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Thesis in full_5.6

Thesis in full_5.6



Academic text on labor market economics. How the minimum wage can create employment

Academic text on labor market economics. How the minimum wage can create employment



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    Thesis in full_5.6 Thesis in full_5.6 Document Transcript

    • Max BerreErik de Regti461865August 18, 2008 The Effects of Statewide Minimum Wages on the US Labor Market from 2002-2007 What Factors Play a Role? Abstract:This paper investigates the effect of US statewide minimum wages on labor markets. Theeffect of sectoral composition of a state’ economy is empirically determined to have a spivotal effect on wage-earning employment elasticity using 2002-2007 BLS data. Theexplanation behind this phenomenon is linked theoretically to tradability as well ascapital/labor substitution elasticity. The effect of statewide minimum wages on a state’ slabor market is explained empirically by a state economy’ sectoral profile. s 1
    • 1: IntroductionThe relationship between minimum wages and employment figures documented by Cardand Krueger’ works in both 1994 and 2000, as well as responses to Card and Krueger’ s s1994 work considered for reply in 2000, focused solely in the fast-food sector, and in justtwo states, Pennsylvania and New Jersey.Beyond Pennsylvania and New Jersey, the minimum wage at the statewide level is anissue that draws attention across the US. Until the second half of 2007, the US federalminimum wage remained unchanged at $5.15 an hour for over 10 years. Meanwhile, theminimum wage in several states across the US increased, while in other states, theminimum wage underwent no change whatsoever. This phenomenon leads one toreasonably question the effects of these statewide minimum wage increases.The QuestionsQuestions arise with respect to the relationship between employment levels and minimumwages proposed by Card and Krueger. First, does a relationship between minimum wagesand employment exist beyond Pennsylvania and New Jersey or in industries and sectorsbeyond the fast food industry? One possibility may be that perhaps the effect describedby Card and Krueger may be specific to New Jersey and Pennsylvania, or to the fast-foodindustry, while the relationship may be of wildly varying magnitude and direction on theaggregate level.Second, what is the explanation for the relationship which was found? To address thisquestion one must consider the effect of the minimum wage on both the labor demandfunction, on effective demand. Statewide variations in tradability and in capital/laborsubstitution elasticity expressed along sectoral lines must also be taken into account.The major purpose of this study is to empirically address these two questions. Inparticular, this study seeks to shed light onto factors determining the shape and nature ofthe relationship between minimum wages and employment. In the next section, part 2,previous research on the minimum wage topic is explored. Part 3 explores the theoretical 2
    • underpinnings of the wage-employment relationship via an examination of theemployment function. Next, part 4 presents the estimation strategy implemented by thisstudy and part 5 explains the factors included in the estimation model. Subsequently, part6 presents the summary statistics, and provides a look into the data set. The empiricalresults of the econometric analysis are outlined in part 7, and are discussed in part 8.Finally, part 9 provides the conclusion of this study, as well as suggestions for furtherresearch into the minimum wage topic.2: Literature ReviewHamermesh (1986) provides a summary of various theoretical labor-demand models, andtheir appropriate derivation. These are derived form various production models. Inparticular, the Hamermesh examines basic two-factor models, constant elasticity ofsubstitution models, Cobb-Douglas models, and multi-factor models. This theoreticalanalysis can be used to examine the employment effects of the minimum wage.Perhaps the most controversial empirical authors examining the employment effects ofthe minimum wage are Card and Krueger. Card and Krueger (1994) found a positiverelationship between minimum wages and employment in the fast-food sector in NewJersey and Pennsylvania in the aftermath of minimum wage increases in New Jersey in1992. Card and Krueger attribute this outcome to monopsony power in the fast-foodindustry of these two states. This positive relationship was based on survey data of acase-study, an approach which then came under severe criticism from emanating fromboth academia in the form of revisionist research, and from conservative think-tanks,mostly in the form of opinion editorials. In response, Neumark and Wascher (2000)concluded a relative decline in employment based on a revision using payroll data, whileclaiming that Card and Krueger (1994) was invalid because of the relative informality ofthe data set used. In response to this, Card and Krueger (2000) re-examine the NewJersey and Pennsylvania phenomenon using data from the Bureau of Labor statistics, andconcluded that the 1992 change in the New Jersey minimum wage had most probably noeffect on total employment, and possibly a small positive effect, while reaching a similarconclusion using Neumark and Wascher’ data set, controlling for employer dummies. s 3
    • Neumark and Wascher (2007) is a meta-study which examines dozens of studies,considering 33 of these to be of a credible rigor and caliber, respond by questioning thevalidity of the case-study approach all-together. Of these studies, 85% point to a negativewage/employment relationship. Neumark and Wascher are prolific empirical authorsknown for a skeptical point of view on minimum wage legislation, and in this study faultsome authors for diverging from the competitive model explaining the wage/employmentrelationship. Setting this opinionated stance aside, Neumark and Wascher (2007) providea thorough critique of the several studies. Among the key issues that surface in thisreview are credibility of data, bindingness of minimum wages, and credibility ofsecondary controls. According to their critique, all data should be from a credible officialsource, bindingness of minimum wages must be controlled for in order to connect theempirical results to theoretical discourse on wages and employment, and secondarycontrols must be clearly justified.Stewart (2002) examines the effects the 1999 reintroduction of a national minimum wagein the UK by means of econometric analysis. Central to this paper’ argument is a smeasurement of the effect of the reimplementation of the minimum wage across differentareas of the UK, whose wage rates had diverged since the minimum wage was abolishedin 1993. The bindingness of the minimum wages was explored therefore, and considereda major potential factor affecting the effect of employment changes in the wake ofminimum wage reimplementation. This paper comes to the conclusion that the effect ofthe reimplementation of minimum wage legislation was largely contained within thelowest income quartile, that there was no statistically significant difference between theeffects of the legislation in high-income, and low-income areas, where the new minimumwage was most binding, and that there was no systemic adverse effect on employment.Singell and Terborg (2005) examine empirically the effect of minimum wage legislationon employment changes in states of Oregon and Washington in the US. Specifically,Singell and Terborg examine the hotel and lodging industry as well as the restaurant andbar industry, with the intention of determining the effect of bindingness of minimum 4
    • wages on the effect of minimum wage changes on employment. Singell and Terborg findthat employment elasticities are in fact industry-specific. In fact, his study finds a positiveemployment elasticity in the hotel industry.Addison et al. (2008) examine the impact of changes in minimum wage legislation onemployment in the restaurant and bar industries in the US using Bureau of LaborStatistics county-level quarterly data. Additionally, this study provides a theoreticalbackground within which to frame the minimum wage debate, stressing the importance ofminimum wage bindingness. Also, Addison et al. find that labor demand elasticity variesby industry. The conclusion explains that labor-demand elasticity is lower in therestaurant industry than in other industries due to the importance of location. i.e., due tolower degree of tradability. This study also mentions a shortcoming of county-level datain that minimum wage changes occur mostly at the state level and are therefore state-wide in their effect. Thus, Addison et al. conclude that state-dummy cross-sectional andpanel data should be considered as primary estimation tools.Rodrik (1997) is an empirical text which outlines various sources of tension surroundingglobalization. One of the more controversial topics covered by Rodrik is a link betweeneconomic openness and labor demand elasticity. Rodrik empirically demonstrates thatwith increased tradability, substitutability between domestic labor and overseas laborincreases, thus increasing labor demand elasticity as a result of increased tradability.3: Theoretical AnalysisIn relation to Card and Krueger (1994), it must be said that the monopsony rationaleexplaining wage and employment relationship which Card and Krueger discovered withinthe fast-food sector in New Jersey and Pennsylvania is not a plausible explanation for asimilar relationship in the aggregate US labor market. One cannot assume thatprospective employees withdraw their offers to sell their labor simply by excludingthemselves from the labor market. In a region-specific and sector-specific analysis suchas Card and Krueger (1994), prospective employees can withdraw their offers of labor byexiting the specific sector or region towards another sector or region. In analyzing the 5
    • entire US labor market however, such an explanation cannot be considered valid. Analternative explanation for this phenomenon must be considered.In theory, there are several effects which take place on the labor market when wageschange. When wages increase, the output effect takes place in the short run. That is, aswages expand, output will decrease. Next, a substitution effect takes place, whereby aportion of the labor input is substituted with capital. Thus, as a result of these twoeffects, the labor demand function gives rise to a downward-sloping curve, as illustratedin figure 1:Figure 1: Output and Substitution Effects Capital K2 K1 Labor Wage w2 w1 Employment L2 L1 6
