The Effect of Technology and Business Cycle on Regional Labor Market in the United States

The Effects of Minimum Wages on U.S. Labor Market over the Business Cycles
Oudom Hean

Introduction
The employment effects of minimum wage have always been a heated debate among economists and policymakers as the studies on minimum wage are burgeoning. At the heart of the debate, the contention is closely linked to the underlying structure of the U.S. labor market. Theoretically, while minimum wage unambiguously exerts a disemployment effect in the competitive labor market setting, minimum wage could have a null effect or even positive impact on the monopsonistic labor market.
One possible explanation which could resolve the debate but has not received full attention in the literature is the dynamic effects of minimum wage over the course of business cycle. The recent empirical work by Depew and Sørensen (2013) sheds light on the evolution of firms’ market power over the business cycle. Consistent with the job search model, they find that firms’ market power is countercyclical. Intuitively, there is relatively high friction in the labor market during recession because of the low job arrival rate and high job destruction rate. This friction in the labor market grants firms relatively high bargaining power in the labor market during an economic recession.
In this paper, I study the employment effects of minimum wage in the period around the Great Recession, which began in December 2007 and ended in June 2009. The Great Recession had a very long-lasting impact on the U.S. labor market. Figure 1.A shows that U.S. real GDP sharply dropped from 2008 to 2009 but bounced back at the beginning of 2010. Yet Figure 2.A. shows that the U.S. employment rate remained relatively low compared to 2007. To gauge a casual effect of minimum wage, I use a cross-border discontinuity approach of Dube, Lester and Reich (2010; 2016). I find that an increase in minimum wages during the pre-period of the Great Recession, from 2002 to 2007, exerted a significantly negative impact on teen employment; however, minimum wages did not have any significant impact on employment of this population during the Great Recession. For the employment of restaurant workers, the estimates effects of minimum wage are imprecise. However, the estimates suggest that minimum wages exerted a higher disemployment effect on restaurant workers. Furthermore, a careful look at the employment by sex, I find that female workers suffer more from the disemployment effect of minimum wages. These findings corroborate Depew & Sørensen (2013) and the job search model with relatively high friction during recession.
Figure 1.A Figure 1.B

Note: Figure 1.A shows the quarterly real GDP; while Figure 1.B. shows the quarterly employment rate. The data are obtained from the Federal Reserve Bank of St. Louis: https://fred.stlouisfed.org.

