1

Max Berre

Erik de Regt

i461865

August 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. The

effect of sectoral composition of a state’s economy is empirically determined to have a

pivotal effect on wage-earning employment elasticity using 2002-2007 BLS data. The

explanation behind this phenomenon is linked theoretically to tradability as well as

capital/labor substitution elasticity. The effect of statewide minimum wages on a state’s

labor market is explained empirically by a state economy’s sectoral profile.

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1: Introduction

The relationship between minimum wages and employment figures documented by Card

and Krueger’s works in both 1994 and 2000, as well as responses to Card and Krueger’s

1994 work considered for reply in 2000, focused solely in the fast-food sector, and in just

two states, Pennsylvania and New Jersey.

Beyond Pennsylvania and New Jersey, the minimum wage at the statewide level is an

issue that draws attention across the US. Until the second half of 2007, the US federal

minimum wage remained unchanged at $5.15 an hour for over 10 years. Meanwhile, the

minimum wage in several states across the US increased, while in other states, the

minimum wage underwent no change whatsoever. This phenomenon leads one to

reasonably question the effects of these statewide minimum wage increases.

The Questions

Questions arise with respect to the relationship between employment levels and minimum

wages proposed by Card and Krueger. First, does a relationship between minimum wages

and employment exist beyond Pennsylvania and New Jersey or in industries and sectors

beyond the fast food industry? One possibility may be that perhaps the effect described

by Card and Krueger may be specific to New Jersey and Pennsylvania, or to the fast-food

industry, while the relationship may be of wildly varying magnitude and direction on the

aggregate level.

Second, what is the explanation for the relationship which was found? To address this

question one must consider the effect of the minimum wage on both the labor demand

function, on effective demand. Statewide variations in tradability and in capital/labor

substitution elasticity expressed along sectoral lines must also be taken into account.

The major purpose of this study is to empirically address these two questions. In

particular, this study seeks to shed light onto factors determining the shape and nature of

the 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

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underpinnings of the wage-employment relationship via an examination of the

employment function. Next, part 4 presents the estimation strategy implemented by this

study and part 5 explains the factors included in the estimation model. Subsequently, part

6 presents the summary statistics, and provides a look into the data set. The empirical

results 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 further

research into the minimum wage topic.

2: Literature Review

Hamermesh (1986) provides a summary of various theoretical labor-demand models, and

their appropriate derivation. These are derived form various production models. In

particular, the Hamermesh examines basic two-factor models, constant elasticity of

substitution models, Cobb-Douglas models, and multi-factor models. This theoretical

analysis can be used to examine the employment effects of the minimum wage.

Perhaps the most controversial empirical authors examining the employment effects of

the minimum wage are Card and Krueger. Card and Krueger (1994) found a positive

relationship between minimum wages and employment in the fast-food sector in New

Jersey and Pennsylvania in the aftermath of minimum wage increases in New Jersey in

1992. Card and Krueger attribute this outcome to monopsony power in the fast-food

industry of these two states. This positive relationship was based on survey data of a

case-study, an approach which then came under severe criticism from emanating from

both 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, while

claiming that Card and Krueger (1994) was invalid because of the relative informality of

the data set used. In response to this, Card and Krueger (2000) re-examine the New

Jersey and Pennsylvania phenomenon using data from the Bureau of Labor statistics, and

concluded that the 1992 change in the New Jersey minimum wage had most probably no

effect on total employment, and possibly a small positive effect, while reaching a similar

conclusion using Neumark and Wascher’s data set, controlling for employer dummies.

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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 the

validity of the case-study approach all-together. Of these studies, 85% point to a negative

wage/employment relationship. Neumark and Wascher are prolific empirical authors

known for a skeptical point of view on minimum wage legislation, and in this study fault

some authors for diverging from the competitive model explaining the wage/employment

relationship. Setting this opinionated stance aside, Neumark and Wascher (2007) provide

a thorough critique of the several studies. Among the key issues that surface in this

review are credibility of data, bindingness of minimum wages, and credibility of

secondary controls. According to their critique, all data should be from a credible official

source, bindingness of minimum wages must be controlled for in order to connect the

empirical results to theoretical discourse on wages and employment, and secondary

controls must be clearly justified.

Stewart (2002) examines the effects the 1999 reintroduction of a national minimum wage

in the UK by means of econometric analysis. Central to this paper’s argument is a

measurement of the effect of the reimplementation of the minimum wage across different

areas of the UK, whose wage rates had diverged since the minimum wage was abolished

in 1993. The bindingness of the minimum wages was explored therefore, and considered

a major potential factor affecting the effect of employment changes in the wake of

minimum wage reimplementation. This paper comes to the conclusion that the effect of

the reimplementation of minimum wage legislation was largely contained within the

lowest income quartile, that there was no statistically significant difference between the

effects of the legislation in high-income, and low-income areas, where the new minimum

wage was most binding, and that there was no systemic adverse effect on employment.

Singell and Terborg (2005) examine empirically the effect of minimum wage legislation

on 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 and

bar industry, with the intention of determining the effect of bindingness of minimum

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wages on the effect of minimum wage changes on employment. Singell and Terborg find

that employment elasticities are in fact industry-specific. In fact, his study finds a positive

employment elasticity in the hotel industry.

Addison et al. (2008) examine the impact of changes in minimum wage legislation on

employment in the restaurant and bar industries in the US using Bureau of Labor

Statistics county-level quarterly data. Additionally, this study provides a theoretical

background within which to frame the minimum wage debate, stressing the importance of

minimum wage bindingness. Also, Addison et al. find that labor demand elasticity varies

by industry. The conclusion explains that labor-demand elasticity is lower in the

restaurant industry than in other industries due to the importance of location. i.e., due to

lower degree of tradability. This study also mentions a shortcoming of county-level data

in 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 and

panel data should be considered as primary estimation tools.

Rodrik (1997) is an empirical text which outlines various sources of tension surrounding

globalization. One of the more controversial topics covered by Rodrik is a link between

economic openness and labor demand elasticity. Rodrik empirically demonstrates that

with increased tradability, substitutability between domestic labor and overseas labor

increases, thus increasing labor demand elasticity as a result of increased tradability.

3: Theoretical Analysis

In relation to Card and Krueger (1994), it must be said that the monopsony rationale

explaining wage and employment relationship which Card and Krueger discovered within

the fast-food sector in New Jersey and Pennsylvania is not a plausible explanation for a

similar relationship in the aggregate US labor market. One cannot assume that

prospective employees withdraw their offers to sell their labor simply by excluding

themselves from the labor market. In a region-specific and sector-specific analysis such

as Card and Krueger (1994), prospective employees can withdraw their offers of labor by

exiting the specific sector or region towards another sector or region. In analyzing the

6

entire US labor market however, such an explanation cannot be considered valid. An

alternative explanation for this phenomenon must be considered.

In theory, there are several effects which take place on the labor market when wages

change. When wages increase, the output effect takes place in the short run. That is, as

wages expand, output will decrease. Next, a substitution effect takes place, whereby a

portion of the labor input is substituted with capital. Thus, as a result of these two

effects, the labor demand function gives rise to a downward-sloping curve, as illustrated

in figure 1:

Figure 1: Output and Substitution Effects

L 1L 2

Wage

Employment

Capital

Labor

w 1

w 2

K 1K 2

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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) production

function 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

curve is given by1:

L = Y( /w)

Labor demand elasticity incorporating both the output and the substitution effect is2

(Hamermesh, 1986):

LL = -[1- - j

j represents elasticity on the product market. Naturally, an increase in wages increases

the cost or production, leading to an increase in price on the product market, leading to

less quantity demanded of the good in question.

This approach considers the effect of wages exclusively as a cost factor. Because wages

are also a form of income, their demand effect must also be taken into account. In order

to take the demand effect into account, we must consider the effect of a change in wages

on consumption, the effect of consumption changes on output, and the effect of the

change 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.

