Heterogeneous Impacts of the Minimum Wage

Transcription

1 Heterogeneous Impacts of the Minimum Wage Peter Brummund University of Alabama Michael R. Strain American Enterprise Institute October 31, 2015 [Preliminary Results. Do not cite] Abstract Two features of minimum wages can be used to further our understanding of their economic effects. First, the federal minimum wage is legislated as one nominal value. Since prices vary across geographic regions, the real value of the minimum wage also varies across regions. Second, some states index minimum wages to inflation (a permanent minimum wage), while other states do not. This study seeks to understand how minimum wages impact the labor market through the lens of these two features of minimum wages. We study whether the employment effect of the federal minimum wage is stronger in states with relatively lower prices and in states which index minimum wages to inflation. Our findings go beyond documenting the magnitude of the employment effect and offer a possible explanation for it: firms facing a temporary increase in their wage bill may behave differently than firms facing a permanent increase. The preliminary results show that a permanent minimum wage heightens the negative impact on employment and that the negative impact of the minimum wage is greater in counties with low price levels. Keywords: Minimum wage, inflation, price levels. JEL Classifications: E31, J08, J38. peter.brummund@ua.edu michael.strain@aei.org

2 1 Introduction The vast literature on minimum wages is unsurprising given their importance for assessing different models of the labor market and their prominence in policy debates. It is a credit to today s economists that, despite hundreds of existing studies 1, in the past decade the minimum wage literature continues to grow, introducing productive debate over new empirical methods (Dube, Lester, Reich, 2010; Neumark, Salas and Wascher, 2014) and extending minimum wage analysis to study new topics including, among others, the effect of minimum wages on prices, profits, turnover, and worker performance (Hirsch, Kaufman, and Zelenska, 2015), on poverty (Sabia and Burkhauser, 2010), on where immigrants choose to locate (Orrenius and Zavodny, 2008), on worker flows (Gittings and Schmutte, forthcoming), on job growth (Meer and West, 2015), and even on youth drinking and drunk driving (Sabia, Pitts, and Argys, 2014) often motivated by a richer understanding of the economics of minimum wages. We build on these developments by continuing to move the literature beyond the employment impacts of minimum wages. This paper studies heterogeneity, both across geography and across policy design. Specifically, this paper asks whether three factors local prices, local mobility rates, and the indexing of minimum wages to inflation lead to heterogeneous employment effects of minimum wages. We find evidence that they do. States that index minimum wages to inflation have larger negative employment effects than those that do not. To the best of our knowledge, our paper is the first to study the effects of this minimum-wage policy design. In addition, we find that counties with relatively low prices have larger disemployment effects than those with higher prices. And less mobile counties have larger disemployment effects of minimum wages than higher mobility counties. Given costly capital investment, firms may be reluctant to change their labor force in 1 A Google Scholar search in the summer of 2015 found 5,240 papers with the exact phrase minimum wage in the title of the article.

3 response to a nominal minimum wage increase under the expectation that such an increase will be temporary, eaten away as prices rise (Sorkin 2015). This suggests that indexing minimum wages to inflation and thereby making them permanent could induce a very different response to minimum wage increases on the part of firms. If firms thinks they will have to live with higher and growing minimum wages into the medium term, they may be much more willing to adjust their production function, including their labor forces, in response to the increase. We find that permanent minimum wages do have stronger disemployment effects than nominal minimum wages. Our estimates for the traditional impact of the minimum wage on employment in the restaurant sector find small negative impacts, ranging from to Our preferred specification focuses on the county-pair sample, including controls for both the county and county-pair, and finds a statistically significant negative impact on employment of Our estimates of the impact of the permanent minimum wage on employment range from to Our preferred specification finds a significant estimate of Lower-wage counties should be expected to respond relatively more strongly to minimum wage increases because their effect on relative prices will be stronger among areas with lower local wages. While local wages have long been included as a control in minimum wage studies, to our knowledge, we are the first to explicitly allow this effect to freely vary. We find that the disemployment effect of minimum wages is relatively smaller in counties with relatively higher local prices. Finally, we study whether lower-mobility counties are differentially affected by minimum wages. Here are results are less strong, but they do provide suggestive evidence that lowermobility counties (as determined by Chetty et al., 2014) experience stronger disemployment effects from minimum wages than do higher-mobility counties. We speculate that this result could be driven by the bargaining power of local firms. This paper uses data from the Quarterly Census of Employment and Wages (QCEW) 2

4 program, which contain labor market data on workers who are covered by the Unemployment Insurance program. We study employment in privately owned restaurants from 1990Q1 to 2012Q3. We construct two analysis samples. The first covers all counties in the United States. The second is based on Dube, Lester, and Reich (2010) and is restricted to county-pairs in which both counties in the pair share a border but are located in different states. We estimate difference-in-difference models on both samples using a variety of controls and, in the countypair models, exploiting the structure of the dataset. We pay particular attention to the need to control for state-specific linear trends, providing multiple tests of the appropriateness of their inclusion. 2 Related Literature The economics literature on minimum wages is massive in size, and we do not attempt to survey it here. For excellent surveys, see Neumark and Wascher (2008), Card and Krueger (1995), and Brown (1999). We provide a broad review of the literature that is directly relevant to our paper. Specifically, we survey the literature as it relates to inflation-adjusting minimum wages, how the employment effects of minimum wage increases might vary across counties with different average wages, how employment effects may vary across areas characterized by differing rates of economic mobility, and whether it is econometrically appropriate to include state-specific linear trends in estimating the employment effects of minimum wage increases. 2.1 Permanent Minimum Wages Economics majors are often surprised by the saw-tooth pattern of inflation-adjusted minimum wages over time. This commonly used graph is a useful heuristic to teach undergraduates the important lesson that inflation erodes nominal quantities over time. It is less remarked upon both by economists and the policy community that the saw- 3

