The impact of immigration on the labour market outcomes of New Zealanders
4. Production Function Estimates
4.1 Nativity-groups are perfect substitutes within skill-groups - CES estimates
We begin by estimating a simple CES production function, as in Card (2001) and Borjas (2003), that allows for substitutability between workers from different skill-groups, but assumes that, within skill-groups, recent migrants, earlier migrants and the New Zealand-born are perfect substitutes. We assume that output in LMA k at time t (Ykt) is produced by a competitive industry with a production function
` Y_(kt)=F(K_(kt),L_(kt)), (2)
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where Kkt is a vector of non-labour inputs (capital, land, etc.) and Lkt is a CES-type aggregate of labour units Ljkt from different skill-groups (j):
` L_(kt)=[∑_(j)((theta_(jk)+theta_(jt)+theta_(kt))L_(jkt))^(((sigma-1))/sigma)]^(sigma/((sigma-1)). (3)
The variable θjk represents time-invariant skill-group/LMA-specific productivity differences, θjt represents time-varying skill-group-specific productivity shocks for the aggregate economy and θkt represents time-varying LMA-specific productivity shocks that affect all skill-groups equally, while the parameter σ is the (common) elasticity of substitution between skill-groups.
Solving this model yields factor demand equations of the form:
` 1n w_(jkt)=alpha_(jk)+alpha_(jt)+alpha_(kt)+gamma1n(L_(jkt)/L_(kt)) (4)
where Ljkt/Lkt is skill-group j's share of employment at time t in LMA k, αjk is an intercept that is specific to each skill-group/LMA combination and controls for heterogeneity in wage levels across skill-groups in different LMAs, αjt is a time fixed effect for each skill-group that controls for aggregate skill-group-specific wage changes between census years, and αkt is a time fixed effect for each LMA that controls for skill-group invariant wage changes between census years in each LMA.[19] The parameter γ is the wage elasticity of demand for skill-group j, indicating the percentage change in wage in response to a percentage change in that skill-group's share of employment and is equal to the negative inverse of the elasticity of substitution between skill-groups (eg. γ = -1/σ). The lower the elasticity of substitution, the more an increase in the employment share for a particular skill-group will reduce the wages for that skill-group. If skill-groups are infinitely substitutable, wages are unaffected by how much of total employment is accounted for by any skill-group, and the wage impact of a change in employment share will be zero.
Following Card (2001), we allow for a log-linear labour supply function for each skill-group/LMA:
` 1n(L_(jkt)/P_(jkt))=epsilon1n w_(jkt) (5)
where Ljkt/Pjkt is the employment rate for skill-group j at time t in LMA k. Combining equations (4) and (5), we obtain expressions for the log wage, ln wjkt, and log employment rate, ln(Ljkt/Pjkt), for each skill-group/LMA/time-period, in terms of skill-group population shares, ln(Pjkt/Pkt), in that LMA/time-period:
` 1n w_(jkt)=[1/(sigma+epsilon)((alpha_(jk)+alpha_(jt)+alpha_(kt)+sigma+1n(L_(kt)/P_(kt))]-(1/(sigma+epsilon))1n P_(jkt)/P_(kt)
` 1n (L_(jkt)/P_(jkt))=[epsilon/(sigma+epsilon)((alpha_(jk)+alpha_(jt)+alpha_(kt)+sigma+1n(L_(kt)/P_(kt))]-(epsilon/(sigma+epsilon))1n P_(jkt)/P_(kt) (6)
These two equations form the basis of our empirical model, with the coefficients on the skill-group population shares jointly identifying the elasticity of substitution σ and the labour supply elasticity ε. The inclusion of skill-group/LMA fixed effects, skill-group/time fixed effects and LMA/time fixed effects means that these parameters are identified solely from changes over time in local skill-group population shares and changes in relative employment rates and wages for these skill-groups.
Adding white-noise error terms, subsuming all constant terms into the appropriate fixed effects and substituting for the coefficients on the skill-group population shares in each equation, our regression equations can be written as:
` 1n w_(jkt)=Beta_(1)1n(P_(jkt)/P_(kt))+delta_(jk)+delta_(jt)+delta_(kt)+epsilon_(jkt)
` 1n(L_(jkt)/P_(jkt))=Beta_(2)1n(P_(jkt)/P_(kt))+gamma_(jk)+gamma_(jt)+gamma_(kt)+u_(jkt), (7)
where ejkt and ujkt are standard white-noise error terms. In the first equation, wjkt is calculated as the mean (imputed) log wage in each skill-group/LMA/year and, in the second equation, Ljkt/Pjkt is calculated as the ratio of FTE employment to population, where FTE employment is calculated as the number of full-time workers plus one-half the number of part-time workers in each skill-group/LMA/year.[20] The labour supply elasticity ε can be calculated from the coefficients on the skill-group population share as β2/β1 and the elasticity of substitution σ equals -1/β1 - ε.
