the state of New York. Predictably, a similar trend exists for both minimum wage and unemployment as seen in Ohio. 4. Econometric Model In order to determine if changes in minimum wage can help forecast changes in unemployment, I evaluate two different model structures. The first model structure with be an auto-regressive model for unemployment, where the current value of unemployment is represented by past values of itself plus a disturbance term. The second model necessary to evaluate is a distributed-lag model where unemployment is represented as not only a function of its past values, but also past values of minimum wage. First we evaluate the autoregressive model (AR). This time series model is a regression where the explanatory variables are past values of the current dependent variable along with an error tem: X = +β X + β X + + β X + ε (1) In this case, X t represents unemployment in time period t, X t-1 X t-n represents past values of unemployment in prior periods 1 through n, and ε t represents an error term. The series of coefficients β 1 β n determines the extent to which each previous period contributes to the current value of unemployment. Thus, unemployment in time t is the sum total of varying degrees of contribution of past values along with ε t which can be interpreted as a series of random shocks. 7

When deriving an AR model, determining the appropriate number of lags (n) is important. For this analysis, lags of n=2, n=4, and n=8 were chosen 5. To ease comparison of the results, the same n is used for all states. For each state in the US, rolling regressions of AR(2), AR(4) and AR(8) models were fitted, Each state has 384 monthly observations of unemployment, state minimum wage and/or federal minimum wage (monthly data for 32 years of coverage). A regression model for each lag is estimated on the first 333 observations 6 and utilizing the coefficients from the estimation, a pseudo out-of-sample one step forecast is made to estimate the value of the 334th observation. Utilizing a series rolling regressions with 333 observations, moving forward one observation at a time, models and forecasts are generated via the method described above for the remaining 50 observations in the each dataset. How these data will be leveraged for the analysis will be described later in this section. The second model for the analysis is a distributed-lag (DL) model. Similar to the AR model, the DL model finds that the effects of the independent variable are spread across time. However, the difference in the DL model is that the independent variables are not just past values of the dependent variable, but of another variable as well. For this analysis, the following form of a DL model is utilized: X = +α Y + +α Y +β X + +β X +ε (2) Just as in the AR model, X t represents unemployment in time t, X t-1 X t-n are the values of unemployment in previous periods 1 through n, and β 1 β n are the coefficients on the lagged values of unemployment. The addition to this DL model is Y t-1 Y t-n, which represents the value of minimum wage in previous periods 1 through n, α 1 α n are the coefficients on the lagged minimum wage terms and dictate how much they contribute to the current value of unemployment. Finally, ε t is an error term that represents a series of random shocks. In addition to generating the forecasts with the DL model, we will also employ a Granger Causality test to determine if minimum wage has explanatory power for unemployment. The impact we are searching for (Granger-Causality) is not of the general cause-and-effect type 5 n=12 was also tested for the 16-24 year old group. 6 The number of in-sample observations varies based on the number of lags. For n=2, there are 331 in-sample observations. For n=4 there are 329, n=8 there are 325, and for n=12 there are 321 in-sample observations. 8

where we determine that a change in one variable will lead to a specific change in another. Rather the test is to determine if a particular variable comes before another 7 in a time series dataset. The Granger Causality test will evaluate the following hypothesis: : = = = =0 (3) The null hypothesis states that past values of minimum wage do not have an effect on the current value of unemployment. If we are able to reject the null hypothesis, then we can infer that changes in minimum wage have some effect on the future state of unemployment. Additionally I will test if the long-run propensity of minimum wage is equal to zero. The long-run propensity of minimum wage is the sum of the coefficient estimates of minimum wage in the model and indicates the total impact that changes in minimum wage have on unemployment. The hypothesis will be defined as: : + + + =0 (4) Just as with the AR models, the same number of lagged observations were selected for both unemployment and minimum wage in the DL models. A similar set of rolling regressions was implemented to generate a forecast value for the last 50 observations of each state dataset. An evaluation of the forecast error for each out-of-sample period will be used to determine which model offers the best forecast. The prediction error for each out-of-sample observation will be defined as: ε = X X (5) Where X t is the value of unemployment in time t and X t is the forecasted value of unemployment for period t. This forecast error will be calculated for all 50 forecast values of each of the six models. For determining an overall prediction error for the models, I calculate the Mean Absolute Squared Prediction Error (MASPE): 7 http://www.statisticshowto.com/granger-causality/ 9