5 tooth pattern indicates that the real value of the minimum wage has had a (relatively) flat trend since the 1960s. In other words, in real terms, the minimum wage hasn t experienced an increase of any sustained length of time in decades. 2 Figure 1: Time Trend in Federal Minimum Wage This fact has significant implications for interpreting the existing literature on minimum wages. The minimum wage literature estimates short-run employment responses often contemporaneous, within quarter. Short-run responses don t leave much room for employment effects that are driven by the slower process of substituting capital for labor, or by other adjustments that likely take longer than three months (Baker, Benjamin, and Stranger, 1999; Hamermesh, 1995). Still, the literature s focus on the short-run response of employment to minimum wage increases is reasonable given relatively high turnover rates and hours flex- 2 The inflation-adjusted trend is obviously sensitive to the measure of inflation used in the calculation. But broadly speaking, the point remains. 4

6 ibility in industries that employ large numbers of minimum wage workers (Brown, Gilroy, and Kohen, 1982; Card and Krueger, 1995). In addition, the literature s focus on the short-run response is reasonable if firms expect the increase to be temporary, and therefore don t engage in structural changes to their production functions in response to it. But the employment elasticity of inflation-adjusted permanent minimum wage increase may be very different than the employment elasticity of a nominal, temporary minimum wage increase (Sorkin 2015). These issues were understood clearly seven decades ago by Richard A. Lester, writing in the American Economic Review in March 1946: From much of the literature the reader receives the impression that methods of manufacture readily adjust to changes in the relative costs of productive factors. But the decision to shift a manufacturing plant to a method of production requiring less or more labor per unit of output because of a variation in wages is not one that the management would make frequently or lightly. Such action involves the sale (at a loss?) of existing facilities not usable under the new method and the purchase of new facilities and equipment to replace those discarded, to say nothing of retraining workers and readapting the whole organization. Such new investment presumably would not be undertaken simply to reduce a current and expected net loss, or if there was a likelihood that the wage change would only be temporary or that the cost relationships between factors would be considerably altered again in the near future (italics ours). Minimum wage increases have been temporary for the entire existence of modern empirical labor economics until the last few years. The literature stretching back at least to Lester suggests that forward-looking firms may react quite differently to a permanent increase in the cost of low-skilled labor than they do to temporary increases. We seek to test that in this paper. 5

7 2.2 Real Minimum Wages Economists have been interested in the bite of the minimum wage for decades (e.g., Kaitz, 1970) and that interest continues to the present day (Garnero, Kampelmann, and Rycx, 2013; Clemens and Wither, 2014; Hirsch, Kaufman, and Zelenska, 2014). It has been common in the literature to include control variables for macroeconomic conditions, such as overall demand, in order to avoid confounding employment effects from minimum wage increases with other drivers of employment changes. And papers often limit their estimation sample to industries and types of workers for which the minimum wage will plausibly have an effect e.g., by focusing on employment among teenagers and young adults (Neumark and Wascher, 1992), employment among lesser-skilled workers (Burkhauser, Couch, and Wittenburg, 2000a), or employment among low-wage industries (Dube, Lester, and Reich, 2010). In addition, the early papers of the new minimum wage literature featured debate over how to properly measure changes in the minimum wage itself, out of concern for appropriately capturing its bite. Should the Kaitz index be used, or the log of the binding minimum wage in each state (e.g., Neumark and Wascher, 1992; Card, Katz, and Krueger, 1994; Neumark and Wascher, 1994)? Should year effects be included (Burkhauser, Couch, and Wittenburg, 2000b)? Some authors include a measure of the adult wages, both to capture macroeconomic conditions that would impact youth employment rates and because economic theory suggests it belongs in a labor demand equation (Card and Krueger, 1995; Burkhauser, Couch, and Wittenburg, 2000b). More recent research uses identification strategies that include geographic and time effects to control for these confounding factors. We take a different approach. Rather than trying to control for the bite which yields an average effect, giving more weight to regions with bigger bite we attempt to estimate and quantify the differential employment impact of minimum wage increases across counties, thereby allowing regions with different bites to have different employment effects. 6

