The Minimum Wage Effect on Youth Employment in Canada: Testing
the Robustness of Cross-Province Panel Studies
James Ted McDonald and Anthony E. Myatt
May 18, 2004
Department of Economics
University of New Brunswick
P. O. Box 4400
Fredericton
New Brunswick
E3B 5A3
CANADA
Acknowledgements: The authors would like to thank, without implicating, Michael Baker,
Vaughan Dickson, and Morley Gunderson, for very helpful suggestions.
The Minimum Wage Effect on Youth Employment in Canada: Testing
the Robustness of Cross-Province Panel Studies
ABSTRACT
A series of papers have established that minimum wages have negative employment effects on
teenagers in Canada. All of these papers use panel data methodology, and most use pooled
provincial time series data. Implicit in the panel-data methodology are restrictive assumptions:
first, about the structure of time and province unobserved effects; and second, on the stability of
the regression coefficients both over time and across provinces. Although we find the negative
employment effect to be robust to changes in lag structure and the inclusion of a range of
additional variables, our main finding is that the implicit assumptions underlying the use of the
panel-data methodology are soundly rejected. The marked non-robustness of the results to the
relaxation of these fundamental assumptions calls into question the validity of the negative
employment effect of minimum wages that has been found in most of the Canadian literature.
2
I. Introduction
Surveys of economists consistently find the most consensus on microeconomic nonnormative issues. But on one particular issue – the effects of minimum wages – the degree of
consensus has significantly weakened over the 1990s (see table 1). This may well reflect the
influence of the work of Card, Katz and Krueger1 that challenges conventional wisdom. Their
results, that minimum wages typically have a zero or positive impact on employment, have been
the subject of a lively debate, of which there are several interesting features.
First, it is striking how narrow is the debate. It is not concerned with the wider welfare
effects of minimum wages – for example who ultimately pays and benefits, or how they affect
income inequality, or how minimum wages compare to other redistributive tools (such as EI,
welfare assistance, or child benefits) and whether they are a useful complement to them.2 These
questions are relatively neglected compared to the research effort devoted to establishing whether
or not there are disemployment effects.
Second, the heat in the debate is surprising given how little is at stake theoretically. The
empirical work is testing the predictions of a standard textbook competitive model of the labour
market; but even slight modifications to this model – a friction here or there – relieve it of clearcut predictions. For example, adding monitoring costs gives rise to an efficiency wage model, or
adding job search costs gives rise to a dynamic monopsony model.3 Effectively, the debate is
1
Card (1992a, 1992b), Katz and Krueger (1992), Card, Katz and Krueger (1994), Card and Krueger (1994, 1995,
2000).
2
Of the ‘wider’ aspects, the effect of minimum wages on school enrollment and on the job training has received the
most attention. See Baker (2003) and the references contained therein. Fortin and Lemieux (2004) consider the
redistributive consequences of minimum wages, and find they are about as progressive as all government transfer
programs considered together.
3
Manning (2003) points out that the dynamic monopsony model can explain a wide array of phenomena that the
competitive labour market model cannot.
3
about how important these frictions are in the real world; and the heat probably reflects not only
the academic objective to provide sound advice to policy makers, but also real world struggles
over income distribution.4
Third, it is interesting that the evidence is mixed for almost every country in the world –
except Canada. Evidence is mixed for the United States, France, the United Kingdom, New
Zealand, and Portugal (see Neumark and Wascher (2004) for references). Only in Canada is the
evidence consistent – and shows significant and increasingly important negative employment
effects of minimum wages. The most often cited explanation is Hammermesh’s (2002)
observation that Canada is “a desirable laboratory” for testing minimum wage effects because
minimum wages are set provincially, which gives more identifying variation. The list of studies
yielding significant negative employment effects in Canada includes Swidinsky (1980),
Schaafsma and Walsh (1983), Grenier and Seguin (1991), Baker, Benjamin and Stanger (1999),
Baker (2003), Yuen (2003), Campolieti, Fang, and Gunderson (2004), and Campolieti,
Gunderson and Riddell (2004). The only study which found no effect was by Goldberg and
Green (1999), but this one anomalous result has a ready explanation – the authors used a
logarithmic specification that Baker et. al. (1999) have shown to be inappropriate. All but two of
these studies combine aggregate time-series provincial data into a panel data set. The exceptions
– by Yuen (2003), and Campolieti et. al. (2004) – both use individual panel data sets.
Our main purpose in this paper is to re-examine the common finding that minimum wages
4
The heat of the debate can gauged by Valentine (1996) accusing Card and Krueger of practising “politically
correct” economics, and of using suspect data in their 1994 case study. The latter claim was also made by Neumark
and Wascher (2000), and refuted by Card and Krueger (2000). For their part, Card and Krueger (1995, page 186)
present evidence of “publication bias” (against results contrary to conventional wisdom) – though this is denied by
Neumark and Wascher (1998). Finally, Levine (2001) recognised the importance of “author biases” (where
conscious or unconscious biases in searching for a “robust” equation explains why one team of authors consistently
finds different results to another team) and committed Industrial Relations to a “pre-specified” research design to try
to cut through the problem.
4
negatively impact the employment rates of teenage Canadians. Specifically, we evaluate the
robustness of results based on province-level panel data when key assumptions underpinning
estimation of panel-data models are relaxed. Since studies based on person-level micro data sets
often embody the same assumptions, our analysis suggests caution is appropriate in the context of
their results too.
In the next section, we outline a functional form for estimation of minimum wage effects
highlighting the assumptions typically made in the literature. In order to benchmark our data and
analysis against the existing empirical literature, we begin by replicating the results reported in
Baker et. al. (1999) – hereafter referred to as BBS. Following this, we consider a series of
variations to the basic model that have been considered in the Canadian and international
literature, specifically: 1) the sensitivity of the results to changes in the lag structure, and 2) the
sensitivity of the results to the inclusion of additional control variables – in particular, EI
generosity, union density, real interest rates, and other measures of the business cycle. In Section
III, we revisit the main assumptions underlying most panel-data estimation by examining the
stability and robustness of the estimated equation, both through time and across provinces. In
Section IV, we summarize our main findings and suggest avenues for further research.
II.
Replication, Lag Structure, and Additional Control Variables
A general functional form for studies using provincial panel data, is the following:
Eit = α + βit·MINWit + ϕit ·Xit + ηit + εit
(1)
where the subscripts denote province i and year t. E is the teenage employment-population ratio;
MINW, the ratio of the minimum wage to the average hourly wage in manufacturing; and X is a
vector of control variables. The standard control variables (which are also the ones used by BBS)
5
are: the prime-aged male unemployment rate and the level of real GDP – both used to control for
aggregate economic activity; and the population share of teenagers relative to the working age
population 15-64 – used to control for supply variation.5 The ηit are unobserved systematic timevarying province effects, and the εit are unobserved random shocks
Clearly, equation (1) cannot be estimated as written and requires identifying restrictions
on both the coefficients and the error structure. When estimating equation (1) as a panel data set,
the βit and ϕit matrices are invariably constrained to be constant across provinces and over time:
βit = β and ϕit = ϕ. (One exception in the literature is Williams (1993) who allows for regionally
specific minimum wage effects.) As far as the error term is concerned, the deterministic part of
the regression cannot be identified separately from the systematic part of the error term. To deal
with this problem, the usual assumption is that ηit be written as:
ηit = σi + γt
(2)
where σi are time-invariant province-specific effects, and γt are province-invariant time effects.
