## wpiea2019301-print-pdf - 0.18 percent over the period (see Text Table)

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### Main empirical conclusion on immigration and wages
- After controlling for observable differences, the estimated competition effect of immigration implies an increase of aggregate wages of 0.26 percent per year over 2012–2016 because the stimulating effects on complement workers outweigh dampening effects on substitute workers.
- The substitution effect dominates for incumbent foreign workers, placing downward pressure on their wages.
- Overall conclusion: immigration had only a negligible impact on aggregate wage growth in Germany over the sample; the Phillips curve accounts for the bulk of wage dynamics and suggests no role for immigration on aggregate wage developments.
- Separate statistic reported in the text: 0.18 percent over the period (see Text Table).

### Microdata corroboration and decomposition (IAB social security panel, 2012–2016)
- Data and approach:
  - Panel covers 38 million employees over 2012–2016, grouped into 14,960 cells per year and 154 wage groups at 50 euro intervals.
  - Restricted weighted least squares (WLS) panel estimation of log wages with extensive dummies (sex, age, nationality, qualification, sector, region, working time) and time fixed effects.
  - Migration intensity by sector (mig/all) lagged one period (mig/all)_{m,t−1}.
- Key empirical outcomes (selected exact coefficient estimates from Table 3):
  - migrant intensity (t-1): 0.001 0.001 0.153 (below median); 0.007 0.003 0.011 (above median).
  - German: 0.003 0.000 0.000 (below); 0.003 0.000 0.000 (above).
  - Europe without EU: -0.006 0.003 0.033 (below); -0.067 0.006 0.000 (above).
  - EU: -0.031 0.003 0.000 (below); -0.042 0.004 0.000 (above).
  - 8 asylum countries: -0.087 0.009 0.000 (below); -0.124 0.029 0.000 (above).
  - other migrants: -0.048 0.005 0.000 (below); -0.077 0.009 0.000 (above).
  - male: 0.013 0.001 0.000 (below); 0.063 0.001 0.000 (above).
  - female: -0.011 0.001 0.000 (below); -0.086 0.001 0.000 (above).
  - Year fixed effects examples: 2013 7.185 0.008 0.000 (below); 8.010 0.013 0.000 (above). 2014 7.212 0.009 0.000 (below); 8.031 0.014 0.000 (above). 2015 7.236 0.009 0.000 (below); 8.050 0.014 0.000 (above). 2016 7.255 0.010 0.000 (below); 8.064 0.014 0.000 (above).
- Interpretation:
  - Being German associated with +0.3 percent deviation relative to national wage average.
  - All non-German groups have wages below the national average after controls (e.g., 8 asylum countries: -8.7 percent and -12.4 percent).
  - Coefficient of the immigration variable interpreted as: 0.0071 for the upper half of wage distribution (text reports 0.0071); 0.0014 for the lower wage half (text reference).
  - Sample sizes and fit: N = 43,300 (below median) and N = 13,963 (above median); Root MSE = 0.011 and 0.014 respectively; Prob > F = 0.000.

### Composition versus competition (shift-share) decomposition
- Marginal effects interpretation:
  - Overall wages would increase by 0.71 (0.14) percent if the immigration rate increased by 1 percentage point of total population (upper-half and lower-half coefficients respectively).
- Sectoral migration intensity and translation:
  - Migration induced a yearly increase in sectoral migrant shares of 0.48 percentage point of total employment.
  - Applying the 0.48 percentage point yearly increase to estimated coefficients yields an overall yearly wage increase of 0.26 percent.
- Within-group competition among non-German groups:
  - Panel regression across four non-German groups yields coefficient -0.033 (p-value = 0.00).
  - Average migrant intensity of these four groups rose from 1.79 percent in 2012 to 2.37 percent in 2016, or 0.14 percentage points per year.
  - Using -0.033 and 0.14 percentage points per year implies a negative yearly wage effect of -0.48 percent for workers within these migrant groups.
- Shift-share (composition) results (2012–2016):
  - Constructed counterfactual with no immigration between 2012 and 2016; multiplied estimated dummy coefficients by actual-minus-counterfactual structure differences in 2016.
  - Aggregate composition effect (2012–2016): -0.49 percent (equivalent to -0.12 percent per year).
  - Composition effect contributions to total -0.49:
    - nationality: -0.18
    - sex: 0.02
    - age: -0.05
    - qualification: 0.01
    - sector: -0.24
    - job/working time: -0.08
    - region: 0.02
    - Total: -0.49

