Thesis in full_5.6

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’ economy is empirically determined to have a
s
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’ sectoral profile.
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1

1: Introduction
The relationship between minimum wages and employment figures documented by Card
and Krueger’ works in both 1994 and 2000, as well as responses to Card and Krueger’
s 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

2

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’ data set, controlling for employer dummies.
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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 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’ argument is a
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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

4

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

5

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

Capital

K2
K1

Labor

Wage

w2

w1

Employment
L2 L1

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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
1
curve 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 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.

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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 c 1w > 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

w2

w1

L1 L2
Employment

3
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
s
system’ I depends on Yo which is determined after changes in output.
s
4
See Appendix 1 for derivation.

8

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 from
domestic 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:
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 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

12

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’ economy. These are by comparison of employment
s
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 chosen
to represent the manufacturing sector, while the services-sector employment represents a compilation of
several 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 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 0.1419

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 basis
of hours worked per pay period. Non-wage-earning employment in the US is mostly salary-based, although
the non-wage-earning employment figure also covers all other non-wage earning employment, such as
contractual employment and self-employment.

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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
ja

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.

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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 07

Figure 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

$4.00

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’ $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 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’ results, the regression of wage-earning employment on a minimum wage
s
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 explanatory
variable, and the lagged control parameters.

18

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 employment Non-wage Periods
X = Minimum wage Min. Wage Services Manufacturing A.H.E. Employment F-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 - - 3.1900
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 - -

FE (Bindingness
Controls) -0.0571 - - 0.1341 -0.5398 24.8000
P value 0.0110 - - 0.0030 0.0000 0.0000
SE 0.0225 - - 0.0450 0.0140
R-sq 0.6927 - -
Overall R-sq 0.9457 - -

FE (all controls) 0.0120 1.5109 0.0996 -0.0044 -0.6324 12.1000
P value 0.2590 0.0000 0.0000 0.8350 0.0000 0.0000
SE 0.0107 0.0317 0.0116 0.0214 0.0069
R-sq 0.9319
Overall R-sq 0.9915

Panel GLS (Hetero) 0.0558 1.3746 0.1420 -0.3719 -0.5575 348.9500
P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
SE 0.0112 0.0092 0.0022 0.0136 0.0090
Wald-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

19

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)

20

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,

21

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

22

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
X = Minimum wage Min. Wage Services Manufacturing Avg. wage Employment F-test
Panel GLS(Hetero) 0.0558 1.3746 0.1420 -0.3719 -0.5575 348.9500
P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
SE 0.0112 0.0092 0.0022 0.0136 0.0090
Wald-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 an
OLS estimation. Thus, the R-squared does not represent proportion of total dependent variable variation
explained by the GLS model. Ergo, is a less useful diagnostic tool when using a GLS rather than an OLS
estimator. (Statacorp, 2003) The Wald statistic is a hypothesis testing tool which follows a chi-square
distribution 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
s
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’ share of
s
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.

24

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

25

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

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 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

27

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

28

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

29

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.

30

10: References

Addison, John, et al. (2008) “ Effect of Minimum Wages on Wages and Employment:
The
County-Level Estimates for the United States” Institute for the Study of Labor, Bonn
Germany, Discussion Paper No. 3300

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

31

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’ Minimum
s
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

32

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.

33

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)

34

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)]

35

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
0.20

0.15

0.10

0.05

0.00
Indiana Ohio New Missouri California Virginia Maryland Hawaii
H pshire
am

Figure 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

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an

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37

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 employment Non-wage
X = Change Dummy Dummy Services Manufacturing Avg. wage Employment
log-log 0.0068 1.3465 0.1403 -0.3204 -0.5351
P value 0.5190 0.0000 0.0000 0.0000 0.0000
SE 0.0105 0.0206 0.0050 0.0197 0.0193
R-sq 0.9938
Lagged Control Parameters
Change Dummy 0.0005 1.1023 0.1375 -0.3413 -0.2928
P value 0.9690 0.0000 0.0000 0.0000 0.0000
SE 0.0137 0.0264 0.0063 0.0249 0.0246
R-sq 0.9903
Lagged Change Dummy 0.0111 1.1004 0.1377 -0.3439 -0.2910
P value 0.4020 0.0000 0.0000 0.0000 0.0000
SE 0.0132 0.0264 0.0063 0.0250 0.0247
R-sq 0.9903