This allows the modeling of the province specific (fixed) effects as:
N −1
∑π
σi =
i =1
i
⋅PROVi
(3)
where PROVi is an indicator variable for province i. The time effects, γt, are typically either
captured by a quadratic in time,
β5·TRENDt + ß6·TREND2t
(4)
or by a set of year dummy variables:
T −1
∑φ
t =1
t
⋅ YEARt
(5)
5
There is small problem in the BBS study, in that they actually deflate teenage population by total population 15
years of age and over; whereas they state it is deflated by total population of working age, 15-65.
6
Imposing these sets of restrictions on equation (1), we obtain the following equations:
Eit = α + β·MINWit + ϕ ·Xit +
N −1
∑π
i =1
i
⋅PROVi + β5·TRENDt + ß6·TREND2t + εit
(6a)
and
Eit = α + β·MINWit + ϕ ·Xit +
N −1
∑π i ⋅PROVi +
i =1
T −1
∑φ
t =1
t
⋅ YEARt + εit
(6b)
In order to benchmark our data to the current literature, we estimate equations (6a) and
(6b) using pooled provincial time-series data. Column (1) of Table 2 reports the results from
these baseline specifications, using the same sample period (1976-93) as BBS. The top panel
parameterizes time-effects as a quadratic in time, while the bottom panel uses the set of year
dummies. Both minimum wage estimates are almost identical to what is reported in BBS. Using
the quadratic in time, our minimum wage elasticity is -0.259 while BBS report –0.264. Using
year dummies, we get –0.250, compared to BBS’s estimate of –0.242.6
In column (2) we estimate the same specification but over the longer time period 19762002, and the magnitude of the estimated minimum wage elasticity increases marginally (from –
0.259 to –0.326). It is also notable that lengthening the time period has significant effects on
some of the other estimated coefficients; for example, the coefficient on real GDP is now
negative but not significant.7 The next two columns expand the basic specification to reflect
refinements in the lag structure suggested in the recent literature. For example, Neumark’s (2001)
“prespecified research design” includes a lagged minimum wage term, while Neumark and
Wacher (2004) capture dynamic elements by including a lagged dependent variable. Column (3)
6
However, we obtain different coefficient estimates for the teenage population share and real GDP. The former
arises because of the different denominator used (see footnote 5). The latter arises from different provincial real GDP
data. See the data appendix for further discussion.
7
shows that the effect of including a lagged minimum wage term is to increase the size of the
long-run minimum wage elasticity to -0.401, and column (4) shows that the inclusion of a lagged
dependent variable has the effect of further increasing the long-run elasticity to –0.421. (We
employ the Arellano-Bond GMM method to estimate this dynamic panel-data model.). In the
bottom panel of Table 2, we keep the same specifications as the top half of the table, but replace
the quadratic in time with a set of year dummies. The pattern of results mirrors that in the top half
of the table, although in each case the size of the minimum wage elasticity is somewhat smaller.
For example, with the lagged minimum wage term (column 3) the effect of year dummies is to
reduce the long-run minimum wage elasticity from –0.401 to –0.342; and with a lagged
dependent variable the long-run elasticity is reduced from –0.421 (with trend and trend squared)
to –0.371 (with a set of year dummies). While this confirms BBS’s result that the long-run effect
of minimum wages is larger than the short-run effect, none of these changes has a substantial
impact on either the size or significance of the minimum wage coefficient.
In Table 3, we extend the base specification to include controls for other variables that
have been included in recent minimum wage research. These controls include EI generosity,
union density, real interest rates, and several measures of the business cycle. These variables are
chosen for several reasons. First, it is well established that EI generosity has an important
influence on employment and unemployment – not only affecting their dynamics through time
(Milbourne et. al., 1991), but also having a greater impact on some provinces than others (Myatt,
1992). Moreover, Coe and Snower (1997) show that more generous EI benefits, or greater
bargaining strength for incumbent employees (proxied by union density), tend to exacerbate the
negative employment effects from an increase in the minimum wage.
7
Restricting the sample to the period 1983-2000, we obtain an estimated minimum wage effect of –0.552, which is
very close to what is reported in Baker (2004). This result suggests that there is some sensitivity in the magnitude of
8
Properly capturing the business cycle is a potentially critical issue. An upturn in economic
activity may cause both an increase in average hourly earnings (and hence a decrease in the
minimum wage ratio) and an increase in teenage employment. Failure to account fully for the
business cycle could therefore lead to spurious negative correlation between employment and the
minimum wage ratio. In the baseline regression, the business cycle is captured both through the
prime-aged male unemployment rate, and through the level of real GDP. However, the existence
of part-time workers wanting full-time work (but who are counted as fully employed), and
discouraged workers dropping out of the labour force, could lead the unemployment rate to
underestimate the business cycle. With regard to the level of real GDP, its coefficient will reflect
divergences from trend, since trend (and trend squared) are included as separate regressors. But
trend (and trend squared) would measure only the common trend for all provinces. Therefore, if
each province has a different trend, as is the case in Canada, this variable will not well capture
the business cycle that each province experiences. Moreover, simply including province-specific
trend and trend squared terms (as do Neumark and Wascher, 2004) would not be an adequate
solution. We know that there are significant differences in industrial structure across provinces
that translate into differences in provincial labour intensity and input/output ratios. So, a given
percentage reduction in provincial GDP would not produce the same percentage reduction in
employment in each province. Hence, real-GDP may not well measure the differential
employment effects of the business cycle in each province. For these reasons we also include
several other measures of the business cycle: first, the prime-aged male employment rate; second,
Y-gapi, which is an estimate of each province’s output gap [(Y – Yf)/Yf], where Yf is estimated
by separately regressing provincial real-GDP on trend and trend squared and taking the predicted
value; and third, the real interest rate. This last term is not only highly correlated with the
the minimum wage effect to the choice of time period from which the data are drawn, a point we return to later.
9
business cycle (see Smithin, 1996), but may also measure real shocks that have province specific
effects (see Myatt, 1992).
As before, the top panel of Table 3 parameterizes time-effects as a quadratic in time,
while the lower panel uses a set of year dummies. For brevity, in the lower panel we only report
the results for the minimum wage coefficient. As can be seen in column (1) Table 3, the EI
subsidy rate is a significant determinant of teenage employment, although union density is not.