8

The output-effects of wage changes can be boiled down entirely to consumption

changes.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 c1w > c (Andini,

2007), leading to an increase in consumption in all cases in which the positive direct

wage effects on consumption outweigh the negative indirect effects on consumption

caused by changes in employment. Increases in output then cause an increase labor

demand:

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

3 I and G are held constant and assumed to be exogenous factors within this model. According to Klein(1947), the neoclassical system’s I depends on interest rate as a determining factor, while the Keynesiansystem’s I depends on Yo which is determined after changes in output.4 See Appendix 1 for derivation.

Employment

w 2

w 1

L 1 L 2

9

Thus, the employment effects of demand changes depend on changes in output as a result

of changes in consumption. This effect amounts an outward shift in the labor demand

curve as in figure 2. Therefore, overall employment elasticity taking into account the

substitution effect, the output effect, and effective demand takes the functional form:

ew = LL + LY Yw

Thus, 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 Tradability

Increased tradability, which may take the form of increased openness to trade, or

logistical improvements which make trade flow more smoothly, has an influential effect

on employment elasticity. Both Rodrik (1997) and Slaughter (2001) document an

increase 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, the

effect that wage increases have on output are moderated by the consumption of imports in

the 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 < 1

In short, is increased by trade due to the wider variety of production technology

available in the world market, j is increased by trade and Y(w) is decreased by trade

because 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.

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consumption. As tradability increases, the output and substitution effects trend towards

infinity, while the demand effect trends towards zero.

Because both and differ within each sector of the economy, this model assumes

sector-specific and leading to sector-specific production functions and employment

elasticities. Thus:

Y = Ys

Ys = [ Ls s + (1- )Ks s]1/ s

And: 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, increased

labor cost which reduces the quantity demanded of labor, and increased effective demand

stemming from consumption of higher wages which leads to increased demand for

output. How far the quantity demanded for labor decreases with a wage increase is

sector-specific and depends on ease of labor/capital substitution. Whether the increased

wage-income is channeled into domestic consumption or import-consumption is also

sector-specific and depends on tradability. Whether the effect of a given wage increase is

positive or negative ultimately depends on whether the employment effect of increased

output demand is larger than the employment effect of decreased quantity demanded of

labor.

4: Estimation Strategy

As a primary and central method of econometric estimation, this study makes use of the

fixed-effects panel generalized least-squares model (GLS).

Fixed-effects estimation is used as the basic estimation technique due primarily to the

rejection of poolability by means of joint significance testing. Additionally, periods are

controlled for by means of quarterly period dummies. Furthermore, because in this data

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set, States > Periods > 2, the fixed-effects estimator is the Best Linear Unbiased

Estimator 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 a

situation, both Dougherty(2002) and Wooldridge (2006) recommend the use of the panel

generalized 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-Sector

employment (state) / h(state) + 4 Man.-sector employment(state) h(state) + 5 Non-wage-earning

employment(state) h(state) + 6 Period Dummies(state) h(state) + error (state) h(state)

The generalized least-squares model and notation above are borrowed directly from

Wooldridge (2006), in which h represents the weighted heteroskedastic error-correction

term which is proportional to the standard deviation. Wooldridge (2006) succinctly

explains that:

Var(u|x) = 2 h(x)

where h(x) is a function of the explanatory variables that determines heteroskedasticity.

(Wooldridge, 2006)

5: Factors in the Estimation Model

Wage-Earning employment is used as the dependent variable. In the US, wage-earning

jobs account for the lowest employment incomes. It is in this subset where all those

directly affected by the minimum wage, as well as changes therein can be found.

Additionally, several control parameters are included in the estimation model. Following

Neumark and Wascher (2007), bindingness and average income are controlled for in

order 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 is

drawn from the Bureau of Labor Statistics.

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Control Parameters

As displayed in the estimation model, several factors are controlled for the regressions.

Taking these factors into account eliminates wage-earning employment changes due to

other factors and isolates the wage-earning employment of the effect of the minimum

wage. Additionally, the minimum wage is properly weighted, ensuring that the

estimations match the theoretical discourse on wages and labor demand.

Periods

Period dummies are included in order to control for natural exogenous changes in

employment. Periods effects wholly contain the seasonal variation, as well as cyclical

trends within the dataset. Inclusion of is supported by joint significance F-test results.

Minimum Wage Coverage

As Addison et al.(2008), Singell and Terborg (2005), and Stewart (2002) all highlight the

importance of bindingness measures in order to correctly gauge the employment effect of

the a change, it is evident that a way to measure the coverage level of the minimum wage

must be included in this study.

The standard way in which minimum wage coverage is measured is via the minimum

wage spike, a ratio comparing minimum wage employment to overall employment

figures. (Downes et al., 2000) Since actual statewide quarterly minimum wage

employment numbers were unavailable during data collection, a proxy is used instead.

The proportion of wage-earning employment relative to all employment within a given

state can effectively be measured by comparing the Current Population Survey (CPS)

data set, which records wage-earning employment with the Quarterly Census

Employment and Wages (QCEW) data set, which records aggregate and sectoral

statewide and countywide employment data. In the US, wage-earning jobs occupy the

lower end of the income scale, and all minimum jobs which remunerate at the minimum

wage are counted within wage-earning employment figures. Thus, a partial measure of

bindingness and coverage is achieved. This measure is useful because minimum wage

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employers in the US also keep a large cohort of employees at slightly above the

minimum wage. In such workplaces, an increase in the minimum wage effectively shifts

the entire wage scale upwards. Thus, it is not only employees actually at the minimum

who are affected by it. Accordingly, this is a measure of all those affected by the

minimum wage.

This control parameter must be expressed as statewide total employment figure because

use of a ratio instead would include wage-earning employment as its numerator, leading

to endogeneity problems. There remains however, a problem of overlap in that total

employment figures include wage-earning employment as a subset. Therefore, this

dilemma is addressed by utilizing using the opposite employment subset, rather than the

overall 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 for

flow from wage-employment to salary-employment with minimum wage changes, thus

eliminating some of the noise present within the data set by account for this tradeoff.

Relative Weighting Minimum Wage Values – Kaitz Index

In order to properly measure the effect of minimum wage changes, a proper minimum

wage weighting scheme is necessary in order to measure real magnitude of the minimum

wage. This means that the minimum wage be first be inflation-adjusted, and then

weighted against other factor costs within the economy. For said purpose, this study

employs the Kaitz index, a measure of the distance between the mean wage and the

minimum wage, weighted by coverage. Thus, the Kaitz index tracks the extent to which

the minimum wage and the average income move together. This weighting measure is an

important tool which filters out any noise from the minim wage and employment

estimation. It may be helpful to think of the Kaitz index as the “minimum wage put into

context”. 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 minimum

wage, the coverage rate, and the average earning rates. (Downes et al., 2000) Because of

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the log-transformation, average hourly earning is used as a control parameter to correctly

weight the minimum wage. Since the A.H.E. coefficient is always negative, the minimum

wage value is successfully weighted. Since minimum wage coverage is already accounted

for, it does not need to be repeated in order to make the Kaitz index effective. Together

with minimum wage coverage, the weighting measure is referred to as a bindingness

control parameter. (Downes et al., 2000)

Controlling for Relative Influence of Sectors

Because the employment function model outlined in the theoretical section describes an

economy composed of various sectors, and because has a different level of tradability and

degree substitutability within each sector, relative sectoral influence must be accounted

for in order to reconcile the empirical analysis of the effect of the minimum wage with

the theoretical analysis.6 Empirically, there are two viable ways in which the relative

influence of sectors within a state’s economy. These are by comparison of employment

share, or by comparison of employment share within the state workforce. The

performance of these two control methods is compared in the empirical results section.