    • The downward-sloping labor demand curve this study uses is derived from total output.Output is expressed as a two-factor constant elasticity of substitution (CES) productionfunction borrowed directly (with slightly different notation) from Hamermesh (1986): Y = f(K, L) Y = [ L + (1- )K ]1/and: = 1/(1- )In this model represents the elasticity of capital/labor substitution. The labor demand 1curve is given by : L = Y( /w)Labor demand elasticity incorporating both the output and the substitution effect is 2(Hamermesh, 1986): LL = -[1- - j j represents elasticity on the product market. Naturally, an increase in wages increasesthe cost or production, leading to an increase in price on the product market, leading toless quantity demanded of the good in question.This approach considers the effect of wages exclusively as a cost factor. Because wagesare also a form of income, their demand effect must also be taken into account. In orderto take the demand effect into account, we must consider the effect of a change in wageson consumption, the effect of consumption changes on output, and the effect of thechange in output on employment. Thus, the employment function takes the form: L = f(w, Y(w))1 See Appendix 1 for derivation of the labor demand curve.2 See Appendix 1 for derivation of the elasticity function. 7
    • The output-effects of wage changes can be boiled down entirely to consumptionchanges.3 In a closed economy4: Y(w) = f(C)And: C/ w = c1w[L + w( L/ w)] - c [L + w( L/ w)]Because = PQ- wL- rK, a redistribution of income occurs from profit-earners to wage-earners. Nevertheless, Keynesian scholars concur that fundamentally c 1w > c (Andini,2007), leading to an increase in consumption in all cases in which the positive directwage effects on consumption outweigh the negative indirect effects on consumptioncaused by changes in employment. Increases in output then cause an increase labordemand: L/ Y = ( /w)Therefore: L/ Y L/ w = ( /w) (c1w[L + w( L/ w)] - c [L + w( L/ w)])Figure 2: Shift in Labor Demand Caused by Increased Demand w2 w1 L1 L2 Employment3 I and G are held constant and assumed to be exogenous factors within this model. According to Klein(1947), the neoclassical system’ I depends on interest rate as a determining factor, while the Keynesian ssystem’ I depends on Yo which is determined after changes in output. s4 See Appendix 1 for derivation. 8
    • Thus, the employment effects of demand changes depend on changes in output as a resultof changes in consumption. This effect amounts an outward shift in the labor demandcurve as in figure 2. Therefore, overall employment elasticity taking into account thesubstitution effect, the output effect, and effective demand takes the functional form: ew = LL + LY YwThus, overall employment elasticity is given by: ew = -[1- ] - j + (w/L)( /w) (c1w[L+w( L/ w)] - c [L+w( L/ w)])The Role of TradabilityIncreased tradability, which may take the form of increased openness to trade, orlogistical improvements which make trade flow more smoothly, has an influential effecton employment elasticity. Both Rodrik (1997) and Slaughter (2001) document anincrease in labor-demand elasticity as a result of increased tradability. This happens vis-à-vis both the substitution effect and the output effect. (Slaughter, 2001) Moreover, theeffect that wage increases have on output are moderated by the consumption of imports inthe place of domestic output. To outline the effect of tradability in a simplistic way5: ew = -[1- ] /(1- ) - j/(1- )+ (1- )(w/L)( /w) (c1w[L+w( L/ w)] - c [L+w( L/ w)])Where tradability is: 0 <1In short, is increased by trade due to the wider variety of production technologyavailable in the world market, j is increased by trade and Y(w) is decreased by tradebecause consumption is diverted away from domestic output and toward import-5 Although the effect of tradability must interact with relative price changes in order to become effective,price level increases are assumed as a result of both wage increases and output increases. Under the Homo-Economicus assumption, any relatively cheaper foreign price change causes substitution away fromdomestic goods and/or production factors. 9
    • consumption. As tradability increases, the output and substitution effects trend towardsinfinity, while the demand effect trends towards zero.Because both and differ within each sector of the economy, this model assumessector-specific and leading to sector-specific production functions and employmentelasticities. Thus: Y= Ys Ys = [ Ls s + (1- )Ks s]1/ sAnd: ews = -[1- s/(1- s)- js/(1- s) + (1- s)(w/L)( /w) s (c1w[L+w( L/ w)] - c [L+w( L/ w)])Put into words, the theoretical argument can be summarized as follows:The employment effect of a wage change is subject to two opposing forces, increasedlabor cost which reduces the quantity demanded of labor, and increased effective demandstemming from consumption of higher wages which leads to increased demand foroutput. How far the quantity demanded for labor decreases with a wage increase issector-specific and depends on ease of labor/capital substitution. Whether the increasedwage-income is channeled into domestic consumption or import-consumption is alsosector-specific and depends on tradability. Whether the effect of a given wage increase ispositive or negative ultimately depends on whether the employment effect of increasedoutput demand is larger than the employment effect of decreased quantity demanded oflabor.4: Estimation StrategyAs a primary and central method of econometric estimation, this study makes use of thefixed-effects panel generalized least-squares model (GLS).Fixed-effects estimation is used as the basic estimation technique due primarily to therejection of poolability by means of joint significance testing. Additionally, periods arecontrolled for by means of quarterly period dummies. Furthermore, because in this data 10
    • set, States > Periods > 2, the fixed-effects estimator is the Best Linear UnbiasedEstimator in the absence of heteroskedasticity and serial correlation according to Li(2007) Westbrook (2007), and Wooldridge (2002, 2006).Heteroskedasticity is however present and widespread within the data set. In such asituation, both Dougherty(2002) and Wooldridge (2006) recommend the use of the panelgeneralized least squares estimator, which takes the theoretical form: (Wooldridge,2006), Dougherty (2002)Wage-earning employment (state) h(state) = 0 h(state) + 1Minwage(state) h(state) + 2 Average hourly earning(state) h(state) + 3 Service-Sectoremployment (state) / h(state) + 4 Man.-sector employment(state) h(state) + 5 Non-wage-earningemployment(state) h(state) + 6 Period Dummies(state) h(state) + error (state) h(state)The generalized least-squares model and notation above are borrowed directly fromWooldridge (2006), in which h represents the weighted heteroskedastic error-correctionterm which is proportional to the standard deviation. Wooldridge (2006) succinctlyexplains that: 2 Var(u|x) = h(x)where h(x) is a function of the explanatory variables that determines heteroskedasticity.(Wooldridge, 2006)5: Factors in the Estimation ModelWage-Earning employment is used as the dependent variable. In the US, wage-earningjobs account for the lowest employment incomes. It is in this subset where all thosedirectly affected by the minimum wage, as well as changes therein can be found.Additionally, several control parameters are included in the estimation model. FollowingNeumark and Wascher (2007), bindingness and average income are controlled for inorder to connect the empirical results to theoretical discourse on wages and employment,sectoral controls are justified due to their effect on employment elasticity, and all data isdrawn from the Bureau of Labor Statistics. 11
    • Control ParametersAs displayed in the estimation model, several factors are controlled for the regressions.Taking these factors into account eliminates wage-earning employment changes due toother factors and isolates the wage-earning employment of the effect of the minimumwage. Additionally, the minimum wage is properly weighted, ensuring that theestimations match the theoretical discourse on wages and labor demand.PeriodsPeriod dummies are included in order to control for natural exogenous changes inemployment. Periods effects wholly contain the seasonal variation, as well as cyclicaltrends within the dataset. Inclusion of is supported by joint significance F-test results.Minimum Wage CoverageAs Addison et al.(2008), Singell and Terborg (2005), and Stewart (2002) all highlight theimportance of bindingness measures in order to correctly gauge the employment effect ofthe a change, it is evident that a way to measure the coverage level of the minimum wagemust be included in this study.The standard way in which minimum wage coverage is measured is via the minimumwage spike, a ratio comparing minimum wage employment to overall employmentfigures. (Downes et al., 2000) Since actual statewide quarterly minimum wageemployment numbers were unavailable during data collection, a proxy is used instead.The proportion of wage-earning employment relative to all employment within a givenstate can effectively be measured by comparing the Current Population Survey (CPS)data set, which records wage-earning employment with the Quarterly CensusEmployment and Wages (QCEW) data set, which records aggregate and sectoralstatewide and countywide employment data. In the US, wage-earning jobs occupy thelower end of the income scale, and all minimum jobs which remunerate at the minimumwage are counted within wage-earning employment figures. Thus, a partial measure ofbindingness and coverage is achieved. This measure is useful because minimum wage 12