Table 6 presents estimates of the wage (β1) and employment rate (β2) elasticities for age/qualification (left panel) and predicted occupation skill-groups (right panel). We also report the implied substitution (σ) and labour supply (ε) elasticities. All regressions are variance weighted by the employed population in each skill-group/LMA in a particular year and skill-group/LMAs are dropped from a regression when there are no employed individuals in that cell in any census year. The bottom panel of the table shows the maximum number of observations that could be used in a particular regression, the actual number of observations used (ie. the cells containing workers in all three census years) and the percentage of total employment covered by these observations. In each specification, even though a number of cells are dropped, the data used captures at least 99.95% of all employment.
Table 6: CES employment and wage elasticities for skill-groups
The first row of the first panel of Table 6 presents the employment rate elasticities (β2) derived from estimating equation (7) for 140 LMAs. As an age/qualification skill-group increases its share of the population in one of 140 LMAs by 10%, the group's employment rate is estimated to decrease by 0.34%. The employment effect is also negative within local predicted occupation groups. As a predicted occupation skill-group increases its share of the population in one of 140 LMAs by 10%, the group's employment rate is estimated to decrease by 1.52%. The larger effect obtained when using the predicted occupation skill-definition is consistent with occupation being a more appropriate skill definition, with workers competing more strongly within rather than between occupation groups.
The second panel presents wage elasticities - showing the proportional change in a skill-group's wage in response to a proportional increase in the skill-group's local population share. The first row presents the results for 140 LMAs. Examining the first column, OLS estimates of β1 indicate that that a 10% increase in an age/qualification skill-group's population share in a LMA is associated with that group having insignificantly higher wages (0.05%) - essentially unchanged.[21] This very small own-wage effect suggests a relatively high degree of substitutability between local age/qualification skill-groups. Similarly for predicted occupation skill-groups, the own-wage effect is essentially zero, suggesting that workers in different predicted occupations are highly substitutable for each other.
However, these estimates are biased if there are skill-group-specific demand shocks in particular local labour markets in particular time-periods, eg. if individuals in particular skill-groups are attracted to local labour markets with the strongest employment or wage growth for their group in a particular time-period. Maré et al. (2007) show that region of birth migrant networks are the most important factor in the settlement decisions of recent migrants to New Zealand. Thus, following the approach taken in Card (2001), we instrument the supply of both recent and earlier migrants in a local labour market area with the concentration of past immigrants from the same region of birth in that area.[22] We use a similar approach to instrument for the supply of the New Zealand-born in each labour market, using the concentration of New Zealand-born with the same ethnicity to create the instrument. If social networks are (weakly) stratified by ethnicity, then the ethnic concentration in a particular area should act as a pull-factor that is independent from local demand shocks. If each of these pull-factors is independent from the local demand for individuals with particular skill-levels, instrumental variables (IV) will produce consistent estimates even if there are skill-group specific local demand shocks.
The IV estimates, shown in the first row and second and fourth column of Table 6, are more strongly negative than the OLS estimates, although the estimates for predicted occupation skill-groups are insignificantly different from the OLS estimate (and from zero).[23] This suggests that OLS estimates are biased upward by endogenous location choice of individuals in different skill-groups.[24] The IV estimates imply that a 10% increase in a skill-group's local population share lower that group's employment rate by 2.1%. The group's wages also decline, although the magnitudes of the estimated decline differs across the two skill-group definitions. For age/qualification skill-groups, wages are 0.56% lower, whereas for predicted occupation skill-groups, the decline is estimated to be 16.7%. The smaller wage impact for the age/qualification groups implies that these groups are relatively highly substitutable. The implied elasticity of substitution of 14.1 is shown in the third panel. Occupation groups are less substitutable, with an estimated elasticity of substitution of only 0.5. The declining wage is accompanied by a drop in the employment rate, implying a positive labour supply elasticity, of 3.58 for the age/qualification groups and of 0.13 for the occupation groups.
As emphasised by Borjas (2003), the area variations approach may fail to pick up negative wage effects of immigration if competition occurs between rather than within areas or if immigration to particular locations causes reallocations of resources across sectors and adjustments in interregional trade (ie. a Heckscher-Ohlin effect), thus leading to diffuse impacts on all areas of the country. To gauge the strength of between-area competition, the remaining rows in each panel present results for increasingly aggregated definitions of local labour markets, 75 TAs, 58 LMAs, and 16 RCs. In contrast to the findings in Borjas (2003), our results show no evidence of increased competition within skill-groups as we examine more aggregated labour markets. Overall, the estimated wage and employment rate elasticities are qualitatively similar for both skill-group definitions across each definition of local labour markets. In a companion paper, Stillman and Maré (2007), we examine the impact of recent migrants on the geographic mobility of other individuals and find no evidence that inflows of recent migrants displace either the New Zealand-born or earlier migrants with similar skills. Combined, these results suggest that, in New Zealand, competition occurs mainly within local labour market areas and thus the area variation approach should produce unbiased estimates of the impact of immigration on labour market outcomes for the New Zealand-born and earlier migrants.