1 50 (6) The squaring of the prediction error prior to taking the mean is to ensure that errors of similar magnitude but opposite signs do not offset one another. The value of the MASPE will be used to evaluate the best forecast model for each state. If the DL models tend to have a lower MASPE than the AR models, then the inclusion of past minimum wage values into the model improved the forecast, suggesting this variable should be included when forecasting unemployment. If the AR models tend to have lower MASPE, then one might conclude nothing is gained by adding minimum wage to the forecast. One last comparison of the accuracy of the forecast models will be comparing the calculated MASPE metric to the standard deviation of a new data series: first-difference of unemployment. In a naïve random walk, the first out-of-sample observation would simply be the previous value of unemployment. By creating a new data series of the first-difference of unemployment, we can compare the ratio of the MASPE to the standard deviation of the new data series. If the ratio is less than one, then the forecast model outperforms the naïve random walk. If the ratio value is greater than one, then the model is no better than the random walk. We can also compare the ratio across the varying models to see which model performed best. 5. Results The MASPE for each state/model of total unemployment is listed in Table 3. The results are mixed as to which model form provided the smallest forecast error. In eleven states the model with the smallest forecast error was an AR model with 8 lagged variables for unemployment. Another nine states found the AR(4) model provided the smallest forecast error while six more states found the AR(2) model to be the best. The remaining states found some form of the DL model to provide the smallest error. In total, 26 states found an AR model to perform best at out-of-sample forecasts while 24 states were best evaluated with DL model. In table 3a, the MASPE for each state/model of unemployment for 16-24 year olds is provided. The results are somewhat similar, albeit reversed, in that 26 states found a DL model to perform best while 24 states did better with an AR model. There was a nearly symmetric breakdown by the model/lag combination that performed best. There were six states each that 10

found either an AR(12) or DL(12) model as the best performing. Twelve states each found an AR(8) or DL(8) model as the best. Five states found an AR(4) model was best while four preferred a DL(4) model. Lastly, the DL(2) model offered the best out-of-sample forecast for four states while only one state had an AR(2) model perform best. Existing research in the minimum wage space would suggest that the addition of minimum wage to a forecast of unemployment should indeed improve the forecast (regardless of the directional impact of minimum wage on unemployment). Even in the research on the topic, there is a good share of results that are not statistically significant, which makes the lack of finding a specific forecast model less surprising. Although the method employed defined the better model, there is not a significant difference in the errors across models. Figure 2 shows the prediction errors across observations for Ohio for the DL(4) and AR(4) models for 16-24 years old unemployment rate. Although the AR(4) model produced a smaller MASPE than the DL(4) model, the forecast error was only 0.4% better. Additionally, the forecast errors are highly correlated and both models over and under-predict the actual value of unemployment in the same pattern. A similar trend is seen with the prediction errors in New York, where an AR(4) model provided the smallest forecast error. Figure 4 displays the prediction errors for the DL(4) and AR(4) model in New York for 16-24 years old unemployment. The results of the Granger-Causality test for total unemployment can be found in Table 4. In only 7% of cases can the null hypothesis of no Granger-Causality be rejected at 95% confidence, indicating that minimum wage does not add a significant amount of in-sample explanatory power for total unemployment. This result is not surprising given the small percentage of the total workforce that minimum wage jobs represent. The results of the Granger-Causality test for unemployment of 16-24 year olds can be found in Table 4a. Here we can reject the null hypothesis of no Granger-Causality in 30% of all cases. However, our ability to reject the null hypothesis decreases as the number of lagged observations increases. When evaluating the results for the n=2 models, we can reject the null hypothesis at 95% in 50% of the cases (25 out of 50 state). However, at n=12, we are only able to reject the null hypothesis 14% of the time (7 out of 50 states). While the results of the test do not allow us to overwhelmingly reject the null hypothesis of no Granger-Causality, the fact that we are able to do so in more cases for 16-24 year olds 11

