## 1. Wage Determinants in Japan (Prefectural Panel), Regression Results Using Instrumental

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---

### Introduction and research question
- Objective: empirically assess the effectiveness of the government plan to raise the minimum wage by 3 percent per year until it reaches 1,000 JPY per hour, focusing on pass-through from the minimum wage to average wages.
- Dataset: prefectural panel covering 1997-2014, with separate analysis for men and women.
- Estimation approach: Instrumental Variables regression used to control for endogeneity in the relationship between minimum wages and average wages.
- Dependent variables: hourly average total wage, hourly average male wage, hourly average female wage.

### Key stylized facts and policy background
- Prime Minister Abe announced a target to increase nominal GDP by 20 percent to reach 600 trillion JPY by 2020.
- Government plan: raise the national weighted average minimum wage by 3 percent per year; this would raise the average minimum wage from 798 JPY to over 1,000 JPY per hour by fiscal year 2023.
- Fiscal year 2016: advisory panel recommended raising the country’s average minimum hourly wage by 24 yen, or 3 percent; prefectural decisions produced an actual increase of 25 yen to 823 yen per hour on average.
- Historical context:
  - The minimum wage has not grown past 3 percent since 1994.
  - Nominal wage growth has been below 3 percent since 1993.
  - Full-time wages have increased 0.3 percent since 1995 (Everaert and Ganelli (2016) cited).
- Labor market distributional facts:
  - Share of non-regular workers rose gradually to reach almost 40 percent of total employees; share of part-time positions in new job openings reached 60 percent.
  - Japan’s minimum wage relative to average wages of full-time workers ranks fourth lowest in the OECD.
  - JILPT estimate (2014): 13.4 percent of total workers earn less than “1.15 x prefectural minimum wage” (4.7 percent of full-time workers; 39.2 percent of part-time workers).
  - Cabinet Office estimate (2014): number of workers paid the minimum wage plus 20 yen was 3.4 million (about 6.5 percent of the working population); number paid the minimum wage plus 40 yen was 5.1 million (almost 10 percent of the working population).
  - If full-time workers work 168.4 hours per month, workers earning less than 179,900 yen per month (179,900/168.4 hours = 1,068 yen) are about 10 percent of total male full-time workers and about 29 percent of total female full-time workers.
  - For part-time workers, the share of workers below the minimum wage (calculated as below 999 yen per hour) is about 54 percent for men and 66 percent for women.

### Main empirical findings (pass-through and gender differences)
- Pass-through estimates:
  - A one percent increase in the minimum wage could lead to about a 0.5 percent increase in total wages.
  - The increase in average wages is more pronounced on male wages than on female wages.
- Gender-specific Instrumental Variables pass-through estimates:
  - Total: 0.48 percent increase in hourly average wage for a 1 percent increase in the minimum wage (0.48** (1.92)).
  - Women: 0.42 percent increase (0.42** (2.28)).
  - Men: 0.66 percent increase (0.66** (2.42)).
- OLS estimates (comparison) substantially larger and overestimate pass-through:
  - Log Minimum Wage coefficients: total 1.05*** (9.63); women 1.22*** (15.37); men 1.06*** (8.05).
- Policy scenario implication:
  - Stepping up minimum wage growth from 2 percent to the planned 3 percent per year could raise wage growth by an additional 0.5 percent annually.
- Additional quantitative note:
  - A 1 percent increase in the hourly minimum wage is estimated to increase the hourly average wage by about 0.48 percent (Instrumental Variables estimate).

### Data, controls, identification and instruments
- Data:
  - Prefectural-level data from Japan’s Ministry of Health, Labour and Welfare; period: 1997 to 2014.
  - Dependent variables: average monthly wages for men, women, and total weighted average (full-time workers only; do not include bonuses).
  - Wages converted to hourly by dividing monthly wages by number of hours worked each month including overtime; adjusted for inflation (CPI).
  - Minimum wage variable: prefectural-level hourly minimum wage, adjusted by CPI.
- Controls included: unemployment rate, CPI, prefectural real GDP, share of part-time work applicants (proxy for duality), share of employment in manufacturing, average age of workers.
- Endogeneity concern:
  - Durbin-Wu-Hausman test indicates endogeneity between minimum wages and average wages.
- Instruments (2SLS/IV):
  - Number of male and female applicants to social welfare in each prefecture divided by total social welfare applicants in Japan (proxy for demand for public assistance).
  - Rationale: public welfare demand affects minimum wage setting but not average earnings directly.