4.2 Nativity-groups are imperfect substitutes within skill-groups - CES estimates
The estimates in the previous subsection assume that migrants are perfect substitutes within skill-groups. However, as discussed above, there are a number of reasons why migrants might actually be imperfect substitutes for non-migrants with the same skills. Thus, as in Ottaviano and Peri (2006), Manacorda et al. (2006) and Peri (2007), we next extend the CES model to allow for substitutability between workers from different nativity-groups within skill-groups in a hierarchical CES production function. Ljkt is now further defined as a CES-type aggregate of labour units Ljknt from the three different nativity-groups n (eg. equation (8) is nested in equation (3)):
` L_(jkt)=[∑_(n)((theta_(njk)+theta_(njt)+theta_(njk)+theta_(nkt))L_(njkt))^(((p-1))/p)]^(p/((p-1)) , (8)
The variables θnjk represent time-invariant nativity-, LMA- and skill-group-specific productivity differences, θnjt represents time-varying nativity/skill-group-specific productivity shocks that affect all LMAs and θnkt represents time-varying productivity shocks that affect all nativity-skill-groups in a LMA, while the parameter ρ is the (common) elasticity of substitution between nativity-groups within skill-groups.
With this addition, our regression equations can now be written as:
` 1n w_(njkt)=Beta_(1)1n(P_(njkt)/P_(jkt))+lambda_(njk)+lambda_(jkt)+lambda_(nkt)+lambda_(njt)+epsilon_(njkt)
` 1n L_(nkjt)/P_(nkjt)=Beta_(2)1n(P_(njkt)/P_(jkt))+delta_(njk)+delta_(jkt)+delta_(nkt)+delta_(njt)+upsilon_(njkt) (9)
The inclusion of nativity/skill-group/LMA-specific fixed effects (njk) means that the β parameters are identified solely from changes over time in local population shares of each nativity-group within each skill-group. Furthermore, the other fixed effects control for changes over time in the demand for local skill groups (jkt) and nativity groups (njt) and for national level changes in outcomes for different nativity-skill groups (nkt). Again, the labour supply elasticity ε can be calculated from the coefficients on the nativity-group population share as β2/β1 and the elasticity of substitution between nativity-groups within skill-groups ρ equals -1/β1 - ε.
Table 7 presents estimates of the wage (β1) and employment rate (β2) elasticities across nativity groups disregarding skill-groups (left panel), for nativity groups within age/qualification skill-groups (center panel) and for nativity groups within predicted occupation skill-groups (right panel). Again, we also report the implied substitution (ρ) and labour supply (ε) elasticities for each set of estimates, all regressions are variance weighted by the employed population in each nativity/skill-group/LMA in a particular year, and nativity/skill-group/LMAs are dropped from a regression when there are no employed individuals in that combination in any census year.[25]
Table 7: CES employment and wage elasticities for nativity groups
We first examine the overall substitutability of nativity groups disregarding skill-groups to judge, in general, the degree to which migrants compete with the New Zealand-born and with earlier migrants. If skill-group stratification is important in the economy, as we are suggesting, then we should expect to find that nativity groups are only moderately substitutable, as Tables 1 and 3 show that recent migrants are concentrated in different skill-groups than the New Zealand-born and earlier migrants. Our results show a moderate-to-strong degree of substitutability between nativity groups. The elasticity of substitution implied by the IV estimates range from 5.4 to 7.3, with lower substitutability in larger areas. The substitutability of nativity groups is thus less than for age-qualification groups, but considerably stronger than the substitutability of predicted occupation skill groups.
We next turn to the within skill-group results. First, examining the results for nativity-groups within age/qualification-groups, the IV estimates indicate that a 10% change in a nativity-group's share of population within an age/qualification-group in a local area has a significant negative impact on that nativity group's employment rates (-1.42% to -2.14%), and a smaller negative effect (-0.58% to -0.68%) on their wages. The wage results indicate that there is a very high degree of substitutability between nativity-groups within age/qualification-skill-groups, with the implied substitution elasticity being between 12 and 25. The results for predicted occupation skill groups are similar, although with somewhat stronger wage and employment effects. A 10% increase in a nativity group with a local predicted occupation skill group lowers their employment rate by between 2.2% and 2.9%, and their wages by between 1.7% and 3.0%.