8 Our specification allows the employment effect of the minimum wage to vary across counties with different local wages. This is of interest because it is plausible that the minimum wage has quite different employment effects in lower-wage counties than it does in higher-wage counties, either because of direct differences in wage differences or because wage differences reflect general differences in prices. 2.3 Minimum Wages and Mobility Whether relatively vulnerable groups of workers have been disproportionately impacted by minimum wage increases has been a significant question in the minimum wage literature (Burkhauser, Couch, and Wittenburg, 2000a). Today, there is much concern in the public debate over economic mobility, and there is growing evidence that an individual s environment matters significantly to his economic outcomes (Chetty, Hendren, and Katz, 2015; Chetty et al., 2014). We seek to test whether the employment effects of the minimum wage vary by the economic mobility of counties. The merits of minimum wage increases are surely driven in part by their employment effects among vulnerable populations, including among populations living in low-mobility areas. In our analysis, we measure mobility following Chetty et al. (2014) and use the measure of mobility generously provided by them on their paper s website. This measure computes the percentile rank in the income distribution of the ith child (c i ) and of the ith s child s parents (p i ) and regresses the child s rank against the parent s rank, generating what Chetty et al. define as the rank-rank slope, which measures the relationship between a child s position in the income distribution and his parents position. Parent income is defined as average income over the five years from 1996 to Child income is defined as average income in the two years, 2011 and 2012, when children are in their early 30s. The rank-rank slope is defined at the county level. See Chetty et al. for a detailed description. 7

9 2.4 State-Specific Linear Trends There is currently a lively debate among labor economists over the appropriate econometric specification of minimum wage studies. It is clearly the case that state minimum wages are not random, and unobserved factors that influence state minimum wages may also influence employment (Allegretto et al., 2015). The canonical two-way fixed effects econometric model using within-state and within-time-period variation validly identifies the effect of the minimum wage on employment provided that the treatment and control states are on parallel employment trends prior to the minimum wage increase. In a seminal paper, Card and Krueger (1994) provided a case study of New Jersey s 1992 minimum wage increase by comparing New Jersey employment with employment in neighboring Pennsylvania, both before and after the increase. Dube, Lester, and Reich (2010) significantly advanced this empirical approach by generalizing it to the entire nation. In their paper, they compare counties that share a border but are located in different states and whose workers are thus subject to different minimum wage laws to estimate the employment effect of minimum wage increases. Concerned that time effects that are constant across counties rules out heterogeneous trends, they also include state-specific linear trends in some of their models. They are unable to find a statistically significant effect of minimum wages on employment. Allegretto, Dube, and Reich (2011) also provides support for the inclusion of state-specific linear trends in minimum wage research designs, which are used in some minimum wage specifications by Gittings and Schmutte (2015) as well. Because these specifications include hundreds of fixed effects and dozens of linear trends, it is natural to ask whether these models are oversaturated. In a paper colorfully titled Revisiting the Minimum Wage-Employment Debate: Throwing Out the Baby with the Bathwater, Neumark, Salas, and Wascher (2014) write the following: We think the central question is whether, out of their concern for avoiding minimum wage variation that is potentially confounded with other sources of employment change, [Allegretto, Dube, and Reich (2011)] and [Dube, Lester, and Reich (2010)] have thrown out so much useful and poten- 8

10 tially valid identifying information that their estimates are uninformative or invalid; that is, have they thrown out the baby along with or worse yet, instead of the contaminated bathwater? Our analysis suggests they have. Meer and West (2015) provide evidence that state-specific (really, jurisdiction-specific) time trends bias estimates of the effect of minimum wage increases towards zero. The results estimated by Clemens and Wither (2014) are robust to including state-specific linear time trends, though the authors write that they share Meer and West s concern that, because of the dynamics with which minimum wage induced employment losses may unfold, direct inclusion of state-specific trends is not a particularly attractive method for controlling for the possibility of differential changes in the economic conditions of each state over time. In a completely separate context an investigation of whether unilateral divorce laws raise divorce rates Wolfers (2006) succinctly summarizes the potential problem with including jurisdiction-specific time trends in models designed to estimate the effect of a policy that likely has dynamic effects: A major difficulty in difference-in-difference analyses involves separating out preexisting trends from the dynamic effects of a policy shock. Wolfers observes that state-specific trends may pick up the effects of a policy and not just preexisting trends. Helpfully, Dube, Lester, and Reich (2010) provide a formal test for the presence of preexisting trends that pose a threat to the valid estimation of employment effects. We utilize their test, discussed more completely in section 4, in order to determine whether to include state-specific linear trends in our models. 3 Empirical Approach We start by following the standard approach in the literature and estimate a differencein-differences model of the form: ln(y it ) = α + βln(mw it ) + δln(pop it ) + φ i + τ t + ɛ it (1) 9

11 where y it is either the log of the average weekly wage in the restaurant sector for county i in quarter t or the log of the number of people employed in the restaurant sector. The independent variable of interest is the log of the relevant minimum wage in that county at time t. All models include county fixed effects φ i and period fixed effects τ t, and when estimating employment effects, we also control for the log of county-level population ln(pop it ). Many papers have extended this basic formulation in various ways. The extension that our data allows us to incorporate is the analysis of county-pairs as pioneered by Dube, Lester, Reich (2010). This model limits the sample to counties that are along state lines bordering counties in other states. Each pair of counties that share a state boundary are linked through a unique pair-id. The analogous specification for this sample is: ln(y ipt ) = α + βln(mw it ) + δln(pop it ) + φ i + τ t + ɛ ipt (2) where y pit represents the employment in the restaurant sector in county i that is part of county-pair p at time t. For each of the specifications used in the following analysis, we estimate both the standard all-county specification and also the county-pair specification. Since the models are very similar, the following discussion will only present the county-pair specification (just remove the p subscript to see the all-county specification). We extend these models to allow for heterogeneous impacts of the minimum wage by interacting a variable which captures the characteristic of interest (permanent, local prices, or mobility) with the minimum wage variable. In the permanent treatment, the interaction term captures whether the impact of the minimum wage on wages and employment differs in states which have indexed their minimum wage to inflation as compared to states which have not done so. This model specification is: ln(y ipt ) = α + βln(mw it ) + γ 1 [ln(mw it ) perm it ] + η perm it + δln(pop it ) + φ i + τ t + ɛ ipt (3) where γ captures the differential impact of a minimum wage policy that has been indexed 10