    • employers in the US also keep a large cohort of employees at slightly above theminimum wage. In such workplaces, an increase in the minimum wage effectively shiftsthe entire wage scale upwards. Thus, it is not only employees actually at the minimumwho are affected by it. Accordingly, this is a measure of all those affected by theminimum wage.This control parameter must be expressed as statewide total employment figure becauseuse of a ratio instead would include wage-earning employment as its numerator, leadingto endogeneity problems. There remains however, a problem of overlap in that totalemployment figures include wage-earning employment as a subset. Therefore, thisdilemma is addressed by utilizing using the opposite employment subset, rather than theoverall employment figure. That is, the use of non-wage-earning jobs as a control factor.Besides overcoming problems of overlap and endogeneity, this parameter controls forflow from wage-employment to salary-employment with minimum wage changes, thuseliminating some of the noise present within the data set by account for this tradeoff.Relative Weighting Minimum Wage Values –Kaitz IndexIn order to properly measure the effect of minimum wage changes, a proper minimumwage weighting scheme is necessary in order to measure real magnitude of the minimumwage. This means that the minimum wage be first be inflation-adjusted, and thenweighted against other factor costs within the economy. For said purpose, this studyemploys the Kaitz index, a measure of the distance between the mean wage and theminimum wage, weighted by coverage. Thus, the Kaitz index tracks the extent to whichthe minimum wage and the average income move together. This weighting measure is animportant tool which filters out any noise from the minim wage and employmentestimation. It may be helpful to think of the Kaitz index as the “minimum wage put intocontext” Thus, it is this tool that ensures that the minimum wage represented in the .empirical results section matches the wage level represented in the theoretical analysis.The Kaitz index can be constructed with three basic ingredients. These are, the minimumwage, the coverage rate, and the average earning rates. (Downes et al., 2000) Because of 13
    • the log-transformation, average hourly earning is used as a control parameter to correctlyweight the minimum wage. Since the A.H.E. coefficient is always negative, the minimumwage value is successfully weighted. Since minimum wage coverage is already accountedfor, it does not need to be repeated in order to make the Kaitz index effective. Togetherwith minimum wage coverage, the weighting measure is referred to as a bindingnesscontrol parameter. (Downes et al., 2000)Controlling for Relative Influence of SectorsBecause the employment function model outlined in the theoretical section describes aneconomy composed of various sectors, and because has a different level of tradability anddegree substitutability within each sector, relative sectoral influence must be accountedfor in order to reconcile the empirical analysis of the effect of the minimum wage withthe theoretical analysis. 6 Empirically, there are two viable ways in which the relativeinfluence of sectors within a state’ economy. These are by comparison of employment sshare, or by comparison of employment share within the state workforce. Theperformance of these two control methods is compared in the empirical results section.Sectors are controlled for individually in order to avoid endogeneity problems. Hence thisstudy includes separate control variables for the manufacturing sector and the servicessector. For purposes of this study, more detailed industry-level controls are not necessarybecause while each industry may have different and values, inter-industry differenceswithin a given sector are small in comparison to inter-sector comparison, and hence donot contribute much added value to this study. 7The regression equation therefore directly poses the first question, as stated in theintroduction: Does a relationship between minimum wages and employment exist? Aswith Card and Krueger (1994), the estimation now focuses only on those jobs whichminimum wage workers would get, as opposed to overall employment.6 Mirroring the theoretical analysis, the substitutability and tradability assumptions are: s< m and s< m7 Employment data is available by industry, from which, manufacturing employment data has been chosento represent the manufacturing sector, while the services-sector employment represents a compilation ofseveral industries intending to approximately capture the totality of services-sector. 14
    • 6: Summary StatisticsThe data set analyzed in this text consists of 1034 observations drawn from two Bureauof Labor Statistics surveys. In total, the sample includes 47 states and 22 quarters from2002q1-2007q2. The sectoral and overall statewide employment information was drawnfrom the BLS Quarterly Census of Employment and Wages (QCEW), a quarterly,sectoral employment and wage survey recorded at the federal, state, and municipal levels.Wage-earning employment data was drawn from the Current Population Survey (CPS), amonthly household survey on minimum wages, wage-earning employment andunemployment in the US at the federal and statewide level. Key variables in this data setare displayed in table 1. Aggregate employment is divided into two groups, wage-earningand non wage-earning employment by comparing the CPS against the QCEW. 8Table 1: Summary Statistics Variable Obs. Mean Std. Dev. Min Max Median Statewide Employment 1034 2742640 2785896 272405 15700000 1841620 Wage-Earning Employment 1034 1567454 1552908 160000 8942000 1113500 Non-Wage Employment 1034 1175186 1256124 81405 7158000 785870 Service Sector Employment 1034 2231389 2360704 192167 13200000 1374321 Service Sector Jobs % 1034 0.788 0.060 0.635 0.936 0.781 Man. Sector Employment 1034 304368 292799 7850 1647646 304368 Man. Sector Jobs % 1034 0.111 0.041 0.024 0.209 0.109 Inflation-Adjusted Minwage 1034 $5.56 $0.73 $5.10 $7.90 $5.15 Inflation-Adjusted A.H.E. 1034 $17.71 $3.09 $11.98 $34.73 $17.24 Kaitz Index 1034 0.3196 0.0478 0.1878 0.4394 0.3164 m_s_ratio 1034 0.1712 0.1436 0.0282 0.9259 0.1419All wages and earnings represent real income. They have been inflation adjusted usingthe Consumer Price Index for Wage-Earners (CPI-W), the index employed by US laborunions to calculate inflation for bargaining purposes. Average hourly earnings arecalculated from both wage-earners and non-wager earners and is abbreviated A.H.E. inall tables. M/S ratio is a sectoral employment distribution ratio comparing manufacturingjobs to service jobs.8 Wage-earning employment pays an hourly wage, and pay-period remuneration is calculated on the basisof hours worked per pay period. Non-wage-earning employment in the US is mostly salary-based, althoughthe non-wage-earning employment figure also covers all other non-wage earning employment, such ascontractual employment and self-employment. 15
    • Figure 3: Sectoral Distribution and Wage/Non-Wage Earning Employment US Sectoral Employment 2500000 2000000 1500000 Services 1000000 Manufacturing 500000 0 Jan 02 Jan 03 Jan 04 Jan 05 Jan 06 Jan 07 Jul 02 Jul 03 Jul 04 Jul 05 Jul 06 Employment in US 2800000 2600000 2400000 2200000 2000000 Wage Emp. 1800000 Total Emp. 1600000 1400000 1200000 1000000 4 2 04 5 07 03 06 3 6 02 05 l-0 l-0 l-0 l-0 l-0 n- n- n- n- n- n- ju ju ju ju ju ja ja ja ja ja jaDuring the 2002q1-2007q2 period, both minimum wages and employment increasedgradually. With respect to employment figures, there were increases in both overallemployment and wage-seeking employment. Both overall employment and wage-seekingemployment display clear seasonal effects, as do service-sector employment figures. Interms of seasonal/quarterly effect on the data, this effect controlled for with the inclusionof period dummies. Additionally, employment figures show an increase in the magnitudeof its seasonal fluctuation after January 2004. The minimum wage illustration in figureA3 displays the average statewide minimum wage in the US along with the highestminimum wage as of 2007 q2 and one of the lowest As all states with a statewideminimum wage lower than the federal minimum wage of $5.15 per hour were normalizedto the federal minimum wage, as the federal law would take effect in such states, therewere several states either whose statewide minimum wage or functional minimum wagestayed at $5.15 per hour during the entire period of this study. Real statewide minimumwages have increased on average, over the 2002q1-2007q2 period. 16
    • Figure 4: Average Statewide Real Minimum Wage (2002 Dollars) Statewide Minimum Wages (USD) Inflation Adjusted $8.00 $7.50 $7.00 $6.50 U Average S $6.00 Georgia $5.50 Oregon $5.00 $4.50 $4.00 Jan Jul Jan Jul Jan Jul Jan Jul Jan Jul Jan 02 02 03 03 04 04 05 05 06 06 07Figure 5: 2002-2007 Average Real Minimum Wage by State (2002 Dollars) 2002-2007 Avg. Minimum Wage by State $7.50 $7.00 $6.50 $6.00 $5.50 $5.00 $4.50 $4.00In terms of the state-specific averages, cross-sectional distribution of the statewide realminimum wage displayed in figure 5, variation is somewhat larger. Minimum wagesrange from Washington state’ $7.25 per hour on the high end to the federal minimum of s$5.15 per hour shared by approximately a third of all states in the US during this timeperiod. Likewise, sectoral share variation within the state economies, displayed in figuresA1 and A2 show wider variation than does average US statewide sectoral employmentshare displayed in figure 3. Florida has the largest service sector employment share at92% of its workforce, while Indiana has the highest manufacturing sector share at 20% ofits workforce. At the lower end are Wyoming with a service sector employment share of63%, and Delaware with a manufacturing sector employment share of 0%. 17
    • 7: Empirical ResultsDummy VariablesIn Card and Krueger (2000), one of the tools employed to measure the effect of aminimum wage change on employment was the regression of employment on a changedummy representing whether or not a minimum wage change occurred. While in this casethe data set contains several changes in the minimum wage, a dummy analysis may stillbe indicative of wage-earning employment effects. The regressions displayed in table A1regress wage-earning employment on a minimum wage change dummy. The empiricalresults are reported in a manner which permits examination of both independent variablecoefficient, P-value and standard error, and those of the control parameters as well.Additionally, table A1 includes a partially-lagged hybrid regression9. Unlike Card andKruger’ results, the regression of wage-earning employment on a minimum wage schange dummy does not indicate any significant relationship between minimum wages.While the control factors are generally significant, the minimum wage change dummy’ scoefficient is too close to zero to achieve any sort of serious significance or predictivepower in all cases but one. In the regressions displayed in table A2, wage-earningemployment is regressed on the dummy variable flat, which takes a value of one whenthe minimum wage has remained unchanged for the previous two years. It is constructedthis way to take both short and medium-term effects of minimum wage changes intoaccount. Again, the coefficients resulting from these regressions are too close to zero toyield any significance.Continuous VariablesThe effect on wage-earning employment caused by minimum wage increases is moreaccurately revealed via analysis of continuous variables. The estimations are log-transformed and inflation adjusted using CPI-W. Estimations in this section are tested forautocorrelation using the Wooldridge test. Rejection of the null hypothesis indicatesautocorrelation. These models are also tested for group-wise heteroskedasticity using9 In the hybrid lagged regression, the dependent variable is regressed on the present value explanatoryvariable, and the lagged control parameters. 18