Contrary to expectations, the inclusion of these variables has little effect on the minimum wage
coefficient. In contrast, including additional business cycle measures (the prime-aged male
employment rate, Y-gap, and the real interest rate) reduces the magnitude of the minimum wage
elasticity to –0.083, and causes it to lose statistical significance. Furthermore, both the primeaged male employment rate and Y-gap are correctly signed and significant. This suggests that the
minimum wage coefficients reported in the top panel of Table 2 are partly reflecting cyclical
effects that are not captured by the standard business-cycle controls. When we add all the
additional variables, shown in column (3), the minimum wage elasticity returns to being
statistically significant at the 10 percent level, though it is still somewhat small (-0.099).
Turning to the lower panel of Table 3, we see that the introduction of year dummies
somewhat restores the minimum wage effect. In particular, column (2) shows that the minimum
wage coefficient is once again statistically significant at the 5 percent level when the new
business cycle variables are combined with year dummies. Finally, combining year dummies
with the full set of new control variables (column 3) causes the minimum wage elasticity to
“bounce back” to close to its original level (–0.235).
In summary, our analysis suggests that the base specification is not robust to additional
measures of the business cycle when time effects are modeled using a quadratic in time.
10
However, when we model time effects using a full set of year dummy variables, the base
specification is robust to additional controls. This suggests that the additional variables are not
necessary provided we avoid modeling time effects using the parsimonious quadratic in time. In
brief, when using a full set of year dummies to model time effects, our results (up to this point)
are generally consistent with the extant literature on minimum wages in Canada.
III.
Stability across time and space
Implicit in the results obtained thus far is the assumption that the underlying relationship
between the explanatory variables and the dependent variable is stable across provinces and time
periods. Unobserved provincial variations (the σi from equation 2) are assumed to be time
invariant and are controlled with a set of province dummy variables. Unobserved variations over
time (the γt from equation 2) are assumed to be constant across provinces and are controlled by
using some parameterization of time (either a quadratic or a set of year dummy variables.)
Alternatively put, all provinces are assumed to have the same time profile of unobserved shocks,
albeit with different intercepts (coming from the province-specific dummies), and the same
functional relationship between the explanatory variables and teenage employment. Violation of
this assumed structure can result in inconsistent and misleading estimates, but is rarely subject to
any sort of statistical testing. In this section we examine the empirical validity of this assumed
structure.
Stability through time:
To investigate stability over time, we divide the data into four sub-periods of seven years
each: 1976-82, 1983-89, 1990-96, and 1997-02.8 These sub-periods are short enough to allow
8
Because we have 27 years in total, the last sub-period has only six years.
11
investigation of possible structural change, but are long enough both to capture the low-frequency
effects emphasized by BBS, and offer enough degrees of freedom. The results are reported in
Table 4.
Comparing the upper and lower parts of Table 4, it is apparent that the results are not
affected by the choice of quadratic in time versus fixed time effects. However, comparing
columns we see that the coefficient estimates vary markedly across time periods. Focusing on the
effects of minimum wages, the coefficient is positive (though insignificant) for every sub-period
except 1990-96. Indeed, the 1990-96 period seems to be exceptional. It is only during this period
that the minimum wage coefficient is large, negative and highly significant. Perhaps not
surprisingly, coefficient estimates for teenage population and real GDP are similarly sensitive to
the particular sub-period, although the coefficient on the prime-age male unemployment rate is
consistently significantly negative. A test of constant coefficient estimates across the sub-periods
is strongly rejected (p-value = 0.0000).
The general conclusion from Table 4 is that the assumption that the determinants of
teenage employment are stable over time is not valid. Whether this is due to the presence of timevarying unobserved provincial effects or parameter instability, the main point is that the use of
different time periods can give rise to markedly different inferences about the relationship
between minimum wages and teenage employment. This is an important caveat even for those
minimum wage studies that use micro-level data: in particular, estimated results based on microdata from the early to mid-1990s may not necessarily generalize to other years.
In order to shed more light on the time instability of the parameter estimates, we estimate
the base specification (using fixed year effects) across a rolling seven-year window, and plot the
estimated minimum wage coefficient at the midpoint of each seven-year period. This is shown in
12
Figure 1, along with a plot of the prime-aged male unemployment rate. The results are striking.
The estimates of the minimum wage coefficient move inversely with the unemployment rate,
implying that the estimated minimum wage effect is at its most negative when the unemployment
rate is highest.9 What could explain this result?
We pointed out in Table 3 that the relationship between minimum wages and teenage
employment is sensitive to the business cycle. Thus, one possible explanation is that the business
cycle is not being properly controlled. However, we find that including the prime-aged male
employment to population ratio has no effect on the pattern depicted in Figure 1. Nor is this
pattern affected by including an interaction term between minimum wages and the
unemployment rate, nor alternatively, the employment rate. (Both variables are always
insignificant and have no effect on the other coefficients.) It appears that the inverse relationship
between the minimum wage coefficient and the unemployment rate is not a statistical artifact, but
rather is reflecting something real about the economy.
Another possibility is that minimum wages are most binding when unemployment is high.
To investigate this idea, Figures 2 and 3 presents the wage distribution for teenagers in 1995 – a
year of relatively high unemployment (9.3 percent) – and in the year 2000 – a year of relatively
low unemployment (6.4 percent). The dotted line indicates the minimum wage, and it is evident
that for most provinces there is a prominent spike at this wage rate or within 25 cents of it.
Comparing Figure 2 and 3 shows no evidence that the minimum wage is any less binding in the
low unemployment year. Indeed, it appears more binding in certain provinces (such as British
Columbia) in the year 2000 than in 1995.
We explore this issue further in Figures 4A and 4B, which present the proportion of
teenagers who earn less than the minimum wage plus 25 cents, between 1993 and 2001. Since the
9
A similar pattern is evident if we plot minimum wage elasticities instead of coefficient estimates.
13
data presented in these figures show no obvious or clear pattern, we used OLS to test for a
relationship between the proportion of teenagers earning less than the minimum wage (plus 25
cents) and the business cycle, where the latter is measured using the prime-aged male
unemployment rate. Table 5 contains the results of various permutations: with or without
provincial dummy variables, a time trend, or fixed year effects. In none of the seven equations is
the unemployment rate significant; nor does the dependent variable exhibit any significant time
trend.
While the evidence presented in Figures 2-4 and Table 5 is only partial, it does not seem
to support the view that minimum wages are more binding in recession than in boom years. Thus,
there is no obvious alternative explanation for the sensitivity of the minimum wage coefficient
across sub-periods – apart from non-robustness across time. It appears the effect is peculiarly
centered on the early to mid-1990s.
