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---

### II. THEORY AND LITERATURE REVIEW
- Rationale:
  - Firms offer implicit insurance by reducing hours but maintaining stable incomes grounded in efficient contract theory (Azariadis (1975)): firm insures worker in return for a lower average wage.
- Frictions and implications:
  - Financing and liquidity constraints, and imperfect contract enforceability, can induce firms to adjust on the headcount (extensive) margin rather than hours (intensive) margin, producing excessive layoffs relative to first-best.
  - Stylized production and cost-minimization setup:
    - Production function: y = n^α h^β
    - Cost minimization: min_{n,h} Λ = n (F + ω(h) h) s.t. y̅ = n^α h^β
    - First-order conditions (as given):
      - h = (β/α) F (ε_{hω} / ω)
      - n = y̅^{1/α} ( (β/α) F (ε_{hω} / ω) )^{-1/α}
    - ε_{hω} = (dω/dh) (h/ω) is the wage elasticity w.r.t. average working hours.
    - Implication: scale changes in y̅ lead mainly to changes in n, leaving h fixed; borrowing constraints yield job losses in downturns.
- Welfare role for government:
  - Subsidizing reductions in hours (short-time work benefits, STW) or taxing firings (employment protection) can be welfare-enhancing to counteract excessive layoffs.
- Literature highlights (select):
  - Theoretical: Hall and Lazear (1984); Burdett and Wright (1985).
  - Empirical/cross-country: Abraham and Houseman (1994); Hijzen and Venn (2011); Boeri and Bruecker (2011).
  - Non-linear effects: Brey and Hertweck (2020) — diminishing returns with higher take-up and stronger effects at start of deep recessions.
  - Germany-specific mixed evidence: Burda and Hunt (2011); Bohachova et al (2011); Balleer et al. (2016); Gehrke and Hochmuth (2021).

### III. INSTITUTIONAL SETUP (Kurzarbeit features and pandemic changes)
- Program nature:
  - Permanent government subsidy to employees working reduced hours; features adjustable by Federal government in downturns.
- Eligibility:
  - Only workers contributing to social security are eligible (excludes marginal workers and some self-employed).
  - Normal minimum threshold: at least one-third of employees in a firm must be placed on reduced hours with ≥10 percent loss of gross monthly earnings.
  - Pandemic change: minimum threshold fully waived in March 2020 and not reinstated until end-September 2021.
- Replacement rate (exact parameters):
  - Normal: 60 percent (rising to 67 percent for employees with children).
  - Pandemic: raised to 70 percent (77 percent for parents) starting from the fourth month under STW, and to 80 percent (87 percent for parents) starting from the seventh month.
  - Note: unemployment benefit pays 60 percent of net income (comparable to usual Kurzarbeit rate).
- Employer costs and related waivers:
  - Normally employers pay 80 percent of social security contributions on reduced work hours.
  - Pandemic change: employer social security contribution requirement waived.
  - Private working-time accounts requirement normally binding was waived during pandemic.
- Duration:
  - Normal maximum: 6 months.
  - Pandemic change: extended to 24 months.
- Aggregate effect:
  - Easier and less costly access for firms; benefits more generous and prolonged for workers; fiscal cost per reduced working hour increased sharply for government.