12 to inflation. Similarly, to capture how the impact of the minimum wage policy depends on local price levels, we interact the minimum wage with a measure of local price levels, price it. ln(y ipt ) = α + βln(mw it ) + γ 2 [ln(mw it ) price it ] + η price it + δln(pop it ) + φ i + τ t + ɛ ipt (4) In this specification, price it is a continuous variable, whereas the perm it variable above is a dummy variable. Therefore γ 2 estimates the gradient of the relationship between minimum wages and employment as influenced by local prices. For example, an estimate of ˆγ 2 > 0 would indicate that the minimum wage has a more positive impact (or less of a negative impact) on wages or employment in counties with higher local prices. The last characteristic that we think influences how a minimum policy may impact wages and employment is the level of economic mobility in that county, mobility it. ln(y ipt ) = α + βln(mw it ) + γ 3 [ln(mw it ) mobility it ] + δln(pop it ) + φ i + τ t + ɛ ipt (5) In order to interpret the γ coefficients as the differential impact of the minimum wage according to the characteristics we consider, we need to assume that the interaction term is uncorrelated with unobserved determinants of the trends in wages and employment (ɛ pit ). One way to assess the validity of this assumption to is analyze the trends in wages and employment before the treatment occurred. While this validity check is easier in a pure event study framework, it can still be performed when there are many treatment dates by examining the leads and lags of the impact of the independent variable. We follow Dube, Lester, Reich (DLR, 2010) and estimate the model: 7 ln(y ipt ) = α + [β 2j 2 ln(mw i,t+2j )] + β 16 ln(mw i,t 16 ) + δln(pop it ) + φ i + τ t + ɛ ipt (6) j= 4 This specification provides estimates of the impact of the minimum wage spanning 25 11

13 quarters, from 16 quarters after to the minimum wage change to 8 quarters prior. As in DLR, 2 represents a two-quarter different operator, so the coefficients represent cumulative changes to each of the leads and lags of the minimum wage. We estimate this model for each of the dependent variables (wages and employment), each of the samples (all-county and county-pair) and each of the specifications (base, permanent, local prices, and mobility). For this base specification, with no interactions, the β coefficients are plotted in Figure 2. In the case of the specifications with interactions, the above specification can easily be modified to also analyze the leads and lags of both the interaction term and the main effect of the characteristic of interest (C {perm, prices, mobility}). 7 ln(y ipt ) = α + [β 2j 2 ln(mw i,t+2j )] + β 16 ln(mw i,t 16 ) (7) + + j= 4 7 {γ 2j 2 [ln(mw i,t+2j ) C i,t+2j ]} + γ 16 [ln(mw i,t 16 ) C i,t 16 ] j= 4 7 [η 2j 2 C i,t+2j ] + η 16 C i,t 16 j= 4 +δln(pop it ) + φ i + τ t + ɛ ipt In this specification, the γ s capture the cumulative impact of the interaction term on the outcome. We plot these γ s for each of the specifications and outcome variables in Figures 3-5. Another way to interpret the inherent assumption of the difference-in-differences technique is that the pre-treatment trends for the treatment and control groups are the same. This assumption can be analyzed graphically by looking at whether the trends in the graphed coefficients differ significantly from 0 before the treatment period, t. While this is just a visual test, the vast majority of the graphs seem to show that the impact of the minimum wage policy before it was implemented is not significantly different from zero. It is also possible to more formally test for the pre-treatment trend. We do so by esti- 12

14 mating a model similar to the one used by Dube.et al. (2010). We estimate ln(y ipt ) = α + η 12 ln(mw i,t+12 ) + η 4 ln(mw i,t+4 ) (8) +η 0 ln(mw i,t ) + δln(pop it ) + φ i + τ t + ɛ ipt for the base case, and also ln(y ipt ) = α + β 12 ln(mw i,t+12 ) + β 4 ln(mw i,t+4 ) + β 0 ln(mw i,t ) (9) +γ 12 C i,t+12 + γ 4 C i,t+4 + γ 0 C i,t +η 12 [ln(mw i,t+12 ) C i,t+12 ] + η 4 [ln(mw i,t+4 ) C i,t+4 ] + η 0 [ln(mw i,t ) C i,t ] +δln(pop it ) + φ i + τ t + ɛ ipt for each characteristic of interest (C {perm, prices, mobility}). In Table 3 below we report both η 12 and η 4, and also the difference between the two, which would capture any trend in the variable of interest between 3 years prior to the minimum wage change and 1 year prior. The top panel shows the results for the base specification and also the permanent treatment, while the bottom panel shows the results for the local price and mobility treatments. For each treatment, the pre-existing trend is tested for the all county sample and the county pair sample. We also include a specification that controls for state-linear trends as well as extra region controls (specifically census division by time period dummies) that was used by DLR. The results of Table 3 indicate that the pre-existing trend is only cause for concern in the mobility treatment, all county sample, without the extra controls. And while we show the results when using the extra regional controls and state linear trends, the results of Table 3 indicate they are unnecessary in this context. In the specifications including all counties, the treatment variable is constant within each state. We therefore cluster the standard errors at the state level to account for this bias. In the county-pair specifications, some observations will be repeated for each pair they are a 13