Sectors are controlled for individually in order to avoid endogeneity problems. Hence this

study includes separate control variables for the manufacturing sector and the services

sector. For purposes of this study, more detailed industry-level controls are not necessary

because while each industry may have different and values, inter-industry differences

within a given sector are small in comparison to inter-sector comparison, and hence do

not contribute much added value to this study.7

The regression equation therefore directly poses the first question, as stated in the

introduction: Does a relationship between minimum wages and employment exist? As

with Card and Krueger (1994), the estimation now focuses only on those jobs which

minimum wage workers would get, as opposed to overall employment.

6 Mirroring the theoretical analysis, the substitutability and tradability assumptions are:s < m and s < m

7 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.

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6: Summary Statistics

The data set analyzed in this text consists of 1034 observations drawn from two Bureau

of Labor Statistics surveys. In total, the sample includes 47 states and 22 quarters from

2002q1-2007q2. The sectoral and overall statewide employment information was drawn

from 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), a

monthly household survey on minimum wages, wage-earning employment and

unemployment in the US at the federal and statewide level. Key variables in this data set

are displayed in table 1. Aggregate employment is divided into two groups, wage-earning

and non wage-earning employment by comparing the CPS against the QCEW. 8

Table 1: Summary Statistics

Variable Obs. Mean Std. Dev. Min Max Median

Statewide Employment 1034 2742640 2785896 272405 15700000 1841620Wage-Earning Employment 1034 1567454 1552908 160000 8942000 1113500Non-Wage Employment 1034 1175186 1256124 81405 7158000 785870Service Sector Employment 1034 2231389 2360704 192167 13200000 1374321Service Sector Jobs % 1034 0.788 0.060 0.635 0.936 0.781

Man. Sector Employment 1034 304368 292799 7850 1647646 304368Man. Sector Jobs % 1034 0.111 0.041 0.024 0.209 0.109Inflation-Adjusted Minwage 1034 $5.56 $0.73 $5.10 $7.90 $5.15Inflation-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 0.3164m_s_ratio 1034 0.1712 0.1436 0.0282 0.9259 0.1419

All wages and earnings represent real income. They have been inflation adjusted using

the Consumer Price Index for Wage-Earners (CPI-W), the index employed by US labor

unions to calculate inflation for bargaining purposes. Average hourly earnings are

calculated from both wage-earners and non-wager earners and is abbreviated A.H.E. in

all tables. M/S ratio is a sectoral employment distribution ratio comparing manufacturing

jobs 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.

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Figure 3: Sectoral Distribution and Wage/Non-Wage Earning Employment

During the 2002q1-2007q2 period, both minimum wages and employment increased

gradually. With respect to employment figures, there were increases in both overall

employment and wage-seeking employment. Both overall employment and wage-seeking

employment display clear seasonal effects, as do service-sector employment figures. In

terms of seasonal/quarterly effect on the data, this effect controlled for with the inclusion

of period dummies. Additionally, employment figures show an increase in the magnitude

of its seasonal fluctuation after January 2004. The minimum wage illustration in figure

A3 displays the average statewide minimum wage in the US along with the highest

minimum wage as of 2007 q2 and one of the lowest As all states with a statewide

minimum wage lower than the federal minimum wage of $5.15 per hour were normalized

to the federal minimum wage, as the federal law would take effect in such states, there

were several states either whose statewide minimum wage or functional minimum wage

stayed at $5.15 per hour during the entire period of this study. Real statewide minimum

wages have increased on average, over the 2002q1-2007q2 period.

US Sectoral Employment

0

500000

1000000

1500000

2000000

2500000Ja

n 02

Jul 0

2

Jan

03

Jul 0

3

Jan

04

Jul 0

4

Jan

05

Jul 0

5

Jan

06

Jul 0

6

Jan

07

Services

Manufacturing

Employment in US

1000000

1200000

1400000

1600000

1800000

2000000

2200000

2400000

2600000

2800000

jan-0

2jul

-02

jan-0

3jul

-03

jan-0

4jul

-04

jan-0

5jul

-05

jan-0

6jul

-06

jan-0

7

Wage Emp.Total Emp.

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Figure 4: Average Statewide Real Minimum Wage (2002 Dollars)

Statewide Minimum Wages (USD)Inflation Adjusted

$4.00$4.50$5.00$5.50$6.00$6.50$7.00$7.50$8.00

Jan02

Jul02

Jan03

Jul03

Jan04

Jul04

Jan05

Jul05

Jan06

Jul06

Jan07

US AverageGeorgiaOregon

Figure 5: 2002-2007 Average Real Minimum Wage by State (2002 Dollars)

2002-2007 Avg. Minimum Wage by State

$4.00

$4.50

$5.00

$5.50

$6.00

$6.50

$7.00

$7.50

In terms of the state-specific averages, cross-sectional distribution of the statewide real

minimum wage displayed in figure 5, variation is somewhat larger. Minimum wages

range from Washington state’s $7.25 per hour on the high end to the federal minimum of

$5.15 per hour shared by approximately a third of all states in the US during this time

period. Likewise, sectoral share variation within the state economies, displayed in figures

A1 and A2 show wider variation than does average US statewide sectoral employment

share displayed in figure 3. Florida has the largest service sector employment share at

92% of its workforce, while Indiana has the highest manufacturing sector share at 20% of

its workforce. At the lower end are Wyoming with a service sector employment share of

63%, and Delaware with a manufacturing sector employment share of 0%.

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7: Empirical Results

Dummy Variables

In Card and Krueger (2000), one of the tools employed to measure the effect of a

minimum wage change on employment was the regression of employment on a change

dummy representing whether or not a minimum wage change occurred. While in this case

the data set contains several changes in the minimum wage, a dummy analysis may still

be indicative of wage-earning employment effects. The regressions displayed in table A1

regress wage-earning employment on a minimum wage change dummy. The empirical

results are reported in a manner which permits examination of both independent variable

coefficient, P-value and standard error, and those of the control parameters as well.

Additionally, table A1 includes a partially-lagged hybrid regression9. Unlike Card and

Kruger’s results, the regression of wage-earning employment on a minimum wage

change dummy does not indicate any significant relationship between minimum wages.

While the control factors are generally significant, the minimum wage change dummy’s

coefficient is too close to zero to achieve any sort of serious significance or predictive

power in all cases but one. In the regressions displayed in table A2, wage-earning

employment is regressed on the dummy variable flat, which takes a value of one when

the minimum wage has remained unchanged for the previous two years. It is constructed

this way to take both short and medium-term effects of minimum wage changes into

account. Again, the coefficients resulting from these regressions are too close to zero to

yield any significance.

Continuous Variables

The effect on wage-earning employment caused by minimum wage increases is more

accurately revealed via analysis of continuous variables. The estimations are log-

transformed and inflation adjusted using CPI-W. Estimations in this section are tested for

autocorrelation using the Wooldridge test. Rejection of the null hypothesis indicates

autocorrelation. These models are also tested for group-wise heteroskedasticity using

9 In the hybrid lagged regression, the dependent variable is regressed on the present value explanatoryvariable, and the lagged control parameters.

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both the modified Wald-chi test, and likelihood-ratio test. (Greene, 2003). The basic

regressions displayed in table A3 demonstrate that the effect of the minimum wage is

generally positive, and zero in the case of first difference models. In the absence of

control parameters, the explanatory power of the minimum wage on wage-earning

employment is low.

Table 2: Fixed Effects Estimations Comparing Control Parameters

Y = wage employmentX = Minimum wage Min. Wage Services Manufacturing A.H.E.

Non-wageEmployment

PeriodsF-test

FE 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 0.9915

Panel 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

Additionally, autocorrelation is present in two these estimations, while heteroskedasticity

is present in all three. The regressions in table 2 display a comparison of the various

estimation models employed in order to examine the wage-employment demand

elasticity. Because the fixed-effects estimator would be the best unbiased estimator in the

absence of heteroskedasticity, table 2 compares fixed-effects estimations with various

20

control parameters.10 This table compares models including some controls and all

controls, as well as OLS models and heteroskedasticity-correction GLS models. Beyond

empirical theory, it makes sense the within estimator would deliver different results than

other 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 another

state as a result of a statewide minimum wage change. A statewide minimum wage

change which positively impacts statewide employment might do so in part by attracting

employees from neighboring states, causing them to register lower employment figures

than they otherwise would, thus registering an employment increase in one state, and an

employment decrease in a neighboring state.