### IV. EMPIRICAL STRATEGY AND DATA
- Research question:
  - Whether and by how much Kurzarbeit reduced unemployment during the COVID-19 crisis.
- Identification challenges:
  1. Need exogenous labor demand shock y that varies across states and is orthogonal to state-specific labor supply; GDP growth is endogenous.
  2. Kurzarbeit (KA) take-up is endogenous to labor market conditions (pro-cyclical firm behavior), biasing estimates toward zero.
- Baseline empirical relationship:
  - z_{st} = α_z + η_{z,st} y_{st} + α_3' X_{st} + γ_s + ε_{st}
  - η_{z,st} = ∂ z_{st} / ∂ y_{st}; if KA works: η_{z,st} = α_1 + α_2 KA_{st}.
  - Substitution yields: z_{st} = α_z + α_1 y_{st} + α_2 (y_{st} × KA_{st}) + α_3' X_{st} + γ_s + ε_{st}
  - Hypotheses on signs:
    - If z = employment growth: α_1 > 0 and α_2 < 0.
    - If z = change in unemployment: α_1 < 0 and α_2 > 0.
- Data and timing:
  - Monthly state-level unemployment and employment data; monthly retail trade turnover index; focus on monthly changes during 2020.
  - Observed peak: share of 10-15 percent of employed workers across states placed in KA in April 2020; share declined by roughly half by the third quarter.
- Construction of exogenous labor demand shocks (shift-share/Bartik):
  - Two alternative metrics:
    i. Contact-intensive exposure:
       - y_{st}^{CI} = ΔRetail&Rec Mobility_t × empshr_{s,t-1}^{CI}
       - ΔRetail&Rec Mobility_t from Germany-wide Google Community Mobility Report.
       - empshr^{CI} is pre-existing state employment share in Accommodation & Food, Retail & Wholesale Trade, Culture & Arts.
    ii. Accommodation & Food exposure:
       - y_{st}^{AF} = ΔlnTurnover_A&F_t × empshr_{s,t-1}^{A&F}
       - ΔlnTurnover_A&F_t is Germany-wide monthly change in volume turnover in accommodation and food services.
  - Both series show sharp decline at pandemic onset in March 2020, partial recovery over Q3, renewed slump toward end of year.
- Addressing KA endogeneity:
  - Use regional monthly variation and Bartik shocks; instrument interaction terms with pre-existing share of social-security-contributing workers (ssc share) in 2019.

### Identification and Instrument (Appendix Figure 2 summary)
- Instrument:
  - Pre-existing share of workers subject to social security contributions (ssc) in the same month one year earlier (2019).
  - Rationale: eligibility requires social security contributions; pre-existing ssc share predicts KA take-up conditional on state exposure to contact-intensive sectors.
- Diagnostics:
  - First-stage: endogenous variable strongly positively correlated with pre-existing ssc share; first-stage F-statistics high, close to thirty.
  - Over-identification: interaction of the labor demand shock with ssc share used as additional instrument; Hausman test rejects OLS validity at the 5 percent significance level.

### V. LABOR MARKET IMPACT (OLS and 2SLS results)
- OLS qualitative findings:
  - Decreases in labor demand from mobility restrictions or A&F shutdowns significantly increase unemployment and reduce employment growth.
  - Stronger KA take-up mitigates adverse demand impact: interaction term positive and significant in unemployment specifications and negative and significant in employment growth specifications.
- OLS quantitative magnitudes (median shocks, 2020Q2):
  - A 10 percentage point increase in KA take-up (the average take-up across states over 2020Q2):
    - For contact-intensive median shock: dampened rise in unemployment by 1.1 ppt; raised employment growth by 1.3 ppt.
    - For hospitality (A&F) median shock: dampened rise in unemployment by 1.2 ppt; boosted employment growth by 1.3 ppt.
- Endogeneity and 2SLS amplification:
  - 2SLS instruments interaction term with pre-existing ssc share and its interaction with labor demand shocks.
  - 2SLS estimates on the interaction term are more than twice as large (in absolute value) compared to OLS.
- Counterfactual unemployment (2020Q2 relative to Jan 2020 baseline) using 2SLS:
  - Unemployment rate would have increased by an additional 2.9 percentage point on average across states if KA take-up was unchanged during 2020Q2 relative to pre-crisis levels.
  - Largest impacts in Hamburg and Bremen: unemployment would have increased by an additional 3.5 - 4 percentage points.
  - More rural states or states with lower ssc share would have seen a less pronounced, though still significant, increase.
  - Counterfactual results similar using alternative shift-share metric y_st_AF.

- Key reported coefficients (preserve exact table values):
  - Table 1 (OLS main coefficients; Observations = 192):
    - Column (1) DV: Change in UR
      - y_ci_st = -0.124*** (0.033)
      - y_ci_st*KA_st = 1.450*** (0.145)
    - Column (2) DV: Employment growth
      - y_ci_st = 0.315*** (0.082)
      - y_ci_st*KA_st = -1.667*** (0.153)
    - Column (3) DV: Change in UR
      - y_af_st = -0.218*** (0.023)
      - y_af_st*KA_st = 2.935*** (0.259)
    - Column (4) DV: Employment growth
      - y_af_st = 0.253*** (0.042)
      - y_af_st*KA_st = -3.247*** (0.409)
    - R-squared: 0.643, 0.654, 0.726, 0.720 respectively.
  - Table 2 (2SLS main coefficients; Observations = 192):
    - y_ci_st = -0.308 (0.242) and 0.535* (0.302)
    - y_ci_st*KA_st = 3.841*** (0.750) and -4.531*** (0.816)
    - y_af_st = -0.820*** (0.109) and 0.790*** (0.133)
    - y_af_st*KA_st = 6.535*** (1.022) and -7.059*** (1.245)
    - First-stage sscshr_s,t-1 coefficients: 14.753*** (2.268) and 8.568** (1.251)
    - F-stat (p-val): 28 (0.00) and 29 (0.00)
    - Sargan overid test statistics: 0.794, 0.767, 0.907, 0.503

