# 7 Estimation results

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The *ŷ*_{it}'s obtained from
the first stage estimation regression described in the previous
section can be used to estimate parameters of a more flexible model
discussed in Section 4, using a generalized method of moments (GMM)
minimum distance estimator in (13).

We first consider three models with common *σ*^{2}_{α},
σ^{2}* _{β}*,

*σ*,

_{α β}*σ*and

_{α γ}*σ*for all cohorts. This specification is almost identical to the specification in Baker and Solon (2003) but with a different set of explanatory variables. Instead of 'potential experience' used in most earnings inequality and earnings instability studies, the set of explanatory variables is chosen to be more consistent with the context of immigrant studies. The total potential experience is divided into 'Canadian experience' (also the age of the cohort) and 'potential foreign experience,' simply defined as the age at arrival minus 25.

_{βγ}Table 4 shows the estimation results for two models using
equal-weighted and sample-weighted GMM estimators. In the first
model, *var*(*v _{it}*) is a quartic function
of

*t*; in the second model,

*var*(

*v*) is also allowed to depend on potential foreign experience. For identification, the first-year factor loadings are normalized to 1 (that is,

_{it}*p*

_{1983}=1 and λ

_{1984}=1).

Consider first the coefficients related to the permanent
variance component, which include *σ*^{2}_{α},σ^{2}_{β},σ^{2}_{γ},σ_{αβ},σ
_{βγ},σ _{αγ},σ
_{r} 2 and *p _{t}*. The first
parameter,

*σ*

^{2}

*, reflects the intercept heterogeneity in (10) and is assumed to be common for all cohorts. Given the*

_{α}*p*

_{1983}=1 normalization, it also represents the 1983 permanent variance component for immigrants from the 1980-to-1982 arrival cohort who had no potential foreign experience (

*t*and

*Z*equal zero and

*p*=1 in [11]). The estimates of

_{t}*σ*

^{2}

*,*

_{α}*σ*

^{2}

*and*

_{β},σ_{αβ}*σ*

^{2}

*are significant at the 95% level in all three models. Consistent with previous studies on earnings inequality, the estimates of σ*

_{r}_{αβ}are significantly negative. In the immigrant context this trade-off between entry earnings and subsequent earnings growth is quite intuitive: those whose entry wages are higher may expect lower earnings growth rates. The estimate of the variance of the random walk component is 0.010 to 0.011 in all models.

Arriving in a new country at an older age may affect the
economic progress of immigrants in more ways than one. The
estimates of σαγ are positive and significant in
all models, meaning that arrival age is positively correlated with
entry earnings. However, the estimates of
*σ _{αγ}* are negative and
significant: the earnings of those who arrive at an older age are
likely to grow at a slower pace than the earnings of those who
arrive at a younger age. The direct effect of the arrival age
heterogeneity on earnings variance appears to be weak. In both
models, the estimates of

*σ*are very small and not significant at the 95% level.

^{2}_{γ}The profile of yearly factor loadings *p _{t}*
gives us some idea about the changes in the persistent variance
component of immigrants' earnings during the 1983-to-2004
period. All models show declining yearly effects during the 1980s,
rising sharply during the recession of the early 1990s. The
results, based on equally-weighted minimum distance estimators,
suggest a substantial decline in inequality in the late 1990s; the
results based on sample-weighted estimators show a much smaller
decline in the late 1990s and subsequent rise in earning inequality
at the beginning of the 2000s.

Figures 1-1 and 1-2 underscore the main problem with the
previous analysis: the three starting points of the profile, for
instance, are estimated only for those immigrants who arrived in
Canada from 1980 to 1982, and had just entered the labour market.
The last three points, on the other hand, are estimated on the mix
of all arrival cohorts in the sample: those who arrived recently as
well as those who had lived in Canada for a considerable period of
time. Hence, although it appears that the early 1980s were years
with high levels of earnings inequality, compared with the mid- and
late 1990s, this result is clearly related to the fact that this
portion of the profile is estimated on cohorts that had arrived
just prior to this period. Therefore, given the nature of the
sample, Figures 1-1 and 1-2 provide a somewhat misleading picture
of immigrant earnings inequality dynamics. An alternative is to
focus on cohort-specific profiles by considering a more flexible
model with cohort-specific *σ
^{2}_{α},σ
^{2}_{β},σ_{αβ},σ_{
αγ}* and

*σ*.