This paper relates to several strains of the minimum wage literature. First, I attempt to reconcile the debate on minimum wage on U.S. employment. One continuous disagreement is the correct methodologies used to quantify the impacts of minimum wage on employment. On the one hand, advocates of conventional fixed effects model always find that minimum wages have a significant effect on the employment of low-wage workers (Neumark & Wascher, 1992, 2000). On the other hand, studies using state-border discontinuity designs usually find no significant disemployment effects of minimum wages (Card & Krueger, 1994, 2000; Dube, Lester, & Reich 2010, 2016). In this paper, I still find negative effects of minimum wage on particularly total teen employment and female teen employment in the economic expansionary period, even though I employ the state-border discontinuity design of Dube, Lester and Reich (2010; 2016). In fact, the estimated of the minimum wages on teen population and on female teen population during economic expansion are similar to the conventional estimates: a 10 percent increase in minimum wage lead to a reduction of 13-15 percent reduction of teen employment or female teen employment.
Second, this paper also relates to studies that analyze the effects of minimum wage during different phase of business cycles. For examples, Addison, Blackburn and Cotti (2013) examine the effects of minimum wage during recessionary periods dated from 2005 to 2010. They find limited evidence of disemployment effect of minimum wage; however, the authors are reluctant to arrive at this conclusion. Similarly, Sabia (2014) concludes that minimum wage has a greater negative impact on employment at the state level between 1989 and 2002 even though the author’s findings, in actuality, are mixed. One shortcoming of previous works is that estimations of the effects of minimum wage are usually conducted without clearly restricting the samples into the different phases of business cycle. Additionally, these estimations can be biased due to insufficient control for geographic-specific time shocks. For this paper, I define the expansion period to be from 2002 to 2007 and the Great Recession to be between 2008 and 2010. These definitions of expansionary and recessionary periods conforms very well with the NBER definitions. However, because the Great Recession had a long-lasting impact on the U.S. labor market, I also conduct a sensitivity analysis by varying the end period of the recessionary period. I find the results soundly robust. Regarding the estimation strategy, I employ the state-border discontinuity design that could eliminate confounding factors affecting the estimated effects of minimum wages.
Third, this paper contributes to research on monopolistic labor market in the United States. Particularly, I find evidence consistent with Depew and Sørensen (2013). Using intuition derived from the search model of Burdett and Mortensen (1998) and Manning (2003), the authors study labor supply to Ford Motors and A.M. Byers in the period of 1919 to 1940. They find strong evidence indicating that both firms had higher market powers during recessions. I find evidence an increase in minimum wage has a lower disemployment effect during a recession than during an expansion. Furthermore, I also find that female workers are more vulnerable to the disemployment effect of minimum wages.
The remainder of the paper is organized as follows. Section 2 provide a theoretical framework to understand the effects of minimum wages during the different phases of business cycle. Section 3 discusses about the dataset; while Section 4 presents the state-border discontinuity design as the empirical strategy to estimate disemployment effects of minimum wages. Section 5 provides the estimated results, and Section 6 concludes.
Conceptual Framework
To understand the effects of minimum wage on employment over the business cycles, I present the work of Manning (2003), who adopts a simplified job search model developed by Burdett and Mortensen (1998). Using this model, Depew and Sørensen (2013) further discuss how the firm market power changes over the business cycles.
Let s(w) represent the separation rate and R(w) is the total number of new workers recruited by the representative firm at a given time. Both separation rate and total new recruits are functions of wages. The labor supply of the frim at time t is
L_t=[1-s(w)] L_(t-1)+R(w). (1)
If L_t=L_(t-1) in a steady state, then (1) implies
L(w)=R(w)/s(w) . (2)
After taking the log of (2) and differentiating with respect to wage, we obtain the following condition:
ϵ_Lw=ϵ_Rw-ϵ_sw. (3)
Here, ϵ_Lw is the labor supply elasticity. ϵ_Rw is the recruitment elasticity; while ϵ_sw is the separation elasticity. If separations and recruits have common job offer rates and the identical distribution of wages, then ϵ_Rw=-ϵ_sw in the steady state (Manning, 2003). Therefore, ϵ_Lw=-〖2ϵ〗_sw.
A ̀ la Manning (2003), the separation function is defined as
s(w)=δ+λ [1-F(w)], (4)
where δ is the exogenous job destruction rate, and λ is the job offer arrival rate. F(w) is the wage distribution. As shown in Depew and Sørensen (2013), the elasticity of labor supply is
ϵ_LW=2θf(w)w/(1+θ[1-F(w)]) . (5)
Here, θ=λ/delta. Therefore, θ measures the labor market friction which determined by the job destruction rate and offer arrival rate. Low θ implies low friction in the labor market. During an economic recession, the job destruction can be relatively high while the job offer arrival rate is relatively low compared. Therefore, there is more friction in the labor market during an economic recession than during an expansion. It is readily shown that
ϵ_LW=2θf(w)w/(1+θ[1-F(w)]) . (6)
That is, the elasticity of labor supply decreases with a reduction in θ. Therefore, in economic recession, the representative firm has higher market power. As in a standard monopsonistic model, a rise wage can increase employment as long as this wage does not surpass the competitive market wage. Hence, all other things being equal, an increase in minimum wage is less likely to reduce employment during a recession than during an economic expansion.
Figure 2.A: Expansion Figure 2.B: Recession

Figures 2.A and 2.B illustrate the effects of minimum wage on the labor market during economic expansion and recession, respectively. As in a classic monopolistic theory, perfectly competitive wage and labor outcomes, w^c and L^c, are higher than monopsonic wage and labor demand, w^M and L^M. Assume that the labor market is not perfectly competitive, Figure 2.A shows that an implementation of minimum wage during an economic expansion period could lead to a reduction in employment relative to both the monoprotic and perfectly competitive labor demand. Yet Figure 2.B show that similar minimum wage (i.e., a similar magnitude increases from w^M) can instead improve employment during a recession. Given that perfectly completive wage and labor are unknown or ambiguous, imposing the same magnitude increase in minimum wage can have different consequence on employment. That is, an increase in minimum wage during an economic recession is relatively benign than a similar increase in magnitude during economic expansion.
Data
The data used in this chapter is provided by Dube, Lester, and Reich (2016). Their primary dataset is sourced from the Quarterly Workforce Indicators (QWI) which offers essentially a full census of employment and demographics at the county and industry level. The variable of interest is employment, the number of workers on the payroll on the last day of a quarter in a county. The job is defined as ending in quarter t when the employee does not have a valid wage record with the employer in quarter t+1. QWI also provides data on worker characteristics, namely age, education, race, sex, and ethnicity. Dube, Lester, and Reich (2016) also provide data on minimum wages at the state level. Table 1 reports the summary statistics of variables of interest I use in this study.
Observation Mean Standard Error Minimum Maximum
Minimum wage 141,904 5.69 1.03 3.35 9.92
Teen workers 139,170 1,224.03 3,209.69 2.00 103,143
Restaurant workers 136,771 2,588.32 7,549.47 2.00 176,763
Female teen workers 138,778 645.2896 1677.862 1 52,390
Female restaurant workers 136,761 1409.646 3738.577 2 91,366
Table 1: Summary Statistics