### Empirical regression results (Instrumental Variables, logs; 1997–2014) — key coefficients and statistics
- Minimum Wage (log) coefficients:
  - Real wages (total): 0.48** (1.92)
  - Real wages (Women): 0.42** (2.28)
  - Real wages (Men): 0.66** (2.42)
- Other controls (selected):
  - CPI Inflation:
    - Total: -0.008** (-2.36)
    - Women: -0.001 (-0.31)
    - Men: 0.01** (02.31)
  - Prefectural GDP:
    - Total: 0.0003*** (4.33)
    - Women: 0.0004*** (6.20)
    - Men: 0.0004*** (5.09)
  - Share of part-time workers:
    - Total: -0.09 (-0.99)
    - Women: 0.12** (1.65)
    - Men: -0.1 (-0.85)
  - Unemployment Rate:
    - Total: -0.009* (-1.75)
    - Women: 0.002 (0.52)
    - Men: 0.01* (1.69)
  - Share of employment in manufacturing:
    - Total: 0.002*** (3.52)
    - Women: 0.001* (1.78)
    - Men: 0.003*** (3.21)
  - Average female age:
    - Total: -0.03*** (-6.22)
    - Women: -0.02*** (-5.00)
  - Average male age:
    - Total: 0.04*** (5.28)
    - Men: 0.03*** (4.27)
- R-Squared:
  - Total: 0.63
  - Women: 0.70
  - Men: 0.53

### First-stage regression diagnostics (Average Total, Male, Female wages)
- Average Total Wages first-stage (Table A.1):
  - R-squared: 0.7478; Adjusted R-sq: 0.7409; Partial R-Sq: 0.2027
  - F (2,365): 30.9384; Prob > F: 0.0000
  - Interpretation: F-statistic 30.94 exceeds Stock, Wright and Yogo (2002) recommended F=10 for reliable 2SLS inference; passes 2SLS relative bias and 2SLS Size of nominal 5% Wald Test critical values reported.
- Average Male Wages first-stage (Table A.3):
  - R-squared: 0.7445; Adjusted R-sq: 0.7382; Partial R-Sq: 0.2375
  - F (2,365): 37.9969; Prob > F: 0.0000
  - Interpretation: F-statistic 37.99 exceeds recommended thresholds and passes relative bias and size tests.
- Average Female Wages first-stage (Table A.5):
  - R-squared: 0.7477; Adjusted R-sq: 0.7415; Partial R-Sq: 0.2320
  - F (2,366): 36.8583; Prob > F: 0.0000
  - Interpretation: F-statistic 36.85 exceeds recommended thresholds and passes relative bias and size tests.

### Over-identifying restrictions and instrument validity tests
- Average Total Wages (Table A.2):
  - Sargan chi2(1) = 7.3 p= 0.0069
  - Basmann chi2(1) = 7.24 p= 0.0071
  - Wooldridge (score) chi2(2) = 8.25 p = 0.0161
  - Interpretation: Wooldridge test does not reject instrument validity at 1% but instruments are rejected at 5%.
- Average Male Wages (Table A.4):
  - Sargan chi2(2) = 4.36 p= 0.1131
  - Basmann chi2(1) = 4.293 p= 00.1169
  - Wooldridge chi2(2) = 5.00398 p = 0.0819
  - Interpretation: Sargan and Basmann do not reject instrument validity at 1%, 5% and 10%; Wooldridge rejects at 10%.
- Average Female Wages (Table A.6):
  - Sargan chi2(2) = 0.85916 p= 0.6508
  - Basmann chi2(1) = 0.83225 p= 0.6576
  - Wooldridge chi2(2) = 0.897377 p = 0.6385
  - Interpretation: Sargan, Basmann, and Wooldridge do not reject instrument validity at 1%, 5% and 10%.