_{βγ}Before we consider a more flexible specification that allows for
cohort-specific parameters in the permanent variance component, let
us examine the parameters related to the transitory variance
component. This variance component is determined by the
'initial variances'
σ^{2}_{ε0}, factor loadings
*λ*_{2}, parameters *g*_{0}*, g*_{1}*, g*_{2}*,
g*_{3} and *g*_{4}, and parameter
*m* in the second model. By allowing cohort specific initial
variances, we are effectively separating cohort effects captured by
*σ ^{2}_{ε0}* from yearly
effects captured by

*λ*

_{t}.

The initial variances capture the earnings instability of
immigrants in each arrival cohort in the first post-arrival year,
that is, 1983 for the 1980-to-1982 cohort, 1986 for the
1983-to-1985 cohort, and so on. More recent cohorts appear to have
much larger initial variances than earlier cohorts; in fact, the
estimates of the
*σ ^{2}_{ε}*

_{2001}are about twice as large as the estimates of

*σ*

^{2}

_{ε1983}.

The estimate of the autoregressive parameter is around 0.46 to
0.47 in all models, which is slightly lower than the parameter
estimate reported by Baker and Solon (2003) and Haider (2001) for
all workers. The estimates of *g*_{0} and
*g*_{2} are positive and significant in all models;
the estimates of *g*_{1} and *g*_{3}
are negative and significant. The estimates of
*g*_{4} are positive and not significant. In the
second model, the estimates of *m* are negative for both
equally weighted (EW) and sample weighted (SW) estimators.

The shape of the *λ*_{t} profile
appears highly pro-cyclical ( *λ*_{1984} is 1
for identification), much more so than the factor loading profile
of the persistent variance component. The profile peaks in 1992 (
*λ*_{1992} is about 1.53 for EW models and
1.51 and 1.52 for SW models);
*λ*_{t} declines from 1992 to 1998
and rises in from 1999 to 2004. The
*λ*_{t} profile, however, does not
tell the whole story of immigrant earnings instability. As initial
variances that determine the starting point of each cohort's
profile vary considerably, it is clear that cohort-specific
profiles will be different.

We now turn to the models with a more flexible specification for the permanent variance component. Just as in the models above, where we assumed cohort-specific initial variances, we can also consider a model with cohort-specific variances and covariances in the permanent variance component, as discussed in Section 4. The estimation results based on the full model using EW and SW estimators are presented in Appendix B, Table B.2.

Table 5 shows the permanent and transitory variance component
profiles computed for a hypothetical immigrant from each arrival
cohort with five years of potential foreign experience (
*Z _{cji}*=5) using the SW parameter estimates in
Appendix B, Table B.2. There seems to be considerable evidence of
cohort effects in earnings inequality, which is consistent with the
descriptive results that show the presence of cohort effects and
higher levels of earnings inequality for more recent cohorts.
Compared with the earnings inequality (permanent component)
profiles of the pre-1992 cohorts, the earnings inequality levels of
the post-1992 cohorts are substantially higher in the first year
after arrival and they remain higher in the next several years
during which these cohorts are observed. The inequality levels of
all pre-1992 cohorts rose in 1991 and 1992 and then declined during
the 1993-to-1995 period. For all immigrants in the sample, with the
exception of the 1980-to-1982 and 1998-to-2000 arrival cohorts, the
permanent variance was rising during the first four years of the
current decade. Unlike the earlier cohorts, the earnings inequality
of recent cohorts appears to be rising slowly but steadily after
declining during the first post-arrival years.