indicates that minimum wage has a greater potential for in-sample estimation on this group than on total unemployment. Finally we take a look at the long-run propensity (LRP) of minimum wage. The LRP results can be viewed in Table 5. The sum of the minimum wage coefficients is reported along with the p-value of the hypothesis test that the LRP of minimum wage is equal to zero. For the hypothesis test, I find that as more lagged values are added the less likely we are to reject the null hypothesis of no LRP. When evaluating the models with 2 lagged values of minimum wage, the null hypothesis can be rejected in thirty-two states at the 0.05 significance level. However, when evaluating models with 8 and 12 lags, I am only able to reject the null hypothesis in fifteen states. This trend makes sense as some effects from changes in minimum wage will likely become more prevalent over time as firms are more able to make adjustments to labor allocation over a longer time horizon than immediately following an increase 8. Shifting focus to the sign of the coefficient, regardless of significance of hypothesis test, we see that almost unanimously the cumulative effect of minimum wage on unemployment is positive. For models with lags of 2 and 4, all states show a positive effect between minimum age and unemployment. Even for models with 8 and 12 lags, forty-nine states have a positive sum of the minimum wage coefficients. This relationship is consistent with the theory that the existence of wage floors in the labor market will lead to lower employment levels than without (or in this case, higher unemployment). Again, the results here are not consistently significant but rather directionally consistent with the more traditional view of minimum wage effects on employment. LRP results also display another trend consistent with minimum wage theory. Table 7 lists average wages by state based on the 2016 CPS data for hourly workers. The table provides wages for the 5 th percentile, 10 th percentile and median (50 th percentile) as well as the average wage in each state. A total of twelve states 9, or 24%, were able to reject the LRP null hypothesis of zero effect at the 0.05 level for all distributed-lag models. Of those twelve states, 75% have a 5 th percentile wage ranking in the bottom half of all states. Only Nebraska, Washington and Wisconsin have 5 th percentile wages in the upper half of all states. When evaluating the average 8 Arguments exist for the immediate impact on employment from changes in minimum wage based on the fact the changes are known well in advance giving firms time to adjust. Even with this extended lead time, shifts between labor and capital are such that they can be expected to take place well after the minimum wage is increased. 9 AL, ID, KY, LA, MS, NC, NE, NM, PA, TN, WA, WI are states where the null hypothesis of zero LRP could be rejected for all models tested. 12

wage in these twelve states, we find that 83% 10 have an average wage ranking in the bottom half of all states. Lower wage states may potentially have a larger share of minimum wage jobs, especially for low wages with respect to the 5 th percentile. If a state has a larger share of minimum wage jobs, then it is unsurprising that changes in the minimum wage may indeed have a long-run impact on unemployment in that state. 6. Conclusion Based on the selection criterion of MASPE, the results of this analysis suggest that minimum wage may not be a uniformly useful variable for forecasting unemployment as the inclusion of lagged minimum wage terms to an autoregressive model of unemployment does not regularly improve the forecast error. When examining unemployment of 16-24 year olds, there was a slight favoring of the distributed lag models 11 as compared to total unemployment which slightly favored autoregressive models 12. Additionally, the MASPE of each model was almost unanimously larger than the standard deviation of the first-difference of unemployment, indicating that the unemployment forecast models tested do not outperform a naïve random walk of unemployment. When evaluating Granger-Causality, we cannot conclusively state that minimum wage offers significant in-sample explanatory power to the unemployment models as evaluated here. We can only reject the null hypothesis of no Granger-Causality in seven percent of the instances for total unemployment. The rejection of the null hypothesis increases to thirty percent when evaluating unemployment for 16-24 year olds. The fact that we do find more in-sample explanatory power in an unemployment model for 16-24 year olds is consistent with economic theory as minimum wage jobs are more prevalent in this cohort. While we might be unable to broadly assert that minimum wage has a significant impact on unemployment, through in-sample explanatory power or out-of-sample forecasting ability, we do find that the long-run propensity (LRP) of minimum wage is statistically different from zero in twelve states. Of those twelve states, 83% of them have an average wage in the bottom half of 10 When evaluating median wages, Washington and Wisconsin again rank in the top half of all states. 11 When evaluating unemployment of 16-24 year olds, 26 states found a DL model to offer the lowest MASPE. 12 When evaluating total unemployment, 26 states found an AR model to offer the lowest MASPE. 13

all states. If the low wages in these states are driven by a higher share of minimum wage jobs, then it is unsurprising that we are finding a long-term impact of minimum wage on unemployment. Furthermore, when evaluating the directional impact of LRP we find a positive relationship between minimum wage and unemployment, which is consistent with the theory that increases in minimum wage adversely affect employment levels. While we were unable to reject LRP being zero in all states, the fact that the sum of minimum wage coefficients was positive in 99% of all models tested is an interesting finding in-and-of itself. Further research into the relationship of minimum wage and employment should focus on finding a definitive and directionally consistent in-sample association between the two. One area to explore would be how the effect of minimum wage changes varies by state. It is likely that uniform increases in minimum wage would be inappropriate as some states have a higher preponderance of minimum wage jobs and thus would be affected differently than states with a smaller percentage of these jobs. Being able to consistently and precisely quantify the impact of changes in minimum wage on employment, be it within an particular industry, across industries within a specific demographic or with consideration of both these factors within a state, would seem to have the most benefit and can help better evaluate competing legislative priorities. 14