### B. IMPACT ON DOMESTIC DEMAND (Retail turnover)
- Mechanisms:
  - KA may support consumption via higher replacement rates during the pandemic and by preserving job retention, reducing idiosyncratic risk and precautionary saving.
  - Pandemic KA replacement increases after four months exceeded unemployment benefit replacement.
- Evidence and magnitudes:
  - Scatter shows adverse labor demand shock had important impact on private consumption, especially in deepest contractions (April 2020).
  - Regression results (Table 3; Observations = 188):
    - OLS (y_ci baseline):
      - y_ci_st = 0.005 (0.006)
      - y_ci_st*KA_st = 0.054*** (0.013)
    - 2SLS (y_ci baseline):
      - y_ci_st = 0.024** (0.012)
      - y_ci_st*KA_st = -0.159* (0.088)
    - OLS (y_af baseline):
      - y_af_st = -0.000 (0.004)
      - y_af_st*KA_st = 0.098*** (0.029)
    - 2SLS (y_af baseline):
      - y_af_st = 0.071** (0.032)
      - y_af_st*KA_st = -0.663* (0.343)
    - 1-st stage F-stat (p.val): 9.1 (0.00) and 3.7 (0.03)
    - R-squared vary: 0.704, 0.289, 0.742, 0.531
  - Counterfactual retail turnover:
    - Absent expanded KA take-up:
      - Retail trade turnover would have declined by three times as much as it actually did in April 2020.
      - For 2020Q2 as a whole, retail trade turnover would have been 15 percent lower than actual.

### VI. ROBUSTNESS AND ADDITIONAL RESULTS
- Alternative export demand shock (y_ex):
  - OLS (median export shock, 2020Q2): observed KA take-up dampened unemployment by 0.4 pp and boosted employment growth by 1.2 pp.
  - 2SLS: KA impact of 0.8 pp for unemployment and 1.4 pp for employment growth.
  - IV approach with ssc share does not exhibit strong first-stage results for export shock.
- Month-by-month pooled panels (March, April, May across 2009–2020):
  - March panel shows much larger estimated dampening impact of KA on unemployment—strong automatic stabilizing role at downturn start.
  - Results similar or stronger than baseline; limited bias from autocorrelation.
- Pre-shock trends inclusion (May 2019–Dec 2020; ten months before and ten months during crisis):
  - Baseline 2SLS with accommodation and food shock yields interaction coefficients:
    - unemployment rate: 7.4 compared to 6.5 (baseline);
    - employment growth: -9.6 compared to -7.1 (baseline).
  - Conclusion: baseline estimates robust to pre-crisis dynamics.
- Robustness in specifications and instrument validity:
  - Columns 3–4 in Table 6 show qualitatively consistent but smaller magnitudes.
  - Controlling for regional industry mix (shares in contact-intensive, hospitality, exports, manufacturing) does not materially change main second-stage estimates; first-stage remains strong.
  - First-stage coefficient for manufacturing employment share impacts KA take-up but does not affect main second-stage coefficients.