The earnings instability profiles can also be computed for each
cohort (second column). Most profiles show that earnings
instability is particularly high among immigrants just entering the
labour market but it falls sharply during the subsequent two or
three years. As in previous models, the instability profiles are
highly pro-cyclical. The 1989-to-1991 cohort, which consists of
immigrants who arrived right before or during the recession of the
early 1990s, has the highest initial transitory variance (0.63);
the 1986-to-1988 cohort has the lowest (0.33). For all cohorts,
transitory variance declines sharply in the first two to three
years after entering the labour market (a notable exception is the
1986-to-1988 cohort, which entered the labour market right before
the recession). The 1980-to-1982 and 1983-to-1985 cohorts, observed
for the longest period of time, show rising instability at the end,
which is likely to be related to the aging of these
cohorts.^{7}

Table 6 shows the predicted total variance—the sum of
permanent and transitory components— and the unconditional
variance of *ŷ _{cjit}* . Overall, the cohort
profiles of the predicted total variance are fairly close to the
profiles of

*var*(

*ŷ*) (see Figure 2). Clearly, the total earnings variance in the first several post-arrival years is mostly driven by the transitory component, while the permanent component becomes predominant as immigrants settle down in their new country.

_{cjit}Hence, it is not surprising that the recession of the early 1990s had a greater impact on the total earnings volatility of the 1989-to-1991 and 1986-to-1988 cohorts than on previous cohorts; for these recently arrived cohorts, the transitory component played a more important role in their total earnings volatility.

An interesting question is to what degree immigrants share larger trends in earnings inequality and earnings instability in Canada, and whether immigrant profiles are similar to the profiles of the Canadian-born workers who entered the labour market at around the same time. Morissette, Myles and Picot (1994), Beach, Finnie and Gray (2003) and Baker and Solon (2003) show that, generally, earnings inequality in Canada fell gradually in the mid-1980s, and increased rapidly in the late 1980s and early 1990s, which is consistent with the trends in earnings inequality of immigrants found in this study. The comparison for the 1992-to-2004 period is more difficult. Beach, Finnie and Gray find only a slight increase in earnings inequality from 1990 to 1997 compared with from 1982 to 1989 for young men entering the labour market, while Morissette and Ostrovsky (2005) show that the family earnings inequality and earnings instability was generally higher from 1996 to 2001 than it was from 1986 to 1991, although the increase was not universal across different age and income groups. In sum, the information about general trends in earnings inequality and earnings instability in Canada in the 1990s and 2000s appears to be insufficient to make a more thorough comparison with the immigrant trends. Such a comparison may be a subject of future research.

^{
7
} Higher earnings instability of older immigrants
is consistent with generally higher earnings instability of older
male workers (see Beach, Finnie and Gray 2003). Older workers may
experience higher earnings instability due to, for instance,
greater earnings losses and/or lower probability of finding new
employment after a layoff; it may also reflect gradual retirement
of some workers.

## 7.1 The effects of foreign education, language ability and the place of birth

Although the profiles of immigrant earnings inequality and earnings instability are interesting in themselves, the linkage between the Longitudinal Administrative Databank and the Longitudinal Immigration Database allows us to take the analysis a step further and consider the effects of foreign education, the ability to speak an official language and the place of birth on immigrant earnings inequality and earnings instability.

Given that these variables are available for immigrants, we can estimate the full model with cohort-specific variances and covariances in the permanent growth component using the four samples described in Section 6: the first sample is based on the residuals from the first-stage regression, with foreign education as a control variable; the second sample is based on the first- stage regression, with the ability to speak one of the official languages as a control variable; the third sample is based on the first-stage regression, with the place of birth as a control variable; and, finally, the fourth sample is based on the first-stage regression, in which all the above mentioned variables are controlled for. The estimation results are shown in Appendix B, Table B.3.