Stability across space:
Next, we focus on the cross-sectional dimension. Specifically, we examine the validity of
the assumptions that unobserved differences in the determinants of teenage employment across
provinces can be captured by a set of time-invariant provincial fixed-effects, and that the
coefficients in equation (6a) and (6b) are stable across provinces.
Table 6 presents estimates of the base specification using a set of year dummy variables
(fixed time effects) for various sub-samples of provinces. Column (1) of Table 6 is based on all
nine provinces (PEI, Nunavut, and the Territories are excluded) and is the same as the lower
panel of column (2) in Table 2. In the second column we exclude data from BC, which results in
a large fall in the size of the coefficient (from –0.31 to –0.14), though it remains significantly
14
negative at the 5 percent level. On the other hand, excluding Ontario (shown in column (3))
causes the coefficient to increase from the base specification. When we exclude both BC and
Ontario (column (4)), the “BC effect” wins out – though the smaller coefficient is still
significantly negative at the 5 percent level. Column (5) shows that a reduction in size and
significance occurs when both BC and Quebec are excluded. Finally, column (6) shows that
when BC, Ontario, and Quebec are all excluded the minimum wage effect becomes
insignificantly different to zero in the remaining 6 provinces.10
One response to this “instability across space” would be to argue that the panel data setup
enhances identification because it exploits variation across provinces, not just across time.
Tossing out a province or two potentially causes a loss of identification if there is not enough
variation across the remaining provinces.
To investigate this possibility, Table 7A presents a decomposition of the variance in
minimum wage rates. Column (1) shows that in the entire data set, the provincial fixed effects
account for about 38 percent of the variation in the minimum wage ratio, the time fixed effects
(the year dummy variables) account for about 41 percent, leaving around 19 percent as a residual
to be explained by the rest of the model. Dropping provinces certainly affects the size of this
residual. And it is true that when British Columbia, Ontario and Quebec are all dropped, the size
of the residual (to be explained by the rest of the model) falls to just over 7 percent. Is this still
enough to ensure identification? Unfortunately, the literature offers no clear guidelines as to how
much variation is “enough”. However, column (4) of Table 7A shows that when we drop only
British Columbia and Ontario the residual variation is also only 7 percent; yet the minimum wage
coefficient is significant in this case. Furthermore, columns (2) and (3) show that the residual to
10
Pooling data from BC, Quebec, and Ontario and estimating the basic specification gives rise to a large negative
and highly significant coefficient estimate on the minimum wage variable (-0.529 with year dummy variables).
15
be explained by the rest of the model is around 15 percent whether either BC or Ontario are
dropped, and in either case the minimum wage coefficient remains significant at the 5 percent
level. Yet, the choice as to which province to drop has a dramatic effect on the size of the
coefficient. Without Ontario, the size of the minimum wage effect for the remaining 8 provinces
is nearly –0.4; whereas, dropping BC, the size of the minimum wage effect for the remaining 8
provinces is only around –0.14.
At this point it is worth backtracking a little, to ask whether the lack of residual variation
in the minimum wage could be responsible for the time instability discussed in the previous
subsection. The data is presented in Table 7B. Columns (1) and (2) show that there are grounds
for concern. In particular, in the first two sub-periods the residual variation in the minimum
wage, not explained by fixed effects, is quite small – only 2.5 percent between 1976-82 and 5.7
percent between 1983-89. In contrast, between 1990 and 1996, the period where the minimum
wage coefficient was large, negative and significant, the residual variation in the minimum wage
is over 9 percent. However, between 1997 and 2002 the residual variation in the minimum wage
is even higher, over 18 percent, and no significant minimum wage effect was found for this
period. Thus, it would appear that lack of identifiable variation in the minimum wage is not
explaining either the non-robustness across time or space.
Returning to the issue of non-robustness across space, we complete our analysis by
estimating the teenage employment equation separately for each of the nine provinces using a
system of seemingly unrelated regressions (SUR).11 Clearly, this throws out all the crossprovince variation, and relies on time series variation for identification. But the point is that this
11
We parameterize time effects by using a quadratic trend term. It is not possible to include year dummy variables
and identify the other variables since the only variation in the variables for a particular province is across time. This
is a generalization of the specification estimated in Neumark and Wacher (2004) who allow a separate quadratic in
time for each country in their pooled country-level panel dataset.
16
method allows us to test the assumptions that the provinces have similar structures and identical
coefficients. The results are reported in Table 8. Looking across the top row of Table 8, it is clear
that there are marked differences in the minimum wage effect across provinces. The estimated
minimum wage coefficient is large, negative, and significant for BC and Newfoundland; positive
and significant for Manitoba, Quebec, and Nova Scotia; and not significant for the other
provinces. This could suggest instability in the estimated relationship between teenage
employment and the explanatory variables across the Canadian provinces – and in particular
instability of the minimum wage effect. The final column of Table 8 tests whether each
explanatory variable has an identical coefficient across the nine provinces. In each case, the null
hypothesis of constant coefficients is strongly rejected, including the hypothesis of a constant
minimum wage effect across the nine provinces; this is rejected with a p-value of 0.0000.
One might think that the results of Table 8 could be used to make sense of those of Table
6 – that is, knowing how the provinces behave individually might help us predict the effect on the
remaining panel data of omitting one or two provinces. But such is not the case. The results of
Table 6 are unstable in unpredictable ways. For example, Table 8 shows us that minimum wages
have their largest negative effect (and the most significant) in British Columbia. But omitting this
province from the panel data set has hardly any effect on the minimum wage coefficient for the
remaining provinces. (It falls marginally from –0.374 to –0.353.) On the other hand, Ontario on
its own has a positive and insignificant minimum wage effect. Yet dropping this province from
the panel data set causes a moderate reduction in the minimum wage coefficient for the remaining
provinces (from –0.374 to –0.296). Even more surprising then is that when both of these
provinces (B.C and Ontario) are dropped from the panel data set, the minimum wage coefficient
for the remaining provinces becomes small (-0.128) and insignificant.
17
It is worth emphasizing that the seemingly unrelated regression model – estimated
imposing constancy of coefficients across provinces – is almost identical statistically to an unweighted pooled provincial panel-data model. This point is brought out in Table 9. Column (1)
shows the results of the SUR regression imposing constant coefficients across the provinces for
all variables except the intercept term. (The non-constant intercept term serves the same role as
the provincial dummy variables in the panel-data model.) Column (2) shows the un-weighted
estimation of the panel data model, while column (3) shows the equivalent panel data model
weighted by provincial population share and is the same as that shown in column (2), Table 2.
The estimated coefficients are very close. The explanation for the difference in coefficients
between columns (1) and (2) is that the constrained SUR model allows more flexibility in the
variance-covariance matrix of the error term. Understanding the similarity between the
constrained SUR model and the panel-data model underscores the importance of the fact that all
the constraints imposed on the SUR model are resoundingly rejected.