### Interpretation of mechanisms and additional empirical insights
- Mechanisms through which minimum wage affects wages:
  - “Truncation” effect: employment loss for workers paid less than the new minimum, truncating the lower tail.
  - “Spike” effect: firms retain low-wage workers and raise their wages, creating a spike around the minimum.
  - Spillover effect: substitution toward higher-skilled workers raises their wages.
- Age and seniority effects:
  - Male average age positively correlated with wages consistent with seniority wage system.
  - Female average age negatively correlated with wages reflecting dropout/re-entry patterns and spousal tax deduction incentives.
- Duality and labor supply effects:
  - Duality proxy (share of part-time new job applications) is positive and significant for women, implying scarcity of full-time female labor pushes up full-time female wages; negative (not statistically significant) for men and total wages.
- Tax and social security thresholds:
  - Spousal tax deduction (income cap at 1.03 million yen) and October 2016 changes (eligibility to pay into national health insurance and pension if working at least 20 hours/week for firms with 501+ employees and earning at least 1.06 million yen) affect work-hour decisions, especially among married women.
  - Risk that wage increases without tax and social security reform could encourage non-regular work as part-time workers reduce hours to avoid thresholds.

### Policy implications and recommendations
- Minimum wage increases are helpful to stimulate wage growth but are insufficient alone to reach desired wage-inflation dynamics.
- Given the Bank of Japan’s inflation target of 2 percent and an assumed productivity growth of 1 percent, nominal wage growth of 3 percent is desirable.
- Recommended complementary measures:
  - Adopt a “soft target” through a “comply or explain mechanism” for wage growth.
  - Increase public wages.
  - Introduce stronger tax incentives or penalties as a last resort.
  - Possibly conduct an additional wage bargaining round.
  - Strengthen the central government’s role in setting the minimum wage.
  - Coordinate income policies with tax and social security reforms to avoid increasing labor market duality and to mobilize more female labor into regular jobs (e.g., reconsider spousal tax deduction and social insurance thresholds).

*Source: _wp16232 - 1. Wage Determinants in Japan (Prefectural Panel), Regression Results Using Instrumental*

### 1. Wage Determinants in Japan (Prefectural Panel), Regression Results Using Instrumental

### _wp16232 - 1. Wage Determinants in Japan (Prefectural Panel), Regression Results Using Instrumental

### Introduction and research question
- Objective: empirically assess the effectiveness of the government plan to raise the minimum wage by 3 percent per year until it reaches 1,000 JPY per hour, focusing on pass-through from the minimum wage to average wages.
- Dataset: prefectural panel covering 1997-2014, with separate analysis for men and women.
- Estimation approach: Instrumental Variables regression used to control for endogeneity in the relationship between minimum wages and average wages.
- Dependent variables: hourly average total wage, hourly average male wage, hourly average female wage.

### Key stylized facts from the paper
- Policy background:
  - Prime Minister Abe announced a target to increase nominal GDP by 20 percent to reach 600 trillion JPY by 2020.
  - Government announced plan to raise the national weighted average minimum wage by 3 percent per year, which would raise the average minimum wage from 798 JPY to over 1,000 JPY per hour by fiscal year 2023.
  - For fiscal year 2016, the government advisory panel recommended raising the country’s average minimum hourly wage by 24 yen, or 3 percent; prefectural decisions produced an actual increase of 25 yen to 823 yen per hour on average.
- Historical context:
  - The minimum wage has not grown past 3 percent since 1994.
  - Nominal wage growth has been below 3 percent since 1993.
  - Full-time wages have increased a mere 0.3 percent since 1995 (Everaert and Ganelli (2016) cited).
- Labor market structure and distributional facts:
  - Share of non-regular workers rose gradually to reach almost 40 percent of total employees; share of part-time positions in new job openings reached 60 percent.
  - Japan’s minimum wage relative to average wages of full-time workers ranks fourth lowest in the OECD (only the U.S., Mexico and Czech Republic are lower).
  - JILPT estimate (2014): 13.4 percent of total workers earn less than “1.15 x prefectural minimum wage” (4.7 percent of full-time workers; 39.2 percent of part-time workers).
  - Cabinet Office estimate (2014): number of workers paid the minimum wage plus 20 yen was 3.4 million (about 6.5 percent of the working population); number paid the minimum wage plus 40 yen was 5.1 million (almost 10 percent of the working population).
  - If full-time workers work 168.4 hours per month, workers earning less than 179,900 yen per month (179,900/168.4 hours = 1,068 yen) are about 10 percent of total male full-time workers and about 29 percent of total female full-time workers.
  - For part-time workers, the share of workers below the minimum wage (calculated as below 999 yen per hour) is about 54 percent for men and 66 percent for women.