    • both the modified Wald-chi test, and likelihood-ratio test. (Greene, 2003). The basicregressions displayed in table A3 demonstrate that the effect of the minimum wage isgenerally positive, and zero in the case of first difference models. In the absence ofcontrol parameters, the explanatory power of the minimum wage on wage-earningemployment is low.Table 2: Fixed Effects Estimations Comparing Control ParametersY = wage employment Non-wage PeriodsX = Minimum wage Min. Wage Services Manufacturing A.H.E. Employment F-testFE 0.1262 - - - - -P value 0.0000 - - - - -SE 0.0322 - - - -R-sq 0.0153 - - - -overall R-sq 0.0007 - - - -FE (Sectoral Controls) -0.0050 1.2014 -0.1011 - - 3.1900P value 0.8810 0.0000 0.0050 - - 0.0000SE 0.0333 0.0982 0.0356 - -R-sq 0.3317 - -Overall R-sq 0.9687 - -FE (BindingnessControls) -0.0571 - - 0.1341 -0.5398 24.8000P value 0.0110 - - 0.0030 0.0000 0.0000SE 0.0225 - - 0.0450 0.0140R-sq 0.6927 - -Overall R-sq 0.9457 - -FE (all controls) 0.0120 1.5109 0.0996 -0.0044 -0.6324 12.1000P value 0.2590 0.0000 0.0000 0.8350 0.0000 0.0000SE 0.0107 0.0317 0.0116 0.0214 0.0069R-sq 0.9319Overall R-sq 0.9915Panel GLS (Hetero) 0.0558 1.3746 0.1420 -0.3719 -0.5575 348.9500P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0112 0.0092 0.0022 0.0136 0.0090Wald-Chi DF = 26 689838.0600Additionally, autocorrelation is present in two these estimations, while heteroskedasticityis present in all three. The regressions in table 2 display a comparison of the variousestimation models employed in order to examine the wage-employment demandelasticity. Because the fixed-effects estimator would be the best unbiased estimator in theabsence of heteroskedasticity, table 2 compares fixed-effects estimations with various 19
    • control parameters.10 This table compares models including some controls and allcontrols, as well as OLS models and heteroskedasticity-correction GLS models. Beyondempirical theory, it makes sense the within estimator would deliver different results thanother estimators, even when time trends are taken into account. This is because a fixed-effects estimation does not take into account employment changes that happen in anotherstate as a result of a statewide minimum wage change. A statewide minimum wagechange which positively impacts statewide employment might do so in part by attractingemployees from neighboring states, causing them to register lower employment figuresthan they otherwise would, thus registering an employment increase in one state, and anemployment decrease in a neighboring state.The Regressions Including Control ParametersRelative Sectoral DistributionThe regressions presented in table A4 represent an estimation of wage-earningemployment elasticity, controlling for sectoral employment share. As demonstrated in thetable, regressions controlling for sectoral employment share, the employment effects ofthe minimum wage become insignificant, and are upstaged by the sectoral relationship ineffect on wage-earning employment. The exception lies in the first-difference model,where none of the coefficients is significant, and no effect on wage-earning employmentis detected. The indication is that sectoral employment share is the primary factoraffecting wage-earning employment, not the minimum wage. Moreover, the sectoralbalance is such that the effect of the minimum wage is neutral. Again, heteroskedasticityis present in the estimation.Bindingness ParametersIn the regressions displayed in table A5, bindingness measures are taken into account ascontrol parameters. Again, considerable heteroskedasticity is present in the panel sample.Additionally, autocorrelation is present within this estimation.10 Because N > t and t > 2, the fixed-effects estimator outperforms the first-difference estimator.(Wooldridge, 2002), (Wooldridge, 2006) Fixed-effects is the best linear unbiased estimator in this situation.(Westbrook, 2007), (Li, 2007) 20
    • All Control Parameters SimultaneouslyDisplayed in table A6, are OLS regressions with all controls. The displayed resultsclosely resemble the results including only the bindingness parameters, indicating that thesectoral parameters do not in fact completely dominate the effect of the minimum wageonce bindingness is taken into account. With that said, it is evident that there is someoverlap between the sectoral share controls and the bindingness controls. Fortunately, theoverlap partially resolves itself in that both bindingness parameters carry negativecoefficients, while the sectoral-share parameters carry positive ones. Thus the two sets ofparameters partially cancel each other. Alternately, one may chose to cancel theindependent variable and some of the control parameters. Doing so would most likelyleave non-wage-earning employment as the dependent variable. While the data do alsoindicate a positive relationship between the statewide minimum wage, and non-wage-earning employment figures in a within-state context, and such a relationship is alsosupported by the underlying theoretical analysis, the focus of this study rests ultimatelyon the wage-earning employment. Wage-earning employment is ultimately influenced byall of the control parameters, a fact which is important to measure, despite some overlap.Tables A6b and A6c offer comparison of OLS regressions which include all controlparameters displayed in table A6 with similar estimations performed with lagged controlparameters in table A6b and lagged independent variable and control parameters in tableA6c. Diverging from table A6, the likelihood ratio test finds no heteroskedasticity presentin tables A6b and A6c. The test value is considerably lower, as are number ofobservations, and the degrees of freedom. The modified Wald test however, makes use ofall observations and finds almost identical test values in all three tables.The cross-sectional dimension of the data set is larger than the time dimension. Ergo, thefixed effects estimator is the preferred estimator when comparing between fixed effectsand first-difference, given that the errors uit are serially uncorrelated as they are here. (Li,2007) It is also is the best least unbiased estimator in this situation if errors are normallydistributed. (Westbrook, 2007) However, heteroskedasticity is present in every regressionconducted with this data set. With respect to the accuracy of the estimations in tables A6, 21
    • A6b, and A6c, the present value regressions displayed table A6 are upheld as the mostaccurate because of the larger R-squared values of the present value estimation. Thepresent value estimation is also superior due to its higher adjusted R-squared values.(Greene, 2003) This outcome is corroborated by the heteroskedasticity-correcting GLSmodel, where the present-value estimation is also the most accurate.Heteroskedasticity Correcting Cluster Robust Standard Error and GLS EstimationsAccording to both Wald testing and likelihood-ratio testing, the data sample examined forthis study has considerable panel heteroskedasticity. Because heteroskedasticity is presentin the data set, estimation errors are not identically distributed. Due to autocorrelation,errors are also not always independently distributed. Ergo, the iid assumption is violated.One method which can be used to address this issue cluster robust standard errorregression. Results of the cluster-robust regressions are displayed in table A9.Another method to correct for heteroskedasticity is the heteroskedasticity-correctingpanel fixed-effects GLS estimation. Because the fixed-effects estimator would be the bestlinear estimator in the absence of heteroskedasticity, a heteroskedasticity-correctingfixed-effects model makes a good choice as an estimator for this dataset. Furthermore,the fixed-effect GLS estimator is preferred heteroskedasticity correction estimator inStata given the existence of panel heteroskedasticity. (Statacorp, 1999)In table A10, regressions controlling only for the manufacturing and services relationshipare re-estimated using a heteroskedasticity-correction panel GLS. These estimations arecarried out because the Wald-Chi test and the likelihood-ratio test disagree on thepresence of heteroskedasticity within the model. As in the regression results displayed intable 2, any employment effects caused by the minimum wage are rendered insignificantand completely overshadowed by controlling for sectoral employment. Additionally,there is almost no difference between the lagged and the present value GLS model. This 22
    • is because the average statewide sectoral distribution changed little during the course ofthe period. 11Table 3 : Present Value GLS Regression Including all Control Parameters –The Best Linear Unbiased EstimationY = wage employment Non-wage PeriodsX = Minimum wage Min. Wage Services Manufacturing Avg. wage Employment F-testPanel GLS(Hetero) 0.0558 1.3746 0.1420 -0.3719 -0.5575 348.9500P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0112 0.0092 0.0022 0.0136 0.0090Wald-Chi DF = 26 689838.0600The regressions in table A11 resemble approximately the standard ordinary least-squaresregression including all of the control parameters displayed in table A6. Given the Waldstatistic, this most likely represents the most accurate regression result. In table A11, thepresent value regression using the present independent variable and control parameters iscompared with, a lagged value regression using the lagged independent variable andcontrol parameter, and a partially-lagged hybrid regression. Despite similar coefficientsand identical P-values, the present value regression displayed in the top portion of tableA11 (also displayed in table 3), displays smaller standard error as well as a considerablylarger Wald statistic, indicating that it is the most accurate regression among the threeestimated in table A11. In comparison with the cluster-robust standard error regressionsdisplayed in table A9, the standard error is smaller in the GLS estimation, indicating thatthe cluster robust estimation perhaps slightly overestimates the employment elasticity.The present-value panel GLS estimation using both sectoral-employment share controlsand bindingness controls is therefore the overall best unbiased estimator for calculatingwage-earning employment elasticity with respect to minimum wages. Accordingly, saidestimation is displayed in table 3 above.Alternate Sector Control Factors11 When executed in STATA, the fixed-effects GLS estimator reports a Wald statistic rather than an R-squared value. This occurs because R-squared does not behave the same with a GLS estimation as with anOLS estimation. Thus, the R-squared does not represent proportion of total dependent variable variationexplained by the GLS model. Ergo, is a less useful diagnostic tool when using a GLS rather than an OLSestimator. (Statacorp, 2003) The Wald statistic is a hypothesis testing tool which follows a chi-squaredistribution whereby the number of restrictions represents the degrees of freedom to compute the chi-square test. (Wooldridge, 2006) Significance of the Wald test validates the model. 23