V.
Conclusion
In contrast to most other countries, a significant and negative effect of minimum wages on
teenage employment has been consistently found for Canada. The most commonly accepted
explanation for this is that Canada is a “desirable laboratory” for minimum wage research.
However, the typical model estimated in the literature assumes that coefficients (both for
minimum wages and other variables) are constant (both across provinces and over time), and that
all provinces have the same time profile of unobserved shocks, albeit with different intercepts
(coming from the province-specific dummies). Our analysis suggests that this set of assumptions
18
does not hold in practice. In particular, we have shown that the coefficients of the teenage
employment equation are unstable both across time and space.
One response is to argue that in periods and/or provinces in which the minimum wage
effect disappears, identification has been lost – either because the minimum wage is not binding
in certain time periods, or because there is insufficient variation in minimum wages across certain
provinces. We have investigated both of these possibilities and tentatively rejected them. We
have good data on the distribution of wages beginning in the early 1990s, which suggests that the
extent to which minimum wages “bite” has not changed much between 1991 and 2002. In
contrast, the estimated minimum wage coefficient does change from being large, negative and
highly significant in the 1990-96 period, to being small, positive and insignificant in the 1997-02
period. With regard to the instability across provinces, it is true that dropping certain provinces
does reduce the amount of cross-province residual variation in the minimum wage ratio not
explained by fixed effects. But it is not clear whether the remaining variation is “enough” without
guidelines as to what “enough” might mean. Moreover, when we exclude both BC and Ontario a
residual variation in the minimum wage of 7.2 percent is enough to find a significant minimum
wage effect at the 5 percent level. But when we exclude BC, Ontario and Quebec we have the
same amount of residual variation in minimum wages (not explained by fixed effects), but can
find no significant minimum wage effect.
Finally, when we test for constancy of coefficients across provinces, these restrictions are
resoundingly rejected. The literature seems to regard these restrictions as necessary for
identification; but rather than regarding them as necessary identifying restrictions, we argue they
should be regarded as rejected constraints.
19
The issue hinges on how heterogeneous the provinces are, and how this heterogeneity is
handled statistically. The literature recognizes this heterogeneity but attempts to control for it
using fixed province effects and fixed time effects. We suggest that such an approach is
inadequate. It is interesting that in other contexts, fixed effects are also being criticized. For
example, in reviewing the literature that attempts to account empirically for cross-country
differences in growth, Wacziarg (2002, page 915) writes: “To conclude on this point, the use of
fixed effects is neither conceptually nor economically an appealing way to address the issue of
technological heterogeneity.” We feel the same is true for attempts to control for structural
heterogeneity across Canadian provinces.
Since we reject the assumptions underpinning the provincial time-series panel-data
models, our analysis calls into question the validity of the negative minimum-wage effect that is
found in most of the Canadian literature. Moreover, it calls into question results based not only
on the current generation of pooled provincial panel-data models, but also results based on those
studies using individual micro-level data that embody similar overly restrictive assumptions on
time/province effects and coefficient stability.
Up to this point, the literature has seen the use of panel data sets as offering the best
chance to pin down the effects of minimum wages. That may still be true. But we are suggesting
that the assumptions underlying the current generation of models using this approach are rarely
tested, and may be rejected in practice. If we are right, what is the best way forward? The current
literature focuses on a standard reduced-form regression emphasizing the same four control
variables – the minimum wage ratio, real-GDP, prime-aged male unemployment rate, and the
teenage population share. Perhaps it is time for a change of focus. But instead of replacing the
standard equation with ‘fishing expeditions’ for additional controls, more effort might be put into
20
deriving the theoretically appropriate reduced-form equation from a properly specified model –
and then testing all its implications.
For example, if increases in minimum wages cause decreases in the employment of
teenage or unskilled workers, we need to know what this labor is replaced with. Is it replaced
with skilled (or adult) workers? If so, then there should be positive employment effects for these
workers – yet this is never shown. Are they replaced with physical capital? Then we should be
including measures of the rental cost of capital in the regressions, and presumably there should be
indirect job gains in the capital goods sector. Or, if the increase in the minimum wage causes
such a large negative scale effect that it dominates these substitution effects, there should be
testable predictions about its effects on industry mix. Similarly, if the jobs are lost to overseas
workers there should again be testable predictions about its effect on industry mix, and
corroborating evidence in the sectors concerned.
This discussion implies that a properly specified model should not be an economy-wide
generalization of a partial equilibrium model. There are two important points to make in this
regard. First, it is worth noting that stability normally requires (in two-sector macro models) that
the capital goods sector be more labour intensive than the consumer goods sector (see Scarth
(1983)), so the net result of replacing teenage labour with capital might be more jobs. Second, our
rolling five-year regressions indicate that minimum wages may only have negative employment
effects in a recession, when unemployment is high; and, Fortin and Lemieux (2004) argue that
minimum wages are a useful redistributive tool. If so, reducing minimum wages may adversely
affect one of the economy’s automatic stabilizers, making the economy more vulnerable to
unemployment, and more (rather than less) susceptible to adverse minimum wage effects. These
macroeconomic general-equilibrium effects should not be overlooked.
21
The bottom line may well be, that to resolve the minimum wage debate, we need to be
able to explain (and test) the mechanisms through which minimum wages are supposed to have
their effects in a wider, more comprehensive framework.
22
Data Appendix:
Our full dataset spans the years 1976-2002 and includes all Canadian provinces except Prince
Edward Island and Nunavut.
The minimum wage ratio:
Minimum wages for Canadian adult workers since 1965 are to be obtained from the Human
Resources Development Canada website: http://labour-travail.hrdcdrhc.gc.ca/psait_spila/lmnec_eslc/eslc/salaire_minwage/report2/report2_e.cfm
This was deflated by average hourly earnings (including overtime) of workers paid by the hour,
in manufacturing industries.
$
The 1983 to 2000 data was obtained from Cansim II, Table 2810004, series numbers (for
B.C., Alberta, Saskatchewan, Manitoba, Ontario, Quebec, New Brunswick, Nova Scotia
and Newfoundland respectively) are as follows: V312117, V305588, V299343, V293744,
V287442, V279936, V273156, V268142, V259846.
$
The above series are the same as that used by Baker, Benjamin and Stanger (1999). They
obtained data prior to 1983 from special tabulations performed by Stats Canada. We are
grateful to them for sharing their data with us.
$
Since the series in Table 281004 were discontinued in 2000, we updated our series using
Table 2810030. The series used (from B.C. to Newfoundland) were: V1807323,
V1807171, V1807060, V1806904, V1806717, V1806534, V1806455, V1806369,
V1806255.