References Brown, Charles, Curtis Gilroy, and Andrew Kohen. The Effect of the Minimum Wage on Employment and Unemployment. In: Journal of Economic Literature. Vol. 20, No. 2 (June), pp. 487-528. Card, David, Lawrence F. Katz, and Alan B. Krueger. Comment on David Neumark and William Wascher, Employment Effects of Minimum and Subminimum Wages: Panel Data on State Minimum Wage Laws. In: Industrial and Labor Relations Review (1994) Vol. 47, No. 3 (April), pp. 487-96. Card, David, and Alan B. Krueger. Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania. In: American Economic Review (1994) Vol. 84, No. 5 (December), pp. 772-93. Card, David, and Alan B. Krueger. Myth and Measurement: The New Economics of the Minimum Wage. In: Princeton, NJ: Princeton University Press (1995). Card, David, and Alan B. Krueger. Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania: Reply. In: American Economic Review (2000) Vol. 90, No.5 (December), pp. 1397-1420. Goldfarb, Robert S. The Policy Content of Quantitative Minimum Wage Research. In: Proceedings of the Industrial Relations Research Association Vol. 27, pp. 261-68. Hamermesh, Daniel S. Myth and Measurement: The New Economics of the Minimum Wage: Comment. In: Industrial and Labor Relations Review (1995) Vol.48, No.4 (July), pp. 830-834. Minimum Wage Study Commission. 1981. Report of the Minimum Wage Study Commission. (1981), Vol. 1, Washington, D.C. Neumark, David, and William Wascher. Minimum Wages and Employment: A Review of Evidence from the New Minimum Wage Research. In: Working Paper 12263. National Bureau of Economic Research. Neumark, David, and William Wascher. The Effect of New Jersey s Minimum Wage Increase on Fast-Food Employment: A Reevaluation Using Payroll Records. In: American Economic Review (2000) Vol.90, No.5 (December), pp. 1362-96. Stigler, George J. The Economics of Minimum Wage Legislation. In: American Economic Review (1946) Vol. 36, No. 3 (June), pp. 358-65. Statistics How To. Granger Causality: Definition, Running the Test. 6 June 2017. http://www.statisticshowto.com/granger-causality/. 15

A Tables Table 1 - State Minimum Wage Descriptives 1983-2014 State Minimum Maximum Mean Std Dev Alabama No State Minimum Wage Alaska $3.85 $7.75 $6.02 $1.53 Arizona $6.75 $7.90 $7.57 $0.40 Arkansas $2.95 $6.25 $4.94 $1.21 California $3.35 $8.00 $6.00 $1.78 Colorado $2.50 $8.00 $5.21 $2.02 Connecticut $3.37 $8.70 $6.16 $1.97 Delaware $3.00 $7.25 $5.50 $1.58 Florida $6.40 $7.93 $7.48 $0.52 Georgia $1.25 $5.15 $4.13 $1.10 Hawaii $3.35 $7.25 $5.67 $1.45 Idaho $2.30 $7.25 $5.09 $1.75 Illinois $2.30 $8.25 $5.69 $1.98 Indiana $2.00 $7.25 $4.77 $1.98 Iowa $3.35 $7.25 $5.82 $1.23 Kansas $1.60 $7.25 $3.76 $2.18 Kentucky $2.60 $7.25 $5.18 $1.58 Louisiana No State Minimum Wage Maine $3.35 $7.50 $5.61 $1.57 Maryland $3.35 $7.25 $5.30 $1.46 Massachusetts $3.35 $8.00 $5.95 $1.82 Michigan $3.35 $7.40 $5.29 $1.71 Minnesota $3.35 $6.15 $5.03 $1.06 Mississippi No State Minimum Wage Missouri $3.80 $7.50 $5.86 $1.31 Montana $2.75 $7.90 $5.46 $1.69 Nebraska $1.60 $7.25 $5.03 $1.83 Nevada $2.75 $8.25 $5.50 $1.92 New Hampshire $3.35 $7.25 $5.33 $1.46 New Jersey $3.35 $8.25 $5.68 $1.71 New Mexico $3.35 $7.50 $5.15 $1.69 New York $3.35 $8.00 $5.48 $1.74 North Carolina $3.35 $7.25 $5.25 $1.51 North Dakota $3.40 $7.25 $5.66 $1.32 Ohio $2.30 $7.95 $5.05 $2.07 Oklahoma $3.35 $7.25 $5.28 $1.46 Oregon $3.10 $9.10 $6.37 $2.13 Pennsylvania $3.35 $7.25 $5.37 $1.50 Rhode Island $3.35 $8.00 $5.87 $1.66 South Carolina No State Minimum Wage 16