    • As an alternative to considering each sector’ employment share, the effect which the smanufacturing and services sectors have on employment elasticity can be examinedthrough the relative GDP share of each sector. This approach however is less precisebecause differences between the sectors in terms of GDP share can be caused by eitherdifferences in employment levels or income levels. In any case, it is worthwhile toexamine the sectoral influence from more than one angle. Controlling for statewidesectoral GDP-shares remains a plausible means of further examination of theemployment and wage relationship. An alternate method of controlling the relative sizeand influence of each sector is especially useful in estimating the effect of minimumwage changes on employment within a specific sector, where controlling for employmentshare rival sectors may be problematic. With the exception of the manufacturing sectorcontrol coefficient, the regression coefficient results when bindingness controls areincluded parameters displayed in table A8 closely resemble regression results which donot include bindingness control parameters displayed in table A7. Interestingly, it is nowthe manufacturing sector, rather than the services sector which has the dominantinfluence over the dependent variable, despite its relatively smaller size. Additionally,there is a pronounced difference in R-squared statistics reported in tables A6 and A7.This indicates that the majority of the explanatory power of this alternate sectoral controlestimation model, in fact lies with the inclusion of controls for bindingness.While autocorrelation is present in both regressions in which each sector’ share of sstatewide GDP, the Wald-Chi test for heteroskedasticity and the likelihood ratio test,which both test for heteroskedasticity in panel data do not agree. The relationship istherefore re-estimated using various panel GLS estimations. Given that sectoral GDP-share controlling OLS estimation models suffer from both autocorrelation andheteroskedasticity, as well as the fact that the sectoral GDP-share controlling OLSestimation models are outperformed in terms of both R-squared and standard error vis-à-vis the by the sectoral GDP-share controlling OLS estimation models, sectoral GDP-share controls must be considered sub-optimal in with respect to sectoral employment-share controls in terms of properly controlling for the effects of respective sector size. 24
    • Autocorrelation and Heteroskedasticity Correcting GLS EstimationWooldridge testing indicates that autocorrelation is present in some places within the dataset. In the regressions displayed in table A12, autocorrelation is corrected by twoalternate means, via panel GLS regression with first-order autocorrelation correctionsettings and via a panel Prais-Winsten regression which also includes first-orderautocorrelation correction settings. The estimation results between the two estimators arealmost identical, producing nearly identical coefficients. The standard errors, P-values,and Wald values indicate however that the panel GLS model is preferred in this instance.While the emergence of autocorrelation is stronger when bindingness control parametersare included, it is also present when they are excluded, indicating that the GDP-sharebased sectoral controls are sub-optimal tools to control for sectoral size and influence.Additionally, both autocorrelation and heteroskedasticity problems are discovered in tworegressions. Therefore, panel GLS is used here because it is a fixed-effects estimatorwhich can simultaneously correct for both heteroskedasticity and autocorrelation. Theoutput for the autocorrelation and heteroskedasticity-correcting GLS is displayed at thebottom of table A12. Because the modified Wald-Chi test and the likelihood ratio test donot agree on the presence of heteroskedasticity within the fully controlled regressionGDP-share sectoral estimation, a separate panel GLS regression is conducted in order tocorrect for both autocorrelation and heteroskedasticity. The results of this regressionclosely match the autocorrelation-correction GLS results. Upon comparison of the Waldstatistics of these two regressions, as well as the standard error terms, it is evident that thelast estimation, which controls for both autocorrelation and heteroskedasticity is the mostaccurate of the three estimations in table A12. Clearly, the original sectoral GDP-sharecontrolling model outlined in table outlined in table 10 does in fact have aheteroskedasticity problem.Breaks in the Data SetIn Card and Krueger (2000), a natural experiment methodology was employed.Accordingly, the data set was broken into several geographical areas -each with auniform minimum wage- for which regressions were conducted separately. This 25
    • difference-in-differences approach is attempted in this study as well. This data set wasdivided into two data sets based on their flat value. The flat value was used in order toinclude medium and long run effect. This division did not however pass the Chow test,indicating that the natural experiment approach cannot be applied here.The US statewide employment data set was Chow-tested a second time and subsequentlydivided along the median into two sets based on sectoral concentration. These aremanufacturing-heavy states, and services heavy states, based on relative sectoralemployment figures. Interestingly, the two data subsets displayed in the lower half oftable A13 indicate different wage elasticities, as well as different quarterly period dummyeffects. In the more services sector dependent states, there exists a stronger positiverelationship between minimum wages and wage-earning employment.Sector-Specific Effects of Minimum Wage ChangesThe effect of the minimum wage on employment is sector-specific. In the case of both theservices sector and manufacturing sector, employment levels are responsive to minimumwage changes. Controls include the rival sector of the economy in order to take thesectoral relationship into account, and non-wage employment as a measure forbindingness. Average hourly earning proves wildly insignificant as a control parameter inthis regression model. Thus, it was dropped as a control parameter in the estimation.In table A14, the data reveal a positive relationship between wage-earning employmentand minimum wages in the services sector, while revealing a considerably strongernegative relationship in the manufacturing sector. The services sector however, isapproximately eight times the size of the manufacturing sector. Consequently, a 1%employment change in the services sector signifies many times more jobs than a 1%change in the manufacturing sector. The data reveal that employment is created in theservices sector, while employment is simultaneously lost in the manufacturing sector as aresult of an increase in statewide minimum wages, as outlined in table A14. Because asectoral employment shift occurs as a result of changes minimum wage, futureemployment elasticity with respect to the minimum wage is affected. The regression 26
    • displayed in table A15 directly measures the sectoral shift caused by the minimum wage.The table indicates a measurable sectoral employment shift caused by the minimum wagetowards services sector employment.. The second regression displayed in table A15however, demonstrates that the relationship between sectoral employment distributionand the minimum wage is overshadowed by the effect of average hourly earning. Sincethe average has both a lower P-value and a larger coefficient than the minimum wagecoefficient, the implication is that while the minimum wage has some effect on thesectoral employment distribution, the majority of the effect reported in the first regressionis in fact contained within the state average hourly earning rather than the statewideminimum wage. The negative coefficients here indicate a shift away from manufacturing-sector employment and towards service-sector employment. As demonstrated in tablesA13, A14, and A15, this shift is manifested via an increase in services sector employmentcoupled with a simultaneous decrease in manufacturing sector employment.Effect of the Minimum Wage on Overall Employment FiguresThe effects of the statewide minimum wage on overall statewide employment are zero. Inthe regression outlined in table A16, the employment elasticity coefficient isapproximately one half the value of the standard error. Thus, the effect of minimum wagechanges on overall statewide employment figures is zero.8: DiscussionGenerally, continuous variable estimations reveal either a slight positive effect of theminimum wage on levels of wage-earning employment, or no effect whatsoever. Whileanalysis of dummy variables indicates no discernable effect of the minimum wage onemployment figures, it must be said that dummy variables only take into account whethera minimum wage change occurred. Once the proportion of the minimum wage change istaken into account, estimations demonstrate that on average, slight increases in wage-earning-employment occurred due to an increase in the minimum wage. This effecthowever is nearly too small to measure and sufficiently small that it is eclipsed ininfluence by the control parameters. Certainly, the best estimator in this study, the fixed-effects panel GLS estimation displayed in table A11 finds a slight positive elasticity 27