### POST-CRISIS REALLOCATION: LESSONS FROM THE GFC AND MISALLOCATION RESULTS
- Motivation:
  - Assess medium- and long-term reallocation effects of STW given critiques that STW may impede efficient reallocation and productivity growth.
- Descriptive and cross-country evidence:
  - Simple correlation between STW take-up and change in unemployment is negative (Figure 7).
  - For three OECD countries with highest STW take-up (Belgium, Italy, Germany) there is no systematic larger widening of labor misallocation relative to low-STW countries (Portugal, UK, US) over 2009–2017.
  - Cross-sectional regression for 26 OECD countries shows no statistically significant correlation for change in misallocation at standard horizons (Appendix Figure 4).
- Empirical test (Table 8; t = 2009 horizons):
  - Regression: ∆Misallocation_{c,t→t+j} = c + α Misallocation_{c,t} + β STW_{c,t} + γ Misallocation_{c,t} × STW_{c,t} + ε_{c,t+j}
  - Key coefficients (selected horizons):
    - Misalloc_t coefficients (t+3 to t+8): -0.614*** (0.146), -0.925*** (0.133), -0.706*** (0.175), -0.967*** (0.280), -0.681** (0.293)
    - STW_t coefficients: -0.019 (0.032), -0.105*** (0.030), -0.110*** (0.022), -0.117*** (0.036), -0.074** (0.032)
    - Misalloc_t*STW_t interaction: 0.001 (0.091), 0.230*** (0.070), 0.293*** (0.050), 0.274*** (0.083), 0.166** (0.075)
  - Interpretation:
    - Positive interaction and negative standalone STW coefficient imply non-linearity: when pre-existing misallocation is high, high STW take-up associated with greater subsequent misallocation.
    - Largest estimated interaction magnitude for j = 6 and j = 7.
    - If initial misallocation below threshold (as for Germany), STW usage not associated with greater subsequent misallocation.
  - Authors treat these results as exploratory, suggesting a trade-off in economies entering a crisis with high misallocation.

### CONCLUSION AND POLICY IMPLICATIONS
- Evidence summary:
  - Germany’s Kurzarbeit (KA) was very powerful in reducing unemployment and stabilizing aggregate demand during the COVID-19 pandemic using state-level variation in KA take-up.
  - Preliminary cross-country GFC evidence indicates greater STW use in 2009 is associated with greater misallocation several years later, but only above a threshold of initial misallocation.
- Policy implications and recommendations:
  - A well-designed job-retention program can effectively stabilize labor markets and aggregate demand in a crisis.
  - Policymakers should recognize a potential trade-off: in economies with large initial cross-sector productivity differences, STW may hinder medium-term reallocative efficiency.
  - Recommendation for future research: focus on mediating the trade-off between short-run stabilization benefits of STW and medium-run reallocation costs.

*Source: wpiea2021242-print-pdf*

### Section IV details the empirical strategy, and Section V provides baseline results. Section VI

### Appendix Figure 2.

### Appendix Figure 2 (wpiea2021242-print-pdf)

### Identification and Instrument
- Data and challenge:
  - KA take-up is strongly correlated with the business cycle during 2020, creating an identification challenge: OLS of unemployment on KA take-up will typically underestimate any mitigating impact of KA, biasing the coefficient toward zero.
- Instrumental variable:
  - Instrument: the share of workers subject to social security contributions (ssc) in the same month one year earlier, in 2019.
  - Rationale: Only contributors to the social security system are eligible for KA benefits; the pre-existing eligibility pool in 2019 should predict state-specific KA take-up given a labor demand shock while being plausibly unrelated to the severity of the pandemic shock in 2020, conditional on state exposure to contact-intensive sectors.
  - Exclusion restriction: state-specific exposure to contact-intensive sectors is controlled for.
  - First-stage diagnostics: the endogenous variable is strongly positively correlated with the pre-existing share of ssc workers; first-stage F-statistics are high, close to thirty.
  - Over-identification and endogeneity tests: using the interaction of the labor demand shock with ssc share as an additional instrument allows an over-identification test suggesting instrument validity; a Hausman test rejects the null hypothesis of OLS validity at the 5 percent significance level.

### A. Labor Market Impact (OLS and 2SLS results)
- OLS qualitative findings:
  - A decrease in labor demand from mobility restrictions in contact-intensive sectors, or shutdowns in Accommodation and Food, significantly increases the unemployment rate and reduces employment growth.
  - Stronger KA take-up mitigates the adverse demand impact: interaction term is positive and statistically significant for unemployment rate specifications and negative and statistically significant for employment growth specifications.
- OLS quantitative magnitudes (median shocks, 2020Q2):
  - For the median shock to contact-intensive labor demand in 2020Q2, an increase in KA take-up of 10 percentage points (the average take-up across states over 2020Q2):
    - dampened the rise in the unemployment rate by 1.1 ppt;
    - raised employment growth by 1.3 ppt.
  - For the median shock to the hospitality sector, the same 10 percentage point increase in KA take-up:
    - dampened the rise in unemployment by 1.2 ppt;
    - boosted employment growth by 1.3 ppt.
- Endogeneity and 2SLS:
  - OLS estimates are likely downwardly biased (in absolute value) because firms in more adversely affected states expanded KA take-up more.
  - 2SLS strategy instruments the interaction term with the pre-existing ssc share and its interaction with each labor demand shock.
  - 2SLS results:
    - Coefficient estimates on the interaction term between the labor demand shock and KA take-up, properly instrumented, are more than twice as large (in absolute value) compared to OLS.
- Counterfactual unemployment (2020Q2 relative to Jan 2020 baseline):
  - Applying the estimated 2SLS coefficient to observed changes yields:
    - The unemployment rate would have increased by an additional 2.9 percentage point on average across states if KA take-up was unchanged during 2020Q2 relative to pre-crisis levels.
    - Largest impacts in states dominated by a single metropolis with large services sectors—Hamburg and Bremen—where unemployment would have increased by an additional 3.5 - 4 percentage points.
    - More rural, less densely populated states and/or states with a lower share of ssc workers would have seen a less pronounced, though still significant, increase in unemployment.
  - Counterfactual results are similar using the alternative shift-share metric 푦_st_AF for labor demand (Appendix Figure 3).