15 part of, inducing a mechanical correlation across county-pairs. We follow Dube, Lester, and Reich (2010) and cluster the standard errors on the state and border segment separately. 4 Data The Quarterly Census of Employment and Wages (QCEW), formerly known as the ES- 202 program, is a cooperative statistical program administered by the Bureau of Labor Statistics (BLS) and State Employment Security Agencies (SESAs). 3 The data provide monthly employment levels, quarterly wages, and quarterly establishment counts by industry for the US as a whole and at the state and county levels. The QCEW data are based on quarterly reports that are submitted by nearly all employers in the US, Puerto Rico, and the US Virgin Islands. 4 Included in the employment numbers are workers who are covered by US Unemployment Insurance laws, regardless of full- or part-time status and temporary or permanent position. The BLS reports that this covers 97% of all wage and salary civilian employment in the US. 5 Workers who are not in the QCEW employment count include self-employed workers, most agricultural workers on small farms, all members of the Armed Forces, elected officials in most states, most employees of railroads, some domestic workers, most student workers at schools, and employees of certain small nonprofit organizations. 6 In this paper, we focus on county-level QCEW data by industry from the first quarter of 1990 through the third quarter of Following Dube, Lester, and Reich (2010) (DLR), we restrict our data to privately owned restaurants which include the industry groups full-service restaurants and limited-service eating places. 8 Restaurant earnings is the average across the 3 Quarterly Census of Employment and Wages. U.S. Bureau of Labor Statistics. 4 See question 14 at Quarterly Census of Employment and Wages Frequently Asked Questions. U.S. Bureau of Labor Statistics. 5 QCEW Frequently Asked Questions, Q1. 6 QCEW Frequently Asked Questions, Q14. 7 We downloaded the NAICS-Based QCEW data from the BLS. For more information, see Quarterly Census of Employment and Wages Data Files. U.S. Bureau of Labor Statistics. 8 The QCEW uses the North American Industry Classification System (NAICS). From 1990 through 14

16 QCEW s average weekly wage in those industries. To calculate quarterly employment, we take the average across the three months of employment data in each quarter. We then sum across the two industries in our data to obtain total restaurant employment. In our samples, we exclude observations for which the QCEW s disclosure code is non-missing; a non-missing disclosure code indicates that the data are suppressed to protect confidentiality. 9 We create two samples for our analysis. The first sample is a county-level dataset that includes 1,056 counties in the US. The second sample consists of 208 adjacent border county pairs; we use the list of county pairs provided by DLR to create this dataset. 10 Both samples are unbalanced panels, with at most 91 quarters of data between the first quarter of 1990 and the third quarter of In both cases, Puerto Rico and the US Virgin Islands are excluded from the sample. In addition to using data from the QCEW, our analysis relies on state minimum wage data and population data. From 1990 through 2007, we use the minimum wage data provided by DLR. We compile minimum wage data from federal and state government websites for the period between 2008 and Beginning in 2004, San Francisco started setting its minimum wage independent of the state of California. We incorporate its minimum wage levels at the county-level. 12 We obtain county-level estimates for the land area in square miles, population per square mile, and the resident population as of April 1, 2010 from the 2010 Census. 13 The US 2006 and from 2007 through 2010, the QCEW uses NAICS 2002 and NAICS 2007, respectively. After 2010, the QCEW uses NAICS Full-service restaurants and limited-service eating places change codes from NAICS 2002/2007 to NAICS 2012; they shift from 7221 to and 7222 to , respectively. See the robustness section for analyses on other industries: Accommodation and food services (NAICS 72), retail trade (NAICS 44-45), and manufacturing (NAICS 31-33). 9 QCEW Frequently Asked Questions, Q Arindrajit Dube, T. William Lester, and Michael Reich, Replication data for: Minimum Wage Effects across State Borders: Estimates Using Contiguous Counties, Version See the robustness section for the results using balanced panels. 12 For more information on San Francisco s minimum wage, see Minimum Wage Ordinance (MWO). City and County of San Francisco. Santa Fe, New Mexico and Albuquerque, New Mexico also set their own minimum wages independent of that state. We do not take into account those city s minimum wages as they are not set at the county level. 13 The data are from the 2010 Census Summary File 1, Population, Housing units, Area, and Density: County - County Subdivision and Place. To download the data, see Download Center. US Census Bureau American FactFinder. 15

