Regression Analysis of Youth Labour
Market Variables
A weakness of the approach taken above is that it fails to control
systematically for all the factors which might explain the regional
differences in youth labour market performance. That is, the analysis
made above may be misleading because it does not allow us to
control for all the relevant variables which might account for the
behaviour of key youth labour market statistics. In order to partially
correct for other influences which might affect these variables, we
estimated "reduced form" regression models of the youth
unemployment rate, the youth employment rate, and the youth labour
force participation rate, controlling for general economic conditions,
provincial real minimum wage rates, and province specific effects. In
order to make our data set as large as possible, we used pooled time
series-cross sectional data for each of the 10 provinces over the
sample period from 1976 to 1996.
The idea behind regression analysis is to estimate the impact of a
number of explanatory variables on a particular variable of interest.
What makes empirical economics difficult is that we cannot observe
directly the process which generates our data. Another confounding
factor is that there are generally several variables which might affect
the behaviour of a particular variable of interest. For instance, the
unemployment rate among youth in Canada may be related in some
way to the adult unemployment rate. However, other factors in
addition to the adult unemployment rate may also influence the youth
unemployment rate. Limiting our analysis to the adult and youth
unemployment rate may give us misleading inferences because we
have not "controlled" for the effect that other variables have on the
youth unemployment rate. Hence, the purpose of regression analysis
is to estimate the impacts of particular variables on the variable of
interest, while controlling for the fact that other variables may also
affect that variable. Regression analysis therefore allows us to
determine the direction and magnitude by which one variable affects
another, holding all other variables constant.
A "reduced form" regression model is sometimes called a "nonstructural" regression model. The distinction between structural and
non-structural (or reduced form) regression models is very important.
When we estimate a reduced form model, we are simply trying to
determine the direction of effect a number of independent variables
have on a particular dependent variable. In contrast, the motivation
behind a structural model is to uncover particular structural
parameters (or economic "primitives") which govern economic
behaviour. Structural models are based on a specific theoretical
model and hence, provide the most direct way of testing a particular
economic theory. In contrast, reduced form models are, in
themselves, atheoretical. While the particular choice of explanatory
variables to include in a reduced form may be governed by economic
theory, no effort is made to uncover the structural parameters which
are buried within the estimated reduced form coefficients. A
weakness of this approach is that it is not invariant to shifts in policy
regime. That is, because the structural parameters which generate
the data are not directly estimated, the reduced form coefficients may
be unstable when policy regimes change. Because of this inherent
weakness in reduced form models, caution should be exercised when
making specific policy recommendations on the basis of reduced form
coefficient estimates.
However, there are some advantages to using the reduced form
method as opposed to the structural method. One advantage is that,
under some assumptions, it still enables us to answer some
questions, such as how one variable affects another, while
maintaining a reasonably agnostic approach as to how the data is
generated. Another advantage is that reduced form regression
models are easier to construct and estimate than structural models
(Davidson and MacKinnon 1993). In order to estimate a structural
econometric model, one must explicitly derive an economic model
and try to identify the structural parameters. Since our interest is
simply to discover how some variables affect youth unemployment,
employment and labour force participation rates, we will limit our
attention to the reduced form approach.
Table 5 presents coefficient estimates from a reduced form
regression of provincial youth unemployment rates on provincial adult
unemployment rates (UN), the real provincial minimum wage rate
(W), and cross sectional dummies representing the 10 provinces. We
incorporate adult unemployment rates in order to control for the effect
of provincial economic conditions on the youth unemployment rate.
The real provincial minimum wage rate is included because economic
theory suggests that high real minimum wages should reduce the
employment prospects of relatively unskilled workers. Since most
empirical studies have found that minimum wages have a statistically
significant impact on youth labour markets, it is important to control
for this factor. Finally, cross sectional dummy variables are included
for each provinces. These dummy variables essentially capture any
province-specific difference which cannot be accounted for by
minimum wages or general macroeconomic conditions. Ideally, we
would like to be more explicit about these province-specific variables
(which might include rates of unionization, welfare benefit rates,
employment insurance rates, demographic variables) and estimate
their impacts individually. However, because of data limitations, we
were restricted to using dummy variables.
Table 5: Reduced Form Model of the Youth Unemployment Rate, Estimated by
Ordinary Least Squares
Variable Name
Coefficient Estimate
Standard Error
T-Ratio
UN
1.2356
0.07284
16.96
W
0.3453
0.1015
3.403
BC
4.1229
1.022
4.034
AB
2.5232
0.8335
3.027
SK
4.0407
0.7873
5.133
MB
3.7084
0.8439
4.394
ON
3.9029
0.9539
4.097
PQ
4.0303
1.177
3.423
NB
5.9347
1.135
5.277
NS
6.1129
1.111
5.503
PE
3.0238
1.276
2.369
NF
8.2672
1.406
6.897
R-Squared Adjusted = 0.9050
Note: Standard errors were estimated using White’s (1980) heteroskedasticity
consistent covariance matrix estimator (HCCME).
Calculations: The Fraser Institute.