### Net effect on aggregate wages and interpretation
- Competition (interaction/complementarity) effect: +0.26 percent per year (from sectoral coefficient application).
- Composition effect annualized: -0.12 percent per year.
- Loose aggregate combination: overall effect on net wages ≈ +0.14 percent per year (0.26 − 0.12 percent).
- Interpretation:
  - Composition effect reflects lower pay of foreigners and concentration in younger, lower-skilled cohorts and low-paid sectors (sector contribution -0.24).
  - Competition effects raised wages for relatively skilled and native workers complementary to migrants, offsetting composition-driven downward pressure.
  - Negative wage pressure observed within migrant groups concentrated in low-wage sectors, but aggregate effect is modestly positive or negligible.
  - Overall conclusion: no evidence of downward pressure on aggregate wages from immigration; net result (very) slightly positive.

### Labor market stylized facts and Phillips curve evidence
- Unemployment and Hartz reforms:
  - Germany’s unemployment rate trended upward to a peak of 11 percent in 2005 (highest among the G7).
  - Hartz I–III enacted 2003–2005 improved matching; Hartz IV implemented January 2005 reformed unemployment insurance.
  - Reforms reduced long-term unemployment assistance, lowered reservation wages, shifted the Beveridge curve inward after 2005.
  - Decline in unemployment between 2005 and 2008 reflects improved matching efficiency; coincided with downward shift of real unit labor costs between 2000 and 2007 and accelerated wage moderation.
- Labor tightness measurement:
  - Vacancy-to-unemployed ratio (V/U) and NAIRU-based unemployment gap track similarly up to 2009 but diverge thereafter; V/U may overestimate tightness when firms can access non-domestic jobseekers.
  - Paper relies on NAIRU to compute unemployment gap; considers a swath of NAIRU estimates by running HP filters with lambda between 1’000 and 1’000’000.
- Phillips curve findings:
  - Controlling for shifts in the NAIRU reinstates the negative relationship between wage inflation and labor market slack.
  - The Phillips curve remains central in explaining wage inflation in Germany over the sample.
  - Empirical specifications from NK microfoundations show unemployment gap and change in unemployment gap are large, highly significant and of expected sign.
  - Inflation expectations (lagged price inflation) positively related to wage inflation.
  - Coefficients related to immigration on aggregate wage growth are statistically non-significant in most specifications; exception noted (column II Table 1) judged spurious in text.
  - Error-correction term negative: positive deviations of wages from long-term productivity-driven equilibrium dampen subsequent wage growth.
  - Table 1 model fit (selected exact figures):
    - Sample 1992-17 Observations 103 Adj. R-squared 0.69.
    - Sample 1995-17 Observations 91 Adj. R-squared 0.47.
    - Alternate specifications sample 1992-17 Observations 103 Adj. R-squared 0.73.
    - Alternate specifications sample 1995-17 Observations 91 Adj. R-squared 0.55.
  - Recursive/rolling estimates: Phillips-curve slope converges to stable, significant negative value (Figure 9.1).
  - Decomposition (Figure 9.2): unemployment gap dominant in early 1990s and Hartz reforms period; unemployment gap pointing towards higher wages since 2016; model explains wage inflation well except pre-crisis and 2014-2015.

### Immigration patterns and contextual statistics
- Stocks and flows:
  - In 2010, less than 15 million people with a migrant background in Germany; by 2017 the figure rose to 19 million — almost 24 percent of the population.
  - Average total net migration per year over 2011-2017: 526,000 persons, up from roughly 132,000 over 1995-2010.
  - In 2015 alone, 2.1 million people migrated to Germany, while 1 million left, net inflow 1.1 million.
  - In 2015, number of asylum seekers increased by 39 percent, and by another 54 percent in 2016.
  - In 2018, of the total stock of immigrants, 70% were from European countries, in particular from the European Union (44 percent).
- Comparative perspective:
  - Many other advanced economies experienced similar or larger immigration flows post-crisis.
  - Spain experienced a supply-push immigration story (foreign unemployment gap rose); Germany’s relative unemployment rate of foreign workers remained roughly constant from 2012 to 2018 (demand-pull story), implying smaller downward pressure on wages in Germany than in Spain.