Identification Strategy
Consistent with previous studies, I focus on teens (ages 14-18) and restaurant sector (NAICS722). I follow Dube, Lester and Reich (2010, 2016) by estimating the following specification:
y_ipt=α_1 □ln log (MW_ipt ) +α_2 X_(ipt )+ϕ_i+ϕ_pt+e_ipt . (7)

Here, y_ipt is the employment of specific population in county i, in time t, and in pair p. MW is the minimum wage implemented in time t. The population of interest is either the total teen employment or restaurant workers. All estimations control for natural log of total private sector employment and population in each county. As in Dube, Lester, and Reich (2016), I control for the total population of teenage in the teen employment regression. Dube, Lester and Reich (2010, 2016) show that the state-border discontinuity design yield similarity of control groups. They also find that cross-border spillovers effects are very small.
To assess heterogeneous effects of minimum wages, I study effects of minimum wages on the employment of these workers by different types of sex. For the female (male) teen employment regression, I control for the total female (male) teen population. I estimate these models separately for two different periods, 2002-2007 (expansion), and 2008-20010 (the Great Recession).
Empirical Results
Table 2: Minimum Wage Effects on Teen and Restaurant Workers
Log teen workers Log restaurant workers
Expansion Great Recession Expansion Great Recession
(1) (2) (3) (4)
Log minimum wage -0.13* 0.05 -0.09 0.14
(0.071) (0.201) (0.084) (0.269)
Controls Yes Yes Yes Yes
County effects Yes Yes Yes Yes
Pair-specific time effects Yes Yes Yes Yes
Number of observation 43,577 22,392 40,697 27,735
Note: All regressions control for natural log of county population and total private sector employment. Specification (1) and (2) also control for natural log of teen population. Robust standard errors are clustered at the state and border-segment levels for all regressions.

Table 2 reports the estimated effects of minimum wages on the employment of teen and restaurant workers. For teen employment, minimum wages exert a significant negative impact on teen workers during the expansionary period; however, there is no significant impact on teen employment during the Great Recession. For restaurant workers, the estimations are imprecise. Yet the evidence suggests that minimum wages have a higher disemployment effect during the expansion than during the Great Recession. I also conduct a sensitivity analysis by limiting the observations of the Great Recession to span from 2008 to 2009 or extending the observation data from 2008 to 2011. The estimated effects of minimum wages in this analysis are similar to those tabulated in Table 2.
Table 3: Minimum Wage Effects on Female and Male Teen Workers
Log female teen workers Log male teen workers
Expansion Great Recession Expansion Great Recession
(1) (2) (3) (4)
Log minimum wage -0.15** -0.06 -0.10 0.17
(0.074) (0.185) (0.074) (0.278)
Controls Yes Yes Yes Yes
County effects Yes Yes Yes Yes
Pair-specific time effects Yes Yes Yes Yes
Number of observation 42,433 21,768 42,407 21,747
Note: All regressions control for natural log of county population and total private sector employment. Specification (1) and (2) control for natural log of female teen population; while (4) and (5) control for natural log of male teen employment. Robust standard errors are clustered at the state and border-segment levels for all regressions.