### B. Impact on Domestic Demand (Retail turnover)
- Mechanisms:
  - KA may or may not boost consumption relative to layoffs because unemployment benefits can provide similar net replacement in principle; however:
    - Replacement rate through KA was significantly increased during the pandemic to levels substantially above unemployment benefit replacement after four months on short-time work.
    - KA participation preserves job retention, reducing idiosyncratic risk and precautionary saving, potentially supporting consumption.
- Evidence:
  - Scatter of monthly retail trade turnover growth against shock to contact-intensive labor demand shows a positive slope: adverse labor demand shock had an important impact on private consumption, steepening where contraction was deepest (April 2020).
- Regression results (OLS and 2SLS) using monthly retail trade volume turnover index:
  - KA take-up is highly endogenous to demand conditions; OLS and 2SLS yield opposite signs for the key interaction term.
  - IV remains strong and valid; OLS rejected at 5 percent significance level.
- Economic magnitudes (counterfactual retail turnover):
  - Absent an expanded take-up of KA:
    - Retail trade turnover would have declined by three times as much as it actually did in April 2020.
    - For 2020Q2 as a whole, retail trade turnover would have been 15 percent lower than actual.
  - Interpretation: KA contributed to stabilizing both the labor market and domestic demand by providing income support and reducing uncertainty for firms and workers.

### VI. Robustness and Additional Results
- Alternative export demand shock:
  - Constructed shift-share variable 푦_st_Ex = ∆ln exp_t × expshr_s,t−1 (Germany-wide export growth × pre-existing state-level export share).
  - OLS (median export shock, 2020Q2): observed average KA take-up dampened unemployment by 0.4 pp and boosted employment growth by 1.2 pp.
  - 2SLS: KA impact of 0.8 pp for unemployment and 1.4 pp for employment growth.
  - Comparison: export-shock identification delivers consistent but quantitatively smaller dampening impacts than the services-sector demand shock.
  - Note: the IV approach with ssc share does not exhibit strong first-stage results for the export shock.
- Month-by-month pooled panels (March, April, May across 2009-2020):
  - March panel shows a much larger estimated dampening impact of KA on unemployment, suggesting KA’s automatic stabilizing role was most pronounced at the beginning of the downturn.
  - Overall, month-by-month pooled panels deliver results similar or stronger than baseline, indicating limited bias from autocorrelation.
- Including pre-shock trends (May 2019 to December 2020 sample; ten months before and ten months during the crisis):
  - Baseline 2SLS regression with accommodation and food shock yields coefficient estimates on key interaction term similar to baseline and slightly larger:
    - unemployment rate: 7.4 compared to 6.5 (baseline);
    - employment growth: -9.6 compared to -7.1 (baseline).
  - Conclusion: baseline estimates are robust to controlling for pre-crisis dynamics.