These estimates of the substitutability of nativity-groups within skill-groups can be used to calculate the impact that inflows of recent migrants, as well as changes in the population of earlier migrants and the New Zealand-born, have on the wages and employment rate of similarly skilled New Zealand-born, earlier migrants and recent migrants. Differentiating equation (9) with respect to the population of a particular nativity-group in the overall population reveals that cross-elasticities (ie. ` (theta 1n w_(i))/(theta 1n P_(j)) and ` (theta 1n (L/P)_(i))/(theta 1n P_(j)) are calculated by multiplying the appropriate coefficient from Table 7 (eg. either β1 for the impact on wages or β2 for the impact on employment rates) by -(Pj/P), while own-elasticities (eg. ` (theta 1n w_(j))/(theta 1n P_(j)) and ` (theta 1n (L/P)_(j))/(theta 1n P_(j)) are calculated by multiplying the appropriate coefficient from Table 7 by 1-(Pj/P).
Table 8 summarises the implied own- and cross- elasticities using the IV estimates from Table 7 for the 140 LMAs. In all cases, the largest impact is the effect inflows of recent migrants have on their own labour market outcomes. For example, the results for age/education skill-groups indicate that a 10% increase in the population of recent migrants in a local labour market decreases wages by 0.7% and employment rates by 1.6% for recent migrants in that area. The results for predicted occupation skill-groups indicate that a 10% increase in the population of recent migrants in a local labour market decreases wages by 2.1% and employment rates by 2.1% percent for recent migrants in that area. Changes in the population of earlier migrants have similar, but smaller, impacts on their own wages and employment rates, whereas the impact of population changes of New Zealand-born on their own outcomes are only one-fifth as large, in the range of -0.1 to 0.4. We find no evidence that inflows of recent migrants negatively impact labour market outcomes for the New Zealand-born; looking across both skill-group definitions, a 10% increase in the population of recent migrants in a local labour market is estimated to increase employment rates by 0.08-0.11% and wages by 0.03-0.11% for the New Zealand-born.
Table 8: CES cross wage elasticities between nativity groups in 140 LMAs (IV)
As discussed earlier, the CES model assumes that a single parameter can summarise the substitutability between factors at a particular level of the production function, here nativity-groups within skill-groups. The wage and employment effects then depend only on the factor share of each labour input. One implication of this restriction is that own-wage and own-employment rate elasticities must have the opposite sign to the corresponding cross-elasticities. Thus, as an increase in the recent migrant share of the population causes a decrease in the shares of other population groups and we estimate negative own-wage and own-employment rate elasticities, this increase must, by the assumptions of the CES model, lead to increased employment rates and wages for the New Zealand-born and for earlier migrants.[26] We next extend our analysis to estimate models that relax this assumption and allow there to be a less constrained relationship between changes in factors shares and changes in wages within a particular level of the production function.
4.3 Nativity-groups are imperfect substitutes within skill-groups - generalised Leontief estimates
In this section, we relax the implicit CES restriction that own-group and cross-group elasticities are of opposite sign, and are both derived from the same estimated parameter. Specifically, we utilise a generalized Leontief (GL) production function (Diewert 1971), which is a second order approximation to an arbitrary twice-differentiable production function:[27]
` Y_(kt)=∑_(j)∑_(n)∑_(m)gamma_(nm)(L_(njkt)L_(mjkt))^(1/2), (10)
where n and m index each of the nativity-groups within skill-groups and the parameters γnm describe the production technology. Under the assumptions of profit maximisation and constant prices, the factor demand equations implied by this technology take the following convenient form:
` w_(njkt)=gamma_(nn)+Sigma/(m≠n)gamma_(nm)(L_(njkt)L_(mjkt))^(1/2) , (11)
The coefficients from this model can also be used to derive estimates of the Hicks (Hicks 1970) partial elasticity of complementarity between any two nativity-groups cnm:[28]
` c_(nm)=gamma_(nm)/(2(s_(n)s_(m)w_(n)w_(m))^(1/2) , (12)
where sn is nativity-group n's share of the overall wage-bill (e.g. ` s_(n)=w_(n)L_(n)/(Sigma_(n) w_(n)L_(n)) ). A positive value of cnm indicates that nativity-groups n and m are complements, whereas a negative value indicates substitutability. For example, a finding that cNZ,RM < 0 would imply that an increase in the number of recent migrants lead to a lowering of wages for the New Zealand-born. Own- and cross-wage elasticity estimates are conveniently obtained as
` eta_(nm)=(d 1n w_(n))/(d 1n L_(m))=s_(m)c_(nm). (13)
Adding error components to (11), results in the following regression model which we estimate:
` w_(njkt)=Sigma/(m≠n)gamma_(nm)(L_(mjkt)/L_(njkt))^(1/2)+alpha_(njk)+alpha_(njt)+alpha_(nkt)+epsilon_(njkt) (14)
where wnjkt and Lnjkt are defined as above, αnjk is a nativity/skill-group/LMA fixed effect, αnjt is a time-varying nativity/skill-group-specific fixed effect and αnkt is a time-varying nativity/LMA-specific fixed effect. The inclusion of these fixed effects controls for unobservable time-invariant differences in the wages paid to different nativity-groups in different skill-groups and local labour markets and for unobservable differences in the wages paid over time to different nativity/skill-groups and to different nativity-groups in different LMAs.