Minimum wages can exert different impact on male and female population. Table 3 shows the effect of minimum wages on female and male teen employment during the expansionary period and the Great Recession; while Table 4 shows the estimated effects of minimum wage on female and male restaurants workers.
Table 4: Minimum Wage Effects on Female and Male Restaurant Workers
Log female restaurant workers Log male Restaurant workers
Expansion Great Recession Expansion Great Recession
(1) (2) (3) (4)
Log minimum wage -0.11 0.096 -0.097 0.23
(0.112) (0.221) (0.083) (0.245)
Controls Yes Yes Yes Yes
County effects Yes Yes Yes Yes
Pair-specific time effects Yes Yes Yes Yes
Number of observation 42,060 21,584 41,617 21,410
Note: All regressions control for natural log of county population and total private sector employment. Robust standard errors are clustered at the state and border-segment levels for all regressions.

Conclusion

The study of minimum wage has been amongst the most contentious topic in both academic and political arenas. Theoretically, the debate revolves around the structure of labor market: competitive versus monopsonistic labor markets.
In this paper, I examine the effects of minimum wages on the U.S. labor market during the Great Recession. Using the state-border discontinuity design of Dube, Lester, and Reich (2010, 2016), I find that minimum wages exert a significant negative impact on teen employment, especially on the female teen employment. These estimates of the disemployment effects of minimum wages are similar to those estimated using conventional fixed effects models. Yet minimum wage does not exert any no significant on teen employment during the Great Recession. For restaurant workers, the esimates are imprecise, although there is suggestive evidence that the disemployment effect of minimum wages are larger during the expansionary period. These findings corroborate Depew and Sørensen (2013) who finds that firms’ market power is counter-cyclical.
References
Addison, J. T., Blackburn, M. L., & Cotti, C. D. (2013). Minimum wage increases in a recessionary environment. Labour Economics, 23, 30-39.
Burdett, K., & Mortensen, D. T. (1998). Wage differentials, employer size, and unemployment. International Economic Review, 257-273.
Card, D., & Krueger, A. (1994). Minimum wages and employment: A case study of the New Jersey and Pennsylvania fast food industries. The American Economic Review, 84(4), 772–793.
Card, D., & Krueger, A. (2000). Minimum wages and employment: A case study of the New Jersey and Pennsylvania fast food industries: Reply. The American Economic Review , 90(5), 1397-1420.
Depew, B., & Sørensen, T. A. (2013). The elasticity of labor supply to the firm over the business cycle. Labour Economics, 24, 196-204.
Dube, A., Lester and Michael Rei, W. T., & Reich, M. (2016). Minimum wage shocks, employment flows, and labor market frictions. Journal of Labor Economics, 34(3), 663-704.
Dube, A., Lester, W. T., & Reich , M. (2010). Minimum wage effects across state borders: Estimates using contiguous counties. The Review of Economics and Statatistics, 92(4), 945-964.
Manning, A. (2003). Monopsony in motion: Imperfect competition in labor markets. Princeton, N.J.: Princeton University Press.
Neumark, D., & Wascher, W. (1992). Employment Effects of Minimum and Subminimum Wages: Panel Data on State Minimum Wage Laws. Industrial and Labor Relations Review , 46(1), 55-81.
Neumark, D., & Wascher, W. (2000). Minimum Wages and Employment: A Case Study of the FastFood Industry in New Jersey and Pennsylvania: Comment. American Economic Review , 90(5), 1362–1396.
Sabia, J. J. (2014). The effects of minimum wages over the business cycle. Journal of Labor Research, 35(3), 227-245.

The Effects of Minimum Wages on U.S. Labor Market over the Business Cycles
Oudom Hean

Introduction
The employment effects of minimum wage have always been a heated debate among economists and policymakers as the studies on minimum wage are burgeoning. At the heart of the debate, the contention is closely linked to the underlying structure of the U.S. labor market. Theoretically, while minimum wage unambiguously exerts a disemployment effect in the competitive labor market setting, minimum wage could have a null effect or even positive impact on the monopsonistic labor market.
One possible explanation which could resolve the debate but has not received full attention in the literature is the dynamic effects of minimum wage over the course of business cycle. The recent empirical work by Depew and Sørensen (2013) sheds light on the evolution of firms’ market power over the business cycle. Consistent with the job search model, they find that firms’ market power is countercyclical. Intuitively, there is relatively high friction in the labor market during recession because of the low job arrival rate and high job destruction rate. This friction in the labor market grants firms relatively high bargaining power in the labor market during an economic recession.
In this paper, I study the employment effects of minimum wage in the period around the Great Recession, which began in December 2007 and ended in June 2009. The Great Recession had a very long-lasting impact on the U.S. labor market. Figure 1.A shows that U.S. real GDP sharply dropped from 2008 to 2009 but bounced back at the beginning of 2010. Yet Figure 2.A. shows that the U.S. employment rate remained relatively low compared to 2007. To gauge a casual effect of minimum wage, I use a cross-border discontinuity approach of Dube, Lester and Reich (2010; 2016). I find that an increase in minimum wages during the pre-period of the Great Recession, from 2002 to 2007, exerted a significantly negative impact on teen employment; however, minimum wages did not have any significant impact on employment of this population during the Great Recession. For the employment of restaurant workers, the estimates effects of minimum wage are imprecise. However, the estimates suggest that minimum wages exerted a higher disemployment effect on restaurant workers. Furthermore, a careful look at the employment by sex, I find that female workers suffer more from the disemployment effect of minimum wages. These findings corroborate Depew & Sørensen (2013) and the job search model with relatively high friction during recession.
Figure 1.A Figure 1.B