    • coefficient whose influence is outweighed by the control parameters. The data reveal thatsectoral distribution, average earning, and non-wage-earning employment figures aremore influential in determining wage-earning employment than is the minimum wage.Furthermore, the data indicate that minimum wages have no measurable effect on overallUS labor market employment.The findings in this paper emerge along similar lines as Addison et al. (2008) The effectof the minimum wage on the labor market is sector-specific, with different employmentelasticities for each sector. This effect is demonstrated in tables A13-A15. Ergo, stateswith different sectoral distribution have different sensitivity to minimum wage changes.Moreover, the data reveal that the minimum wage also has a small measurable effect onsectoral employment distribution. The result is a shift towards service-sector employmentcaused by an increase in the minimum wage. Thus, future employment elasticity forwage-earning labor will be affected by changes in the minimum wage, causing furtherchanges in the wage-earning employment figures as a result of future minimum wagechanges.In light of the sensitivity of the relationship between statewide minimum wages andwage-earning employment to sectoral employment distribution within a given state, it isevident that the sectoral distribution, as well as the and characteristics of the sectorsinvolved in this analysis are the more pivotal and influential factors in determining therelationship between wage-earning employment figures and the minimum wage. Thedegree of substitutability has a pivotal effect on the shape of the employment/wagerelationship, as does of product tradability. The manufacturing sector, aside from beingthe most capital-intensive sector, is also the sector of the economy where tradability isleast restricted, logistically speaking. Not only does the manufacturing sector have highsubstitutability with domestic capital stock; but also with foreign labor and foreign capitalstock.With respect to the two questions posed in the introduction, it is confirmed that arelationship between the minimum wage and wage-earning employment exists at the state 28
    • level in the US. The data indicate a very slight positive average relationship betweenwage-earning employment and minimum wages across the US. Nonetheless, the data alsoindicate a neutral relationship between overall employment and the minimum wage. Interms of explanatory factors, the data indicate that both bindingness measures andsectoral distribution are influential determining factors in the wage/employmentrelationship. That is, when properly weighted to measure how much the labor market isactually affected by the minimum wage, the sectoral profile of the economy is the maininfluential factor in determining the relationship between the minimum wage, andemployment.9: ConclusionsThe answer to the central questions posed in this study are clear: The relationshipbetween minimum wages and wage-earning employment can be either positive ornegative. The data indicate that the average statewide employment elasticity is positive.The explanation for this phenomenon is that the overall relationship between thestatewide minimum wage and wage-earning employment figures depends on thebindingness of the statewide minimum wage, and the sectoral make-up of the economy.This study seeks to demonstrate that the employment elasticity can be manipulated bycapital/labor substitutability, and the degree of tradability, -expressed via sectoraldistribution given that sectors examined feature diverging substitutability and tradability-are analyzed. Thus, this study leaves some matters unanswered, raising possibilities forfurther study. The QCEW data set includes quarterly industry-level data on a massivenumber of industries and could be further analyzed. Also, it is possible that otherexogenous factors may have influence on employment elasticity. Population density maybe an determining factor for employment elasticity. A further possibility for future studylies in the investigation of employment and income effects of minimum wage changes indifferent income quintiles. This way, economic mobility aspects of the minimum wagecan be measured. In fact, the data in this study indicate that changes may affect individualincome groups differently. Table A11 demonstrates that minimum wages have a positive 29
    • effect on wage-earning employment figures, whereas table A16 points out that minimumwages have a neutral average effect on the statewide employment overall.While the relationships explored in this study could benefit from additional research, thisstudy presents conclusive evidence regarding the relationship between the minimumwage and wage-earning employment. This study concludes by stating that the evidenceindicates that circumstances such as tradability, substitutability expressed via sectoralcomposition are considerably more influential in determining wage-earning employmentthan is the minimum wage, whose influence depends on these parameters. 30
    • 10: ReferencesAddison, John, et al. (2008) “ Effect of Minimum Wages on Wages and Employment: TheCounty-Level Estimates for the United States” Institute for the Study of Labor, BonnGermany, Discussion Paper No. 3300Andini, Corrado (2007) “Teaching Keynes’ Principle of Effective Demand within the sReal Wage vs. Employment Space” Centro de Estudos de Economia Aplicada doAtlantico, Working Paper No. 06/2007Card, David and Krueger, Alan B. (1994) “Minimum Wages and Employment: A CaseStudy of the Fast-Food Industry in New Jersey and Pennsylvania.”American EconomicReview, Vol. 84 pp. 772-793Card, David and Krueger, Alan B. (2000) “Minimum Wages and Employment: A CaseStudy of the Fast-Food Industry in New Jersey and Pennsylvania: Reply” AmericanEconomic Review, Vol. 90 pp. 1397-1420Dougherty, Christopher, (2002) “Introduction to Econometrics: Second Edition”OxfordUK. Oxford University Press.Downes, Andrew, et al.(2000) “Labor Market Regulation and Employment In theCaribbean” Washington DC, Inter-American Development Bank, Research NetworkWorking Paper No. R-388Greene, William H. (2003) “Econometric Analysis” Upper Saddle River, New Jersey,Prentice Hall, Pearson Education InternationalHamermesh, Daniel, (1986) “Demand for Labor in the Long Run” Michigan StateUniversity. Elsevier Science Publishers, Handbook of Labor Economics, edition 1, Vol.1,chapter 8, pp. 429-471 31
    • Hamermesh, Daniel, (1993) “Labor Demand” Princeton, New Jersey, PrincetonUniversity PressKlein, Lawrence R. (1947) “Theories of Effective Demand and Employment” TheJournal of Political Economy, Vol. 1 No. 2, pp. 108-131Li, Zhigang (2007) “Panel Data Course: Applied Econometrics, Lecture Notes” HongKong S.A.R., China, School of Economics and Finance, the University of Hong KongNeumark, David, and William Wascher. 2000. “The Effect of New Jersey’ Minimum sWage Increase on Fast-Food Employment: A Reevaluation Using Payroll Records.”American Economic Review. Vol. 90, No. 5 (December), pp. 1362-96.Neumark, David and Wascher, William (2007) “ Minimum Wages and Employment”Institute for the Study of Labor, Bonn, Germany, Discussion Paper No. 2570Rodrik, Dani, (1997) “Has Globalization Gone Too Far?” Institute for InternationalEconomics, Washington DCSingell, Larry D., and James R. Terborg. (2005) “Employment Effects of Two NorthwestMinimum Wage Initiatives: Eating and Drinking and Hotel and Lodging.”Unpublishedpaper, University of OregonSlaughter, Mathew J. (2001) “International Trade and Labor Demand – DemandElasticities” Journal of International Economics Vol.54, 27-56,Statacorp, (1999) “How does xtgls differ from regression clustered with robust standarderrors?”Retrieved Aug. 14, 2008, from http://www.stata.com/support/faqs/stat/xtgls_rob.html 32
    • Statacorp, (2003). “R-squared after xtgls, Why does xtgls not report an R-squaredstatistic?” Retrieved Apr. 12, 2008, from http://www.stata.com/support/faqs/stat/xtgls2.html,Stewart, Mark B., (2002) "Estimating the Impact of the Minimum Wage UsingGeographical Wage Variation" Oxford Bulletin of Economics and Statistics, Vol. 64, pp.583-605Westbrook, Dan. (2007) “Applied Econometrics with Stata, E-Lecture Notes.” Ho ChiMinh City, Viet Nam, United Nations Development Programme, Public Policy Educationand Research for Vietnam, Fulbright Economics Teaching ProgramWooldridge, Jeffery M. (2002) “Economic Analysis of Cross Section and Panel Data”Cambridge Massachusetts, The MIT PressWooldridge, Jeffery M. (2006) “Introductory Econometrics, A Modern Approach”Mason Ohio, Thompson Higher Education Press, Thompson South-Western. 33
    • Appendix 1: DerivationsA: Labor Demand CurveY = [ L + (1- )K ]1/ Y/ L = w = (1/ ) [ L + (1- )K ] (1/ -1) L -1) = [ L + (1- )K ] (1/ -1) ( L -1) = Y(1- ) ( L -1) = Y(1- ) ( L-1(1- )) = Y (1- ) /(L(1- )) = (Y/L) (1- ) Y/L = (w/ ) 1/(1- ) L = Y(w/ ) = Y( /w)B: Labor Demand ElasticityThis can be demonstrated via the cost-function approach. Constant returns to scale, and acompetitive market are assumed.Y = [ L + (1- )K ]1/Let L = YCw andK = YCrPrice = Costp=CIf markets clear, D(p) = Y L/ w = YCww + D(p)Cw2C is linear homogeneous, so:Cww = (-r/w) Cwr L/ w = (rK/Y) ( L/wC) + (D(p)L2/Y2) 34
    • Thus, the resulting elasticity is: LL = (-rK/pY) + (pD(p)/Y) (wL/pY) = -[1- - jC: The Effect of Wages on ConsumptionIn the traditional Keynesian consumption function consumption is a function of income:C = c0 + c1YC = c0 + c1wwL + c C/ w = c1w wL/ w) + c w)Via the product rule where f(x) = g(x) +h(x)And: f(w) = c1wwLConstant = c1w Constant = cg(w) = w g(w) = wh(w) = L(w) h(w) = L(w)f(w) = g(w)h(w)+g(w)h(w) f(w) = g(w)h(w)+g(w)h(w)f(w) = L + w( L/ w) f(w) = L + w( L/ w) C/ w = c1w[L + w( L/ w)] - c [L + w( L/ w)] 35
    • Appendix 2: Employment Share and CoverageFigures A1 and A2 display sectoral employment share averages by state across the 2002-2007 time period. Table A3 displays average wage-earning employment ratio by stateacross the same period. Sectoral employment shares are calculated from QCEW data,while the wage-earning employment ratio is calculated by comparing CPS employmentdata with QCEW employment data.Figure A1: 2002-2007 Average Manufacturing Sector Employment Share by State Manufacturing Sector Employment Share by State 0.20 0.15 0.10 0.05 0.00 Indiana Ohio New Missouri California Virginia Maryland Hawaii H pshire amFigure A2: 2002-2007 Average Services Sector Employment Share by State Services Sector Employment Share by State 1.00 0.90 0.80 0.70 0.60 0.50 0.40 Florida Nevada Arizona Utah Montana North Kentucky Mississippi Carolina 36
    • Figure A3: Wage-Earning Employment Share by State W/E Ratio by State 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 a re e n ts a ut an ky in se to an et wa tic ol uc ig ng es us di ar ec ich la nt In ch nn hi C De nn Ke as M rth sa Te Co W as No M 37