Employment, unemployment, and population data:
Data on employment, population, and unemployment were all obtained from Table Number
2820001. Series numbers (for B.C., Alberta, Saskatchewan, Manitoba, Ontario, Quebec, New
Brunswick, Nova Scotia and Newfoundland respectively) are as follows:
$
Teenage population, both sexes, 15 to 19 years: V2097397, V2096717, V2096087,
V2095457, V2094827, V2094197, V2093567, V2092937, V2091668.
$
Total population, both sexes, 15 to 64 years: V2097396, V2096716, V2096086,
V2095456, V2094826, V2094196, V2093566, V2092936, V2091667.
$
Teenaged employment, both sexes, 15 to 19 years: V2097439, V2096759, V2096129,
V2095499, V2094869, V2094239, V2093609, V2092979, V2091710.
$
Prime-aged male employment rate (employed/population), 25-54 years: V2097793,
V2097113, V2096483, V2095853, V2095223, V2094593, V2093963, V2093333,
V2092064.
$
Prime-aged male unemployment rate, 25 to 54 years (unemployed/labour force):
V2097751, V2097071, V2096441, V2095811, V2095181, V2094551, V2093921,
V2093291, V2092022.
$
Aggregate unemployment rate, 15 years and over (used to construct EI generosity series):
V2097536, V2096856, V2096226, V2095596, V2094966, V2094336, V2093706,
V2093076, V2091807.
Real GDP:
Statistics Canada has only published provincial real GDP data since 1981. One option, the one
23
chosen by Baker, Benjamin and Stanger (1999), is to deflate provincial nominal GDP by the
provincial CPI’s.
The option we chose was to use Statistics Canada’s official data post-1981, and to use the
Conference Board of Canada’s estimates prior to 1981. We obtained a consistent series by
calculating GDP growth rates from the Conference Board data, and “backcasting” from the 1981
estimate provided by Stats Canada.
The Stats Canada real provincial GDP data is to found in Cansim II, Table 3840002. The series
numbers (from B.C. to Newfoundland) are: V3840347, V3840301, V3840255, V3840209,
V3840163, V3840117, V3840071, V3840025, V3839933.
EI Generosity:
UI/EI program eligibility and generosity dimensions are captured by the 'subsidy rate'. Following
Lemieux and MacLeod (2000), the subsidy rate is calculated as the replacement rate times the
maximum number of benefits available to a minimally qualified claimant divided by the
minimum weeks of employment needed to qualify for UI/EI. UI/EI program parameters are
obtained from the HRDC website: http://www14.hrdc-drhc.gc.ca/ei-ae/ratesc.htm.
Real interest rate:
This was calculated by subtracting provincial inflation rates from the Canada-wide chartered
bank prime interest rate. The prime interest rate was taken from Table 1760041, series V121796.
Series for provincial CPI’s (B.C. to Newfoudland) are: V736960, V736824, V736689, V736553,
V736417, V736281, V736145, V736010, V735741.
Relative Energy Prices:
This is the provincial energy price index deflated by the provincial CPI. The energy price index
comes from Cansim II, Table 3260001, series (from B.C. to Newfoundland): V736963, V736827,
V736692, V736556, V736420, V736284, V736148, V736013, V735744.
Union density:
$
Union density, 1976 to 1995, was taken from the CALURA survey and can be found in
Cansim I, Matrix 03516, series labels (from B.C. to Newfoundland): D135162, 135159,
D135156, D135153, D135150, D135147, D135144, D135141, D135135.
$
Union density, from 1997 to 2003, was calculated using Labour Force Survey data. In
particular, we divided total employees with union coverage (15 years and over) by total
employees (15 years and over). Both sets of numbers came from Cansim II, Table
2820073. The series for union coverage are (from B.C. to Newfoundland): V3075121,
V3075116, V3075111, V3075106, V3075101, V3075096, V3075091, V3075076. The
series for total employees are: V3075066, V3075061, V3075056, V3075051, V3075046,
V3075041, V3075036, V3075031, V3075018.
$
The two series matched up surprisingly well. Data for the missing year was imputed
using interpolation.
$
Movements in the resulting series over the period 1994 to 1999 were checked using data
in the Directory of Labour Organizations in Canada. Again, the two data sets mirrored
each other surprisingly well.
24
Wage Distribution:
The data on the distribution of wages of teenagers, 1993-2001, was obtained from Stats Canada’s
Survey of Labour Income and Dynamics. We used all the available panels: 1993-98, 1996-2001,
and 1999-01 (at time of writing). Stats Canada provides cross sectional weights, which allowed
all the available data to be used for any given year.
25
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Card, David, Katz, Lawrence, and Alan Krueger, “Comment on David Neumark and William
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Campolieti, Michele, Gunderson, M., and Chris Riddell, “Minimum Wage Impacts from a PreSpecified Research Design” mimeograph, University of Toronto, 2004.
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26
Fuller, D., and Doris Geide-Stevenson, “Consensus Among Economists: Revisited”, Journal of
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Research Design” Industrial Relations, 40(1), January 2001, 121-144.
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the Fast-Food Industry in New Jersey and Pennsylvania: Comment.”American Economic Review,
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27
Youth Employment: A Cross-National Analysis”, Industrial and Labor Relations Review, 57,
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Schaafsma, J., and W. Walsh, “Employment and Labour Supply Effects of the Minimum Wage:
Some Pooled Time-Series Estimates from Canadian Provincial Data”, Canadian Journal of
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Economics, 25, 1993, 1517-28.
28
Table 1: Percent Agreement with the proposition: “minimum wages increase
unemployment amongst young and unskilled workers.”
1979*
1990†
2000Θ
Generally Agreed
68%
62.4%
45.6%
Agreed with provisos
22%
19.5%
27.9%
Disagreed
10%
17.5%
26.5%
* Kearl et. al. 1979; † Alston et. al. 1992; Θ Fuller et. al. 2003
29
Table 2: Benchmarking to the Existing Literature
Minimum wage
Unemployment rate
Teenage Population
Real GDP
Trend
Trend-squared
Minimum wage (lagged)
Lagged dependent variable
Minimum wage
elasticity
Province Dummies
Year Dummies
Weighted
Sample size
(1)
1976-93, OLS
Coef.
Std. Error
**
-0.3109
(.092)
-1.8792**
(.077)
0.1075
(.333)
0.4191**
(.114)
**
0.0069
(.003)
-0.0002*
(.000)
(2)
1976-2002, OLS
Coef.
Std. Error
**
-0.3744
(.060)
-1.8392**
(.112)
**
-2.2469
(.400)
-0.0905
(.066)
-0.0037
(.002)
-0.0001
(.000)
(3)
1976-2002, OLS
Coef.