Note: Figure 1.A shows the quarterly real GDP; while Figure 1.B. shows the quarterly employment rate. The data are obtained from the Federal Reserve Bank of St. Louis: https://fred.stlouisfed.org.

This paper relates to several strains of the minimum wage literature. First, I attempt to reconcile the debate on minimum wage on U.S. employment. One continuous disagreement is the correct methodologies used to quantify the impacts of minimum wage on employment. On the one hand, advocates of conventional fixed effects model always find that minimum wages have a significant effect on the employment of low-wage workers (Neumark & Wascher, 1992, 2000). On the other hand, studies using state-border discontinuity designs usually find no significant disemployment effects of minimum wages (Card & Krueger, 1994, 2000; Dube, Lester, & Reich 2010, 2016). In this paper, I still find negative effects of minimum wage on particularly total teen employment and female teen employment in the economic expansionary period, even though I employ the state-border discontinuity design of Dube, Lester and Reich (2010; 2016). In fact, the estimated of the minimum wages on teen population and on female teen population during economic expansion are similar to the conventional estimates: a 10 percent increase in minimum wage lead to a reduction of 13-15 percent reduction of teen employment or female teen employment.
Second, this paper also relates to studies that analyze the effects of minimum wage during different phase of business cycles. For examples, Addison, Blackburn and Cotti (2013) examine the effects of minimum wage during recessionary periods dated from 2005 to 2010. They find limited evidence of disemployment effect of minimum wage; however, the authors are reluctant to arrive at this conclusion. Similarly, Sabia (2014) concludes that minimum wage has a greater negative impact on employment at the state level between 1989 and 2002 even though the author’s findings, in actuality, are mixed. One shortcoming of previous works is that estimations of the effects of minimum wage are usually conducted without clearly restricting the samples into the different phases of business cycle. Additionally, these estimations can be biased due to insufficient control for geographic-specific time shocks. For this paper, I define the expansion period to be from 2002 to 2007 and the Great Recession to be between 2008 and 2010. These definitions of expansionary and recessionary periods conforms very well with the NBER definitions. However, because the Great Recession had a long-lasting impact on the U.S. labor market, I also conduct a sensitivity analysis by varying the end period of the recessionary period. I find the results soundly robust. Regarding the estimation strategy, I employ the state-border discontinuity design that could eliminate confounding factors affecting the estimated effects of minimum wages.
Third, this paper contributes to research on monopolistic labor market in the United States. Particularly, I find evidence consistent with Depew and Sørensen (2013). Using intuition derived from the search model of Burdett and Mortensen (1998) and Manning (2003), the authors study labor supply to Ford Motors and A.M. Byers in the period of 1919 to 1940. They find strong evidence indicating that both firms had higher market powers during recessions. I find evidence an increase in minimum wage has a lower disemployment effect during a recession than during an expansion. Furthermore, I also find that female workers are more vulnerable to the disemployment effect of minimum wages.
The remainder of the paper is organized as follows. Section 2 provide a theoretical framework to understand the effects of minimum wages during the different phases of business cycle. Section 3 discusses about the dataset; while Section 4 presents the state-border discontinuity design as the empirical strategy to estimate disemployment effects of minimum wages. Section 5 provides the estimated results, and Section 6 concludes.
Conceptual Framework
To understand the effects of minimum wage on employment over the business cycles, I present the work of Manning (2003), who adopts a simplified job search model developed by Burdett and Mortensen (1998). Using this model, Depew and Sørensen (2013) further discuss how the firm market power changes over the business cycles.
Let s(w) represent the separation rate and R(w) is the total number of new workers recruited by the representative firm at a given time. Both separation rate and total new recruits are functions of wages. The labor supply of the frim at time t is
L_t=[1-s(w)] L_(t-1)+R(w). (1)
If L_t=L_(t-1) in a steady state, then (1) implies
L(w)=R(w)/s(w) . (2)
After taking the log of (2) and differentiating with respect to wage, we obtain the following condition:
ϵ_Lw=ϵ_Rw-ϵ_sw. (3)
Here, ϵ_Lw is the labor supply elasticity. ϵ_Rw is the recruitment elasticity; while ϵ_sw is the separation elasticity. If separations and recruits have common job offer rates and the identical distribution of wages, then ϵ_Rw=-ϵ_sw in the steady state (Manning, 2003). Therefore, ϵ_Lw=-〖2ϵ〗_sw.
A ̀ la Manning (2003), the separation function is defined as
s(w)=δ+λ [1-F(w)], (4)
where δ is the exogenous job destruction rate, and λ is the job offer arrival rate. F(w) is the wage distribution. As shown in Depew and Sørensen (2013), the elasticity of labor supply is
ϵ_LW=2θf(w)w/(1+θ[1-F(w)]) . (5)
Here, θ=λ/delta. Therefore, θ measures the labor market friction which determined by the job destruction rate and offer arrival rate. Low θ implies low friction in the labor market. During an economic recession, the job destruction can be relatively high while the job offer arrival rate is relatively low compared. Therefore, there is more friction in the labor market during an economic recession than during an expansion. It is readily shown that
ϵ_LW=2θf(w)w/(1+θ[1-F(w)]) . (6)
That is, the elasticity of labor supply decreases with a reduction in θ. Therefore, in economic recession, the representative firm has higher market power. As in a standard monopsonistic model, a rise wage can increase employment as long as this wage does not surpass the competitive market wage. Hence, all other things being equal, an increase in minimum wage is less likely to reduce employment during a recession than during an economic expansion.
Figure 2.A: Expansion Figure 2.B: Recession