Using the coefficient estimates in Table B.3 we can now construct five earnings inequality profiles for each arrival cohort (Table 7). Figure 3 helps visualize the effect of foreign education, ability to speak an official language and birthplace on earnings inequality. Each of these variables has an impact on immigrant earnings inequality and the effect of the birthplace is generally the largest. However, Figure 3 also illustrates the importance of a dynamic analysis. In contrast to the descriptive analysis, the dynamic models allow us to observe how the effects of different variables on earnings inequality change with time.

Table 7 also shows the percentage decline in the permanent variance component after controlling for education, language and birthplace. Consistent with the descriptive results, the place of birth has the strongest overall impact on inequality. Controlling for immigrants' origins reduces the permanent variance component of the 1980-to-1982 cohort by from 22% to 31%, depending on the period. However, the effect of birthplace is clearly less strong for more recent cohorts; for all post-1992 cohorts the effect of birthplace is less than or equal to 18% in any given period, and for the 1995-to-1997 cohort the effect is less than 16%.

The place of birth is, of course, not just a geographic location; it is a proxy for ethnic, religious and cultural attributes of immigrants. It may also signal the quality of immigrants' education and the relevance of their foreign work experience to potential employers, and may influence their hiring decisions. Interestingly, the effect of the immigrant origins generally increases in the first several years and remains strong long after entrance to the labour market. For the earlier cohorts, which are observed for the longest periods of time, we see that the birthplace effect is actually stronger 10 to 20 years after their arrival than in the first several years.

Table 7 also shows that although foreign education has a
relatively small impact on inequality in the early years after
arrival, its importance increases as the cohort ages. For the
1980-to-1982 cohort, for instance, controlling for language ability
reduces the permanent variance component by 16.7% to 19.4% in the
first three years after arrival, while controlling for foreign
education leads only to a 10.9% to 13.7% reduction. In all years
after 1992, however, the effects of education are greater than the
effects of language competence. Similar to the birthplace, the
effect of education is somewhat weaker for more recent cohorts,
although its relative importance is greater. For the most recent
cohorts, after several years, education plays as important a role
in reducing earnings inequality as the birthplace. All in all,
these results seem to indicate that foreign schooling has a
positive long-term effect and that it plays an increasing role in
reducing earnings inequality.^{8}

In contrast to education, the effect of the language competence does not change much as immigrants settle in their new country; it appears to be at its strongest in the recession years. It also seems weaker for immigrants who arrived in the late 1980s and 1990s compared with the earlier cohorts.

The last two columns in Table 7 show the combined effect of including all three explanatory variables in the first-stage regression. The cohort effects noted earlier remain strong: even after controlling for foreign education, the ability to speak an official language and birthplace. The most recent cohorts have generally higher levels of earnings inequality than those who arrived in the 1980s. Not surprisingly, the total effect is smaller that the sum of individual effects because of collinearity. Although controlling for all three variables leads to a substantial reduction in the permanent variance component, most of the immigrant earnings inequality remains unexplained. It is interesting to note that for the pre-1992-arrival cohorts, the combined effect of the three variables on the permanent variance component increased during the recession years and remained high during the post-recession period.

Finally, the cohort profiles of the transitory variance components based on all five samples are presented in Table 8. The inclusion of extra explanatory variables into the first-stage regression

generally has little effect on the dynamics of the transitory variance component, although we notice the divergence between the first (no controls) and the third (language) column for the 1980-to-1982 and 1983-to-1985 cohorts. However, as with the descriptive analysis, there is a noticeable drop in instability when all additional variables are controlled for.

The similarity of the earnings instability profiles in Table 8 is consistent with our understanding of the nature of earnings instability: the transitory component of the variance of immigrants' earnings is a residual variance component; changes in the skill composition of immigrant cohorts—broadly defined to include education, official language ability, as well as religious and cultural attributes—will affect immigrant earnings inequality but will have little direct effect on earnings instability.

^{
8
} The effects of foreign schooling may also reflect
the effects of unobserved individual characteristics that are
usually correlated with higher education, such as, for instance,
strong motivation.

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