For this model, there is one factor demand equation for each nativity-group and the three equations are estimated simultaneously using Seemingly Unrelated Regression (SUR or Zellner's regression) with cross-equation symmetry of technology parameters imposed. As in the CES case, if individuals in particular nativity-skill-groups are attracted to local labour markets with the strongest wage growth for their group in a particular time-period, OLS estimates will be biased. We again use the supply-pull instruments (properly transformed as square roots of ratios) to estimate models that are consistent even if there are nativity-skill-group-specific demand shocks in particular local labour markets in particular time-periods. These IV regressions are estimated using three-stage least squares. Elasticities of complementarity (cij) and wage elasticities (ηij) are derived by scaling the estimated parameters (γ), as in equations (12) and (13), where s and w are evaluated at sample means.
As employment rate elasticities cannot be conveniently incorporated in the Generalized Leontief (GL) formulation, we restrict our attention in this section to wage elasticities. Table 9 presents SUR (top panel) and IV-3SLS (bottom panel) estimates of GL wage elasticities between nativity groups within age/qualification (left panel) and predicted occupation (right panel) skill-groups for 140 LMAs.[29] Each row reports the (transformed) estimates from one equation of a three-equation system of factor demands. Each equation has as many observations as there are skill-group/area/year combinations and all regressions are variance weighted by the employed population in each skill-group/LMA in a particular year. Because of the cross-equation symmetry restrictions, skill-group/areas need to be dropped when data for any nativity-groups in that cell are missing in any year. The loss of observations is more severe than for the CES estimates, but we still capture 89% of employment for age/qualification skill groups, and close to 100% for predicted occupation skill-groups.
Table 9: GL cross wage elasticities between nativity groups in 140 LMAs
The results for the wage elasticities of nativity groups within age-qualification skill groups are puzzling. The SUR results show own-wage elasticities that are generally positive, and often statistically insignificant. The first entry in the table shows that a 10% increase in the employment of the New Zealand-born raises their own wages by 0.03%. This suggests a lack of identification, as may arise due to local demand shocks. The analogous entry in the IV-3SLS estimates should control for the endogeneity of local employment, but unexpectedly, show a slightly larger positive impact of 0.08%. Although we present these results for completeness, we do not believe that they provide robust inference.[30]
Turning to the results for predicted occupation skill-groups, which still provide coverage for the entire population, the SUR results show no significant own-wage or cross-wage elasticities. Using three-stage least squares to adjust for the potential endogeneity of local employment composition yields generally negative, although insignificant own-wage elasticities. Based on the point estimates, a 10% increase in the number of recent migrants in a local predicted occupation group has the strongest impact on the wages of recent migrants in that group - lowering their wages by 7%. We do estimate a number of significant cross-elasticities. For example, a 10% increase in the number of recent migrants in an occupation group increases the wages of earlier migrants in the local skill-group by 2.5%, suggesting some degree of complementarity. Similarly, there is a very small (0.1%) negative impact of recent migrants on the wages of New Zealand-born workers in the same local skill-group. We also estimate that an increase in the number of earlier migrants raises the wages of similarly-skilled local recent migrants by 7.9%, while an increase in the number of New Zealand-born lowers the wages of similar-skilled local recent migrants by 2.1%.