The Regressions Including Control Parameters

Relative Sectoral Distribution

The regressions presented in table A4 represent an estimation of wage-earning

employment elasticity, controlling for sectoral employment share. As demonstrated in the

table, regressions controlling for sectoral employment share, the employment effects of

the minimum wage become insignificant, and are upstaged by the sectoral relationship in

effect 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 employment

is detected. The indication is that sectoral employment share is the primary factor

affecting wage-earning employment, not the minimum wage. Moreover, the sectoral

balance is such that the effect of the minimum wage is neutral. Again, heteroskedasticity

is present in the estimation.

Bindingness Parameters

In the regressions displayed in table A5, bindingness measures are taken into account as

control 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)

21

All Control Parameters Simultaneously

Displayed in table A6, are OLS regressions with all controls. The displayed results

closely resemble the results including only the bindingness parameters, indicating that the

sectoral parameters do not in fact completely dominate the effect of the minimum wage

once bindingness is taken into account. With that said, it is evident that there is some

overlap between the sectoral share controls and the bindingness controls. Fortunately, the

overlap partially resolves itself in that both bindingness parameters carry negative

coefficients, while the sectoral-share parameters carry positive ones. Thus the two sets of

parameters partially cancel each other. Alternately, one may chose to cancel the

independent variable and some of the control parameters. Doing so would most likely

leave non-wage-earning employment as the dependent variable. While the data do also

indicate a positive relationship between the statewide minimum wage, and non-wage-

earning employment figures in a within-state context, and such a relationship is also

supported by the underlying theoretical analysis, the focus of this study rests ultimately

on the wage-earning employment. Wage-earning employment is ultimately influenced by

all 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 control

parameters displayed in table A6 with similar estimations performed with lagged control

parameters in table A6b and lagged independent variable and control parameters in table

A6c. Diverging from table A6, the likelihood ratio test finds no heteroskedasticity present

in tables A6b and A6c. The test value is considerably lower, as are number of

observations, and the degrees of freedom. The modified Wald test however, makes use of

all 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, the

fixed effects estimator is the preferred estimator when comparing between fixed effects

and 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 normally

distributed. (Westbrook, 2007) However, heteroskedasticity is present in every regression

conducted with this data set. With respect to the accuracy of the estimations in tables A6,

22

A6b, and A6c, the present value regressions displayed table A6 are upheld as the most

accurate because of the larger R-squared values of the present value estimation. The

present value estimation is also superior due to its higher adjusted R-squared values.

(Greene, 2003) This outcome is corroborated by the heteroskedasticity-correcting GLS

model, where the present-value estimation is also the most accurate.

Heteroskedasticity Correcting Cluster Robust Standard Error and GLS Estimations

According to both Wald testing and likelihood-ratio testing, the data sample examined for

this study has considerable panel heteroskedasticity. Because heteroskedasticity is present

in 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 error

regression. Results of the cluster-robust regressions are displayed in table A9.

Another method to correct for heteroskedasticity is the heteroskedasticity-correcting

panel fixed-effects GLS estimation. Because the fixed-effects estimator would be the best

linear estimator in the absence of heteroskedasticity, a heteroskedasticity-correcting

fixed-effects model makes a good choice as an estimator for this dataset. Furthermore,

the fixed-effect GLS estimator is preferred heteroskedasticity correction estimator in

Stata given the existence of panel heteroskedasticity. (Statacorp, 1999)

In table A10, regressions controlling only for the manufacturing and services relationship

are re-estimated using a heteroskedasticity-correction panel GLS. These estimations are

carried out because the Wald-Chi test and the likelihood-ratio test disagree on the

presence of heteroskedasticity within the model. As in the regression results displayed in

table 2, any employment effects caused by the minimum wage are rendered insignificant

and completely overshadowed by controlling for sectoral employment. Additionally,

there is almost no difference between the lagged and the present value GLS model. This

23

is because the average statewide sectoral distribution changed little during the course of

the period. 11

Table 3 : Present Value GLS Regression Including all Control Parameters – The Best Linear Unbiased Estimation

Y = wage employmentX = Minimum wage Min. Wage Services Manufacturing Avg. wage

Non-wageEmployment

PeriodsF-test

Panel 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

The regressions in table A11 resemble approximately the standard ordinary least-squares

regression including all of the control parameters displayed in table A6. Given the Wald

statistic, this most likely represents the most accurate regression result. In table A11, the

present value regression using the present independent variable and control parameters is

compared with, a lagged value regression using the lagged independent variable and

control parameter, and a partially-lagged hybrid regression. Despite similar coefficients

and identical P-values, the present value regression displayed in the top portion of table

A11 (also displayed in table 3), displays smaller standard error as well as a considerably

larger Wald statistic, indicating that it is the most accurate regression among the three

estimated in table A11. In comparison with the cluster-robust standard error regressions

displayed in table A9, the standard error is smaller in the GLS estimation, indicating that

the cluster robust estimation perhaps slightly overestimates the employment elasticity.

The present-value panel GLS estimation using both sectoral-employment share controls

and bindingness controls is therefore the overall best unbiased estimator for calculating

wage-earning employment elasticity with respect to minimum wages. Accordingly, said

estimation is displayed in table 3 above.

Alternate Sector Control Factors

11 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.

24

As an alternative to considering each sector’s employment share, the effect which the

manufacturing and services sectors have on employment elasticity can be examined

through the relative GDP share of each sector. This approach however is less precise

because differences between the sectors in terms of GDP share can be caused by either

differences in employment levels or income levels. In any case, it is worthwhile to

examine the sectoral influence from more than one angle. Controlling for statewide

sectoral GDP-shares remains a plausible means of further examination of the

employment and wage relationship. An alternate method of controlling the relative size

and influence of each sector is especially useful in estimating the effect of minimum

wage changes on employment within a specific sector, where controlling for employment

share rival sectors may be problematic. With the exception of the manufacturing sector

control coefficient, the regression coefficient results when bindingness controls are

included parameters displayed in table A8 closely resemble regression results which do

not include bindingness control parameters displayed in table A7. Interestingly, it is now

the manufacturing sector, rather than the services sector which has the dominant

influence 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 control

estimation model, in fact lies with the inclusion of controls for bindingness.

While autocorrelation is present in both regressions in which each sector’s share of

statewide 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 is

therefore re-estimated using various panel GLS estimations. Given that sectoral GDP-

share controlling OLS estimation models suffer from both autocorrelation and

heteroskedasticity, as well as the fact that the sectoral GDP-share controlling OLS

estimation 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.

25

Autocorrelation and Heteroskedasticity Correcting GLS Estimation

Wooldridge testing indicates that autocorrelation is present in some places within the data

set. In the regressions displayed in table A12, autocorrelation is corrected by two

alternate means, via panel GLS regression with first-order autocorrelation correction

settings and via a panel Prais-Winsten regression which also includes first-order

autocorrelation correction settings. The estimation results between the two estimators are

almost 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 parameters

are included, it is also present when they are excluded, indicating that the GDP-share

based sectoral controls are sub-optimal tools to control for sectoral size and influence.

Additionally, both autocorrelation and heteroskedasticity problems are discovered in two

regressions. Therefore, panel GLS is used here because it is a fixed-effects estimator

which can simultaneously correct for both heteroskedasticity and autocorrelation. The

output for the autocorrelation and heteroskedasticity-correcting GLS is displayed at the

bottom of table A12. Because the modified Wald-Chi test and the likelihood ratio test do

not agree on the presence of heteroskedasticity within the fully controlled regression

GDP-share sectoral estimation, a separate panel GLS regression is conducted in order to

correct for both autocorrelation and heteroskedasticity. The results of this regression

closely match the autocorrelation-correction GLS results. Upon comparison of the Wald

statistics of these two regressions, as well as the standard error terms, it is evident that the

last estimation, which controls for both autocorrelation and heteroskedasticity is the most

accurate of the three estimations in table A12. Clearly, the original sectoral GDP-share

controlling model outlined in table outlined in table 10 does in fact have a

heteroskedasticity problem.