*Source: wpiea2021242-print-pdf - Appendix Figure 2.*

### section II). This is to explore whether differences in program parameters change the

### wpiea2021242-print-pdf - section II)

### Robustness of estimated KA (Kurzarbeit) impacts and instrument validity
- Purpose: explore whether differences in program parameters change the estimated impact of KA.
- Findings from alternative specifications:
  - Columns 3-4 in Table 6 show results qualitatively consistent with the baseline specification but smaller in absolute magnitude.
  - Columns 1-2 together with 3-4 imply that the largest benefits of KA in terms of dampening unemployment occurs at the beginning of the downturn (here March 2020).
  - Inclusion of some months prior to the surge in KA and unemployment is important to capture the early variation when the change in KA take-up was most pronounced.
- Controlling for regional industry mix to strengthen the IV exclusion restriction:
  - Concern: pre-existing share of ssc workers may be driven by regional industry mix, which could also determine exposure to the pandemic lockdown.
  - Approach: both OLS and IV specifications control for the share of employment in the sector subject to the shock:
    - For the baseline contact-intensive sector shock: share of employment in contact-intensive sectors.
    - For the accommodation and food services shock: share of employment in hospitality sectors.
    - For the export shock: share of exports in regional GDP.
  - Joint controls: Table 7 includes all three employment shares plus the share of employment in manufacturing.
  - First-stage result: the employment share in manufacturing has a strong positive impact on KA take-up but does not affect the first-stage coefficients on the instrumental variable, nor the main coefficient estimates of the second stage.
  - Conclusion: main regional characteristics which may determine a state’s exposure to the pandemic shock are not spuriously captured by the IV, though other structural differences cannot be fully ruled out.

### Post-crisis reallocation: lessons from the GFC (Great Financial Crisis)
- Motivation: evaluate medium- and long-term reallocation effects of short-time work (STW) programs given critiques that STW may prevent efficient resource reallocation and lower productivity growth (cited Boeri and Bruecker, 2011; Burdett and Wright, 1989).
- Simple correlations and descriptive evidence:
  - The simple correlation between STW take-up and the change in unemployment is negative (Figure 7).
  - Sectoral misallocation is computed as the change in the standard deviation of log dispersion of MRPL across 2-digit sectors within each country (see notes to Figure 7).
  - Data sources: STW take-up in 2009 from Hijzen and Venn (2011); OECD, EU-KLEMS, IMF WEO and authors’ calculations.
  - For the three OECD countries with the highest take-up of STW schemes (Belgium, Italy, Germany) there is no systematic larger widening of labor misallocation relative to countries with little use of STW (Portugal, the UK, the US) over 2009-2017 (Figure 5, right panel).
  - A simple cross-sectional regression of the change in misallocation at all time horizons after 2009 on STW usage in 2009 for a set of 26 OECD countries does not deliver any statistically significant correlation (Appendix Figure 4 for the 5-year horizon illustration).

### Empirical test of STW and sectoral misallocation dynamics
- Conceptual framing:
  - Labor misallocation proxied by cross-sectoral dispersion in log marginal revenue product of labor (MRPL) following Hsieh and Klenow (2009).
  - Perfect equality of MRPL across sectors represents zero misallocation. Prolonged STW could retain inefficient job matches and impede reallocation.
  - STW could also be productivity-enhancing if it preserves firm- and industry-specific human capital and supports liquidity for investment and hiring during recovery.
- Regression specification (as presented in the source):
  - ∆푀푖푠푎푙푙표푐푎푡푖표푛
    푐,푡→ 푡+푗
    =푐+훼푀푖푠푎푙푙표푐푎푡푖표푛
    푐,푡
    + 훽푆푇푊
    푐,푡
    + 훾푀푖푠푎푙푙표푐푎푡푖표푛
    푐,푡
    ×
    푆푇푊
    푐,푡
    + 휀
    푐,푡+푗
  - Where t = 2009 and the change in misallocation is measured by the change in country-level sectoral standard deviation in log MRPL.
- Key empirical findings (Table 8 summary):
  - The interaction term between initial misallocation and STW take-up is positive, while the standalone STW coefficient is negative.
  - Interpretation: if pre-existing misallocation is high, high STW take-up is associated with greater subsequent misallocation; there exists a threshold of initial misallocation above which higher STW take-up in 2009 led to greater misallocation after 6-7 years.
    - The magnitude of the estimated interaction term is largest for j = 6 and j = 7.
  - If initial misallocation is below the threshold—as it was for Germany—STW usage is not associated with greater subsequent misallocation of resources.
  - The authors view these results as exploratory but indicative of a non-linearity: economies entering a crisis with high misallocation face a trade-off between STW usage to curb unemployment and medium-run allocative efficiency.