17 Census Bureau also provides annual, county-level population estimates. We keep only those estimates that approximate the number of people living in the county as of July 1st of the relevant year. 14 Our analysis seeks to understand how minimum wages affect earnings and employment by taking into account local price variation, minimum wages that are indexed to inflation, and intergenerational mobility. To measure quarterly local price variation, we calculate average county-level wages across all privately owned industries. Between 1998 and 2006, several states passed legislation to tie their minimum wages to inflation. In our sample, these states are Arizona, Florida, Nevada, Oregon, Washington, Colorado, Missouri, Montana, Vermont, and Ohio. 15 We use the relevant state s government website to identify the year and quarter that the inflation adjustment became effective. To account for intergenerational mobility, we use the rank-rank measure calculated in Chetty et al. (2014). Chetty et al. calculate this measure using data from federal income tax records for the period from 1996 through 2012: We use a rank-rank specification similar to that used by Dahl and DeLeire (2008). We rank children based on their incomes relative to other children in the same birth cohort. We rank parents of these children based on their incomes relative to other parents with children in these birth cohorts. We characterize mobility based on the slope of this rankrank relationship, which identifies the correlation between children s and parents positions in the income distribution. The rank-rank coefficient is at the county level and does not vary with time. In the robustness section, we perform our analysis using the absolute upward mobility ranking also used in Chetty et al. (2014). That measure provides the average income rank of children 14 For more information on how the US Census Bureau calculates population estimates, see About Population Estimates. United States Census Bureau. For the estimates, see State and County Intercensal Estimates by County. United States Census Bureau. For the estimates, see Intercensal Estimates of the Resident Population for Counties: April 1, 2000 to July 1, United States Census Bureau. For the estimates, see Annual Estimates of the Resident Population for Counties: April 1, 2010 to July 1, 2012, United States Census Bureau. 15 Table 1 reports years between 1999 and 2007; those are the years the legislation became effective. 16

18 whose parents are in the 25th percentile of the parent income distribution. Summary statistics for our data are presented in Table 2. The first two columns report the mean and standard deviation for the all-county sample, whereas the last two columns show the county-pair sample. Across the U.S., the restaurant sector employs about 3,600 people in each county, and those restaurant workers earn $177 per week. The retail sector employs 4,679 people on average, and pays $335 a week. The manufacturing sector is even larger, employing 5,667 people, and pays higher wages,average $634 a week. Over the years , the average minimum wage is $5.37 per hour. The all-county sample includes counties in Alaska and Hawaii, whereas those counties are excluded from the county-pair sample as they do not share any borders with counties in other states. 5 Results We start by showing the results of our tests of the pre-trend assumption. Table 3 shows the results of the formal test, whereas figures showing the trends for each of the specifications in our analysis are shown in the Appendix. Table 3 estimates equations 8 and 9, with various sets of controls for both the all-county and county-pair samples. The first panel estimates equation 8, looking for pre-trends in the standard treatment of the minimum wage on employment. The second panel estimates equation 9, looking for pre-trends for the permanent treatment. The third panel shows the results for the pre-trend tests for the real treatment and the last panel shows the results for the mobility analysis. For each treatment, column 1 estimates the base specification on the all-county sample, controlling for just period and county effects. Column 2 adds controls for a state-linear trend on the all-county sample, and column 3 then also includes census division by period controls. Columns 4-7 report results on the county-pair sample. Column 4 shows the results for the base specification, with just period and county controls. Column 5 uses period and countypair controls, column 6 uses period, county, and county pair controls, and then column 7 17

19 uses county and county-pair by period controls. Focusing attention on the third coefficient in each panel, which shows the difference between the impact of the minimum wage on employment between periods t 4 and t 12. In the standard treatment, only column 2 shows a significant result for the trend, indicating that when only including state-linear trends, the estimated impact may be biased due to differences in the pre-trends between the treatment and control groups. For the second panel, the coefficients reported are those on the interaction term between the log of the minimum wage and the permanent variable. In this case, the pre-trend test is valid for all specifications since non of the trends are estimated to be significantly different from zero. For the third panel, the coefficients reported are from the interaction term between the log of the minimum wage and the local price level (proxied for by the average local wage). In this treatment, only column 2 reports a failure of the pre-trend test. Finally, in the last panel, the coefficients reported are from the interaction term between the log of the minimum wage and the local economic mobility level (measured by Chetty et al s rank rank variable). In this treatment, both columns 1 and 2 report a failure of the pre-trend test. We will keep these results in mind as we interpret the results below. Table 4 reports the results of the traditional analysis of the minimum wage, measuring its impact on earnings and employment. The top panel shows the results of estimating equation 2, with columns 1-3 using the all-county sample and columns 4-7 using the county-pair sample. In all specifications, the impact of changes in the minimum wage on wages is statistically significant with the estimates ranging from to The bottom panel reports the estimates for the impact of the minimum wage on employment in the restaurant sector. The results we find are consistent with the previous literature, either small in magnitude or not statistically significant. Our preferred specification is column 6, which uses the county-pair sample, and controls for period, county, and county-pair effects. In this specification, the estimated impact is