Std. Error
0.1487
(.142)
-1.8085**
(.109)
**
-2.1891
(.433)
-0.0633
(.068)
**
-0.0076
(.003)
0.0000
(.000)
-0.6090**
(.153)
-0.259
-0.326
-0.401
Yes
No
Yes
162
Yes
No
Yes
243
Yes
No
Yes
234
Minimum Wage
Unemployment Rate
Teenage Population
Real GDP
Minimum wage (lagged)
Lagged dependent variable
-0.2993**
-1.6664**
-0.2529
0.4349**
Minimum wage
elasticity
-0.250
-0.268
-0.342
Yes
Yes
Yes
162
Yes
Yes
Yes
243
Yes
Yes
Yes
234
Province Dummies
Year Dummies
Weighted
Sample size
(.088)
(.120)
(.471)
(.106)
-0.3086**
-1.7028**
-1.4885**
-0.1592**
(.051)
(.130)
(.364)
(.046)
0.0761
-1.7003**
-1.5882**
-0.1332**
-0.4694**
(4)
1976-2002, GMM
Coef.
Std. Error
**
-0.2156
(.042)
-1.1133**
(.080)
**
-1.7634
(.203)
-0.0929
(.061)
**
-0.0078
(.001)
0.0001**
(.000)
0.5554**
-0.421
(.036)
No
Yes
225
(.108)
(.124)
(.352)
(.047)
(.115)
-0.1701**
-0.7237**
-1.1458**
-0.1436**
(.040)
(.106)
(.215)
(.054)
0.6010**
-0.371
(.049)
Yes
Yes
225
Note: ** denotes significance at the 5% level and * denotes significance at the 10% level. Regressions are weighted by province and year-specific population.
30
Table 3: Extending the “Base Specification” to Include Additional Controls.
Minimum Wage
Unemployment Rate
Teenage Population
Real GDP
Trend
Trend-squared
Union density
EI subsidy rate
(1)
1976-2002
-0.3962**
(.061)
-1.5219**
(.139)
-2.6402**
(.400)
-0.0034
(.068)
-0.0098**
(.003)
0.0000
(.000)
0.0636
(.099)
-0.0225**
(.006)
0.0003
(.001)
0.0207**
(.003)
0.0023**
(.001)
(3)
1976-2002
-0.1136*
(.061)
1.2470**
(.338)
-2.1317**
(.361)
0.0161
(.062)
-0.0051*
(.003)
0.0000
(.000)
0.0929
(.085)
-0.0204**
(.005)
0.0004
(.001)
0.0202**
(.003)
0.0023**
(.001)
-0.345
Yes
No
Yes
243
-0.083
Yes
No
Yes
243
-0.099
Yes
No
Yes
243
-0.3939**
(.052)
-0.1856**
(.049)
-0.2695**
(.050)
-0.342
Yes
Yes
Yes
243
-0.161
Yes
Yes
Yes
243
-0.235
Yes
Yes
Yes
243
Real interest rate
Employment Rate
Y-gap
Minimum wage elasticity
Province Dummies
Year Dummies
Weighted
Sample size
Minimum Wage
Minimum wage elasticity
Province Dummies
Year Dummies
Weighted
Sample size
(2)
1976-2002
-0.0953
(.061)
1.0219**
(.345)
-1.7659**
(.363)
-0.0651
(.061)
0.0008
(.002)
-0.0001
(.000)
Note: ** denotes significance at the 5% level and * denotes significance at the 10% level. Regressions are
weighted by province and year-specific population.
31
Table 4: Panel data results by 7-year intervals.
Minimum Wage
Unemployment Rate
Teenage Population
Real GDP
Trend
Trend-squared
Provincial Dummies
Year Dummies
Weighted
Sample Size
Minimum Wage
Unemployment Rate
Teenage Population
Real GDP
Provincial Dummies
Year Dummies
Weighted
Sample Size
(1)
1976-82
0.0755
(.12)
-1.6331**
(.155)
1.7466**
(.66)
1.7026**
(.49)
0.0084*
(.004)
0.0009*
(.0005)
(2)
1983-89
0.0259
(.15)
-1.1951**
(.21)
-2.2062**
(.85)
0.3804**
(.14)
-0.0363**
(.013)
0.0018**
(.0005)
(3)
1990-96
-0.9798**
(.12)
-1.5589**
(.18)
1.3290**
(.57)
-1.0361**
(.23)
0.0202
(.019)
-0.0007
(.0005)
(4)
1997-02†
0.0312
(.16)
-1.3314**
(.37)
-4.4083**
(1.17)
0.5263**
(.207)
-0.0425
(.052)
0.0009
(.001)
Yes
No
Yes
63
(5)
1976-82
0.1046
(.119)
-1.1352**
(.285)
1.8503**
(.66)
1.4345**
(.50)
Yes
No
Yes
63
(6)
1983-89
0.0212
(.15)
-1.0972**
(.224)
-2.7060**
(.868)
0.4021**
(.14)
Yes
No
Yes
63
(7)
1990-96
-1.0045**
(.118)
-1.1847**
(.233)
1.3830**
(.547)
-1.0777**
(.22)
Yes
No
Yes
63
(8)
1997-03
-0.0642
(.18)
-1.2047**
(.45)
-4.2911**
(1.22)
0.4131*
(.242)
Yes
Yes
Yes
63
Yes
Yes
Yes
63
Yes
Yes
Yes
63
Yes
Yes
Yes
63
Note: ** denotes significance at the 5% level and * denotes significance at the 10% level. Regressions are
weighted by province and year-specific population.
† Because the period does not divide up evenly into seven-year intervals, the last interval is only six years.
32
Figure 1: Minimum Wage Coefficients From Rolling 7-Year Regressions.
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
0.08
1983
0
-0.2
1982
0.09
1981
0.4
0.2
1980
0.1
1979
0.6
-0.4
-0.6
0.07
-0.8
-1
0.06
-1.2
0.05
Unemployment Rate
estimate
Unemployment Rate
Minimum wage estimates
7-year moving averages
The minimum wage coefficient is plotted in the mid-point of the sample range. The unemployment rate is the
weighted average of the provincial prime-aged (24-54) male unemployment rates. Regressing the minimum
wage coefficient estimate on the unemployment rate of prime-aged males yields a correlation coefficient of –
0.75. (Note that the estimate plotted for the year 2000 reflects the six-year interval 1996-2002.)
33
Figure 2: Did Minimum Wages “Bite” in 1995?
Data source: Survey of labour income and dynamics.
34
Figure 3: Did Minimum Wages “Bite” in 2000?
Data source: Survey of labour income and dynamics.
35
36
Table 5: Does the Unemployment Rate Determine How Much the Minimum Wage “Bites” (1993-01)?
Dependent Variable: the proportion of teenagers who earn less than the minimum wage plus 25 cents.
(1)
(2)
(3)
(4)
(5)
(6)
Unemployment Rate
-27.01
14.5
59.86
64.92
36.07
58.26
(103.3)
(109.9)
(58.7)
(60.1)
(44.98)
(49.15)
Trend
-0.44
0.3183
(.649)
(.627)
Provincial Dummies
Year Dummies
Weighted
Degrees of Freedom
Yes
No
Yes
70
Yes
Yes
Yes
63
No
No
Yes
78
No
Yes
Yes
71
Yes
No
Yes
71
Data source: Aggregate province-level data drawn from successive years of the Survey of labour income and dynamics.