### Theoretical and empirical approach (modeling highlights)
- Theoretical setup:
  - Builds on Gali (2011) and Calvo (1983) wage-setting with imperfect substitutability and Calvo-style wage stickiness.
  - Derives wage Phillips curve: πt^w = α(1−β)^(−1) + γ π̄_{t−1}^p − δ û_t − ψ1 Δû_t (with parameter sign conventions stated).
  - Empirical linear representation: π_{t,w,4} = a0 + a1 π_{t−1,8} + a2 û_t + a3 Δû_t + ε_t.
- Incorporating immigration:
  - CES aggregate employment: N_t = (δ1 N_{1,t}^ρ + δ2 N_{2,t}^ρ)^{1/ρ}, σ = (1−ρ)^(−1).
  - Extended empirical model (equation (2)): π_{t,w,4} = b0 + b1 π̂_{t−1,8} + b2 û_t + b3 Δû_t + b4 (u_{2,t} − u_t) + b5 u_{2,t} ir_t + b6 u_{2,t} ir_t^2 + ε_t.
  - Two channels: intercept/level effect (u_{2,t} − u_t and ir_t, b4–b6 expected negative) and slope effect (immigrant preferences/elasticities affecting b2 and b3).
- Reduced-form and error-correction:
  - Error-correction augmented (equation (3)): π_{t,w,4} = c0 + c1 π_{t−1,8} + (1−c1) π_{t+8,4} + c2 û_t + c3 ê_{t−4} + ε_t, where ê_{t−4} from log(W_t) regression with dum = 1 for 2005Q1 to 2008Q1.
  - Reduced-form with immigration rate (equation (4)): π_{t,w,4} = d0 + d1 π_{t−1,8} + (1−d1) π_{t+8,4} + d2 û_t + d3 ê_{t−4} + d4 ir_t + ε_t; if foreign labor dampens wage inflation, expect d4 significant and negative.
- Empirical summary:
  - NK-consistent specifications show unemployment gap dynamics and expectations matter; immigration coefficients on aggregate wage growth mostly statistically non-significant.
  - Model explains wage inflation well; deviations largely accounted for by unemployment gap and expectations.

### Appendix highlights
- Appendix A: Derivation of wage Phillips curve from first principles, indexation, AR(2) unemployment-gap dynamics, yielding empirical Phillips form π^w_t = α(1−β)^{-1} + γ π̄^p_{t−1} + ψ_0 û_t + ψ_1 û_{t−1}.
- Appendix AA.2: Micro-founded Phillips curve with immigration—two labor types, differing labor supply elasticities (ϕ_2 > ϕ_1), yields empirical specification including (u_{2,t} − u_t), u_{2,t} ir_t, and u_{2,t} ir_t^2 terms.
- Appendix B: Short- and long-term determinants in Germany:
  - Long-term: nominal compensation per hour follows total output per hour (1991–2017); output per hour roughly doubled and labor compensation increased similarly except 2003–2010.
  - Short-term: Phillips curve operative; dropping inflation expectations helped keep nominal wage growth stable despite falling unemployment; real wage growth peaked at 3.5 percent post-crisis.
  - Relationship between real wage growth and unemployment gap holds when accounting for NAIRU decline.

*Source: wpiea2019301-print-pdf — IMF staff calculations based on Eurostat, The Institute for Employment Research, Bundesbank, Destatis, Federal Employment Agency, Consensus Forecasts, Haver Analytics.*

### 0.18 percent over the period (see Text Table).

### wpiea2019301-print-pdf - 0.18 percent over the period (see Text Table)

### Main empirical conclusion on immigration and wages
- After controlling for observable differences (immigrants’ typically lower wages, gender wage gaps, higher manufacturing wages, and other factors), the estimated competition effect of immigration implies an increase of aggregate wages of 0.26 percent per year over 2012–2016 because the stimulating effects on complement workers outweigh dampening effects on substitute workers.
- The substitution effect dominates for incumbent foreign workers, placing downward pressure on their wages.
- Overall conclusion: immigration had only a negligible impact on aggregate wage growth in Germany over the sample; the Phillips curve accounts for the bulk of wage dynamics and suggests no role for immigration on aggregate wage developments.
- A separate statistic in the text: 0.18 percent over the period (see Text Table).

### Microdata corroboration and decomposition
- Analysis based on social security data (IAB panel covering 38 million employees over 2012–2016) confirms that competition and composition effects broadly cancel out.
- Post-crisis large immigration waves tended to dampen wage growth of foreign labor directly competing with newcomers, but this negative effect was more than offset by higher wage growth for relatively skilled and native workers.
- Immigration flows increased most in sectors where wage increases were highest and where prior migrant representation was greatest (Food and accommodation, I, Support, N, Transport, H and Construction, F), suggesting concentration of any downward pressure in low-skilled, low-pay activities.