Table 1 - State Minimum Wage Descriptives 1983-2014 State Minimum Maximum Mean Std Dev South Dakota $2.80 $7.25 $5.19 $1.58 Tennessee No State Minimum Wage Texas $1.40 $7.25 $4.67 $2.02 Utah $3.80 $7.25 $5.76 $1.22 Vermont $3.35 $8.73 $6.08 $2.00 Virginia $2.65 $7.25 $5.09 $1.71 Washington $2.30 $9.32 $6.23 $2.47 West Virginia $3.05 $7.25 $5.29 $1.55 Wisconsin $3.25 $7.25 $5.32 $1.49 Wyoming $1.60 $5.15 $3.41 $1.78 US - National $3.35 $7.25 $4.95 $1.31 17

Table 2 Unemployment Rate Descriptives 1983-2014 Unemployment Rate for Total Population State Minimum Maximum Mean Std Dev Alaska 6.3 11.2 7.7 1.3 Alabama 3.8 15.4 7.0 2.4 Arkansas 4.2 10.3 6.5 1.5 Arizona 3.7 11.3 6.2 1.8 California 4.7 12.2 7.4 2.1 Colorado 2.7 8.9 5.5 1.6 Connecticut 2.2 9.2 5.4 1.8 Delaware 3.0 8.7 5.0 1.6 Florida 3.1 11.2 6.1 2.0 Georgia 3.4 10.5 6.0 1.8 Hawaii 2.4 7.3 4.7 1.4 Iowa 2.4 9.1 4.6 1.4 Idaho 2.9 10.1 6.0 1.6 Illinois 4.1 13.1 7.0 2.0 Indiana 2.9 12.5 6.0 2.1 Kansas 3.2 7.3 4.8 0.9 Kentucky 4.0 12.1 6.9 1.9 Louisiana 3.9 13.1 7.4 2.3 Massachusetts 2.6 8.9 5.4 1.7 Maryland 3.3 8.0 5.1 1.2 Maine 3.2 8.8 5.7 1.5 Michigan 3.2 16.4 7.8 2.7 Minnesota 2.5 8.9 4.9 1.3 Missouri 3.1 10.6 6.0 1.6 Mississippi 5.0 12.8 7.7 2.0 Montana 2.9 8.8 5.8 1.3 North Carolina 3.0 11.3 5.8 2.1 North Dakota 2.5 6.2 3.8 0.9 Nebraska 2.3 6.3 3.5 0.9 New Hampshire 2.2 7.4 4.3 1.4 New Jersey 3.5 9.8 6.1 1.8 New Mexico 3.7 10.5 6.6 1.4 Nevada 3.7 13.7 6.6 2.7 New York 4.0 9.3 6.4 1.4 Ohio 3.8 14.0 6.6 2.0 Oklahoma 2.9 8.9 5.4 1.4 Oregon 4.7 11.9 7.1 1.8 Pennsylvania 4.0 12.7 6.2 1.7 Rhode Island 2.9 11.3 6.4 2.4 South Carolina 3.5 11.8 6.6 2.0 South Dakota 2.4 5.9 3.7 0.8 18

Table 2 Unemployment Rate Descriptives 1983-2014 Unemployment Rate for Total Population State Minimum Maximum Mean Std Dev Tennessee 3.7 12.9 6.4 1.9 Texas 4.0 9.2 6.3 1.3 Utah 2.3 9.6 4.8 1.5 Virginia 2.1 7.8 4.6 1.3 Vermont 2.6 7.3 4.5 1.1 Washington 4.6 12.0 6.8 1.7 Wisconsin 3.0 11.9 5.5 1.7 West Virginia 4.1 18.8 8.3 3.1 Wyoming 2.7 9.4 5.2 1.5 US - National 3.8 10.4 6.3 1.6 Total population unemployment is defined as all people who are jobless, actively seeking work, and available to take a job. The total unemployment rate is calculated as the number of unemployed divided by the labor force. 19