### Conclusion and policy implications
- Evidence summary:
  - The paper provides early evidence that Germany’s Kurzarbeit (KA) was very powerful in reducing unemployment and stabilizing aggregate demand during the COVID-19 pandemic, using state-level variation in KA take-up.
  - Preliminary cross-country evidence from the GFC indicates greater use of STW during 2009 is associated with greater misallocation several years later, but only in economies above a certain initial-misallocation threshold.
- Policy implications:
  - A well-designed job-retention program can be an effective tool to stabilize labor markets and aggregate demand in a crisis.
  - Where economies exhibit large initial differences in labor market productivity across sectors, policymakers should be aware of the potential trade-off with medium-term rigidities and allocative efficiency.
  - Recommendation for future research: focus on how best to mediate the trade-off between short-run stabilization benefits of STW and medium-run reallocation costs.

*Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021242-print-pdf.pdf*

### 335. Brookings Institute Press.

### 335. Brookings Institute Press.

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### Main empirical estimates (OLS and 2SLS results)
- Estimation sample period: January to December 2020 for 16 states.
- Key regressors and definitions:
  - y_ci_st: contact-intensive demand shock.
  - y_af_st: accommodation & food demand shock.
  - KA = short-time workers in pct of total state employment.
  - DV in Tables 1–4: Change in UR (unemployment rate) and Employment growth.
  - Robust standard errors clustered at state level reported where indicated.

- Table 1 (OLS main coefficients):
  - Column (1) DV: Change in UR
    - y_ci_st = -0.124*** (0.033)
    - y_ci_st*KA_st = 1.450*** (0.145)
  - Column (2) DV: Employment growth
    - y_ci_st = 0.315*** (0.082)
    - y_ci_st*KA_st = -1.667*** (0.153)
  - Column (3) DV: Change in UR
    - y_af_st = -0.218*** (0.023)
    - y_af_st*KA_st = 2.935*** (0.259)
  - Column (4) DV: Employment growth
    - y_af_st = 0.253*** (0.042)
    - y_af_st*KA_st = -3.247*** (0.409)
  - Observations = 192 in all columns.
  - R-squared: 0.643, 0.654, 0.726, 0.720 respectively.

- Table 2 (2SLS main coefficients and first-stage):
  - Columns (1) and (3) DV: Change in UR; (2) and (4) DV: Employment growth.
  - Selected coefficients:
    - y_ci_st = -0.308 (0.242) and 0.535* (0.302)
    - y_ci_st*KA_st = 3.841*** (0.750) and -4.531*** (0.816)
    - y_af_st = -0.820*** (0.109) and 0.790*** (0.133)
    - y_af_st*KA_st = 6.535*** (1.022) and -7.059*** (1.245)
  - First-stage instrument sscshr_s,t-1 coefficients: 14.753*** (2.268) and 8.568** (1.251) reported.
  - F-stat (p-val): 28 (0.00) and 29 (0.00).
  - Sargan overid test statistics: 0.794, 0.767, 0.907, 0.503 as reported.

- Table 3 (KA impact on retail trade turnover):
  - Dependent variable: Year on year monthly percentage change in retail trade turnover index at the state-level.
  - OLS (1) and 2SLS (2) for y_ci baseline:
    - y_ci_st = 0.005 (0.006) and 0.024** (0.012)
    - y_ci_st*KA_st = 0.054*** (0.013) and -0.159* (0.088)
  - OLS (3) and 2SLS (4) for y_af baseline:
    - y_af_st = -0.000 (0.004) and 0.071** (0.032)
    - y_af_st*KA_st = 0.098*** (0.029) and -0.663* (0.343)
  - 1-st stage F-stat (p.val) reported as 9.1 (0.00) and 3.7 (0.03).
  - Observations = 188; R-squared vary across specifications: 0.704, 0.289, 0.742, 0.531.

- Table 4 (alternative export-based labor demand y_ex):
  - y_ex_st coefficients (OLS columns):
    - dUR: -0.089*** (0.022)
    - Emp growth: 0.218*** (0.037)
  - Interaction y_ex_st*KA_s,t-1 (OLS):
    - dUR: 0.550*** (0.129)
    - Emp growth: -1.748*** (0.261)
  - Columns 3–4 report 2SLS with coefficients and standard errors as shown; Observations = 192; R-squared reported per column.