37
No
No
Yes
79
(7)
-0.3128
(.529)
No
No
Yes
79
Table 6: Panel data results by selected provinces, 1976-2002
(1)
All
provinces
-0.3086**
(.051)
-1.7028**
(.130)
-1.4885**
(.364)
-0.1592**
(.046)
(2)
Exclude
BC
-0.1378**
(.070)
-1.8942**
(.166)
-1.6328**
(.388)
-0.2336**
(.052)
Provincial Dummies
Year Dummies
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Weighted
Yes
Yes
Yes
Yes
Yes
Yes
Minimum Wage
Unemployment Rate
Teenage Population
Real GDP
(3)
(4)
(5)
(6)
Exclude Exclude BC, Exclude BC, Exclude BC,
ONT
ONT
PQ
ONT, PQ
-0.3958**
-0.1766**
-0.1434*
-0.0273
(.054)
(.090)
(.079)
(.084)
-1.2299**
-1.4672**
-2.0474**
-1.4989**
(.132)
(.162)
(.168)
(.142)
-2.1831**
-2.7837**
-2.6724**
-1.7606**
(.318)
(.321)
(.439)
(.270)
**
0.1232
-0.0157
-0.1617
-1.1376**
(.120)
(.118)
(.051)
(.134)
234
234
Sample Size
243
225
225
216
Note: ** denotes significance at the 5% level and * denotes significance at the 10% level. Regressions are
weighted by province and year-specific population.
38
Table 7: Decomposition of the Variance in Minimum Wages and Employment
Table 7A: How is the Decomposition Affected by the Analysis Across Space?
Between
Provinces
Between
Years
Residual
Total
Between
Provinces
Between
Years
Residual
Total
Decomposing the Variance in the Minimum Wage Ratio
(1)
(2)
(3)
(4)
(5)
ALL
Exclude Exclude
Exclude
Exclude
PROVINCES
BC
ONT
BC, ONT
BC, PQ
38.4%
35.5%
40.3%
32.5%
21.9%
40.7%
47.9%
43.6%
58.4%
54.1%
(6)
EXCLUDE
BC, ONT. & PQ
29.4%
60.3%
19.6%
15.0%
14.5%
7.2%
22.7%
7.3%
100%
100%
100%
100%
100%
100%
Decomposing the Variance in the Teenage Employment/Population Ratio
ALL
Exclude Exclude
Exclude
Exclude
EXCLUDE
PROVINCES
BC
ONT
BC, ONT
BC, PQ
BC, ONT. & PQ
65.7%
69.3%
75.6%
80.8%
62.4%
89.0%
23.1%
21.3%
14.5%
12.6%
26.6%
6.6%
11.8%
100%
9.8%
100%
10.3%
100%
6.5%
100%
11.5%
100%
4.4%
100%
Table 7B: How is the Decomposition Affected by the Analysis Across Time?
Decomposing the Variance in the Minimum Wage Ratio
(1)
(2)
(3)
(4)
1976-82
1983-89
1990-96
1997-02
Between Provinces
65.2%
93.1%
77.0%
79.5%
Between Years
31.1%
1.2%
14.5%
1.6%
Residual
2.5%
5.7%
9.1%
18.8%
Total
100%
100%
100%
100%
Decomposing the Variance in the Teenage Employment/Population Ratio
1976-82
1983-89
1990-96
1997-02
Between Provinces
90.9%
77.8%
67.1%
76.5%
Between Years
7.1%
19.4%
28.2%
17.6%
Residual
1.8%
2.4%
5.3%
5.4%
Total
100%
100%
100%
100%
39
Table 8: Seemingly unrelated regression results by province, 1976-2002
BC
AB
SK
MN
ON
PQ
-0.6945**
-0.0244
0.1556
0.4077**
0.0133
0.5596**
(.227)
(.121)
(.152)
(.207)
(.145)
(.172)
Unemployment Rate -2.0886** -1.2388** -1.4029**
-0.4696
0.3919
0.0142
(.491)
(.170)
(.257)
(.311)
(.303)
(.362)
Teenage Population -8.7921**
-0.5191
-0.5934
6.0294**
2.1429**
-3.6402**
(1.927)
(.720)
(.439)
(1.198)
(1.037)
(.794)
Real GDP
1.9942
2.2011**
-0.7666
17.5729** 3.2933**
4.1348**
(3.398)
(.934)
(2.192)
(4.055)
(.467)
(1.042)
Trend
-0.0460**
-0.0029
0.0058*
0.0316**
0.0059
-0.0131**
(.012)
(.005)
(.003)
(.008)
(.005)
(.005)
Trend-squared
0.0009**
-0.0003*
-0.0003** -0.0010** -0.0013** -0.0003**
(.000)
(.000)
(.000)
(.000)
(.000)
(.000)
Breusch-Pagan
Test of independent
equations (p-value)
0.0000
Sample Size
243
Note: ** denotes significance at the 5% level and * denotes significance at the 10% level.
Minimum Wage
41
NB
-0.1754
(.219)
-0.5423**
(.224)
3.1692**
(1.175)
42.8587**
(7.713)
0.0030
(.006)
-0.0002
(.000)
NS
0.3383*
(.197)
-1.1337**
(.204)
1.2538
(1.349)
14.1699**
(5.270)
0.0140
(.009)
-0.0005**
(.000)
NF
-0.5997**
(.234)
-0.4985**
(.221)
3.0814
(2.094)
21.2926**
(7.745)
-0.0114*
(.006)
0.0005**
(.000)
Test of
equal
coefficients
p-value
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
Table 9: Constrained SUR compared with OLS estimation of a Pooled
Provincial Panel Data Set, 1976-2002
(1)
SUR
-0.2833**
(.035)
-1.6037**
(.083)
-2.2981**
(.205)
-0.1706**
(.039)
-0.0081**
(.002)
-0.0001*
(.000)
(2)
OLS
-0.3244**
(.062)
-1.7481**
(.110)
-2.4940**
(.293)
-0.1296
(.079)
-0.0081**
(.002)
-0.0001*
(.000)
(3)
OLS
-0.3744**
(.060)
-1.8392**
(.112)
-2.2469**
(.400)
-0.0905
(.066)
-0.0037*
(.002)
-0.0001*
(.000)
Province Dummies
Year Dummies
Weighted by population share
Yes
No
No
Yes
No
No
Yes
No
Yes
Sample size
243
243
243
Minimum wage
Unemployment rate
Teenage Population
Real GDP
Trend
Trend-squared
Note: ** denotes significance at the 5% level and * denotes significance at the 10% level.
43
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