### Labor market stylized facts relevant for wage dynamics
- Unemployment dynamics:
  - Germany’s unemployment rate trended upward from the early 1990s to the mid-2000s, peaking at 11 percent in 2005 (the highest rate among the G7).
  - The Hartz reforms were enacted between 2003 and 2005 (Hartz I–III improved matching; Hartz IV, implemented in January 2005, reformed unemployment insurance).
- Effects of the Hartz reforms:
  - Reforms reduced long-term unemployment assistance and improved matching efficiency, lowering reservation wages and shifting the Beveridge curve inward after 2005.
  - The decline in unemployment between 2005 and 2008 reflects a more efficient labor market (not necessarily tighter).
  - The reforms coincided with a downward shift of real unit labor costs between 2000 and 2007, accelerating wage moderation.
- Labor tightness measurement:
  - The vacancy-to-unemployed ratio (V/U) and NAIRU-based unemployment gap track similarly up to 2009 but diverge thereafter; V/U may overestimate tightness when firms can access large pools of non-domestic jobseekers.
  - The paper relies on the NAIRU to compute the unemployment gap as the preferred measure of labor market slack.
  - NAIRU estimates vary by methodology; the WEO NAIRU lies above HP-filtered NAIRU estimates between 1991 and 2001, while the OECD NAIRU is below; the two converge after the crisis.
  - A swath of NAIRU estimates is considered by running HP filters with lambda parameters between 1’000 and 1’000’000.
- Phillips curve:
  - Controlling for shifts in the NAIRU reinstates the negative relationship between wage inflation and labor market slack characteristic of the Phillips curve.
  - The Phillips curve remains a central mechanism explaining wage inflation in Germany over the sample.

### Immigration patterns and contextual statistics
- Migrant population and flows:
  - In 2010, there were less than 15 million people with a migrant background in Germany; by 2017 the figure rose to 19 million — almost 24 percent of the population.
  - The average total net migration to Germany per year over 2011-2017 was 526,000 persons, up from roughly 132,000 over 1995-2010.
  - In 2015 alone, 2.1 million people migrated to Germany, while 1 million people left, resulting in a net inflow of 1.1 million.
  - In 2015, the number of asylum seekers increased by 39 percent, and by another 54 percent in 2016.
  - In 2018, of the total stock of immigrants, 70% were from European countries, in particular from the European Union (44 percent).
- Comparative perspective:
  - Many other advanced economies experienced similar or larger immigration flows post-crisis.
  - Comparison with Spain: Spain experienced a supply-push immigration story (foreign unemployment gap rose), whereas Germany’s relative unemployment rate of foreign workers remained roughly constant from 2012 to 2018 (demand-pull story), implying smaller downward pressure on wages in Germany than in Spain.

### Theoretical and empirical approach summarized
- Paper structure (as implemented):
  - Section II: Presents stylized facts and argues that the natural rate of unemployment dropped in Germany following the Hartz reforms, with implications for specifying and estimating the wage Phillips curve.
  - Section III: Derives a theoretical specification of the wage Phillips curve that allows immigration to play a distinct role in wage formation.
  - Section IV: Estimates the Phillips curve under competitive specifications and finds that immigration did not play a significant role in explaining overall wage developments in Germany.
  - Section V: Uses administrative micro-data to corroborate Section IV’s conclusions and to decompose competition effects (impact of migration on wages holding migrant shares constant) and composition effects (mechanical impact on aggregate wages from changing shares of lower-paid migrants).

*Source: wpiea2019301-print-pdf - 0.18 percent over the period (see Text Table).*

### 1. Unemployment Rate Differences: Natives and

### 1. Unemployment Rate Differences: Natives and Immigrants

### Key empirical charts and data points
- Figure references and sources:
  - Figure 8. Immigration Looks Like a Demand-Pull Story in Germany. Sources: Eurostat, The Institute for Employment Research; and IMF staff calculations.
  - Figures display: Unemployment Rate Differences (Percent) 1995–2018 for Germany and Spain; Difference Between Immigrant and Total Unemployments (Percent); Foreign born (% of total), 2012; Variation of foreign born in total (%), 2012-16; Wage Decile foreign-born shares; Wage growth 2012-2016 (percent) and Difference in migrant intensity 2012-2016 (percentage points); Migrant intensity 2012 (percent).
- Visual evidence summarized:
  - Time series plots for 1995–2018 show notable differences in unemployment rates between natives and immigrants, with country-level comparison (Germany, Spain).
  - Cross-sectional charts for 2012–2016 show migrant intensity by wage decile and sector and associated wage growth 2012–2016.