Table 2a Unemployment Rate Descriptives 1983-2014 Unemployment Rate for 16-24 Year Olds State Minimum Maximum Mean Std Dev Alaska 4.7 27.1 14.8 3.6 Alabama 5.1 35.1 15.6 4.8 Arkansas 5.8 28.6 14.6 3.8 Arizona 3.8 26.9 12.6 4.8 California 8.4 26.1 14.3 3.7 Colorado 3.4 24.4 11.8 3.4 Connecticut 1.2 23.7 11.1 4.1 Delaware 1.1 22.3 10.3 4.3 Florida 5.6 25.3 12.2 3.5 Georgia 4.3 34.7 13.4 4.3 Hawaii 1.7 27.4 11.1 3.8 Iowa 2.0 18.7 9.5 3.0 Idaho 3.7 25.6 12.2 4.2 Illinois 3.5 25.5 13.6 3.6 Indiana 0.7 26.8 12.6 4.5 Kansas 3.7 23.6 10.3 2.8 Kentucky 5.8 28.0 14.8 3.9 Louisiana 2.7 34.0 15.9 5.0 Massachusetts 3.7 24.0 10.4 3.7 Maryland 2.5 24.7 11.9 3.2 Maine 2.9 24.5 12.1 3.9 Michigan 5.7 28.2 14.3 3.8 Minnesota 2.0 19.5 9.4 2.8 Missouri 4.0 24.5 12.4 3.6 Mississippi 3.3 37.8 18.3 4.9 Montana 4.1 26.3 12.0 3.6 North Carolina 4.9 26.2 13.0 4.5 North Dakota 1.1 19.2 8.1 2.6 Nebraska 0.9 14.6 7.8 2.5 New Hampshire 0.7 21.2 9.3 3.4 New Jersey 5.3 23.8 12.0 3.4 New Mexico 2.5 27.3 14.1 4.2 Nevada 3.3 36.0 12.6 4.8 New York 6.1 21.5 13.4 2.8 Ohio 6.4 26.7 13.1 3.2 Oklahoma 3.9 28.1 11.7 3.4 Oregon 2.9 28.8 14.3 4.1 Pennsylvania 6.2 24.2 12.7 2.8 Rhode Island 2.9 26.5 12.4 4.5 South Carolina 3.9 28.9 15.0 4.4 South Dakota 1.6 15.9 8.2 2.4 20

Table 2a Unemployment Rate Descriptives 1983-2014 Unemployment Rate for 16-24 Year Olds State Minimum Maximum Mean Std Dev Tennessee 4.3 28.5 13.8 4.7 Texas 6.8 19.2 13.4 2.2 Utah 2.9 21.2 9.2 3.1 Virginia 2.7 23.3 11.3 3.7 Vermont 1.2 22.7 10.0 3.4 Washington 4.5 29.5 14.4 4.0 Wisconsin 2.1 20.7 10.7 3.3 West Virginia 2.8 35.4 17.7 5.5 Wyoming 3.9 24.8 12.2 4.0 16-24 year old unemployed are defined as those who are ages 16-24 and are jobless, actively seeking work, and available to take a job. The total unemployment rate for 16-24 year olds is calculated as the number of 16-24 unemployed divided by the total number of 16-24 individuals in the labor force. 21