### Main empirical findings
- Pass-through estimates:
  - A one percent increase in the minimum wage could lead to about a 0.5 percent increase in total wages.
  - The increase in average wages is more pronounced on male wages than on female wages.
- Policy scenario implication from estimates:
  - Stepping up minimum wage growth from 2 percent to the planned 3 percent per year could raise wage growth by an additional 0.5 percent annually.

### Interpretation and policy implications
- Even with the estimated pass-through, the planned minimum wage increases alone are unlikely to generate the vigorous nominal wage growth Japan needs to reach the Bank of Japan’s inflation target:
  - Given the Bank of Japan’s inflation target of 2 percent and an assumed productivity growth of 1 percent, nominal wage growth of 3 percent is desirable.
- Recommended complements to minimum wage policy (described as more “unorthodox” income policies):
  - Adopt a “soft target” through a “comply or explain mechanism” for wage growth.
  - Increase public wages.
  - Introduce stronger tax incentives or penalties as a last resort.
  - Possibly conduct an additional wage bargaining round.
  - Complement income policies with tax reform to avoid increasing labor market duality by pushing more workers into non-regular jobs.

### Methodological notes and scope
- The prefectural panel allows exploitation of cross-prefecture variability and gender-specific labor market characteristics.
- Instrumental Variables estimation is used to address potential endogeneity that could overestimate pass-through effects.
- The paper emphasizes that minimum wage increases have spillover effects across the wage distribution beyond direct effects on minimum-wage earners.

*Source: _wp16232 - 1. Wage Determinants in Japan (Prefectural Panel), Regression Results Using Instrumental*

### 168.4 is the estimated average number of hours worked per month by full-time workers in 2014 by the

### _wp16232 - 168.4 is the estimated average number of hours worked per month by full-time workers in 2014 by the

### Key findings
- A 1 percent increase in the hourly minimum wage is estimated to increase the hourly average wage by about 0.48 percent (Instrumental Variables estimate).
- Gender-specific pass-through estimates (Instrumental Variables):
  - Women: 0.42 percent increase in average wages for a 1 percent minimum wage increase.
  - Men: 0.66 percent increase in average wages for a 1 percent minimum wage increase.
- OLS estimates are substantially larger and overestimate pass-through (Table 2: Log Minimum Wage coefficients: total 1.05 ***, women 1.22 ***, men 1.06 ***).
- The planned 3 percent minimum wage increase (government advisory panel decision in July 2016) would be expected to produce about a 0.5 percent increase in average wages according to the paper’s estimations.
- The paper notes that a wage growth of 3 percent would seem desirable for Japan given the Bank of Japan’s inflation target of 2 percent and assuming productivity growth of 1 percent.

### Context and literature
- Minimum wage effects on wages arise from three mechanisms described:
  - “Truncation” effect: employment loss for workers paid less than the new minimum, truncating the lower tail of the distribution.
  - “Spike” effect: firms retain low-wage workers and raise their wages, creating a spike around the minimum.
  - Spillover effect: substitution toward higher-skilled workers raises their wages.
- Influential referenced studies: DiNardo, Fortin and Lemieux (1996); Lee (1999); Autor, Manning and Smith (2010); Kambayashi, Kawaguchi, and Yamada (2013); Neumark and Wascher (2004); Gramlich (1976); Schmitt (2013); Betcherman (2012); Cunningham (1981); Katz and Krueger (1992); Hungerford (2000).
- Japan-specific literature is scarce; Kambayashi, Kawaguchi, and Yamada (2013) find minimum wage increases reduced inequality for women with negligible employment losses in 1994–2003.