20 Table 5 reports the results of estimating equation 3, analyzing the differential impact of a permanent minimum wage on earnings and employment. The structure of the table is similar to that of Table 4, with columns 1-3 using the all-county sample, and columns 4-7 using the county-pair sample. The coefficient of interest is the third one reported in each panel, on the interaction between the log of the minimum wage and the indicator for whether the minimum wage is permanent. In 5 of the 7 specifications, the coefficient is statistically significant, negative, and greater in magnitude than the main effect of the minimum wage on employment. Our preferred specification is column 6, and finds the impact of a permanent minimum wage on employment to be This is twice as large as the main effect of the minimum wage. These results suggest that firms are responding more to minimum wages that are indexed to inflation than to nominal minimum wages. The results in Table 6 correspond to estimating equation 4, analyzing how the impact of minimum wages may differ according to the local price level. The structure of the table is the same as the previous two, and the coefficient of interest is the third one reported, that on the interaction term between the log of the minimum wage and the local average wage. In 6 of the 7 specifications, there is a positive and statistically significant result, indicating that counties with high average wages, the disemployment effect of the minimum is smaller than it is in counties with low average wages. Next, Table 7 reports the results of estimating equation 5, analyzing how the impact of minimum wages may differ by the local level of economic mobility. The coefficient of interest that on the interaction term between the log of the minimum wage and the measure of economic mobility, the rank rank coefficient. The results presented here paint a less consistent picture. In most of the specifications, the relationship is positive, but three specifications do not find a statistically significant relationship. Our preferred specification does find a significantly positive relationship, indicating that counties with high levels of economic mobility experience less of a disemployment effect of the minimum wage, and counties with low levels of economic mobility experience a greater disemployment effect. 19

21 6 Conclusion This paper continues the recent trend in the literature of moving beyond the employment impact of minimum wages by studying heterogeneous impacts of the minimum wage, both across geography and across policy design. Specifically, this paper asks whether three factors local prices, local mobility rates, and the indexing of minimum wages to inflation lead to heterogeneous employment effects of minimum wages. We find evidence that they do. States that index minimum wages to inflation have larger negative employment effects than those that do not. To the best of our knowledge, our paper is the first to study the effects of this minimum-wage policy design. In addition, we find that counties with relatively low prices have larger disemployment effects than those with higher prices. And less mobile counties have larger disemployment effects of minimum wages than higher mobility counties. 20

22 Table 1: State level adoption of Permanent Minimum Wages State Year Adopted Arizona 2007 Colorado 2007 Florida 2006 Missouri 2007 Montana 2007 Nevada 2007 Ohio 2007 Oregon 2003 Vermont 2007 Washington 1999 Table 2: Descriptive Statistics of QCEW Data, This table reports descriptive statistics for the QCEW data. The first two columns report the mean and standard deviation for the all-county sample respectively. The second two columns report the mean and standard deviation of the contiguous county-pair sample respectively. All-County Sample County-Pair Sample Mean SD Mean SD Variable (1) (2) (3) (4) Population, , ,257 94, ,852 Population Density 261 1, ,348 Land area (square miles) 951 1,303 1,262 2,073 Overall private employment 32, ,740 32, ,926 Overall private average weekly wages ($) Restaurant employment 3,598 9,747 3,424 7,507 Restaurant average weekly wages ($) Accommodation and food services employment 4,527 13,382 4,664 13,271 Accommodation and food services average weekly wages ($) Retail employment 4,679 14,658 4,518 11,528 Retail average weekly wages ($) Manufacturing employment 5,667 18,090 5,396 12,504 Manufacturing average weekly wages ($) Minimum wage Number of counties 3,108 1,138 Number of county-pairs N/A 1,178 Number of states

23 Table 3: Preexisting Trends in Employment, This table reports estimates of log employment on leads of the minimum wage variable 12 and 4 quarters prior. All specifications also include the contemporaneous effect of the minimum wage. The Trend coefficient reports the difference of the first two coefficients. All All All County County County County County County County Pair Pair Pair Pair Sample Sample Sample Sample Sample Sample Sample Base η t * (0.044) (0.020) (0.022) (0.061) (0.313) (0.043) (0.045) η t *** 0.051** ** ** (0.033) (0.025) (0.021) (0.031) (0.086) (0.029) (0.034) Trend *** η t 4 η t 12 (0.033) (0.029) (0.016) (0.046) (0.280) (0.035) (0.035) Permanent η t (0.069) (0.126) (0.100) (0.192) (0.707) (0.138) (0.194) η t ** ** (0.071) (0.078) (0.052) (0.123) (0.384) (0.091) (0.113) Trend η t 4 η t 12 (0.098) (0.162) (0.115) (0.197) (0.676) (0.136) (0.196) Real η t * *** * 0.130* (0.069) (0.046) (0.051) (0.076) (0.249) (0.077) (0.067) η t * 0.220*** *** *** (0.072) (0.045) (0.043) (0.060) (0.192) (0.060) (0.058) Trend *** η t 4 η t 12 (0.123) (0.069) (0.075) (0.122) (0.335) (0.124) (0.079) Mobility η t *** 0.422* ** (0.318) (0.247) (0.273) (0.348) (0.939) (0.309) (0.424) η t ** *** ** * (0.343) (0.321) (0.262) (0.298) (0.516) (0.277) (0.348) Trend *** *** η t 4 η t 12 (0.613) (0.480) (0.462) (0.542) (1.345) (0.479) (0.634) Controls County fixed effects Y Y Y Y Y Y Period fixed effects Y Y Y Y Census Division * Period Y State Linear Trend Y Y County-Pair fixed effects Y Y Pair Id * Period Dummies Y Notes: Robust standard errors, in parentheses, are clustered at the state level for specifications 1, 2, and 3, and at the state and border segment levels for specifications 4 thru 7. 22