Table 3 Forecast Model Errors MASPE Forecast Errors for Total Population Unemployment Rate MASPE MASPE MASPE State AR2 DL2 AR4 DL4 AR8 DL8 Alaska 0.00747 0.00747 0.00738 0.00737 0.00734 0.00734* Alabama 0.00544 0.00544 0.00543 0.00544 0.00534* 0.00534 Arkansas 0.00363 0.00363 0.00362* 0.00363 0.00363 0.00363 Arizona 0.00286 0.00286 0.00281 0.00277 0.00278 0.00276* California 0.00134* 0.00135 0.00137 0.00137 0.00137 0.00137 Colorado 0.00283 0.00291 0.00275* 0.00278 0.00278 0.00277 Connecticut 0.00223 0.00228 0.00216* 0.00219 0.00217 0.00219 Delaware 0.00338 0.00338 0.00332 0.00331* 0.00332 0.00336 Florida 0.00201 0.002* 0.00208 0.00205 0.00208 0.00210 Georgia 0.00201 0.00201 0.00201 0.00201 0.00199* 0.00200 Hawaii 0.00226 0.00224 0.00213 0.00211* 0.00213 0.00213 Iowa 0.00782 0.00782 0.00774* 0.00774 0.00777 0.00778 Idaho 0.00794 0.00798 0.00791 0.00797 0.00776* 0.00778 Illinois 0.00317 0.00320 0.00313 0.00315 0.00304 0.00303* Indiana 0.00269 0.00269 0.00269 0.00269 0.00267 0.00267* Kansas 0.00462 0.00462 0.0046* 0.00461 0.00461 0.00463 Kentucky 0.00433 0.00433 0.00421 0.00421 0.00416 0.00415* Louisiana 0.00607* 0.00608 0.00615 0.00619 0.00625 0.00629 Massachusetts 0.00313 0.00315 0.00312* 0.00313 0.00316 0.00316 Maryland 0.00189 0.00189* 0.00192 0.00193 0.00193 0.00194 Maine 0.00968 0.00968 0.00970 0.00971 0.00967* 0.00969 Michigan 0.00666 0.00668 0.00661 0.00663 0.00657 0.00656* Minnesota 0.00964 0.00964 0.00961 0.00961 0.00958* 0.00961 Missouri 0.00531 0.00530 0.00534 0.00532 0.00528 0.00527* Mississippi 0.00406 0.00406 0.00405 0.00406 0.00407 0.00405* Montana 0.01082 0.01085 0.01084 0.01079 0.01074 0.01064* North Carolina 0.00232 0.00232 0.0023* 0.00233 0.00231 0.00234 North Dakota 0.02575 0.02576 0.02579 0.02575* 0.02598 0.02590 Nebraska 0.00731 0.00734 0.00713 0.00715 0.00710 0.00705* New Hampshire 0.00414 0.00415 0.00406 0.00406* 0.00415 0.00414 New Jersey 0.00209 0.00208 0.00209 0.00209 0.00207 0.00205* New Mexico 0.00339 0.00343 0.00340 0.00343 0.00336 0.00336* Nevada 0.00052 0.00055 0.00044 0.00046 0.00043* 0.00044 New York 0.0022* 0.00220 0.00223 0.00223 0.00222 0.00221 Ohio 0.00475 0.00477 0.00469 0.00471 0.00465 0.00462* Oklahoma 0.00258 0. 00258 0.00252 0.00253 0.00250 0.00249* Oregon 0.00316 0.00318 0.00315 0.00317 0.00315* 0.00315 Pennsylvania 0.00444 0.00445 0.00443 0.00444 0.00438* 0.00438 22

Table 3 Forecast Model Errors MASPE Forecast Errors for Total Population Unemployment Rate MASPE MASPE MASPE State AR2 DL2 AR4 DL4 AR8 DL8 Rhode Island 0.00270 0.00274 0.00254* 0.00256 0.00255 0.00256 South Carolina 0.00248 0.00249 0.00246 0.00246 0.00244* 0.00245 South Dakota 0.01059* 0.01059 0.01067 0.01066 0.01073 0.01072 Tennessee 0.00305 0.00305 0.00303 0.00303 0.00298 0.00298* Texas 0.00268 0.00270 0.00265 0.00266 0.00264 0.00263* Utah 0.00461 0.00467 0.00461 0.00464 0.00461* 0.00466 Virginia 0.0026* 0.00260 0.00261 0.00262 0.00260 0.00262 Vermont 0.00597* 0.00601 0.00598 0.00604 0.00602 0.00606 Washington 0.00279 0.00279 0.00279 0.00277 0.00278 0.00277* Wisconsin 0.00786 0.00789 0.00786 0.00788 0.00778* 0.00787 West Virginia 0.00490 0.00492 0.00489* 0.00490 0.00493 0.00489 Wyoming 0.00837 0.00839 0.00830 0.00829* 0.00840 0.00832 Mean absolute squared prediction error is calculated for each model structure in each state. Total Population, as defined by the CPS, are all people who are jobless, actively seeking work, and available to take a job. *Indicates forecast model with smallest Mean Absolute Squared Percent Error. 23