---

### III. Deriving the Phillips Curve from First Principles
- Theoretical setup (as in Gali (2011)):
  - Households maximize intertemporal utility: E0 ∑ β^t U(Ct, {Nt(i)})∞t=0.
  - Utility specification: U(Ct, {Nt(i)}) = log Ct − ∫0^1 Nt(i)^(1+φ)/(1+φ) di.
  - Budget constraint: Pt Ct + Qt Bt ≤ Bt−1 + ∫0^1 Wi(i) Nt(i) di + Πt.
- Derived traditional wage Phillips curve (theoretical form):
  - πt^w = α(1−β)^(−1) + γ π̄_{t−1}^p − δ û_t − ψ1 Δû_t, for δ>0, γ>0, α>0, 0<β<1 and ψ1<0.
- Empirical linear representation derived from theory (equation (1)):
  - π_{t,w,4} = a0 + a1 π_{t−1,8} + a2 û_t + a3 Δû_t + ε_t.
  - Expectations for coefficients: a1 and a3 positive; a2 negative.
  - Definitions: π_{t,w,4} is a 4-quarter moving average nominal wage inflation; π_{t−1,8} is an 8-quarter moving average quarterly inflation lagged one quarter.

---

### Incorporating Immigration into the NK framework
- Aggregate employment CES specification:
  - N_t = (δ1 N_{1,t}^ρ + δ2 N_{2,t}^ρ)^{1/ρ}, with σ = (1−ρ)^(−1) as elasticity of substitution; N_{1,t} natives, N_{2,t} immigrants.
- Extended empirical model including immigrant unemployment gap and immigration rate (equation (2)):
  - π_{t,w,4} = b0 + b1 π̂_{t−1,8} + b2 û_t + b3 Δû_t + b4 (u_{2,t} − u_t) + b5 u_{2,t} ir_t + b6 u_{2,t} ir_t^2 + ε_t.
- Two channels by which immigration may affect wage setting:
  - Intercept/level effect: Larger immigrant vs native unemployment gap (u_{2,t} − u_t) and higher immigration rate ir_t could exert downward pressure on wages (b4 to b6 expected negative).
  - Slope effect: Different preferences/elasticities of immigrants could alter Phillips curve slope via b2 and b3.

---

### IV. The Phillips Curve: from Theory to Empirics
- Relaxations and reduced-form specifications:
  - Replace model-consistent rational expectations with survey (consensus) measures; allow both backward and forward-looking expectations via parameter c1.
  - Allow for error-correction mechanism to account for deviations from long-term productivity-driven real wage trends.
- Error-correction augmented specification (equation (3)):
  - π_{t,w,4} = c0 + c1 π_{t−1,8} + (1−c1) π_{t+8,4} + c2 û_t + c3 ê_{t−4} + ε_t.
  - ê_{t−4} is the residual from: log(W_t) = μ0 + μ1 * log(YL_t) + μ2 * dum * log(YL_t) + e_t, where dum = 1 for 2005Q1 to 2008Q1 and 0 otherwise.
- Reduced-form with immigration rate (equation (4)):
  - π_{t,w,4} = d0 + d1 π_{t−1,8} + (1−d1) π_{t+8,4} + d2 û_t + d3 ê_{t−4} + d4 ir_t + ε_t.
  - If foreign labor dampens wage inflation, expect d4 significant and negative.

- Estimation summary and findings (textual):
  - Specifications directly from NK microfoundations (equations (1) and (2)) show unemployment gap and change in unemployment gap play roles in explaining aggregate wage dynamics; coefficients are large, highly significant and of expected sign.
  - Inflation expectations (lagged price inflation) positively related to wage inflation.
  - Coefficients related to immigration on aggregate wage growth are statistically non-significant in most specifications, suggesting immigration played no additional role in explaining aggregate wage dynamics in Germany.
    - Exception: column II of Table 1 shows the gap between immigrant unemployment and total unemployment positive and significant, but judged largely spurious in text.
  - Error-correction term negative: positive deviations of wages from long-term equilibrium determined by labor productivity have dampening effects on subsequent wage growth.
  - Table 1: adjusted R-squared reported as 0.69, 0.47, 0.73, 0.55 for four specifications (Samples 1992-17 and 1995-17), with Observations = 103 and 91 depending on sample.
  - Recursive/rolling estimates: the slope of the Phillips curve converges to a long-term, stable, significant and negative value (Figure 9.1).
  - Decomposition (Figure 9.2): unemployment gap dominant in early 1990s and Hartz reforms period; unemployment gap has been pointing towards higher wages since 2016; model explains wage inflation well with limited error term contribution except pre-crisis and 2014-2015.