Breaks in the Data Set

In Card and Krueger (2000), a natural experiment methodology was employed.

Accordingly, the data set was broken into several geographical areas -each with a

uniform minimum wage- for which regressions were conducted separately. This

26

difference-in-differences approach is attempted in this study as well. This data set was

divided into two data sets based on their flat value. The flat value was used in order to

include 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 subsequently

divided along the median into two sets based on sectoral concentration. These are

manufacturing-heavy states, and services heavy states, based on relative sectoral

employment figures. Interestingly, the two data subsets displayed in the lower half of

table A13 indicate different wage elasticities, as well as different quarterly period dummy

effects. In the more services sector dependent states, there exists a stronger positive

relationship between minimum wages and wage-earning employment.

Sector-Specific Effects of Minimum Wage Changes

The effect of the minimum wage on employment is sector-specific. In the case of both the

services sector and manufacturing sector, employment levels are responsive to minimum

wage changes. Controls include the rival sector of the economy in order to take the

sectoral relationship into account, and non-wage employment as a measure for

bindingness. Average hourly earning proves wildly insignificant as a control parameter in

this 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 employment

and minimum wages in the services sector, while revealing a considerably stronger

negative relationship in the manufacturing sector. The services sector however, is

approximately 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 the

services sector, while employment is simultaneously lost in the manufacturing sector as a

result of an increase in statewide minimum wages, as outlined in table A14. Because a

sectoral employment shift occurs as a result of changes minimum wage, future

employment elasticity with respect to the minimum wage is affected. The regression

27

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 wage

towards services sector employment.. The second regression displayed in table A15

however, demonstrates that the relationship between sectoral employment distribution

and the minimum wage is overshadowed by the effect of average hourly earning. Since

the average has both a lower P-value and a larger coefficient than the minimum wage

coefficient, the implication is that while the minimum wage has some effect on the

sectoral employment distribution, the majority of the effect reported in the first regression

is in fact contained within the state average hourly earning rather than the statewide

minimum wage. The negative coefficients here indicate a shift away from manufacturing-

sector employment and towards service-sector employment. As demonstrated in tables

A13, A14, and A15, this shift is manifested via an increase in services sector employment

coupled with a simultaneous decrease in manufacturing sector employment.

Effect of the Minimum Wage on Overall Employment Figures

The effects of the statewide minimum wage on overall statewide employment are zero. In

the regression outlined in table A16, the employment elasticity coefficient is

approximately one half the value of the standard error. Thus, the effect of minimum wage

changes on overall statewide employment figures is zero.

8: Discussion

Generally, continuous variable estimations reveal either a slight positive effect of the

minimum wage on levels of wage-earning employment, or no effect whatsoever. While

analysis of dummy variables indicates no discernable effect of the minimum wage on

employment figures, it must be said that dummy variables only take into account whether

a minimum wage change occurred. Once the proportion of the minimum wage change is

taken into account, estimations demonstrate that on average, slight increases in wage-

earning-employment occurred due to an increase in the minimum wage. This effect

however is nearly too small to measure and sufficiently small that it is eclipsed in

influence 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

28

coefficient whose influence is outweighed by the control parameters. The data reveal that

sectoral distribution, average earning, and non-wage-earning employment figures are

more influential in determining wage-earning employment than is the minimum wage.

Furthermore, the data indicate that minimum wages have no measurable effect on overall

US labor market employment.

The findings in this paper emerge along similar lines as Addison et al. (2008) The effect

of the minimum wage on the labor market is sector-specific, with different employment

elasticities for each sector. This effect is demonstrated in tables A13-A15. Ergo, states

with different sectoral distribution have different sensitivity to minimum wage changes.

Moreover, the data reveal that the minimum wage also has a small measurable effect on

sectoral employment distribution. The result is a shift towards service-sector employment

caused by an increase in the minimum wage. Thus, future employment elasticity for

wage-earning labor will be affected by changes in the minimum wage, causing further

changes in the wage-earning employment figures as a result of future minimum wage

changes.

In light of the sensitivity of the relationship between statewide minimum wages and

wage-earning employment to sectoral employment distribution within a given state, it is

evident that the sectoral distribution, as well as the and characteristics of the sectors

involved in this analysis are the more pivotal and influential factors in determining the

relationship between wage-earning employment figures and the minimum wage. The

degree of substitutability has a pivotal effect on the shape of the employment/wage

relationship, as does of product tradability. The manufacturing sector, aside from being

the most capital-intensive sector, is also the sector of the economy where tradability is

least restricted, logistically speaking. Not only does the manufacturing sector have high

substitutability with domestic capital stock; but also with foreign labor and foreign capital

stock.

With respect to the two questions posed in the introduction, it is confirmed that a

relationship between the minimum wage and wage-earning employment exists at the state

29

level in the US. The data indicate a very slight positive average relationship between

wage-earning employment and minimum wages across the US. Nonetheless, the data also

indicate a neutral relationship between overall employment and the minimum wage. In

terms of explanatory factors, the data indicate that both bindingness measures and

sectoral distribution are influential determining factors in the wage/employment

relationship. That is, when properly weighted to measure how much the labor market is

actually affected by the minimum wage, the sectoral profile of the economy is the main

influential factor in determining the relationship between the minimum wage, and

employment.

9: Conclusions

The answer to the central questions posed in this study are clear: The relationship

between minimum wages and wage-earning employment can be either positive or

negative. The data indicate that the average statewide employment elasticity is positive.

The explanation for this phenomenon is that the overall relationship between the

statewide minimum wage and wage-earning employment figures depends on the

bindingness 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 by

capital/labor substitutability, and the degree of tradability, -expressed via sectoral

distribution given that sectors examined feature diverging substitutability and tradability-

are analyzed. Thus, this study leaves some matters unanswered, raising possibilities for

further study. The QCEW data set includes quarterly industry-level data on a massive

number of industries and could be further analyzed. Also, it is possible that other

exogenous factors may have influence on employment elasticity. Population density may

be an determining factor for employment elasticity. A further possibility for future study

lies in the investigation of employment and income effects of minimum wage changes in

different income quintiles. This way, economic mobility aspects of the minimum wage

can be measured. In fact, the data in this study indicate that changes may affect individual

income groups differently. Table A11 demonstrates that minimum wages have a positive

30

effect on wage-earning employment figures, whereas table A16 points out that minimum

wages have a neutral average effect on the statewide employment overall.

While the relationships explored in this study could benefit from additional research, this

study presents conclusive evidence regarding the relationship between the minimum

wage and wage-earning employment. This study concludes by stating that the evidence

indicates that circumstances such as tradability, substitutability expressed via sectoral

composition are considerably more influential in determining wage-earning employment

than is the minimum wage, whose influence depends on these parameters.

31

10: References

Addison, John, et al. (2008) “The Effect of Minimum Wages on Wages and Employment:

County-Level Estimates for the United States” Institute for the Study of Labor, Bonn

Germany, Discussion Paper No. 3300

Andini, Corrado (2007) “Teaching Keynes’s Principle of Effective Demand within the

Real Wage vs. Employment Space” Centro de Estudos de Economia Aplicada do

Atlantico, Working Paper No. 06/2007

Card, David and Krueger, Alan B. (1994) “Minimum Wages and Employment: A Case

Study of the Fast-Food Industry in New Jersey and Pennsylvania.” American Economic

Review, Vol. 84 pp. 772-793

Card, David and Krueger, Alan B. (2000) “Minimum Wages and Employment: A Case

Study of the Fast-Food Industry in New Jersey and Pennsylvania: Reply” American

Economic Review, Vol. 90 pp. 1397-1420

Dougherty, Christopher, (2002) “Introduction to Econometrics: Second Edition” Oxford

UK. Oxford University Press.

