Shift Share Instruments for the German Labor MarketMarket

The shift share instrument is widely used in the spatial correlation literature on immigration to deal with the endogeneity of the regional settlement of newly arriving immigrants. In what follows, we describe the implementation of two versions of the shift share instrument, both motivated by the idea that newly arriving immigrants tend to settle in regions in which other immigrants already settled earlier, and that the settlement decision of earlier immigrants is uncorrelated with current demand shocks. While the simple version of the instrument only considers the pattern of the overall immigrant settlement (see, e.g., Altonji and Card 1991), the more complex version further takes into account the source countries in the construction of the instrument (see, e.g., Card, 2001, 2007, 2009; Glitz, 2012; Smith, 2012; Peri and Sparber, 2009; Dustmann and Glitz, 2015).

In the simple version of the shift share instrument, we predict the immigrant inflow into a local labor market based on the foreign population density in some initial period to instrument the actual region level changes in immigrant population shares. Formally,

∆I˜_r,88−93^Pop =γ_r,t0 I₉₃^Pop−I₈₈^Pop

(N_r,88^Pop+I_r,88^Pop) ^(A.27) whereγ_r,t0=I_r,t^Pop₀ /It^Pop₀ denotes the share of foreigners in the population that resides in region rin some initial periodt₀,I₉₃^Pop−I₈₈^Popis the nationwide net inflow of immigrants between 1988 and 1993, andPop_r,88is the population in regionrin 1988. The initial yeart₀in our example is 1961, the earliest year for which population data for natives and immigrants are available. We use census information from the GESIS data archive (available online under the file name ZA2472) and combine these data with population data from the German Federal Statistical Office for years 1985-2001, which we reassembled from Statistical Yearbooks and published tables (both available online). To obtain first stage results, we regress the changes in local immigrant employment shares in 1988-1993 on the instrument∆I˜_r,88−93^Pop . The results in Table 2.7 (see last rows) suggest that the historical immigrant settlement pattern is indeed a strong predictor for settlement of immigrants between 1988 and 1993, withF-statistics of 30.24 to 32.56 (depending on the measure for the outcome variable). However, we do not

A.5. SHIFTSHAREINSTRUMENTS FOR THEGERMANLABORMARKET

use this instrument in our main analysis because it is only available for 112 out of 204 local labor markets.

A more sophisticated version of the shift share instrument relies, in principle, on a similar idea, but instead of using the overall share of past immigrant settlements, it uses information on the source country of arriving immigrants to account for more detailed ties between specific ethnic enclaves. Formally, the instrument is constructed by interacting past country-specificimmigrant densities across regions with nationwidecountry-specificnet inflows of immigrants, whereλc,r,t0 =I_c,r,t^Emp₀/I_c,t^Emp₀ denotes the share of all immigrants from source countrycthat work in regionrin some base year, andI_c,93^Pop−I_c,88^Popis the nationwide net inflow of country cimmigrants between 1988 and 1993.⁴ The denominator scales the predicted net change in levels by total employment (natives+immigrants) in regionr in year 1988. We choose 1975 as the initial year because it is the earliest year available in our administrative records, and because it comes as close as possible to the settlement structure underlying our distance instrument (although the latter dates back one more decade). The results are summarized in Table A.3. Somewhat surprisingly, column 1 (which corresponds to column 5 in Table 2.3) shows a low correlation (F-statistic=3.34) between predicted and actual immigrant employ-ment growth, which disqualifies this instruemploy-ment for our analysis. The entries in column 2 demonstrate that the performance of the supply push instrument deteriorates further if we (in analogy to DG) extend the observation period backward and forward to 1985-1995.

The relatively poor performance of the shift-share instrument seems to contradict the evidence in a recent study of DG. They use the shift-share instrument to predict changes in the local skill-specific labor supply, reportingF-statistics well above 20 in their analysis of all skill groups. There is, however, an important conceptual differences between the present analysis and the study of DG. Notably, we do not use skill-specific inflows of immigrants (relying on variation in immigration across regions and skill cells) but instead base our analysis on the overall immigrant inflow. In the following, we show that when we estimate a first stage specification exploiting skill-specific variation in employment growth, we obtain very similar results as DG, yet these appear to be driven by native rather than immigrant employment changes.

We begin by defining the change in skill-specific employment between 1985 and 1995 as the percentage change of the total (native+immigrant) employment of skill groupiin region rbetween 1985 and 1995.⁵ In concordance with the endogenous variable of the first stage model, we define the shift-share instrument to predict theskill-specificinflow of immigrants by interacting the predicted inflow in a region with a nation-wide average skill distribution

4We use five nationality groups defined as (1) Poland, the Former Soviet Union, Romania, and Central and Eastern Europe, (2) Turkey, (3) Italy, (4) Former Yugoslavia, Greece, and Portugal, and (5) Western Europe plus rest of the world.