24 Table 4: Minimum Wage Effects on Wages and Employment, This table reports estimates of the effect of the log minimum wage on average weekly wages and employment in the restaurant sectors. Columns 1-3 report the results from the base specification for the all county sample and columns 4-7 report the results for the county-pair sample. All All All County County County County County County County Pair Pair Pair Pair Sample Sample Sample Sample Sample Sample Sample (1) (2) (3) (4) (5) (6) (7) ln(earnings) ln(minimum wage) 0.219*** 0.180*** 0.178*** 0.228*** 0.294*** 0.224*** 0.206*** (0.030) (0.016) (0.025) (0.027) (0.050) (0.026) (0.029) ln(employment) ln(minimum wage) ** *** * ** (0.076) (0.025) (0.027) (0.087) (0.412) (0.063) (0.050) ln(population) 1.090*** 1.182*** 1.112*** 0.028*** 0.787*** 0.898*** (0.059) (0.044) (0.040) (0.111) (0.069) (.) Controls County fixed effects Y Y Y Y Y Y Period fixed effects Y Y Y Y State linear trend Y Y Census division x period Y County Pair fixed effects Y Y Pair * period dummies Y Observations 174, , , , , , ,627 Notes: Robust standard errors, in parentheses, are clustered at the state level for specifications 1-3, and at the state and border segment levels for specifications

25 Table 5: Permanent Minimum Wage Effects on Wages and Employment, This table reports estimates of the effect of the log minimum wage on average weekly wages and employment in the restaurant sectors. Columns 1-3 report the results from the permanent specification for the all county sample and columns 4-7 report the results for the county-pair sample. All All All County County County County County County County Pair Pair Pair Pair Sample Sample Sample Sample Sample Sample Sample Variables (1) (2) (3) (4) (5) (6) (7) ln(earnings) ln(minimum wage) 0.204*** 0.189*** 0.180*** 0.205*** 0.252*** 0.203*** 0.198*** (0.032) (0.017) (0.026) (0.025) (0.045) (0.025) (0.028) Permanent minimum wage ** (0.112) (0.110) (0.101) (0.167) (0.168) (0.170) (0.117) Perm min wage * ln(min wage) ** (0.057) (0.059) (0.054) (0.085) (0.084) (0.087) (0.059) ln(employment) ln(minimum wage) ** *** ** * (0.064) (0.033) (0.033) (0.081) (0.441) (0.061) (0.054) Permanent minimum wage 0.823*** 1.330*** ** 1.405** 0.644*** (0.138) (0.291) (0.224) (0.224) (0.681) (0.128) (0.293) Perm min wage * ln(min wage) *** *** ** * *** (0.078) (0.162) (0.130) (0.118) (0.333) (0.066) (0.151) ln(population) 1.100*** 1.168*** 1.111*** 0.028*** 0.768*** 0.902*** (0.057) (0.041) (0.039) (0.004) (0.112) (0.069) (.) Controls County fixed effects Y Y Y Y Y Y Period fixed effects Y Y Y Y State linear trend Y Y Census division x period Y County Pair fixed effects Y Y Pair * period dummies Y Observations Notes: Robust standard errors, in parentheses, are clustered at the state level for specifications 1-3, and at the state and border segment levels for specifications

26 Table 6: Real Minimum Wage Effects on Wages and Employment, This table reports estimates of the effect of the log minimum wage on average weekly wages and employment in the restaurant sectors, controlling for the local price levels. Columns 1-3 report the results from the real specification for the all county sample and columns 4-7 report the results for the county-pair sample. All All All County County County County County County County Pair Pair Pair Pair Sample Sample Sample Sample Sample Sample Sample (1) (2) (3) (4) (5) (6) (7) ln(earnings) ln(minimum wage) 0.590*** 0.739*** 0.370** 0.687*** 0.615** 0.709*** (0.189) (0.095) (0.159) (0.240) (0.274) (0.244) (0.254) ln(avg wage) 0.288*** 0.361*** 0.211*** 0.318*** 0.411*** 0.322*** 0.130* (0.056) (0.028) (0.046) (0.071) (0.076) (0.072) (0.076) ln(min wage)*ln(avg wage) * *** * ** (0.029) (0.016) (0.025) (0.037) (0.041) (0.038) (0.041) ln(employment) ln(minimum wage) *** 2.326*** *** *** *** ** (0.329) (0.351) (0.310) (0.584) (1.594) (0.423) (0.790) ln(avg wage) *** 0.568*** *** ** 1.533*** *** ** (0.099) (0.098) (0.081) (0.173) (0.542) (0.123) (0.227) ln(min wage)*ln(avg wage) 0.142** *** 0.156*** 0.262*** 0.476** 0.279*** 0.303** (0.053) (0.058) (0.049) (0.091) (0.235) (0.066) (0.124) ln(population) 1.104*** 1.181*** 1.118*** 0.028*** 0.574*** 0.911*** (0.058) (0.043) (0.040) (0.004) (0.117) (0.064) (.) Controls County fixed effects Y Y Y Y Y Y Period fixed effects Y Y Y Y State linear trend Y Y Census division x period Y County Pair fixed effects Y Y Pair * period dummies Y Observations Notes: Robust standard errors, in parentheses, are clustered at the state level for specifications 1-3, and at the state and border segment levels for specifications