Figures 2.A and 2.B illustrate the effects of minimum wage on the labor market during economic expansion and recession, respectively. As in a classic monopolistic theory, perfectly competitive wage and labor outcomes, w^c and L^c, are higher than monopsonic wage and labor demand, w^M and L^M. Assume that the labor market is not perfectly competitive, Figure 2.A shows that an implementation of minimum wage during an economic expansion period could lead to a reduction in employment relative to both the monoprotic and perfectly competitive labor demand. Yet Figure 2.B show that similar minimum wage (i.e., a similar magnitude increases from w^M) can instead improve employment during a recession. Given that perfectly completive wage and labor are unknown or ambiguous, imposing the same magnitude increase in minimum wage can have different consequence on employment. That is, an increase in minimum wage during an economic recession is relatively benign than a similar increase in magnitude during economic expansion.
Data
The data used in this chapter is provided by Dube, Lester, and Reich (2016). Their primary dataset is sourced from the Quarterly Workforce Indicators (QWI) which offers essentially a full census of employment and demographics at the county and industry level. The variable of interest is employment, the number of workers on the payroll on the last day of a quarter in a county. The job is defined as ending in quarter t when the employee does not have a valid wage record with the employer in quarter t+1. QWI also provides data on worker characteristics, namely age, education, race, sex, and ethnicity. Dube, Lester, and Reich (2016) also provide data on minimum wages at the state level. Table 1 reports the summary statistics of variables of interest I use in this study.
Observation Mean Standard Error Minimum Maximum
Minimum wage 141,904 5.69 1.03 3.35 9.92
Teen workers 139,170 1,224.03 3,209.69 2.00 103,143
Restaurant workers 136,771 2,588.32 7,549.47 2.00 176,763
Female teen workers 138,778 645.2896 1677.862 1 52,390
Female restaurant workers 136,761 1409.646 3738.577 2 91,366
Table 1: Summary Statistics

Identification Strategy
Consistent with previous studies, I focus on teens (ages 14-18) and restaurant sector (NAICS722). I follow Dube, Lester and Reich (2010, 2016) by estimating the following specification:
y_ipt=α_1 □ln log (MW_ipt ) +α_2 X_(ipt )+ϕ_i+ϕ_pt+e_ipt . (7)