Downes, Andrew, et al.(2000) “Labor Market Regulation and Employment In the

Caribbean” Washington DC, Inter-American Development Bank, Research Network

Working Paper No. R-388

Greene, William H. (2003) “Econometric Analysis” Upper Saddle River, New Jersey,

Prentice Hall, Pearson Education International

Hamermesh, Daniel, (1986) “Demand for Labor in the Long Run” Michigan State

University. Elsevier Science Publishers, Handbook of Labor Economics, edition 1, Vol.1,

chapter 8, pp. 429-471

32

Hamermesh, Daniel, (1993) “Labor Demand” Princeton, New Jersey, Princeton

University Press

Klein, Lawrence R. (1947) “Theories of Effective Demand and Employment” The

Journal of Political Economy, Vol. 1 No. 2, pp. 108-131

Li, Zhigang (2007) “Panel Data Course: Applied Econometrics, Lecture Notes” Hong

Kong S.A.R., China, School of Economics and Finance, the University of Hong Kong

Neumark, David, and William Wascher. 2000. “The Effect of New Jersey’s Minimum

Wage 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. 2570

Rodrik, Dani, (1997) “Has Globalization Gone Too Far?” Institute for International

Economics, Washington DC

Singell, Larry D., and James R. Terborg. (2005) “Employment Effects of Two Northwest

Minimum Wage Initiatives: Eating and Drinking and Hotel and Lodging.” Unpublished

paper, University of Oregon

Slaughter, Mathew J. (2001) “International Trade and Labor Demand – Demand

Elasticities” Journal of International Economics Vol.54, 27-56,

Statacorp, (1999) “How does xtgls differ from regression clustered with robust standard

errors?” Retrieved Aug. 14, 2008, from http://www.stata.com/support/faqs/stat/

xtgls_rob.html

33

Statacorp, (2003). “R-squared after xtgls, Why does xtgls not report an R-squared

statistic?” 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 Using

Geographical Wage Variation" Oxford Bulletin of Economics and Statistics, Vol. 64, pp.

583-605

Westbrook, Dan. (2007) “Applied Econometrics with Stata, E-Lecture Notes.” Ho Chi

Minh City, Viet Nam, United Nations Development Programme, Public Policy Education

and Research for Vietnam, Fulbright Economics Teaching Program

Wooldridge, Jeffery M. (2002) “Economic Analysis of Cross Section and Panel Data”

Cambridge Massachusetts, The MIT Press

Wooldridge, Jeffery M. (2006) “Introductory Econometrics, A Modern Approach”

Mason Ohio, Thompson Higher Education Press, Thompson South-Western.

34

Appendix 1: Derivations

A: Labor Demand Curve

Y = [ 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 Elasticity

This can be demonstrated via the cost-function approach. Constant returns to scale, and a

competitive market are assumed.

Y = [ L + (1- )K ]1/

Let L = YCw and

K = YCr

Price = Cost

p = C

If markets clear, D(p) = Y

L/ w = YCww + D'(p)Cw2

C is linear homogeneous, so:

Cww = (-r/w) Cwr

L/ w = (rK/Y) ( L/wC) + (D'(p)L2/Y2)

35

Thus, the resulting elasticity is:

LL = (-rK/pY) + (pD'(p)/Y) (wL/pY) = -[1- - j

C: The Effect of Wages on Consumption

In the traditional Keynesian consumption function consumption is a function of income:

C = c0 + c1Y

C = c0 + c1wwL + c

C/ w = c1w wL/ w) + c w)

Via the product rule where f(x) = g(x) +h(x)

And: f(w) = c1wwL

Constant = c1w Constant = c

g(w) = w g(w) = w

h(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)]

36

Appendix 2: Employment Share and Coverage

Figures 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 state

across the same period. Sectoral employment shares are calculated from QCEW data,

while the wage-earning employment ratio is calculated by comparing CPS employment

data with QCEW employment data.

Figure A1: 2002-2007 Average Manufacturing Sector Employment Share by State

Manufacturing Sector Employment Share by State

0.00

0.05

0.10

0.15

0.20

Indiana Ohio NewHampshire

Missouri California Virginia Maryland Hawaii

Figure A2: 2002-2007 Average Services Sector Employment Share by State

Services SectorEmployment Share by State

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Florida Nevada Arizona Utah Montana NorthCarolina

Kentucky Mississippi

37

Figure A3: Wage-Earning Employment Share by State

W/E Ratio by State

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

Massa

chus

etts

Michiga

n

Conne

cticu

t

North C

arolina

Tenn

esse

e

Washin

gton

Kentu

cky

Delaware

Indian

a

38

Appendix 3: Dummy Regressions

Regressions in table A1 display wage-earning employment on a minimum wage change

dummy. Both standard OLS and first-differenced OLS estimations are undertaken here in

present value terms, lagged terms, and hybrid term.

The regressions in table A2 are of wage-earning employment on the flat dummy which

takes a value of 1 when the minimum wage has gone unchanged for two years. Both

standard OLS and first-differenced OLS estimations are undertaken here in present value

terms, lagged terms, and hybrid term.

Table A1: Change Dummy Regressions Controlling for Bindingness and Sectoral Employment Share

Y = wage employmentX = Change Dummy Dummy Services Manufacturing Avg. wage

Non-wageEmployment

log-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 0.9903

First 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

39

Table A2: Change Dummy Regressions controlling for Bindingness and Sectoral Employment Share

Y = wage employmentX = Flat Dummy Dummy Services Manufacturing Avg. wage

Non-wageEmployment

log-log 0.0055 1.3501 0.1399 -0.3131 -0.5388P value 0.3580 0.0000 0.0000 0.0000 0.0000SE 0.0059 0.0207 0.0050 0.0205 0.0194R-sq 0.9938

Lagged Control ParametersFlat Dummy -0.0039 1.1006 0.1377 -0.3454 -0.2910P value 0.6050 0.0000 0.0000 0.0000 0.0000SE 0.0076 0.0265 0.0063 0.0261 0.0248R-sq 0.9903

Lagged Control ParametersLagged Flat Dummy -0.0055 1.1002 0.1378 -0.3471 -0.2905P value 0.4750 0.0000 0.0000 0.0000 0.0000SE 0.0077 0.0264 0.0063 0.0261 0.0248R-sq 0.9903

First Difference 0.0129 0.2533 -0.0013 -0.0107 -0.2453P value 0.3030 0.0000 0.7660 0.5370 0.0000SE 0.0125 0.0182 0.0044 0.0173 0.0169R-sq 0.2844

Lagged Control ParametersFirst Difference -0.0008 -0.2438 -0.0030 -0.0251 0.2422P value 0.9520 0.0000 0.4930 0.1450 0.0000SE 0.0126 0.0182 0.0044 0.0172 0.0170R-sq 0.2790

Lagged Control ParametersLagged First Difference -0.0004 -0.2399 -0.0050 -0.0315 0.2411P value 0.9740 0.0000 0.2660 0.0750 0.0000SE 0.0125 0.0187 0.0045 0.0177 0.0174R-sq 0.2835

40

Appendix 4: Basic Continuous Variable OLS Regressions

These are basic OLS estimations of wage-earning employment on the statewide

minimum wage. The relationship is estimated without controls, with state controls, and

with period controls. Various estimators are used and all models are tested for both

autocorrelation and heteroskedasticity.