---

### Table 1 highlights (as shown)
- Samples and fit:
  - Sample 1992-17 Observations 103 Adj. R-squared 0.69.
  - Sample 1995-17 Observations 91 Adj. R-squared 0.47.
  - Alternate specifications sample 1992-17 Observations 103 Adj. R-squared 0.73.
  - Alternate specifications sample 1995-17 Observations 91 Adj. R-squared 0.55.
- Notes:
  - Serial correlation and heteroskedasticity-robust Newey-West standard errors in parenthesis.
  - ***/**/* indicate significance at the 1%/5%/10%-level.

---

### V. Immigration and Wages: Evidence from Social Security Data

### A. Panel data, estimation strategy and variables
- Data source and structure:
  - Administrative data from the Federal Employment Agency for 2012–2016.
  - Panel built by grouping workers by characteristics: sex, age, nationality, qualification, sector, region, working time — combinations produce 14,960 different cells per year.
  - For each cell, wages are broken into 154 wage groups at 50 euros intervals.
- Estimation approach:
  - Restricted weighted least squares (WLS) panel estimation of log wages with dummy controls for cross-sectional characteristics (Dt for time fixed effects; dummies for sex, age, nationality, qualification, sector, region, working time).
  - Weighted restrictions imposed so coefficients are deviations from average wage; weights reflect employment share averaged over periods.
  - Time fixed effects capture time-dependent drivers of average wages (productivity growth, inflation expectations).
  - Migration intensity by sector (mig/all) measured as migrant share in total employment; variable lagged by one period (mig/all)_{m,t−1} to mitigate endogeneity.
  - Sample split into below- and above-median wage groups to measure heterogeneous effects across wage distribution.

- Wage equation (equation (5)):
  - w_{ijklmno,t} = ∑_{t=1}^3 β_t D_{time,t} + ∑ β_i D_{sex,i} + ∑ β_j D_{age,j} + ∑ β_k D_{nat,k} + ∑ β_l D_{qual,l} + ∑ β_m D_{sec,m} + ∑ β_n D_{reg,n} + ∑ β_owt D_{owt} + b(mig_all)_{m,t−1} + ε_{ijklmno,t}.
- Additional controls:
  - Minimum wage introduction in 2015 controlled by indicator interacted with time fixed effects (workers earning below minimum wage in 2014).
  - Robustness: distributed lag model with t, t−1, t−2 lags tried with no material changes.

---

### B. WLS panel results (Table 3) — selected coefficients and statistical outcomes
- Sample sizes and overall statistics:
  - N = 43,300 (wage groups below median wage) and N = 13,963 (wage groups above median wage).
  - F(40, 43260) = 4331558.58 (below median); F(37, 13925) = 3689999.04 (above median).
  - Prob > F = 0.000 for both.
  - Root MSE = 0.011 (below median); Root MSE = 0.014 (above median).
- Key coefficient estimates (coefficient, S.E., p value) — selected rows reproduced exactly as reported:
  - migrant intensity (t-1): 0.001 0.001 0.153 (below median); 0.007 0.003 0.011 (above median).
  - German: 0.003 0.000 0.000 (below); 0.003 0.000 0.000 (above).
  - Europe without EU: -0.006 0.003 0.033 (below); -0.067 0.006 0.000 (above).
  - EU: -0.031 0.003 0.000 (below); -0.042 0.004 0.000 (above).
  - 8 asylum countries: -0.087 0.009 0.000 (below); -0.124 0.029 0.000 (above).
  - other migrants: -0.048 0.005 0.000 (below); -0.077 0.009 0.000 (above).
  - male: 0.013 0.001 0.000 (below); 0.063 0.001 0.000 (above).
  - female: -0.011 0.001 0.000 (below); -0.086 0.001 0.000 (above).
  - Age and qualification: e.g., low: -0.063 0.001 0.000 (below); -0.213 0.004 0.000 (above). high: 0.068 0.003 0.000 (below); 0.223 0.001 0.000 (above).
  - Sector examples: Manufacturing 0.113 0.003 0.000 (below); 0.040 0.007 0.000 (above). Accommodation and food service activities -0.189 0.007 0.000 (below); -0.384 0.051 0.000 (above).
  - Working-time and job-type: SVB+full-time 0.499 0.001 0.000 (below); 0.140 0.001 0.000 (above). SVB+part-time -0.067 0.002 0.000 (below); -0.362 0.001 0.000 (above). marginal -0.795 0.002 0.000 (below); 0.000 0.000 0.000 (above).
  - Region: West 0.027 0.000 0.000 (below); 0.008 0.000 0.000 (above). East -0.087 0.001 0.000 (below); -0.065 0.002 0.000 (above).
  - Year fixed effects: 2013 7.185 0.008 0.000 (below); 8.010 0.013 0.000 (above). 2014 7.212 0.009 0.000 (below); 8.031 0.014 0.000 (above). 2015 7.236 0.009 0.000 (below); 8.050 0.014 0.000 (above). 2016 7.255 0.010 0.000 (below); 8.064 0.014 0.000 (above).
  - Minimum wage indicators: 2013-2014 -0.781 0.003 0.000; 2015-2016 -0.773 0.003 0.000 (as reported).
- Textual interpretation of Table 3:
  - Being German is associated with a positive deviation of +0.3 percent relative to the national wage average (small due to large native share).
  - All other nationality groups have wages below the national average after controlling for characteristics; e.g., 8 asylum countries: -8.7 percent (below median) and -12.4 percent (above median).
  - Wages of men are typically higher controlling for other factors; manufacturing sector associated with higher wages.
  - Controlling for all factors, including that wages of foreigners are typically lower, the coefficient of the immigration variable is:
    - 0.001 (S.E. 0.001 p=0.153) for wage groups below median.
    - 0.007 (S.E. 0.003 p=0.011) for wage groups above median.
  - Text conclusion: the coefficient of the immigration variable is positive and equal to 0.0071 for the upper [half of wage distribution] (text reports 0.0071).