4.4 Nativity-groups are imperfect substitutes between and within skill-groups - GL estimates
Our final specification extends the previous subsection's GL model to allow for substitution and complementarity between different nativity-groups both between and across skill-groups. This is done by re-estimating equation (14) with each nativity/skill-group as a separate factor of production, each included in a simultaneous equations model. Increasing the number of factors within the GL framework makes econometric identification increasingly challenging as the number of parameters to be estimated rises with the square of the number of factors, and the number of observations is reduced due to having to drop areas containing any empty nativity-group/skill-group cells. In the light of the estimation issues outlined in the previous section, we confine our analysis to using the predicted-occupation definition of skill with only three skill-groups defined as i) Legislators, Administrators, and Managers; and Professionals; ii) Technicians and Associate Professionals; and Trade Workers; and iii) the remaining five one-digit occupations.[31]
Table 10 presents IV-3SLS estimates of wage elasticities for 140 LMAs. At this level of aggregation only 6 of 420 possible observations are dropped from due to zero employment for one or more factor. Own-wage elasticities are consistently negative, and close to -1 for recent migrants and earlier migrants. Wage elasticities are also more strongly negative for low-skilled than for higher skilled workers within each nativity group. The CES restriction of positive cross-wage elasticities within skill groups does not appear to hold. For instance, within the high-skilled Professional/ Managerial group, all cross-elasticities between nativity groups are negative. In particular, there is a negative impact of high-skilled recent migrants on the wages of high-skilled New Zealand-born workers, with a 10% increase in high skilled recent migrants lowering the wages of similarly skilled New Zealand-born workers by 1.8%. There are also significant interactions across both skill and nativity cells, such as the estimated positive impacts of low skilled recent migrants on earlier migrants in the Associate Professionals and Trade Workers group, or of high-skilled migrants on New Zealand-born Associate Professionals and Trade Workers. Such interactions were constrained in the CES specification to operate only through changes in the overall skill composition.
Table 10: GL wage elasticities between nativity-skill-groups across 140 LMAs (IV-3SLS)
4.5 Simulated impacts of alternative immigration flows
The regression results presented so far summarise the strength of relationships in terms of elasticities. With some further manipulation, they can provide more readily interpretable measures of the impacts of different immigration patterns. In this section, we consider four possible scenarios, as a means of gauging the economic significance of the estimated results. Each of the four scenarios takes as its baseline the observed 2006 population structure, and asks what the impact would have been of receiving a different number or composition of recent migrants in the preceding five years.
The first scenario (A) entails halving the number of recent migrants that arrived between 2001 and 2006, keeping the composition of recent migrants that same as was observed for the actual flow. This resulting smaller inflow is similar in magnitude and composition to the actual inflow that was observed between 1991 and 1996. The second scenario (B) is similar to scenario (A) but assumes a doubling rather than a halving of the 2001-2006 recent migrant inflow. Scenarios (C) and (D) both maintain the same number of recent migrants as were observed between 2001 and 2006, but change the skill composition. Scenario (C) examines the implications of raising the proportion of high-skilled recent migrants to 75%. For the age-qualification definition of skills, this is captured as an increase in the number of recent migrants with post-school or degree qualifications, from the actual level of 64% to 75%. For predicted-occupation skill groups, we examine an increase in the proportion of recent migrants in the three most skilled predicted occupations (Legislators, Administrators and Managers; Professionals, and Technicians & Associate Professionals) from an actual level of 49%, to 75%.
For each of these scenarios, we calculate the change in factor shares, and examine wage and employment effects along two margins. First, we calculate the implied change in skill-group shares that would result from the assumed scenario, and use the estimates from Table 6 to calculate the implied wage and employment rate change for each nativity group. We refer to this as a 'between-skill-group' change. The second source of wage and employment rate change is a result of the changing nativity group mix within skill groups. For this, we use the estimates in Table 7 to calculate the implied change for each nativity group, which we refer to as the 'within skill-group' contribution.
Table 11 summarises the employment and wage rate impacts of each scenario on the New Zealand-born, on earlier migrants, and on the recent migrants themselves, using the CES estimates. Scenarios A and B show impacts that are similar in magnitude but opposite in sign. The reduced recent migrant flows in scenario A lower the population shares of skill groups in which recent migrants are prevalent. Combined with the negative share elasticities for own-skill outcomes as shown in Table 6, this 'between' effect implies increases in recent migrants' employment rates (0.4% for age-qualification groups, and 0.02% for occupation groups) and wages (0.13% for age-qualification groups, and 0.2% for occupation groups). The skill composition of earlier migrants is similar to that of recent migrants, so the impact of the changing skill composition is also positive, and similar to that for the recent migrants. The 'between skill' impacts on the New Zealand born are smaller because the decline in recent migrants raises shares for skill groups where the New Zealand-born are relatively more prevalent, leading to less positive or more negative impacts overall.
Table 11: Simulated impacts of different immigration scenarios (CES estimates)
The 'within skill' impacts resulting from the imperfect substitutability of nativity groups within skill groups for these scenarios are much larger. The negative own elasticities in Table 7 imply that the decline in the number of recent migrants in scenario A will have a positive impact on recent migrant employment and wage rates within skill groups. Table 11 shows that employment rates for recent migrants increase by 10% to 15%, and wage rates rise by 4% to 14% when the inflow of recent migrants is halved. The drop in recent migrant shares within skill groups necessarily raises the shares of the New Zealand-born and earlier migrants, with a consequent decline in their employment rates (-0.7% to -1.0%) and wage rates (-0.3% to -1.0%). The impacts on these groups are lower in part because of their initially larger population shares.[32]
The impacts under scenario B are roughly the negative of those under Scenarios A. The doubling of recent migrant flows increases the population shares of skill groups where recent migrants are most prevalent, leading to declines in their wages and employment rates, and small or positive between-skill effects on outcomes for the New Zealand-born. Numerically larger effects are observed for within-skill effects, for which the increase in recent migrant shares within skill groups lowers their wages and employment rates, and increases the wages and employment rates of earlier migrants and the New Zealand-born.