First Difference 0.0040 0.2526 -0.0013 -0.0108 -0.2447
P value 0.5240 0.0000 0.7730 0.5340 0.0000
SE 0.0063 0.0182 0.0044 0.0174 0.0169
R-sq 0.2839
First Difference 0.0025 -0.2437 -0.0030 -0.0249 0.2421
P value 0.6920 0.0000 0.4920 0.1480 0.0000
SE 0.0063 0.0182 0.0044 0.0172 0.0170
R-sq 0.2792
Lagged First Difference 0.0051 -0.2400 -0.0050 -0.0319 0.2412
P value 0.4510 0.0000 0.2650 0.0720 0.0000
SE 0.0067 0.0187 0.0045 0.0177 0.0174
R-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
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 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
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 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 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. Basic Control for Control for Periods
X = minimum wage Coefficient States States (F-test) periods (F- Test)
log-log 0.1910 0.1262 4901.0300 0.1677 0.0400
P value 0.4070 0.0000 0.0000 0.4890 1.0000
SE 0.2302 0.0322 0.2423
R-sq 0.0007 0.9956 0.0014

FD log -0.1032 -0.1018 0.0700 0.0045 6.8900
P value 0.1670 0.1890 1.0000 0.9520 0.0000
SE 0.0746 0.0776 0.0742
R-sq 0.0019 0.0054 0.1267

RE log 0.1262 0.1262 230000.0000 -0.0477 252.9600
P value 0.0000 0.0000 0.0000 0.1820 0.0000
SE 0.0322 0.0322 0.0357
R-sq 0.0006 1.0000 0.0006

FE log 0.1262 N/A N/A -0.0479 12.0400
P value 0.0000 N/A N/A 0.1810 0.0000
SE 0.0322 N/A N/A 0.0358
R-sq 0.0153 0.0153 0.2197
overall R-sq 0.0007 0.0007 0.0007

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

Wald Test 783.6700 783.6700 Heteroskedasticity 731.3600 Heteroskedasticity
P value 0.0000 0.0000 0.0000

Likelihood-ratio No
test 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 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 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 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
X = Minimum wage Min. Wage Services Manufacturing A.H.E. Employment F-test
log-log 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
Adjusted R-sq 0.9937

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

RE 0.0087 1.4513 0.1164 -0.0248 -0.6337 266.3200
P value 0.4150 0.0000 0.0000 0.2350 0.0000 0.0000
SE 0.0107 0.0160 0.0103 0.0209 0.0069
R-sq 0.9917

FE 0.0120 1.5109 0.0996 -0.0044 -0.6324 12.1000
P value 0.2590 0.0000 0.0000 0.8350 0.0000 0.0000
SE 0.0107 0.0317 0.0116 0.0214 0.0069
R-sq 0.9319
Overall R-sq 0.9915

P value 0.8145

P value 0.0000

Likelihood-ratio test 2999.5900 Heteroskedasticity is present
1034

43

Table A6b: Present-Value OLS Regressions Using Lagged-Value Control Parameters
X = Minimum wage Min. Wage Services Manufacturing Avg. wage Employment F-test
log-log 0.1311 1.0795 0.1395 -0.4029 -0.2673 3.8900
P value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
SE 0.0284 0.0262 0.0062 0.0282 0.0246
R-sq 0.9906
FD 0.0698 -0.2457 -0.0022 -0.0250 0.2431 6.9200
P value 0.3050 0.0000 0.6120 0.1480 0.0000 0.0000
SE 0.0680 0.0183 0.0044 0.0172 0.0170
R-sq 0.2797
RE -0.0027 0.8618 0.1143 -0.2225 -0.0425 135.9700
P value 0.9350 0.0000 0.0000 0.0000 0.0540 0.0000
SE 0.0331 0.0323 0.0187 0.0560 0.0220
R-sq 0.9918
FE -0.0083 1.0741 -0.0425 -0.1264 -0.0261 6.9800
P value 0.8090 0.0000 0.0540 0.0660 0.2390 0.0000
SE 0.0344 0.0954 0.0220 0.0686 0.0221
R-sq 0.3125
Overall R-sq 0.9840

P value 0.8145

P value 0.0000

Likelihood-ratio test 433.7100 No Heteroskedasticity present
987

44

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