### Robustness exercises
- Table 5 (March–May pooled panels 2009–2020, 16 states):
  - Labor demand measures: y_af and y_ex.
  - Selected OLS coefficients (pooled months):
    - y_af_st ranges from -0.786*** (0.124) to -0.335*** (0.090) across columns.
    - y_af_st*KA_st large positive in some pooled months: e.g., 14.250*** (1.731), 13.402*** (1.918), and smaller positive coefficients such as 2.480*** (0.612).
    - y_ex_st coefficients include -0.022*** (0.007) and -0.014* (0.007).
    - y_ex_st*KA_st coefficients include 0.442*** (0.138) and smaller or insignificant values in other columns.
  - Observations = 192; R-squared vary across specifications up to 0.694.
  - Dependent variable: Change in UR; months pooled include March, April, May.

- Table 6 (Including and excluding pre-trends; 2SLS baseline y_af instrumented with sscshr):
  - Sample periods:
    - May 2019 - Dec 2020 (columns 1–2): Observations = 320.
    - March 2020 - Dec 2020 (columns 3–4): Observations = 160.
  - Key coefficients (2SLS first and second stage summary):
    - y_af_st = -0.972*** (0.117) and 1.236*** (0.152) in May 2019 - Dec 2020 specification.
    - y_af_st*KA_st = 7.399*** (1.225) and -9.636*** (1.609) in corresponding columns.
    - sscshr_s,t-1 = 4.758*** (0.771) in first-stage reporting and 8.870*** (1.671) in the shorter-sample first-stage.
  - F-stat (p-val) reported as 22 (0.00) and 20.4 (0.00).
  - Overid test (p-val): 0.725, 0.586, 0.725, 0.589.

- Table 7 (Additional sectoral composition controls; 2SLS with extra controls):
  - Added controls: state-specific shares of employment in accommodation and food services, export/GDP share and employment share in manufacturing.
  - Selected coefficients:
    - y_ci_s,t = -0.279 (0.242) for dUR and 0.507* (0.308) for Emp growth.
    - y_ci_s,t*KA = 3.855*** (0.763) and -4.529*** (0.852).
    - empshr_ci_t-12, empshr_af_s,t-12, expshr_s,t-12, empshr_man_s,t-12 coefficients reported as in table.
  - Observations: 192, 192, 188 across columns.
  - First-stage coefficient for sscshr_s,t-1 reported 24.015*** (2.951) and 14.662*** (2.417) in parts of the table.

### Misallocation and STW (Short-Time Work) take-up
- Table 8 (Cross-sectional model of long-term changes in dispersion of MRPL; t=2009; sources: EU-KLEMS):
  - Dependent variable: Change in misallocation between t & t+j where Misallocation measured by standard deviation of log MRPL.
  - STW_t = share of total employment participating in STW program as in Hijzen and Venn (2011).
  - Selected coefficients across horizons t+3, t+5, t+6, t+7, t+8:
    - Misalloc_t coefficients: -0.614*** (0.146), -0.925*** (0.133), -0.706*** (0.175), -0.967*** (0.280), -0.681** (0.293).
    - STW_t coefficients: -0.019 (0.032), -0.105*** (0.030), -0.110*** (0.022), -0.117*** (0.036), -0.074** (0.032).
    - Misalloc_t*STW_t interaction: 0.001 (0.091), 0.230*** (0.070), 0.293*** (0.050), 0.274*** (0.083), 0.166** (0.075).
  - Observations range: 26, 26, 26, 25, 23. R-squared range: 0.441 to 0.534 to 0.238 across columns.

### Appendix figures (descriptive visuals described in notes)
- Appendix Figure 1: Evolution of retail mobility (Google Community Mobility Report) and turnover in accommodation and food services (DESTATIS/Haver). Time series indexed with Turnover index in accommodation and food services (Volume index, SA, 201701=100) and retail and recreation mobility (Percent change from baseline, range shown from -60 to 10 on axis).
- Appendix Figure 2: Monthly change in the Unemployment Rate across 16 states during 2020. Box plots show cross-sectional distribution of change in unemployment rate across states for each month in 2020 relative to same month in 2019; “x” denotes outside values (1.5 times above the upper interquartile range).
- Appendix Figure 3: KA impact on mitigating labor demand shock using the accommodation and food services shock. Bars show by how much the unemployment rate in each state would have been higher if KA take-up had remained at pre-crisis levels, using 2SLS estimated coefficients; black line is the simple average across 16 states.
- Appendix Figure 4: Change in misallocation 2009-2014 versus STW take-up in 2009.

*Source: wpiea2021242-print-pdf - 335. Brookings Institute Press.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021242-print-pdf.pdf_