Scenario C maintains the same number of migrants but changes the skill composition towards more highly skilled migrants. This has the impact of increasing inflows most strongly for skill-groups where recent migrants are relatively prevalent. As a result, the between-skill impacts on recent migrants are negative. Within skill-groups, recent migrant population shares are raised for high-skilled groups, lowering their wages and employment rates and lowered for low-skill groups, raising their wages and employment rates. Weighting these impacts by initial wage-bill shares, the overall within-skill impact is to raise the employment rates of recent migrants, Wage rates of recent migrants are raised when examining predicted-occupation skill-groups (1.85%), but lowered when examining age/qualification groups (-0.13%). The employment rates impacts on earlier migrants and the New Zealand-born are minimal, with small between-skill and within-skill contributions roughly balancing each other. Estimated wage impacts on other nativity groups are close to zero using the age/qualification skill definition, and are negative using predicted occupations. The more-skilled recent migrant inflow in this scenario leads to lower wages for earlier migrants (-1.4%) and for the New Zealand-born (-0.35%), primarily as a result of changing the ('between-skill') skill composition of the workforce.
Finally, a lower-skilled recent migrant inflow in scenario D leads to generally positive wage and employment impacts across the board because the implied recent migrant inflow is sufficiently different from the existing workforce that skill shares are reduced for the majority of workers, raising outcomes. The within-group wage effects are the opposite sign to those seen in scenario C. Overall, average wages are raised for recent migrants, and either raised (using predicted occupations) or reduced only slightly (age/qualification groups) for earlier migrants and the New Zealand-born.
To gauge whether the less constrained GL specification shows patterns that are substantially different from those found in the more parsimonious CES model, we next examine whether the implied CES changes differ from those calculated using the fully unrestricted GL estimates reported in Table 10. The results are summarised in Table 12. For each scenario, there are nine separate impact estimates - for each combination of three nativity-groups and three skill-groups, defined as in Table 10. Table 12 also shows a weighted average of impacts for each nativity group, using 2006 labour cost shares as weights. This weighted average is comparable to the restricted CES estimate, which is presented in the first column of the table.
Table 12: Simulated wage impacts of different immigration scenarios (GL estimates)
Halving the number of recent migrants under scenario A has a large positive impact on the wages of recent migrants, and negative impacts on both earlier migrants and the New Zealand-born. However, the estimated impacts do vary across skill groups within the New Zealand-born and earlier migrant groups. Negative impacts only occur for medium-skilled New Zealand- born and medium- and high-skilled earlier migrants. Overall, the weighted average of GL impacts for scenario A is qualitatively similar to the estimates obtained from the CES model, although with much larger positive impact on recent migrants (62%) and a somewhat weaker negative impact on the New Zealand-born (-0.23%). In order to capture both of these effects with a single parameter, it appears that the CES estimates understate the impact on recent migrants and overstate the impact on New Zealand-born. Based on the GL estimates, the impacts of scenarios A and B are exactly equal in magnitude but opposite in sign.
Scenario C reflects an increase in the skill-content of recent migration flows. There is a negative impact on high-skilled workers of each nativity group, although the magnitudes of the resulting wage change are quite different: -36% for high-skilled recent migrants; -0.82% for high-skilled earlier migrants; and -1.77% for high-skilled New Zealand-born. Medium-skilled earlier migrants also experience a wage decline, of -0.99%. Averaged over all skill groups, the more highly-skilled recent migrant flow lowers average wages for earlier migrants, and raises them for recent migrants and the New Zealand-born. This is in contrast to the negative implied CES impact of -0.39% for the New Zealand-born.
Finally, a less skilled recent migrant inflow in scenario D raises the wages of high-skilled workers in each nativity group, again by quite different magnitudes, with the largest impact on recent migrants. The overall impacts are positive for recent and earlier migrants, as in the CES estimates, but the average impact on the New Zealand-born of a less-skilled migrant inflow is negative, in contrast to the positive impact implied by the CES estimates. While both high-skilled and low-skilled New Zealand-born benefit from the less-skilled migrant inflow, the average effect reflects the strength of the negative impact on medium-skilled New Zealand-born.