    • Appendix 3: Dummy RegressionsRegressions in table A1 display wage-earning employment on a minimum wage changedummy. Both standard OLS and first-differenced OLS estimations are undertaken here inpresent value terms, lagged terms, and hybrid term.The regressions in table A2 are of wage-earning employment on the flat dummy whichtakes a value of 1 when the minimum wage has gone unchanged for two years. Bothstandard OLS and first-differenced OLS estimations are undertaken here in present valueterms, lagged terms, and hybrid term.Table A1: Change Dummy Regressions Controlling for Bindingness and Sectoral Employment ShareY = wage employment Non-wageX = Change Dummy Dummy Services Manufacturing Avg. wage Employmentlog-log 0.0068 1.3465 0.1403 -0.3204 -0.5351P value 0.5190 0.0000 0.0000 0.0000 0.0000SE 0.0105 0.0206 0.0050 0.0197 0.0193R-sq 0.9938 Lagged Control ParametersChange Dummy 0.0005 1.1023 0.1375 -0.3413 -0.2928P value 0.9690 0.0000 0.0000 0.0000 0.0000SE 0.0137 0.0264 0.0063 0.0249 0.0246R-sq 0.9903 Lagged Control ParametersLagged Change Dummy 0.0111 1.1004 0.1377 -0.3439 -0.2910P value 0.4020 0.0000 0.0000 0.0000 0.0000SE 0.0132 0.0264 0.0063 0.0250 0.0247R-sq 0.9903First Difference 0.0040 0.2526 -0.0013 -0.0108 -0.2447P value 0.5240 0.0000 0.7730 0.5340 0.0000SE 0.0063 0.0182 0.0044 0.0174 0.0169R-sq 0.2839 Lagged Control ParametersFirst Difference 0.0025 -0.2437 -0.0030 -0.0249 0.2421P value 0.6920 0.0000 0.4920 0.1480 0.0000SE 0.0063 0.0182 0.0044 0.0172 0.0170R-sq 0.2792 Lagged Control ParametersLagged First Difference 0.0051 -0.2400 -0.0050 -0.0319 0.2412P value 0.4510 0.0000 0.2650 0.0720 0.0000SE 0.0067 0.0187 0.0045 0.0177 0.0174R-sq 0.2839 38
    • Table A2: Change Dummy Regressions controlling for Bindingness and Sectoral Employment Share Y = wage employment Non-wage X = Flat Dummy Dummy Services Manufacturing Avg. wage Employment log-log 0.0055 1.3501 0.1399 -0.3131 -0.5388 P value 0.3580 0.0000 0.0000 0.0000 0.0000 SE 0.0059 0.0207 0.0050 0.0205 0.0194 R-sq 0.9938 Lagged Control Parameters Flat Dummy -0.0039 1.1006 0.1377 -0.3454 -0.2910 P value 0.6050 0.0000 0.0000 0.0000 0.0000 SE 0.0076 0.0265 0.0063 0.0261 0.0248 R-sq 0.9903 Lagged Control Parameters Lagged Flat Dummy -0.0055 1.1002 0.1378 -0.3471 -0.2905 P value 0.4750 0.0000 0.0000 0.0000 0.0000 SE 0.0077 0.0264 0.0063 0.0261 0.0248 R-sq 0.9903 First Difference 0.0129 0.2533 -0.0013 -0.0107 -0.2453 P value 0.3030 0.0000 0.7660 0.5370 0.0000 SE 0.0125 0.0182 0.0044 0.0173 0.0169 R-sq 0.2844 Lagged Control Parameters First Difference -0.0008 -0.2438 -0.0030 -0.0251 0.2422 P value 0.9520 0.0000 0.4930 0.1450 0.0000 SE 0.0126 0.0182 0.0044 0.0172 0.0170 R-sq 0.2790 Lagged Control Parameters Lagged First Difference -0.0004 -0.2399 -0.0050 -0.0315 0.2411 P value 0.9740 0.0000 0.2660 0.0750 0.0000 SE 0.0125 0.0187 0.0045 0.0177 0.0174 R-sq 0.2835 39
    • Appendix 4: Basic Continuous Variable OLS RegressionsThese are basic OLS estimations of wage-earning employment on the statewideminimum wage. The relationship is estimated without controls, with state controls, andwith period controls. Various estimators are used and all models are tested for bothautocorrelation and heteroskedasticity.Table A3 : Basic Continuous Variable OLS RegressionsY = wage employ. Basic Control for Control for PeriodsX = minimum wage Coefficient States States (F-test) periods (F- Test)log-log 0.1910 0.1262 4901.0300 0.1677 0.0400P value 0.4070 0.0000 0.0000 0.4890 1.0000SE 0.2302 0.0322 0.2423R-sq 0.0007 0.9956 0.0014FD log -0.1032 -0.1018 0.0700 0.0045 6.8900P value 0.1670 0.1890 1.0000 0.9520 0.0000SE 0.0746 0.0776 0.0742R-sq 0.0019 0.0054 0.1267RE log 0.1262 0.1262 230000.0000 -0.0477 252.9600P value 0.0000 0.0000 0.0000 0.1820 0.0000SE 0.0322 0.0322 0.0357R-sq 0.0006 1.0000 0.0006FE log 0.1262 N/A N/A -0.0479 12.0400P value 0.0000 N/A N/A 0.1810 0.0000SE 0.0322 N/A N/A 0.0358R-sq 0.0153 0.0153 0.2197overall R-sq 0.0007 0.0007 0.0007Wooldridge test 10.2480 10.2480 Autocorrelation 3.8280 No AutocorrelationP value 0.0025 0.0025 0.0565Wald Test 783.6700 783.6700 Heteroskedasticity 731.3600 HeteroskedasticityP value 0.0000 0.0000 0.0000Likelihood-ratio Notest 1158.2500 1158.2800 Heteroskedasticity 1066.8100 Heteroskedasticity 1034 0.0041 0.0040 0.2331 40
    • Appendix 5: Controlling for Sectoral Employment Share and Bindingness SeparatelyTable A4 displays are OLS estimations of wage-earning employment on the statewideminimum wage with period and sectoral employment share controls. Various estimatorsare used and the model is tested for both autocorrelation and heteroskedasticity.Table A5 displays OLS estimations of wage-earning employment on the statewideminimum wage with period and bindingness controls. With these regressions, theminimum wage is effectively weighted. Various estimators are used and the model istested for both autocorrelation and heteroskedasticity.Table A4: Regressions Controlling for Sectoral Employment Share Y = wage employment Minimum Periods X = Minimum wage Wage Services Manufacturing F-test log-log -0.0233 0.7396 0.1662 0.6800 P value 0.4110 0.0000 0.0000 0.8544 SE 0.0283 0.0080 0.0068 R-sq 0.9867 FD log 0.0060 -0.0007 -0.0001 6.8800 P value 0.9360 0.8950 0.9870 0.0000 SE 0.0746 0.0053 0.0045 R-sq 0.1268 RE log -0.0145 0.8486 0.0664 51.4800 P value 0.6570 0.0000 0.0030 0.0002 SE 0.0327 0.0278 0.0225 R-sq 0.9871 FE log -0.0050 1.2014 -0.1011 3.1900 P value 0.8810 0.0000 0.0050 0.0000 SE 0.0333 0.0982 0.0356 R-sq 0.3317 Overall R-sq. 0.9687 Wooldridge test 2.5490 No Autocorrelation present P value 0.1172 Wald Test 412.8700 Heteroskedasticity is present P value 0.0000 Likelihood-ratio test 475.9000 No Heteroskedasticity present heteroskedasticity 1.0000 1034 41
    • Table A5: OLS Regressions Controlling for Bindingness Y = wage employment Services Manufacturing Periods X = Minimum wage Min. Wage Employment Employment F-test log-log -0.0233 0.7396 0.1662 0.6800 P value 0.4110 0.0000 0.0000 0.8544 SE 0.0283 0.0080 0.0068 R-sq 0.9870 FD 0.0060 -0.0007 -0.0001 6.8800 P value 0.9360 0.8950 0.9870 0.0000 SE 0.0746 0.0053 0.0045 R-sq 0.1268 POLS -0.0050 1.2014 -0.1011 3.1900 P value 0.8810 0.0000 0.0050 0.0000 SE 0.0333 0.0982 0.0356 R-sq 0.9970 RE -0.0145 0.8486 0.0664 51.4800 P value 0.6570 0.0000 0.0030 0.0000 SE 0.0327 0.0278 0.0225 R-sq 0.9871 FE -0.0050 1.2014 -0.1011 3.1900 P value 0.8810 0.0000 0.0050 0.0000 SE 0.0333 0.0982 0.0356 R-sq 0.3317 Overall R-sq 0.9687 Wooldridge test 0.0560 Autocorrelation P value 0.8145 Wald Test 412.8700 Heteroskedasticity P value 0.0000 Likelihood-ratio test 1454.81 Heteroskedasticity heteroskedasticity 0 1034 42
    • Appendix 6: OLS Regressions Using All Control ParametersTable A6 displays present-value OLS estimations of wage-earning employment on thestatewide minimum wage with period, bindingness, and sectoral employment sharecontrols. Various estimators are used and the model is tested for both autocorrelation andheteroskedasticity. Tables A6b and A6c display are present/lagged hybrid estimationsand lagged-value estimation respectively. The present-value outperforms both the lagged-value and hybrid models.Table A6: Present-Value OLS Regressions Using All Control ParametersY = wage employment Non-wage PeriodsX = Minimum wage Min. Wage Services Manufacturing A.H.E. Employment F-testlog-log 0.0813 1.3382 -0.5243 -0.3584 -0.5243 4.9700P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0226 0.0206 0.0193 0.0223 0.0193R-sq 0.9939Adjusted R-sq 0.9937FD -0.0254 0.8902 0.0646 -0.2248 -0.5820 6.4500P value 0.6670 0.0000 0.0710 0.0000 0.0000 0.0000SE 0.0590 0.0699 0.0357 0.0354 0.0230R-sq 0.4501Adjusted R-sq 0.9918RE 0.0087 1.4513 0.1164 -0.0248 -0.6337 266.3200P value 0.4150 0.0000 0.0000 0.2350 0.0000 0.0000SE 0.0107 0.0160 0.0103 0.0209 0.0069R-sq 0.9917FE 0.0120 1.5109 0.0996 -0.0044 -0.6324 12.1000P value 0.2590 0.0000 0.0000 0.8350 0.0000 0.0000SE 0.0107 0.0317 0.0116 0.0214 0.0069R-sq 0.9319Overall R-sq 0.9915Wooldridge test 0.0560 No Autocorrelation presentP value 0.8145Wald Test 1444.8400 Heteroskedasticity is presentP value 0.0000Likelihood-ratio test 2999.5900 Heteroskedasticity is presentheteroskedasticity 0.0000 1034 43
    • Table A6b: Present-Value OLS Regressions Using Lagged-Value Control ParametersY = wage employment Non-wage PeriodsX = Minimum wage Min. Wage Services Manufacturing Avg. wage Employment F-testlog-log 0.1311 1.0795 0.1395 -0.4029 -0.2673 3.8900P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0284 0.0262 0.0062 0.0282 0.0246R-sq 0.9906Adjusted R-sq 0.9904 Lagged Control ParametersFD 0.0698 -0.2457 -0.0022 -0.0250 0.2431 6.9200P value 0.3050 0.0000 0.6120 0.1480 0.0000 0.0000SE 0.0680 0.0183 0.0044 0.0172 0.0170R-sq 0.2797Adjusted R-sq 0.2610 Lagged Control ParametersRE -0.0027 0.8618 0.1143 -0.2225 -0.0425 135.9700P value 0.9350 0.0000 0.0000 0.0000 0.0540 0.0000SE 0.0331 0.0323 0.0187 0.0560 0.0220R-sq 0.9918 Lagged Control ParametersFE -0.0083 1.0741 -0.0425 -0.1264 -0.0261 6.9800P value 0.8090 0.0000 0.0540 0.0660 0.2390 0.0000SE 0.0344 0.0954 0.0220 0.0686 0.0221R-sq 0.3125Overall R-sq 0.9840Wooldridge test 0.0560 No Autocorrelation presentP value 0.8145Wald Test 14230.2500 Heteroskedasticity is presentP value 0.0000Likelihood-ratio test 433.7100 No Heteroskedasticity presentheteroskedasticity 1.0000 987 44
    • Table A6c: Lagged-Value OLS Regressions Using All Control ParametersY = wage employ. (lag) Non-wage PeriodsX = Minimum wage Min. Wage Services Manufacturing A.H.E. Employment F-testlog-log 0.1362 1.0817 0.1391 -0.4042 -0.2686 3.8600P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0291 0.0261 0.0062 0.0282 0.0246R-sq 0.9906Adjusted R-sq 0.9904 Lagged Control ParametersFD 0.0503 -0.2413 -0.0043 -0.0314 0.2415 7.2300P value 0.4580 0.0000 0.3390 0.0760 0.0000 0.0000SE 0.0678 0.0188 0.0045 0.0177 0.0174R-sq 0.2837Adjusted R-sq 0.2649 Lagged Control ParametersRE -0.0136 0.8618 0.1141 -0.2203 -0.0425 135.7000P value 0.7010 0.0000 0.0000 0.0000 0.0540 0.0000SE 0.0355 0.0322 0.0187 0.0561 0.0220R-sq Lagged Control ParametersFE -0.0194 1.0709 0.0443 -0.1258 -0.0259 6.9900P value 0.6020 0.0000 0.1810 0.0670 0.2430 0.0000SE 0.0372 0.0956 0.0331 0.0686 0.0221R-sq 0.3126Overall R-sq 0.9840Wooldridge test 0.0560 No Autocorrelation presentP value 0.8145Wald Test 14229.8600 Heteroskedasticity is presentP value 0.0000Likelihood-ratio test 435.7900 No Heteroskedasticity presentheteroskedasticity 1.0000 987 45