The results are basically in accord with our prior beliefs about the
behaviour of youth unemployment rates. The high adjusted Rsquared statistic (0.90) suggests that our reduced form model can
explain most of the variance in youth unemployment rates. Increases
in adult unemployment rates (declines in general economic activity)
have a positive and statistically significant effect on youth
unemployment rates (i.e., as adult unemployment rates rise, so do
youth rates). Similarly, increases in real provincial minimum wage
rates also have a statistically significant and positive impact on youth
unemployment rates, albeit by a fairly small amount (i.e., increases in
provincial minimum wages raise youth unemployment rates).
Provincial dummy variables are statistically significant and vary
considerably in magnitude. Hence, it appears that province-specific
factors play a very strong role in determining a province’s
unemployment rate. This is not altogether surprising, since many
policy variables which have a large impact on labour supply and
labour demand decisions (such as welfare rates, payroll taxes,
unemployment insurance benefit rates) differ across provinces. In
accord with our findings from figure 6, the dummy variable for Alberta
is smaller than every other province and the dummy variable for
Newfoundland is higher than every other province. In other words, if
all provinces had the same minimum wage and the same adult
unemployment rate, Alberta would have the lowest youth
unemployment rate and Newfoundland would have the highest.
Table 6 presents coefficient estimates from a reduced form
regression of the youth employment rate on the adult unemployment
rate, the real minimum wage, and provincial dummy variables. Again,
the results are in accord with our expectations. The adult
unemployment rate has a negative impact on youth employment
rates (i.e. the proportion of youth who are employed falls when
general economic conditions decline). The impact of minimum wages
on youth employment rates is also negative and statistically
significant. Also, dummy variables differ significantly across
provinces. Alberta’s provincial dummy is highest while
Newfoundland’s is lowest. In fact, provincial dummy variables appear
to become smaller as one moves farther east. Assuming that all
provinces have identical adult unemployment rates and identical
minimum wages, our estimates suggest that Alberta would have the
highest youth employment rate while the Atlantic provinces would
have the lowest. The high R-squared statistic (0.92) shows that our
independent variables "explain" the bulk of the variation in the youth
employment rate.
Table 6: Reduced Form Model of the Youth Employment Rate
(estimated using ordinary least squares)
Variable Name
Coefficient
Standard Error
T-Ratio
UN
-1.0483
0.1099
-9.561
W
-0.8005
0.1802
-4.442
BC
71.192
1.710
41.64
AB
73.612
1.441
51.07
SK
68.826
1.370
50.23
MB
71.801
1.408
51.00
ON
70.741
1.638
43.18
PQ
65.241
1.942
33.60
NB
60.349
1.805
33.75
NS
63.349
1.760
36.00
PE
68.034
1.971
34.53
NF
54.007
2.080
25.89
R-Squared Adjusted = 0.9192
Standard errors were estimated using White’s (1980) HCCME.
Calculations: The Fraser Institute.
Finally, Table 7 displays coefficient estimates from our reduced form
model of the youth labour force participation rate. In this case, the
coefficient estimates are slightly more difficult to interpret. As one
might expect, the adult unemployment rate is negatively related to the
youth participation rate: the youth labour force shrinks slightly when
general economic conditions decline. Furthermore, the dummy
variables vary considerably across provinces and decline as one
moves eastward. Interestingly, the minimum wage variable is
negatively related to the labour force participation rate. This is
contrary to what standard economic theory would predict: that
increases in wage rates should result in increases in labour supply.
Table 7: Reduced Form Model of the Youth Participation Rate
(estimated using ordinary least squares)
Variable Name
Coefficient
Standard Error
T-Ratio
UN
-0.17555
0.08702
-2.017
W
-0.74223
0.1361
-5.456
BC
74.862
1.347
55.58
AB
76.360
1.143
66.81
SK
72.245
1.138
63.81
MB
75.325
1.115
67.56
ON
74.175
1.255
59.09
PQ
67.503
1.499
45.03
NB
63.442
1.411
44.98
NS
66.802
1.373
49.67
PE
69.901
1.511
46.27
NF
67.633
1.784
38.68
R-Squared Adjusted = 0.8014
As before, standard errors were computed using White’s (1980) HCCME.
Calculations: The Fraser Institute.
The failure of this particular model to achieve results fully consistent
with economic theory is not altogether surprising, however. This is
because the participation rate equation we estimated is not, strictly
speaking, a labour supply equation since we have made no effort to
separately identify labour supply and labour demand shocks. That is,
we have made no effort to solve the "identification problem" which is
so pervasive in applied econometrics. The reason that youth labour
force participation rates appear to be negatively related to the
minimum wage is likely due to the fact that increases in the minimum
wage rate have a stronger effect on labour demand than on labour
supply. That is, when the minimum wage rises, it reduces the
demand for workers and, because fewer youth can now find work,
some youth withdraw from the labour force (Rottemburg 1981). Since
we have not separately identified labour demand and labour supply,
the coefficient estimate on the minimum wage rate in our reduced
form model will likely be inaccurate.
Notwithstanding the weaknesses outlined above, the general
conclusion we can draw from this section are as follows. Provincial
economic performance is an important determinant of youth
unemployment and employment rates. Minimum wages have a small
negative effect on the employment prospects for young Canadians.
Finally, province-specific factors are very important determinants of
youth labour market variables. Controlling for differences in minimum
wages and provincial economic performance, youth unemployment is
higher in the Maritimes than in either central or western Canada.
Hence, youth unemployment is a fairly regional phenomenon in the
Canadian context.