Footnotes
[19] An alternative approach would be to assume a common production function across all LMAs, and restrict αjk to be αj +αk. Given the lack of information on non-labour inputs in our data, we choose to identify γ solely from changes over time in local skill-group shares, rather than using cross-unit variation in shares.
[20] Full-time workers are employed for at least 30 hours in the week prior to the census.
[21] Statistical significance here refers to whether the wage elasticity is significantly different from zero. A zero wage elasticity is commensurate with infinite substitutability of factors.
[22] Formally, let RMgt represent the number of recent migrants from source region g in census t, and let λgkt represent the fraction of earlier migrants from region g that is observed living in LMA k five-years prior to the current census. Finally, let τgst represent the fraction of recent migrants from source region g that is in skill-group s in census t. In the absence of demand factors, the number of recent migrants from region g in skill-group s who would be expected to live in LMA k in census t is τgst * λgkt * RMgt. Summing over all regions, we can calculate the component of the supply of recent migrants in each skill-group and LMA that occurs because of an individual’s desire to live near other migrants from their home region. The same formula is used to determine the supply of earlier migrants in a LMA, except that τgst is calculated for earlier migrants and that RMgt is replace by EMgt, the number of earlier migrants from source region g in census t. In practice, we group individuals into the nine regions tabulated in Table 1 for calculating this instrument.
[23] For age/qualification skill-groups, predicted population shares are strongly related to actual population shares, with the partial R-squared from the unreported first-stage regression 0.154 and the F-stat on the significance of the instrument 1158, where a F-stat of less than 17 indicates potential problems with weak instruments in our model (Stock and Yogo 2002). However, the instrument is much weaker when focusing on predicted occupation groups, with a partial R-squared of 0.006 and a F-stat of 6.9. This is a likely explanation for the lack of precision on the IV estimates that uses this skill-group definition and perhaps calls into question the large estimates wage elasticity. As is noted later on, the instruments are strong for both skill-group definitions when we allow for substitutability between nativity groups, eg. our preferred estimates.
[24] This differs from the finding in Maré et al. (2007) that the settlement decisions of recent migrants are not significantly related to skill-specific local labour market conditions. However, both sets of results are consistent with earlier migrants and/or the NZ-born being attracted to areas with skill-specific demand shocks, while recent migrants are not responsive to these differences.
[25] For nativity groups, the partial R-squared from the unreported first-stage regression is 0.314 and the F-stat on the significance of the instrument is 251. For nativity groups within age/qualification skill-groups, the partial R-squared is 0.054 and the F-stat is 770. For predicted occupation groups, the partial R-squared is 0.050 and the F-stat is 117. Thus, none of the IV estimates is this section appear to suffer from weak instrument problems.
[26] The same point applies when interpreting the results in Ottaviano and Peri (2006), Manacorda et al. (2006) and Peri (2007), each which uses this modelling approach.
[27] There are two downsides to this approach relative to the nested CES model. First, there is not a straightforward way to incorporate labour supply into this model and thus we now assume that labour supply is inelastic and employment is not affected by changing factor shares. Second, this approach is more demanding of the data (for example, for the model examining the impact on nativity groups within age/qualification skill-groups, the CES model estimates 7,270 parameters using 21,847 observations, while the GL model estimates 3,426 parameters using 8,271 effective observations – this is the actually number of observations times three simultaneous equations) and thus the estimates are generally less precise.
[28] The Hicks-Allen elasticity of substitution as estimated by the CES approach measures the change in relative quantities in response to a change in relative marginal productivities, holding other factor prices constant. The elasticity of complementarity provides an alternative view of the same relationship, and is estimated holding other factor quantities constant.
[29] Results from when the model is estimated at other geographies are available from the authors. In general, the finding are sensitive to the chosen aggregation, but given that we found qualitatively similarly results at different aggregations when estimating the CES models, we feel that 140 LMAs is the preferred geography.
[30] One undesirable consequence of the GL specification is that observations need to be dropped if employment is zero in any of the local skill-nativity groups. This restriction is often binding because many of the smaller local age/qualification groups have no recent migrants. Of the 10,080 potential observations, only 2,757 are used in this regression. We examined whether using more aggregated age-qualification skill-groups led to more ‘sensible’ results, but generally this has little impact.
[31] Like the five predicted occupation grouping, this particular aggregation was also chosen by using cluster analysis to group occupations according to the similarity of the individuals employed in them across a wide variety of characteristics, but with a lower threshold of similarity.
[32] For example, in scenario A, the roughly 69,000 decline in the recent migrant population lowers the recent migrant share by about 50% (from 8.7% to 4.5%), but raises the non-recent migrant population by only about 5% for NZ-born (from 74% to 77%) and earlier migrants (from 17.4% to 18.2%).