5Note that, as in DG, we include ethnic Germans and East Germans in this analysis.

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of immigrants who arrived between 1985 and 1995. Formally,

∆I˜_i,r,85−95^Emp = ^{∑cλc,r,t0θc,i}(I_c,95^Pop−I_c,85^Pop)

(N_r,85^Emp+I_r,85^Emp) ^(A.29) The three components in the numerator reflect, for each source countryc, the initial regional distribution of immigrant employment in 1975 (λc,r,t0=I_c,r,t^Emp₀/I_c,t^Emp₀ ), the average skill dis-tribution between 1985 and 1995, and the total net inflow between 1985 and 1995. The denominator scales the predicted inflow by skill-specific employment in the base year (1985).

We use published data from DG to obtain the skill-specific regional immigrants net flows by source country (numerator).⁶

Column 3 in Table A.3 shows the first stage relation between the relative change in skill-specific total employment (natives+immigrants) and the predicted skill-skill-specific inflows of immigrants (conditional on a full set of region and skill group fixed effects). Although our slope parameter is somewhat larger and theF-statistic somewhat smaller compared to DG’s results (slope: 0.448 compared to 0.297 (DG);F-statistic: 16.26 compared to 26.0 (DG)), we arrive at substantially similar conclusions: the instrument works well in this setting.

However, once we decompose the change in total employment into the change in natives and immigrant employment, and regress each component (both divided by total employment) separately on the instrument, we find that the predicted immigrant growth between 1985 and 1995 is highly correlated with native employment changes but virtually uncorrelated with changes in immigrant employment (see columns 4 and 5 in Table A.3).⁷ This seems to contradict the original enclave-based idea of the supply push instrument, which should lead to a positive correlation between the percentage change inimmigrantemployment and the predicted immigrant growth.

In the following, we suggest a possible explanation for why the complex shift share instrument performs worse than a distance-based measure in the German context: first, the initial settlements, especially of former guest workers, were highly concentrated in a relatively small number of regions, leading to exceptionally high immigrant employment rates in some areas, but still low shares in other, geographically close regions; second, immigrants from former Eastern Bloc states were virtually non-existent introducing substantial randomness in the assignment of later flows. For example, based on 1975 data, we find that there are areas of high concentration in Baden-Wuerttemberg and North Rhine-Westphalia as well as the wider

6DG obtain immigrant net flows by source country from the German Federal Statistical Office and the skill distribution from the German Microcensus using information on the year of immigration and the current education level. Note that DG’s data distinguished between 15 nationality groups.

7Note that we focus on the percentage change in immigrant employment rather than the total labor force.

Moreover, we merge medium- and high-skilled workers in the analysis, which stands in contrast to the analysis in DG. However, we repeated the same exercise for the labor force subdivided into three skill groups and obtained very similar results: while estimates using the percentage change in the total labor force are even closer to DG’s results, theF-statistic is close to zero when we use the percentage change in the immigrant labor force. Also note that DG use weights for total labor force (including immigrants) in thetradablesector, whereas we present results based on total employment in all sectors, but exclude immigrants. But again, in unreported results, we found that using the alternative weighting scheme does not have a relevant impact on the results and we arrive at the same conclusions.

A.5. SHIFTSHAREINSTRUMENTS FOR THEGERMANLABORMARKET

area of Munich and some dispersed areas further north (like Hamburg). In contrast, the north and eastern border of Bavaria reveals rather low concentrations of immigrants. Applying the mechanics of the shift share instrument, we can calculate the counterfactual immigrant density that would be observed if future immigrant settlements were determined only by the initial density in 1975 (see Figure A.3). The shift share instrument — using shares in 1975 — overpredicts changes in immigrant shares between 1985 and 1995 in areas that were initially high immigrant regions. That is, later immigrants didnotmove proportionately into areas that were initially high immigrant regions. This points to some spillover effects, possibly because the former guest workers who were granted the right to stay, required further and cheaper housing space as they started to reunify their families in later decades.⁸ In addition, the shift share IV performs particularly bad in many southern regions that either share a border with high immigrant regions as of 1975 or are located further east. This illustrates the inability of the shift share prediction to adequately predict the settlement of Eastern Bloc migrants.

8Anecdotal evidence suggests that housing space was scarce in the hot spots of 1975. As immigrants reunified their families over the subsequent decade, they may have been forced to move to neighboring regions.

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