Online Supplement to The Heterogeneous Effects of the Minimum Wage on Employment Across States

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1 Online Supplement to The Heterogeneous Effects of the Minimum Wage on Employment Across States Wuyi Wang, Peter C.B. Phillips,LiangjunSu Institute for Economic and Social Research, Jinan University Yale University, University of Auckland, University of Southampton, & Singapore Management University School of Economics, Singapore Management University The supplement is composed of two parts. Section A reports some additional empirical results when the classifications are done at the state level. Section B reports the empirical results when the classifications are done at the county level. A Some auxiliary empirical results for the state-level classifications In this section, we report some auxiliary results for the applications in Section 4 of the paper. A.1 Results for Model (4.3) Table A1 report the numeric values for the information criteria used for model (4.3). The number shown in bold denotes the minimum value, which is achieved when =0 10 and =4. Table A1: Values for the information criterion in model (4.3) =1 =2 =3 =4 =5 =6 =7 =8 = = = Table A2 reports the classification results based on the model in (4.3). For Group 1, the increase in the minimum wage is positively correlated with employment. The effect is relatively large a 1% increase in minimum wages associates with a 0.534% increase in employment. We call Group 1 the large positive, large group, which contains 8 member states. For Group 2, the effect of the minimum wage on employment is significantly positive but very small, and the effect of population is marginally smaller than that in Group 1. So we call Group 2 the small positive, large group, which has 15 member states. Similar to Group 2, the effect of the minimum wage on employment is significantly positive but small for Group 3, but the effect of population on employment is also small for Group 3. So we call Group 3 the small positive, small group, which has 17 member states. Group 4 distinguishes itself from all other groups by having negative correlation between the minimum wage and employment after controlling for population. So we call Group 4 the negative group, which contains 11 states. 1

2 Table A2: Classification results of states for mode (4.3) Group 1: large positive, large group( ˆ 1 =8) Alabama District of Columbia Hawaii Louisiana Mississippi Ohio South Carolina South Dakota Group 2: small positive, large group( ˆ 2 =15) Arkansas Connecticut Georgia Maryland Michigan Minnesota Missouri Nevada New York North Carolina North Dakota Rhode Island Tennessee Texas Virginia Group 3: small positive, small group( ˆ 3 =17) Alaska Arizona Delaware Idaho Illinois Kentucky Maine Massachusetts Montana Nebraska New Hampshire New Mexico Oklahoma Pennsylvania West Virginia Wisconsin Wyoming Group 4: negative group( ˆ 4 =11) California Colorado Florida Indiana Iowa Kansas New Jersey Oregon Utah Vermont Washington Figure A1 illustrates the connection between the preliminary estimates and the final groupings for each state. The preliminary estimates are obtained when we minimize the objective function in equation (2.5) without imposing any group structure. The horizontal and vertical axes correspond to the preliminary estimates of s and s, respectively. Recall that s and s are the slope coefficients of ln ( ) and ln ( ) respectively. Groups1,2,3,and4aresignified by red circle, green diamond, blue triangle, and purple square, respectively. The results show that, as might be expected from the classification process, those states with close preliminary estimates of the slope parameters are typically more likely to be classified into the same group. 2

3 4 DC Group 1 3 Group 2 Group 3 Group 4 γ^ NV IA SD TN MD MI CO NJ IN VA MOMN OR NDNY AR KSCA FL DE MT AK NC VT UT ILAZ OK NH WI ME NE ID WA PA KY WY MA CT MS TX SCGA NM WV RI AL OH LA 1 HI η^ Figure A1: The horizontal and vertical axes correspond to the preliminary estimates of and, respectively. Each point represents a state, marked by the standard state abbreviation. For Groups 1, 2, 3, and 4, we use red circle, green diamond, blue triangle, and purple square to denote them, respectively. A.2 Results for Model (4.4) Table A3 report the numeric values for the information criteria used for model (4.4). The number in bold is the minimum value, which is achieved when =0 05 and =4. Table A3: Values for the information criterion in model (4.4) =1 =2 =3 =4 =5 =6 =7 =8 = = = TableA4reportstheclassification results for model (4.4). Groups 1 4 have 7, 17, 14, and 13 member states, respectively. Depending on the values of the estimates, we name Groups 1 4 respectively as the large positive group, small negative group, small positive group, and large negative group. The table suggests that the control of total population brings significant changes to the classification results. Figure A2 illustrates the connection between the preliminary estimates and the final groupings for each state. Now the horizontal and vertical axes correspond to the preliminary estimates of and +, respectively. Groups 1, 2, 3, and 4 are displayed using red circle, green diamond, blue triangle, and purple square, respectively. Unsurprisingly, we find that states with close preliminary estimates of the slope parameters are more likely to be classified into the same group. 3