---

*Italic: Source: wpiea2019301-print-pdf — IMF staff calculations based on Eurostat, The Institute for Employment Research, Bundesbank, Destatis, Federal Employment Agency, Consensus Forecasts, Haver Analytics.*

### 0.0014 for the lower wage half. These coefficients are to be interpreted as marginal effects:

### Composition effect: shift share analysis

### Immigration and wage effects — key empirical findings
- Coefficient estimates to be interpreted as marginal effects: overall wages would increase by 0.71 (0.14) percent if the immigration rate increased by 1 percentage point of total population.
- Sectoral migration intensity:
  - Migration induced a yearly increase in the sectoral migrant’s shares of 0.48 percentage point of total employment.
  - Applying the 0.48 percentage point yearly increase to the estimated coefficients in the two wage halves translates into an overall yearly wage increase of 0.26 percent.
- Heterogeneous effects by wage segment:
  - Complementarity with migrants is more important for the higher-wage jobs segment, producing positive wage effects in the upper-half of the wage distribution.
  - The lower-wage half exhibits smaller positive marginal coefficients (reference to 0.0014 for the lower wage half appears in the source).
- Within-group competition among non-German groups:
  - Panel regression across four non-German groups (Europe without EU, EU, 8 asylum counties, other migrants) yields a coefficient estimate of -0.033 (p-value = 0.00).
  - Average migrant intensity of these four groups rose from 1.79 percent in 2012 to 2.37 percent in 2016, or 0.14 percentage points per year.
  - Using the -0.033 coefficient and the 0.14 percentage points per year increase implies a negative yearly wage effect of -0.48 percent for workers within these migrant groups.
- Aggregate interpretation:
  - While within-group competition can exert negative wage pressure on specific migrant groups, the aggregate effect across the economy is estimated to be positive due to larger wage gains for workers complementary to migrants.

### Shift-share (composition) analysis: methodology and results
- Method:
  - Constructed a counterfactual composition of the labor force under the assumption that no immigration occurred between 2012 and 2016.
  - Multiplied the coefficients for dummy variables in equation 5 (estimated from the whole sample) with the difference between the actual and counterfactual structures in 2016 to compute impacts on wages from changes in gender, age, sectoral composition, qualification, nationality, job/working time, and region.
- Aggregate composition effect (2012–2016):
  - The shift-share analysis suggests that immigration reduced average wage growth by 0.49 percent in Germany over the period 2012-16 (equivalent to -0.12 percent per year).
- Composition effect broken down (contribution to total -0.49):
  - nationality: -0.18
  - sex: 0.02
  - age: -0.05
  - qualification: 0.01
  - sector: -0.24
  - job/working time: -0.08
  - region: 0.02
  - Total: -0.49