    • Appendix 7: OLS Regressions Using Alternate Sectoral GDP-Share Control ParametersTable A7 displays OLS estimations of wage-earning employment on the statewideminimum wage with period and sectoral GDP-share controls. Various estimators are usedand the model is tested for both autocorrelation and heteroskedasticity.The estimations in table A8 are OLS estimations of wage-earning employment on thestatewide minimum wage with period, bindingness and sectoral GDP-share controls.Various estimators are used and the model is tested for both autocorrelation andheteroskedasticity.Table A7: OLS Regressions Using Alternate Sectoral GDP-Share ControlsY = wage employment Services Manufacturing PeriodsX = Minimum wage Minimum Wage GDP ratio GDP ratio F-testlog-log 0.2956 -0.4307 2.3314 0.0800P value 0.2260 0.0000 0.0000 1.0000SE 0.2442 0.0806 0.4451R-sq 0.0076FD 0.0056 -0.0002 0.0053 6.8800P value 0.9400 0.9710 0.8780 0.0000SE 0.0745 0.0063 0.0345R-sq 0.1267RE -0.0489 -0.0057 0.1406 199.7400P value 0.1730 0.8900 0.5510 0.0000SE 0.0359 0.0412 0.2360R-sq 0.0019FE -0.0488 -0.0014 0.1247 9.4200P value 0.1740 0.9740 0.6020 0.0000SE 0.0359 0.0416 0.2387R-sq 0.2199Overall R-sq 0.0017Wooldridge test 4.1690 Autocorrelation is presentP value 0.0469Wald Test 718.4700 Heteroskedasticity is presentP value 0.0000Likelihood-ratio test 1323.5700 Heteroskedasticity is presentheteroskedasticity 0.0000 1034 46
    • Table A8: OLS Regressions Including Alternate Sectoral GDP-Share and Bindingness ControlsY = wage employment Services Manufacturing Non-wage PeriodsX = Minimum wage Min. Wage GDP ratio GDP ratio A.H.E. Employment F-testlog-log 0.2793 -0.2201 1.3186 -0.4238 0.9050 2.7300P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0566 0.0164 0.0894 0.0545 0.0074R-sq 0.9625FD 0.0132 -0.0012 0.0099 0.0014 -0.0042 6.7700P value 0.8600 0.8550 0.7810 0.9400 0.1280 0.0000SE 0.0747 0.0065 0.0356 0.0185 0.0028R-sq 0.1299RE -0.0537 -0.0699 0.7486 0.4296 -0.1169 109.6500P value 0.2390 0.1430 0.0060 0.0000 0.0000 0.0000SE 0.0456 0.0477 0.2733 0.0910 0.0242R-sq 0.5234FE -0.0696 -0.0869 1.3202 -0.0869 1.3202 30.0900P value 0.0010 0.0010 0.0000 0.0010 0.0000 0.0000SE 0.0217 0.0256 0.1502 0.0256 0.1502R-sq 0.7155Overall R-sq 0.8853Panel GLS(hetero, ar1) 0.1318 -0.2254 1.3100 -0.1970 0.8664 85.8900P value 0.0420 0.0000 0.0000 0.0010 0.0000 0.0000SE 0.0648 0.0198 0.1109 0.0604 0.0092 15151.380Wald-Chi DF = 26 0Wooldridge test 18.6170 Autocorrelation is presentP value 0.0001Wald Test 4119.4400 Heteroskedasticity is presentP value 0.0000Likelihood-ratio test 260.2600 No Heteroskedasticity is presentheteroskedasticity 1.0000 1034 47
    • Appendix 8: Heteroskedasticity and Autocorrelation Correction ModelsTable A9 compares standard OLS with cluster-robust standard-error heteroskedasticityand autocorrelation-correcting OLS estimations of wage-earning employment on thestatewide minimum wage with period, bindingness and sectoral employment sharecontrols. The pooled OLS and the first-difference estimator are used.The estimations in tables A10 and A11 are heteroskedasticity-correcting panel GLSregressions of wage-earning employment on the statewide minimum wage. Table A10includes period, and sectoral employment share controls. In table A11, bindingnesscontrols are added as well. Present-value, lagged-value, and hybrid regressions arecompared. The present value model outperforms the other two models in both tables.The estimations in table A12 are autocorrelation-correction regressions of wage-earningemployment on the statewide minimum wage with period, bindingness, and sectoralGDP-share. The table includes autocorrelation-correcting panel GLS and Prais-Winstenestimations, and an autocorrelation and heteroskedasticity-correcting panel GLS model.Table A9: Estimations Correcting for Heteroskedasticity and Autocorrelation Using Cluster Robust Standard Errors Y = wage employment Minimum Non-wage Periods X = min. wage Wage Services Manufacturing A.H.E. Employment F-test POLS 0.0813 1.3382 -0.5243 -0.3584 -0.5243 4.9700 P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SE 0.0226 0.0206 0.0193 0.0223 0.0193 R-sq 0.9939 POLS Cluster Robust SE 0.0813 1.3382 0.1407 -0.3584 -0.5243 16.1800 P value 0.0040 0.0000 0.0000 0.0000 0.0000 0.0000 SE 0.0274 0.0146 0.0092 0.0292 0.0179 R-sq 0.9939 FD -0.0254 0.8902 0.0646 -0.2248 -0.5820 6.4500 P value 0.6670 0.0000 0.0710 0.0000 0.0000 0.0000 SE 0.0590 0.0699 0.0357 0.0354 0.0230 R-sq 0.4501 FD Cluster Robust SE -0.0441 0.2533 -0.0013 -0.0100 -0.2453 21.9200 P value 0.4910 0.0000 0.7120 0.5750 0.0000 0.0000 SE 0.0639 0.0153 0.0036 0.0178 0.0146 R-sq 0.2839 48
    • Table A10: Heteroskedasticity Correction GLS Regressions including only sectoral employment-share controlsY = wage employment StatesX = Minimum Wage Minimum wage Services Manufacturing F-testPanel GLS (hetero) -0.0127 0.7417 0.1675 32.6800P value 0.5340 0.0000 0.0000 0.0498SE 0.0205 0.0052 0.0042Wald-Chi DF = 24 142485.4700 Lagged Control ParametersPanel GLS (hetero) -0.0178 0.7416 0.1671 93.0300P value 0.3970 0.0000 0.0000 0.0000SE 0.0210 0.0054 0.0044Wald-Chi DF = 23 136668.8300 Lagged Control ParametersLagged GLS (hetero) -0.0200 0.7415 0.1671 93.3500P value 0.3550 0.0000 0.0000 0.0000SE 0.0216 0.0053 0.0044Wald-Chi DF = 23 136331.3600Table A11: Heteroskedasticity Correction GLS Regressions Including all Control ParametersY = wage employment Non-wage PeriodsX = Minimum wage Min. Wage Services Manufacturing A.H.E. Employment F-testPanel GLS(Hetero) 0.0558 1.3746 0.1420 -0.3719 -0.5575 348.9500P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0112 0.0092 0.0022 0.0136 0.0090Wald-Chi DF = 26 689838.0600 Lagged Control ParametersPanel GLS (Hetero) 0.0733 1.0609 0.1462 -0.4082 0.1462 160.5100P value 0.0010 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0223 0.0210 0.0048 0.0239 0.0048Wald-Chi DF = 25 154468.9800 Lagged Control ParametersLagged GLS (Hetero) 0.0802 1.0637 0.1458 -0.4113 -0.2447 160.5500P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0230 0.0209 0.0048 0.0241 0.0196Wald-Chi DF = 25 154415.7500 49
    • Table A12: Heteroskedasticity and Autocorrelation Correction GLS Regressions including all Control Parameters Y = wage employment Services Manufacturing Non-wage Periods X = Minimum wage Min. Wage GDP ratio GDP ratio A.H.E. Employment F-test Panel GLS (ar1) 0.1454 -0.2325 1.3512 -0.2036 0.8601 60.4500 P value 0.0560 0.0000 0.0000 0.0050 0.0000 0.0000 SE 0.0762 0.0237 0.1296 0.0724 0.0103 Wald-Chi DF = 26 11498.4800 Panel Prais-Winsten (ar1) 0.1454 -0.2325 1.3512 -0.2036 0.8601 4132.1700 P value 0.0910 0.0000 0.0000 0.0190 0.0000 0.0000 SE 0.0861 0.0221 0.1359 0.0868 0.0153 Wald-Chi DF = 5 8857.1300 Y = wage employment Services Manufacturing Non-wage Periods X = Minimum wage Min. Wage GDP ratio GDP ratio A.H.E. Employment F-test Panel GLS (hetero, ar1) 0.1318 -0.2254 1.3100 -0.1970 0.8664 85.8900 P value 0.0420 0.0000 0.0000 0.0010 0.0000 0.0000 SE 0.0648 0.0198 0.1109 0.0604 0.0092 Wald-Chi DF = 26 15151.3800 50
    • Appendix 9: Breaks in the Data SetThis table analyzes breaks in the data set using a heteroskedasticity-correcting panel GLSmodel. Chow testing reveals no break between states which did and states which did notincrease their minimum wages, ruling-out a natural experiment methodology. Chowtesting also reveals that there is a break in the data set between services-employmentheavy, and manufacturing-employment heavy states.Table A13: Estimation of Breaks in the Data Set Y = wage employment Non-wage Periods X = Minimum wage Min. Wage Services Manufacturing A.H.E. Employment F-test Panel GLS (hetero) Flat = 1 0.2248 1.3497 0.1531 -0.3550 -0.5495 80.8000 P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 SE 0.0402 0.0220 0.0058 0.0264 0.0206 Wald-Chi DF =26 137786.6100 Panel GLS (hetero) Flat = 0 0.3460 1.3395 0.1100 -0.4478 -0.4776 21.5500 P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.4256 SE 0.0650 0.0481 0.0083 0.0404 0.0445 Wald-Chi DF =26 43405.8600 DF loss (numerator) Remaining RSS RSS -1 Agg DF K n-2k 756.0000 232.0000 200.0718 613.2880 986.0000 2.0000 986.0000 Chow Chow Numerator Denom. F(2, 986) Test 1.4598 0.8249 19.4900 1.7697 Not Significant at .05 Y = wage employment Non-wage Periods X = Minimum wage Min. Wage Services Manufacturing A.H.E. Employment F-test Manufacturing-heavy states (GLS hetero) 0.0129 1.5822 0.0839 -0.2951 -0.6937 318.6900 P value 0.3280 0.0000 0.0000 0.0000 0.0000 0.0000 SE 0.0132 0.0133 0.0027 0.0141 0.0124 Wald-Chi DF = 26 695390.6700 Services-heavy states (GLS hetero) 0.0818 1.2723 0.1276 -0.0863 -0.4531 28.7700 P value 0.0000 0.0000 0.0000 0.0010 0.0000 0.1196 SE 0.0168 0.0148 0.0072 0.0268 0.0111 Wald-Chi DF = 26 337665.0300 DF loss (numerator) Remaining RSS RSS -1 Agg DF K n-2k 498.0000 490.0000 285.1213 494.1430 986.0000 2.0000 986.0000 Chow Chow Numerator Denom. F (2, 986) Test 18.5076 0.7903 19.4900 23.4175 Significant at .05 51
    • Appendix 10: Secondary Effects of Minimum Wage ChangesTable A14 analyzes the sectoral employment shift caused by a change in the minimumwage using a heteroskedasticity-correcting panel GLS model. Sector-specificemployment is used as the dependent variable. Periods, bindingness, and the rivaleconomic sector are controlled for.Table A15 analyzes the sectoral employment shift caused by a change in the minimumwage using a heteroskedasticity-correcting panel GLS model. The sectoral employmentdistribution ratio is used as the dependent variable. Periods, and sectoral GDP-shares arecontrolled for.Table A16 analyzes the effects on overall employment caused by a change in theminimum wage using a heteroskedasticity-correcting panel GLS model. Periods, andsectoral employment-share are controlled for.Table A14: Sectoral Shift Caused by Minimum Wages Y = service employment Non-wage Manufacturing Periods X = Minimum wage Minimum Wage Employment Employment F-test Panel GLS(Hetero) 0.1771 0.8889 0.0694 93.8300 P value 0.0000 0.0000 0.0000 0.0000 SE 0.0209 0.0050 0.0044 Wald-Chi DF = 24 191653.1300 Y = Manufacturing employment Non-wage Service Periods X = Minimum wage Minimum wage Employment employment F-test Panel GLS(Hetero) -0.7629 -0.0621 1.1128 195.3900 P value 0.0000 0.0030 0.0000 0.0000 SE 0.0311 0.0212 0.0225 Wald-Chi DF = 24 148728.6200Table A15: Sectoral Shift Caused by Minimum Wages considered with relative GDP-share Y = M/S ratio (employment based) Services Manufacturing Periods X = Minimum wage Min. Wage GDP ratio GDP ratio F-test Panel GLS (hetero) -0.0946 -0.5699 6.8786 22.6400 P value 0.0000 0.0000 0.0000 0.3635 SE 0.0256 0.0103 0.0369 Wald-Chi DF = 24 35831.9000 52
    • Table A16: The Effect of Minimum Wages on Overall Statewide Employment Y = Overall Employment Service Manufacturing Periods X = Minimum wage Minimum wage employment Employment F-test Panel GLS(Hetero) -0.0035 0.8569 0.0985 57.6100 P value 0.6280 0.0000 0.0000 0.0000 SE 0.0073 0.0015 0.0013 Wald-Chi DF = 24 2203375.0000 ( 1) log_Imin = 0 chi2( 1) 0.2400 Prob > chi2 = 0.6277 53