Table A3 : Basic Continuous Variable OLS Regressions

Y = wage employ.X = minimum wage

BasicCoefficient

Control forStates States (F-test)

Control forperiods

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 0.0014

FD 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 0.1267

RE 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 0.0006

FE 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 0.0007

Wooldridge test 10.2480 10.2480 Autocorrelation 3.8280 No AutocorrelationP value 0.0025 0.0025 0.0565

Wald Test 783.6700 783.6700 Heteroskedasticity 731.3600 HeteroskedasticityP value 0.0000 0.0000 0.0000

Likelihood-ratiotest 1158.2500 1158.2800 Heteroskedasticity 1066.8100

NoHeteroskedasticity

1034 0.0041 0.0040 0.2331

41

Appendix 5: Controlling for Sectoral Employment Share and Bindingness Separately

Table A4 displays are OLS estimations of wage-earning employment on the statewide

minimum wage with period and sectoral employment share controls. Various estimators

are used and the model is tested for both autocorrelation and heteroskedasticity.

Table A5 displays OLS estimations of wage-earning employment on the statewide

minimum wage with period and bindingness controls. With these regressions, the

minimum wage is effectively weighted. Various estimators are used and the model is

tested for both autocorrelation and heteroskedasticity.

Table A4: Regressions Controlling for Sectoral Employment Share

Y = wage employmentX = Minimum wage

MinimumWage Services Manufacturing

PeriodsF-test

log-log -0.0233 0.7396 0.1662 0.6800P value 0.4110 0.0000 0.0000 0.8544SE 0.0283 0.0080 0.0068R-sq 0.9867

FD log 0.0060 -0.0007 -0.0001 6.8800P value 0.9360 0.8950 0.9870 0.0000SE 0.0746 0.0053 0.0045R-sq 0.1268

RE log -0.0145 0.8486 0.0664 51.4800P value 0.6570 0.0000 0.0030 0.0002SE 0.0327 0.0278 0.0225R-sq 0.9871

FE log -0.0050 1.2014 -0.1011 3.1900P value 0.8810 0.0000 0.0050 0.0000SE 0.0333 0.0982 0.0356R-sq 0.3317Overall R-sq. 0.9687

Wooldridge test 2.5490 No Autocorrelation presentP value 0.1172

Wald Test 412.8700 Heteroskedasticity is presentP value 0.0000

Likelihood-ratio test 475.9000 No Heteroskedasticity presentheteroskedasticity 1.0000

1034

42

Table A5: OLS Regressions Controlling for Bindingness

Y = wage employmentX = Minimum wage Min. Wage

ServicesEmployment

ManufacturingEmployment

PeriodsF-test

log-log -0.0233 0.7396 0.1662 0.6800P value 0.4110 0.0000 0.0000 0.8544SE 0.0283 0.0080 0.0068R-sq 0.9870

FD 0.0060 -0.0007 -0.0001 6.8800P value 0.9360 0.8950 0.9870 0.0000SE 0.0746 0.0053 0.0045R-sq 0.1268

POLS -0.0050 1.2014 -0.1011 3.1900P value 0.8810 0.0000 0.0050 0.0000SE 0.0333 0.0982 0.0356R-sq 0.9970

RE -0.0145 0.8486 0.0664 51.4800P value 0.6570 0.0000 0.0030 0.0000SE 0.0327 0.0278 0.0225R-sq 0.9871

FE -0.0050 1.2014 -0.1011 3.1900P value 0.8810 0.0000 0.0050 0.0000SE 0.0333 0.0982 0.0356R-sq 0.3317Overall R-sq 0.9687

Wooldridge test 0.0560 AutocorrelationP value 0.8145

Wald Test 412.8700 HeteroskedasticityP value 0.0000

Likelihood-ratio test 1454.81 Heteroskedasticityheteroskedasticity 0

1034

43

Appendix 6: OLS Regressions Using All Control Parameters

Table A6 displays present-value OLS estimations of wage-earning employment on the

statewide minimum wage with period, bindingness, and sectoral employment share

controls. Various estimators are used and the model is tested for both autocorrelation and

heteroskedasticity. Tables A6b and A6c display are present/lagged hybrid estimations

and lagged-value estimation respectively. The present-value outperforms both the lagged-

value and hybrid models.

Table A6: Present-Value OLS Regressions Using All Control Parameters

Y = wage employmentX = Minimum wage Min. Wage Services Manufacturing A.H.E.

Non-wageEmployment

PeriodsF-test

log-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 0.9937

FD -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 0.9918

RE 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 0.9917

FE 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 0.9915

Wooldridge test 0.0560 No Autocorrelation presentP value 0.8145

Wald Test 1444.8400 Heteroskedasticity is presentP value 0.0000

Likelihood-ratio test 2999.5900 Heteroskedasticity is presentheteroskedasticity 0.0000

1034

44

Table A6b: Present-Value OLS Regressions Using Lagged-Value Control Parameters

Y = wage employmentX = Minimum wage Min. Wage Services Manufacturing Avg. wage

Non-wageEmployment

PeriodsF-test

log-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 0.9840

Wooldridge test 0.0560 No Autocorrelation presentP value 0.8145

Wald Test 14230.2500 Heteroskedasticity is presentP value 0.0000

Likelihood-ratio test 433.7100 No Heteroskedasticity presentheteroskedasticity 1.0000

987

45

Table A6c: Lagged-Value OLS Regressions Using All Control Parameters

Y = wage employ. (lag)X = Minimum wage Min. Wage Services Manufacturing A.H.E.

Non-wageEmployment

PeriodsF-test

log-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 0.9840

Wooldridge test 0.0560 No Autocorrelation presentP value 0.8145

Wald Test 14229.8600 Heteroskedasticity is presentP value 0.0000

Likelihood-ratio test 435.7900 No Heteroskedasticity presentheteroskedasticity 1.0000

987

46

Appendix 7: OLS Regressions Using Alternate Sectoral GDP-Share Control Parameters

Table A7 displays OLS estimations of wage-earning employment on the statewide

minimum wage with period and sectoral GDP-share controls. Various estimators are used

and the model is tested for both autocorrelation and heteroskedasticity.

The estimations in table A8 are OLS estimations of wage-earning employment on the

statewide minimum wage with period, bindingness and sectoral GDP-share controls.

Various estimators are used and the model is tested for both autocorrelation and

heteroskedasticity.

Table A7: OLS Regressions Using Alternate Sectoral GDP-Share Controls

Y = wage employmentX = Minimum wage Minimum Wage

ServicesGDP ratio

ManufacturingGDP ratio

PeriodsF-test

log-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 0.0076

FD 0.0056 -0.0002 0.0053 6.8800P value 0.9400 0.9710 0.8780 0.0000SE 0.0745 0.0063 0.0345R-sq 0.1267

RE -0.0489 -0.0057 0.1406 199.7400P value 0.1730 0.8900 0.5510 0.0000SE 0.0359 0.0412 0.2360R-sq 0.0019

FE -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 0.0017

Wooldridge test 4.1690 Autocorrelation is presentP value 0.0469

Wald Test 718.4700 Heteroskedasticity is presentP value 0.0000

Likelihood-ratio test 1323.5700 Heteroskedasticity is presentheteroskedasticity 0.0000

1034

47

Table A8: OLS Regressions Including Alternate Sectoral GDP-Share and Bindingness Controls

Y = wage employmentX = Minimum wage Min. Wage

ServicesGDP ratio

ManufacturingGDP ratio A.H.E.

Non-wageEmployment

PeriodsF-test

log-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 0.9625

FD 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 0.1299

RE -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 0.5234

FE -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 0.8853

Panel 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

Wald-Chi DF = 2615151.380

0

Wooldridge test 18.6170 Autocorrelation is presentP value 0.0001

Wald Test 4119.4400 Heteroskedasticity is presentP value 0.0000

Likelihood-ratio test 260.2600 No Heteroskedasticity is presentheteroskedasticity 1.0000

1034

48

Appendix 8: Heteroskedasticity and Autocorrelation Correction Models

Table A9 compares standard OLS with cluster-robust standard-error heteroskedasticity

and autocorrelation-correcting OLS estimations of wage-earning employment on the

statewide minimum wage with period, bindingness and sectoral employment share

controls. The pooled OLS and the first-difference estimator are used.