### Net effect of immigration on aggregate wages and interpretation
- Comparison of composition and competition effects:
  - Composition effect (total, 2012–2016): -0.49 percent (i.e., wages would have been 0.49 percent higher in 2016 absent net migration).
  - Competition (interaction/complementarity) effect: +0.26 percent per year (from sectoral coefficient application).
  - Translating the composition result to an annualized figure gives -0.12 percent per year (i.e., -0.49 over four years).
  - Loosely combining the annual figures: overall effect on net wages ≈ +0.14 percent per year (0.26-0.12 percent).
- Interpretation and caveats:
  - The composition effect reflects that foreigners tend to be paid less than German workers and that immigrants concentrate in younger, lower-skilled cohorts and low-paid sectors (sectoral concentration contributes -0.24 percent).
  - Competition effects raised wages for better-skilled and better-paid workers who are complements to migrants, more than offsetting composition-driven downward pressure at the aggregate level.
  - Evidence of negative wage pressure is observed within migrant groups concentrated in low-wage sectors, even where aggregate effects are modestly positive.
  - Overall conclusion from the analysis: there is no evidence of downward pressure on aggregate wages from immigration; if anything, the overall effect has been (very) slightly positive.

### Broader conclusions on wage dynamics and the Phillips curve
- Short- and long-term drivers of wage growth in Germany:
  - The Phillips curve remains relevant: in the short term, wage growth reacts to labor market tightness and inflation expectations; in the longer term, real wage developments are driven by productivity growth.
  - The NAIRU declined significantly throughout the 2000s, reflecting labor market reforms and increased efficiency rather than simply tighter labor markets.
- Role of immigration in recent wage trends:
  - More than half of post-crisis employment growth is attributable to foreign labor, motivating the analysis.
  - Empirical evidence combining macro Phillips-curve methods and micro administrative IAB data indicates that immigration did not play an independent role in explaining aggregate wage fluctuations.
  - Composition effects (negative) and within-group competition (negative for specific migrant groups) were outweighed at the aggregate level by positive complementarity effects for higher-skilled workers.
  - Net result: competition effects resulted in upward pressure on wages—especially in the upper-half of the wage distribution—and more than offset composition effects, yielding a negligible if positive aggregate impact of immigration on wage growth.

### Appendix highlights (modeling and theoretical derivations)
- Appendix A (Deriving the Wage Phillips Curve from First Principles):
  - Builds on Gali (2011) and Calvo (1983) wage-setting framework with imperfect substitutability of workers and Calvo-style wage stickiness.
  - Derives a wage inflation equation where wage inflation depends on expected future wage inflation and deviations of the average wage markup from its desired level, culminating in a micro-founded Phillips curve relating wage inflation to unemployment gaps and inflation expectations.
  - Provides log-linearized expressions and shows how indexation and AR(2) unemployment-gap dynamics yield an empirical Phillips-curve form: π^w_t = α(1−β)^{-1} + γ π̄^p_{t−1} + ψ_0 û_t + ψ_1 û_{t−1}, and equivalent reduced-form representations.
- Appendix AA.2 (A Micro-founded Phillips Curve with Immigration):
  - Extends micro-foundations to incorporate two types of labor (native N1_t and immigrant N2_t) and a production function with constant returns to scale.
  - Allows different marginal rates of substitution and labor supply elasticities for immigrants and natives (ϕ_2 > ϕ_1).
  - Derives expressions where changes in real marginal cost and wage dynamics depend on overall unemployment gaps, the difference between foreign and native unemployment rates (u_{2,t} − u_t), the relative labor supply of immigrants (ir_t), and higher-order terms in ir_t.
  - Resulting empirical specification includes terms: π^w_t = τ_0 + τ_1 π̂_{t−1} + τ_2 û_t + τ_3 Δû_t + τ_4 (u_{2,t}−u_t) + τ_5 u_{2,t} ir_t + τ_6 u_{2,t} ir_t^2 + ε_t.
- Appendix B (Short and long-term determinants of wage dynamics in Germany):
  - Long-term: nominal compensation per hour follows total output per hour; from 1991 to 2017, output per hour roughly doubled and labor compensation increased at the same pace except during 2003-2010.
  - Short-term: wage Phillips curve remains operative, but dropping inflation expectations helped keep nominal wage growth stable despite falling unemployment; real wage growth recovered to a peak of 3.5 percent post-crisis.
  - Relationship between real wage growth and the unemployment gap remains clear when accounting for the decline in the natural rate of unemployment (NAIRU).

*Source: wpiea2019301-print-pdf*

### References

### References

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### Methods, measurement, and real-time estimation
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*Source: References section of the content unit "wpiea2019301-print-pdf - References".*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019301-print-pdf.pdf_