Here, y_ipt is the employment of specific population in county i, in time t, and in pair p. MW is the minimum wage implemented in time t. The population of interest is either the total teen employment or restaurant workers. All estimations control for natural log of total private sector employment and population in each county. As in Dube, Lester, and Reich (2016), I control for the total population of teenage in the teen employment regression. Dube, Lester and Reich (2010, 2016) show that the state-border discontinuity design yield similarity of control groups. They also find that cross-border spillovers effects are very small.
To assess heterogeneous effects of minimum wages, I study effects of minimum wages on the employment of these workers by different types of sex. For the female (male) teen employment regression, I control for the total female (male) teen population. I estimate these models separately for two different periods, 2002-2007 (expansion), and 2008-20010 (the Great Recession).
Empirical Results
Table 2: Minimum Wage Effects on Teen and Restaurant Workers
Log teen workers Log restaurant workers
Expansion Great Recession Expansion Great Recession
(1) (2) (3) (4)
Log minimum wage -0.13* 0.05 -0.09 0.14
(0.071) (0.201) (0.084) (0.269)
Controls Yes Yes Yes Yes
County effects Yes Yes Yes Yes
Pair-specific time effects Yes Yes Yes Yes
Number of observation 43,577 22,392 40,697 27,735
Note: All regressions control for natural log of county population and total private sector employment. Specification (1) and (2) also control for natural log of teen population. Robust standard errors are clustered at the state and border-segment levels for all regressions.

Table 2 reports the estimated effects of minimum wages on the employment of teen and restaurant workers. For teen employment, minimum wages exert a significant negative impact on teen workers during the expansionary period; however, there is no significant impact on teen employment during the Great Recession. For restaurant workers, the estimations are imprecise. Yet the evidence suggests that minimum wages have a higher disemployment effect during the expansion than during the Great Recession. I also conduct a sensitivity analysis by limiting the observations of the Great Recession to span from 2008 to 2009 or extending the observation data from 2008 to 2011. The estimated effects of minimum wages in this analysis are similar to those tabulated in Table 2.
Table 3: Minimum Wage Effects on Female and Male Teen Workers
Log female teen workers Log male teen workers
Expansion Great Recession Expansion Great Recession
(1) (2) (3) (4)
Log minimum wage -0.15** -0.06 -0.10 0.17
(0.074) (0.185) (0.074) (0.278)
Controls Yes Yes Yes Yes
County effects Yes Yes Yes Yes
Pair-specific time effects Yes Yes Yes Yes
Number of observation 42,433 21,768 42,407 21,747
Note: All regressions control for natural log of county population and total private sector employment. Specification (1) and (2) control for natural log of female teen population; while (4) and (5) control for natural log of male teen employment. Robust standard errors are clustered at the state and border-segment levels for all regressions.

Minimum wages can exert different impact on male and female population. Table 3 shows the effect of minimum wages on female and male teen employment during the expansionary period and the Great Recession; while Table 4 shows the estimated effects of minimum wage on female and male restaurants workers.
Table 4: Minimum Wage Effects on Female and Male Restaurant Workers
Log female restaurant workers Log male Restaurant workers
Expansion Great Recession Expansion Great Recession
(1) (2) (3) (4)
Log minimum wage -0.11 0.096 -0.097 0.23
(0.112) (0.221) (0.083) (0.245)
Controls Yes Yes Yes Yes
County effects Yes Yes Yes Yes
Pair-specific time effects Yes Yes Yes Yes
Number of observation 42,060 21,584 41,617 21,410
Note: All regressions control for natural log of county population and total private sector employment. Robust standard errors are clustered at the state and border-segment levels for all regressions.

Conclusion

The study of minimum wage has been amongst the most contentious topic in both academic and political arenas. Theoretically, the debate revolves around the structure of labor market: competitive versus monopsonistic labor markets.
In this paper, I examine the effects of minimum wages on the U.S. labor market during the Great Recession. Using the state-border discontinuity design of Dube, Lester, and Reich (2010, 2016), I find that minimum wages exert a significant negative impact on teen employment, especially on the female teen employment. These estimates of the disemployment effects of minimum wages are similar to those estimated using conventional fixed effects models. Yet minimum wage does not exert any no significant on teen employment during the Great Recession. For restaurant workers, the esimates are imprecise, although there is suggestive evidence that the disemployment effect of minimum wages are larger during the expansionary period. These findings corroborate Depew and Sørensen (2013) who finds that firms’ market power is counter-cyclical.
References
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