The estimations in tables A10 and A11 are heteroskedasticity-correcting panel GLS

regressions of wage-earning employment on the statewide minimum wage. Table A10

includes period, and sectoral employment share controls. In table A11, bindingness

controls are added as well. Present-value, lagged-value, and hybrid regressions are

compared. The present value model outperforms the other two models in both tables.

The estimations in table A12 are autocorrelation-correction regressions of wage-earning

employment on the statewide minimum wage with period, bindingness, and sectoral

GDP-share. The table includes autocorrelation-correcting panel GLS and Prais-Winsten

estimations, and an autocorrelation and heteroskedasticity-correcting panel GLS model.

Table A9: Estimations Correcting for Heteroskedasticity and Autocorrelation Using Cluster Robust Standard Errors

Y = wage employmentX = min. wage

MinimumWage Services Manufacturing A.H.E.

Non-wageEmployment

PeriodsF-test

POLS 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 0.9939

POLS ClusterRobust SE 0.0813 1.3382 0.1407 -0.3584 -0.5243 16.1800P value 0.0040 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0274 0.0146 0.0092 0.0292 0.0179R-sq 0.9939

FD -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 0.4501

FD Cluster RobustSE -0.0441 0.2533 -0.0013 -0.0100 -0.2453 21.9200P value 0.4910 0.0000 0.7120 0.5750 0.0000 0.0000SE 0.0639 0.0153 0.0036 0.0178 0.0146R-sq 0.2839

49

Table A10: Heteroskedasticity Correction GLS Regressions including only sectoral employment-share controls

Y = wage employmentX = Minimum Wage Minimum wage Services Manufacturing

StatesF-test

Panel 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 136331.3600

Table A11: Heteroskedasticity Correction GLS Regressions Including all Control Parameters

Y = wage employmentX = Minimum wage Min. Wage Services Manufacturing A.H.E.

Non-wageEmployment

PeriodsF-test

Panel 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

50

Table A12: Heteroskedasticity and Autocorrelation Correction GLS Regressions including all Control Parameters

Y = wage employmentX = Minimum wage Min. Wage

ServicesGDP ratio

ManufacturingGDP ratio A.H.E.

Non-wageEmployment

PeriodsF-test

Panel GLS (ar1) 0.1454 -0.2325 1.3512 -0.2036 0.8601 60.4500P value 0.0560 0.0000 0.0000 0.0050 0.0000 0.0000SE 0.0762 0.0237 0.1296 0.0724 0.0103Wald-Chi DF = 26 11498.4800

Panel Prais-Winsten (ar1) 0.1454 -0.2325 1.3512 -0.2036 0.8601 4132.1700P value 0.0910 0.0000 0.0000 0.0190 0.0000 0.0000SE 0.0861 0.0221 0.1359 0.0868 0.0153Wald-Chi DF = 5 8857.1300

Y = wage employmentX = Minimum wage Min. Wage

ServicesGDP ratio

ManufacturingGDP ratio A.H.E.

Non-wageEmployment

PeriodsF-test

Panel 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 0.0092Wald-Chi DF = 26 15151.3800

51

Appendix 9: Breaks in the Data Set

This table analyzes breaks in the data set using a heteroskedasticity-correcting panel GLS

model. Chow testing reveals no break between states which did and states which did not

increase their minimum wages, ruling-out a natural experiment methodology. Chow

testing also reveals that there is a break in the data set between services-employment

heavy, and manufacturing-employment heavy states.

Table A13: Estimation of Breaks in the Data Set

Y = wage employmentX = Minimum wage Min. Wage Services Manufacturing A.H.E.

Non-wageEmployment

PeriodsF-test

Panel GLS (hetero) Flat = 1 0.2248 1.3497 0.1531 -0.3550 -0.5495 80.8000P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0402 0.0220 0.0058 0.0264 0.0206Wald-Chi DF =26 137786.6100

Panel GLS (hetero) Flat = 0 0.3460 1.3395 0.1100 -0.4478 -0.4776 21.5500P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.4256SE 0.0650 0.0481 0.0083 0.0404 0.0445Wald-Chi DF =26 43405.8600

DF loss (numerator) Remaining RSS RSS -1 Agg DF K n-2k756.0000 232.0000 200.0718 613.2880 986.0000 2.0000 986.0000

Chow NumeratorChowDenom. F(2, 986) Test

1.4598 0.8249 19.4900 1.7697 Not Significant at .05

Y = wage employmentX = Minimum wage Min. Wage Services Manufacturing A.H.E.

Non-wageEmployment

PeriodsF-test

Manufacturing-heavy states(GLS hetero) 0.0129 1.5822 0.0839 -0.2951 -0.6937 318.6900P value 0.3280 0.0000 0.0000 0.0000 0.0000 0.0000SE 0.0132 0.0133 0.0027 0.0141 0.0124Wald-Chi DF = 26 695390.6700

Services-heavy states(GLS hetero) 0.0818 1.2723 0.1276 -0.0863 -0.4531 28.7700P value 0.0000 0.0000 0.0000 0.0010 0.0000 0.1196SE 0.0168 0.0148 0.0072 0.0268 0.0111Wald-Chi DF = 26 337665.0300

DF loss (numerator) Remaining RSS RSS -1 Agg DF K n-2k498.0000 490.0000 285.1213 494.1430 986.0000 2.0000 986.0000

Chow NumeratorChowDenom. F (2, 986) Test

18.5076 0.7903 19.4900 23.4175 Significant at .05

52

Appendix 10: Secondary Effects of Minimum Wage Changes

Table A14 analyzes the sectoral employment shift caused by a change in the minimum

wage using a heteroskedasticity-correcting panel GLS model. Sector-specific

employment is used as the dependent variable. Periods, bindingness, and the rival

economic sector are controlled for.

Table A15 analyzes the sectoral employment shift caused by a change in the minimum

wage using a heteroskedasticity-correcting panel GLS model. The sectoral employment

distribution ratio is used as the dependent variable. Periods, and sectoral GDP-shares are

controlled for.

Table A16 analyzes the effects on overall employment caused by a change in the

minimum wage using a heteroskedasticity-correcting panel GLS model. Periods, and

sectoral employment-share are controlled for.

Table A14: Sectoral Shift Caused by Minimum Wages

Y = service employmentX = Minimum wage Minimum Wage

Non-wageEmployment

ManufacturingEmployment

PeriodsF-test

Panel GLS(Hetero) 0.1771 0.8889 0.0694 93.8300P value 0.0000 0.0000 0.0000 0.0000SE 0.0209 0.0050 0.0044Wald-Chi DF = 24 191653.1300

Y = Manufacturing employmentX = Minimum wage Minimum wage

Non-wageEmployment

Serviceemployment

PeriodsF-test

Panel GLS(Hetero) -0.7629 -0.0621 1.1128 195.3900P value 0.0000 0.0030 0.0000 0.0000SE 0.0311 0.0212 0.0225Wald-Chi DF = 24 148728.6200

Table A15: Sectoral Shift Caused by Minimum Wages considered with relative GDP-share

Y = M/S ratio(employment based)X = Minimum wage Min. Wage

ServicesGDP ratio

ManufacturingGDP ratio

PeriodsF-test

Panel GLS (hetero) -0.0946 -0.5699 6.8786 22.6400P value 0.0000 0.0000 0.0000 0.3635SE 0.0256 0.0103 0.0369Wald-Chi DF = 24 35831.9000

53

Table A16: The Effect of Minimum Wages on Overall Statewide Employment

Y = Overall EmploymentX = Minimum wage Minimum wage

Serviceemployment

ManufacturingEmployment

PeriodsF-test

Panel GLS(Hetero) -0.0035 0.8569 0.0985 57.6100P value 0.6280 0.0000 0.0000 0.0000SE 0.0073 0.0015 0.0013Wald-Chi DF = 24 2203375.0000

( 1) log_Imin = 0 chi2( 1) 0.2400Prob > chi2 = 0.6277