Table 3a Forecast Model Errors MASPE Forecast Errors for 16-24 Year Old Unemployment Rate Mean Absolute Squared Prediction Error (MASPE) State AR2 DL2 AR4 DL4 AR8 DL8 AR12 DL12 Alaska 0.0694 0.0687 0.0682 0.0678* 0.0705 0.0712 0.0737 0.0738 Alabama 0.0638 0.0608 0.0605 0.0593 0.0548 0.0546* 0.0569 0.0565 Arkansas 0.0458 0.0450 0.0449 0.0447 0.0433* 0.0438 0.0458 0.0468 Arizona 0.0872 0.0777 0.0769 0.0715 0.0748 0.0713* 0.0763 0.0720 California 0.0098 0.0098 0.0094 0.0095 0.0093 0.0094 0.0088* 0.0090 Colorado 0.0528 0.0521 0.0507 0.0511 0.0459* 0.0481 0.0474 0.0488 Connecticut 0.0573 0.0531 0.0487 0.0475 0.0447 0.0435* 0.0446 0.0488 Delaware 0.0896 0.0890 0.0745 0.0756 0.0633 0.0668 0.0599* 0.0603 Florida 0.0175 0.0172 0.0170 0.0173 0.0157 0.0171 0.0155* 0.0163 Georgia 0.0597 0.0553 0.0565 0.0545 0.0523 0.0523 0.0522* 0.0527 Hawaii 0.0978 0.0981 0.0985 0.0982 0.0961 0.0960* 0.0984 0.0972 Iowa 0.1149 0.1138 0.1127 0.1123 0.1076 0.1074* 0.1158 0.1159 Idaho 0.0953 0.0865 0.0890 0.0850 0.0807 0.0794* 0.0852 0.0838 Illinois 0.0253 0.0235 0.0233 0.0226 0.0235 0.0228 0.0229 0.0226* Indiana 0.0825 0.0803* 0.0857 0.0851 0.0841 0.0837 0.0842 0.0845 Kansas 0.0946 0.0934 0.0815 0.0807 0.0819 0.0818 0.0774 0.0773* Kentucky 0.0511 0.0489 0.0508 0.0493 0.0478 0.0470* 0.0494 0.0487 Louisiana 0.0724* 0.0751 0.0800 0.0824 0.0854 0.0888 0.0901 0.0961 Massachusetts 0.0906 0.0905 0.0815 0.0814 0.0786* 0.0795 0.0815 0.0820 Maryland 0.0571 0.0549 0.0578 0.0569 0.0536 0.0532* 0.0536 0.0540 Maine 0.0453 0.0445 0.0427 0.0432 0.0376 0.0374* 0.0383 0.0389 Michigan 0.0293 0.0291 0.0257 0.0256 0.0262 0.0262 0.0230* 0.0233 Minnesota 0.0345 0.0322 0.0311 0.0307 0.0298 0.0300 0.0287 0.0284* Missouri 0.0511 0.0491 0.0482 0.0474 0.0464* 0.0468 0.0474 0.0481 Mississippi 0.0715 0.0665 0.0672 0.0638 0.0590 0.05710* 0.0621 0.0599 Montana 0.1138 0.1244 0.1134 0.1231 0.1038* 0.1133 0.1169 0.1303 North Carolina 0.0326 0.0304 0.0306 0.0301 0.0279 0.0278* 0.0292 0.0291 North Dakota 0.1838 0.1904 0.1752* 0.1827 0.1898 0.1960 0.1997 0.2095 Nebraska 0.0695 0.0685 0.0629* 0.0633 0.0674 0.0695 0.0683 0.0716 New Hampshire 0.0514 0.0507 0.0518 0.0508 0.0491 0.0492 0.0473 0.0471* New Jersey 0.0265 0.0298 0.0222 0.0243 0.0206* 0.0225 0.0226 0.0227 New Mexico 0.0911 0.0948 0.0912 0.0945 0.0911* 0.0946 0.0949 0.1008 Nevada 0.0623 0.0513 0.0549 0.0518 0.0462 0.0470 0.0452* 0.0467 New York 0.0202 0.0201 0.0178 0.0177* 0.0179 0.0181 0.0181 0.0181 Ohio 0.0310 0.0309 0.0293* 0.0295 0.0293 0.0298 0.0300 0.0301 Oklahoma 0.0774 0.0773 0.0767* 0.0768 0.0779 0.0794 0.0786 0.0790 Oregon 0.0479 0.0444* 0.0488 0.0467 0.0474 0.0458 0.0498 0.0483 Pennsylvania 0.0260 0.0252* 0.0265 0.0259 0.0280 0.0277 0.0305 0.0302 Rhode Island 0.0499 0.0498 0.0479 0.0476 0.0441* 0.0443 0.0457 0.0460 South Carolina 0.0487 0.0467 0.0466 0.0452 0.0404 0.0402* 0.0420 0.0425 South Dakota 0.1090 0.1055 0.1074 0.1050* 0.1068 0.1057 0.1079 0.1062 24