4 Table A4: Classification results of states for mode (4.4) Group 1: large positive group( ˆ 1 =7) Alabama Georgia Louisiana Mississippi Ohio South Carolina Texas Group 2: small negative group( ˆ 2 =17) Delaware District of Columbia Indiana Maine Maryland Massachusetts Michigan Minnesota Missouri Nevada New Jersey New York North Carolina Rhode Island South Dakota Tennessee Virginia Group 3: small positive group( ˆ 3 =14) Alaska Arizona Arkansas California Connecticut Idaho Illinois Kentucky New Hampshire New Mexico Oklahoma Pennsylvania West Virginia Wisconsin Group 4: large negative group( ˆ 3 =13) Colorado Florida Hawaii Iowa Kansas Montana Nebraska North Dakota Oregon Utah Vermont Washington Wyoming γ^ +δ^ IA DE NV CO ME SD DC RI MI TN MN MO ND VA KS OR FL AR IN HI NY MD CA WI AZ UT IL MT NHOK WA NJ AK PA VT KY WY CT NC ID NM GATX WV SC OH MS LA AL Group 1 Group 2 Group 3 NE Group MA η^ Figure A2: The horizontal and vertical axes correspond to the preliminary estimates of and +, respectively. Each point represents a state, marked by the standard state abbreviation. Groups 1, 2, 3, and 4 are shown using red circle, green diamond, blue triangle, and purple square, respectively. 4

5 B Empirical results for the county-level classifications Following the comment of an anonymous referee, we now consider the classification and estimation by assuming that the latent group structure is present at the county level instead of the state level. Now, the models under our investigation become ln( )= + ln( )+ ln( )+ + + and (B.1) ln( )= + ln( )+ ln( )+ ln( )+ + + (B.2) where =1 =1 =( ) 0 in (B.1) and =( ) 0 (B.2). In either case, has the latent group structure: 1 if 1 =.. (B.3) if where { 1 } forms a partition of all the counties. In the dataset, the number of time periods is =66and the number of individual counties is = 1380 for model (B.1) and = 1378 for model (B.2). Note that is approximately of order 2 3 here. For model (B.1) and model (B.2), the C-Lasso method identifies 5 groups and 2 groups, respectively. This indicates that the classifications at the county level are rather unstable over the two specifications, whichisinsharpcontrasttotheclassifications at the state level. As explained in the main text, this might stem the fact that the number of groups discovered by the C-Lasso method is sensitive to the specification of the model when is approximately proportional to 2 Another reason is that the minimum wage exhibits little or no variations across counties within any given state. The post-classification regression results are reported in Table A5. Despite the fact that different numbers of groups are detected from the two models, we can still observe that the general pattern is the same for the two models: some groups have positive estimate of whereas the opposite is true for the other groups. Specifically, in model (B.1), Groups 1 and 5 have positive estimates of while Groups 2 4 have negative estimates of ; in model (B.2), Group 1 and Group 2 have positive and negative estimates of, respectively. In short, we find minimum wages have heterogeneous effects on employment at the county level. Based on the C-Lasso classification results, we can count the number of counties to be classified into each of the 5 or 2 groups for the above two models. The results are reported in Tables A6 and A7 for Models (B.1) and (B.2), respectively. From Table A6 we can see that the majority of counties in the same state are usually classified into either Groups 1 and 5 (with positive estimate of ) orgroups 2 4 (with negative estimate of ). See, e.g., Alabama, California, Louisiana, and South Carolina. The same pattern also appears in Table A7; see Alabama, Louisiana, Mississippi, Ohio, South Carolina, West Virginia, among others. This is evidence of little degree of heterogeneity within states. 5

6 Table A5: Regression results Model (B.1) Model (B.2) G1 G2 G3 G4 G5 All Group 1 Group 2 All ln( ) (0.009) (0.011) (0.010) (0.015) (0.015) (0.096) (0.009) (0.009) (0.097) ln( ) (0.008) (0.015) (0.013) (0.028) (0.014) (0.060) (0.009) (0.012) (0.086) ln( ) (0.006) (0.008) (0.044) Observations Note:,,and correspond to 10%, 5%, and 1% significance levels, respectively. Table A6: Classification results of counties for model (B.1) State Total G1 G2 G3 G4 G5 State Total No. G1 G2 G3 G4 G5 Alabama Montana Alaska Nebraska Arizona Nevada Arkansas New Hampshire California New Jersey Colorado New Mexico Connecticut New York Delaware North Carolina D.C North Dakota Florida Ohio Georgia Oklahoma Hawaii Oregon Idaho Pennsylvania Illinois Rhode Island Indiana South Carolina Iowa South Dakota Kansas Tennessee Kentucky Texas Louisiana Utah Maine Vermont Maryland Virginia Massachusetts Washington Michigan West Virginia Minnesota Wisconsin Mississippi Wyoming Missouri Sum

7 Table A7: Classification results of counties for model (B.2) State Total G1 G2 State Total No. G1 G2 Alabama Montana Alaska Nebraska Arizona Nevada Arkansas New Hampshire California New Jersey Colorado New Mexico Connecticut New York Delaware North Carolina District of Columbia North Dakota Florida Ohio Georgia Oklahoma Hawaii Oregon Idaho Pennsylvania Illinois Rhode Island Indiana South Carolina Iowa South Dakota Kansas Tennessee Kentucky Texas Louisiana Utah Maine Vermont Maryland Virginia Massachusetts Washington Michigan West Virginia Minnesota Wisconsin Mississippi Wyoming Missouri Sum

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