### Data and empirical strategy
- Dataset:
  - Prefectural-level data from Japan’s Ministry of Health, Labour and Welfare statistics.
  - Period: 1997 to 2014 (17 years).
  - Dependent variables: average monthly wages for men, women, and total weighted average (full-time workers only; do not include bonuses).
  - Wages converted to hourly by dividing monthly wages by number of hours worked each month including overtime; adjusted for inflation (CPI).
  - Minimum wage variable: prefectural-level hourly minimum wage, adjusted by CPI.
  - Controls: unemployment rate, CPI, prefectural real GDP, share of part-time work applicants (proxy for duality), share of employment in manufacturing, average age of workers.
- Endogeneity concern:
  - Average wages and minimum wages may fluctuate together and average wages influence prefectural minimum wage-setting.
  - Durbin-Wu-Hausman test indicates endogeneity between minimum wages and average wages.
- Identification / Instruments:
  - Two-stage least squares (2SLS) with instruments: number of male and female applicants to social welfare in each prefecture divided by total social welfare applicants in Japan (proxy for demand for public assistance).
  - Rationale: public welfare demand affects minimum wage setting (workers’ cost of living) but not average earnings directly, satisfying instrument exogeneity assumption.
  - Appendix reports weak instrument and over-identification tests (Stock, Wright and Yogo (2002); Sargan, Basmann and Wooldridge tests).

### Empirical results (Instrumental Variables, logs; period: 1997-2014)
- Coefficients (Z-statistics in parentheses; significance: * 10% level, ** 5% level, *** 1% level):
  - Minimum Wage:
    - Real wages (total): 0.48** (1.92)
    - Real wages (Women): 0.42** (2.28)
    - Real wages (Men): 0.66** (2.42)
  - CPI Inflation:
    - Total: -0.008** (-2.36)
    - Women: -0.001 (-0.31)
    - Men: 0.01** (02.31)
  - Prefectural GDP:
    - Total: 0.0003 *** (4.33)
    - Women: 0.0004*** (6.20)
    - Men: 0.0004*** (5.09)
  - Share of part-time workers:
    - Total: -0.09 (-0.99)
    - Women: 0.12** (1.65)
    - Men: -0.1 (-0.85)
  - Unemployment Rate:
    - Total: -0.009* (-1.75)
    - Women: 0.002 (0.52)
    - Men: 0.01* (1.69)
  - Share of employment in manufacturing:
    - Total: 0.002*** (3.52)
    - Women: 0.001* (1.78)
    - Men: 0.003*** (3.21)
  - Average female age:
    - Total: -0.03*** (-6.22)
    - Women: -0.02*** (-5.00)
  - Average male age:
    - Total: 0.04*** (5.28)
    - Men: 0.03*** (4.27)
  - R-Squared:
    - Total: 0.63
    - Women: 0.70
    - Men: 0.53
- OLS results (for comparison) show larger coefficients on log minimum wage (Total 1.05*** (9.63); Women 1.22*** (15.37); Men 1.06*** (8.05)) and similar signs on other controls (Table 2).

### Interpretation and additional findings
- The pass-through of minimum wage to average wages is statistically significant and meaningful but less than unity (partial pass-through).
- Age effects reflect Japan’s seniority wage system:
  - Male average age positively correlated with wages.
  - Female average age negatively correlated with wages, reflecting labor market dropout and re-entry patterns linked to childbearing and spousal tax deduction incentives.
- Duality proxy (share of part-time new job applications) is:
  - Positive and significant for women, implying scarcity of full-time female labor pushes up full-time female wages.
  - Negative (but not statistically significant) for men and total wages.
- Tax and social security features matter:
  - Spousal tax deduction (income cap at 1.03 million yen) and changes from October 2016 (eligibility to pay into national health insurance and pension if working at least 20 hours/week for firms with 501+ employees and earning at least 1.06 million yen) influence work-hour decisions, especially among married women.
  - Risk that wage increases without tax and social security reform could encourage non-regular work as part-time workers reduce hours to avoid thresholds.

### Policy recommendations and implications
- Minimum wage increases are helpful to stimulate wage growth but are insufficient alone to reach desired wage-inflation dynamics.
- Complement minimum wage policy with other income policies:
  - A “soft target” for wage growth.
  - Increases in public wages.
  - Strengthening the central government’s role in setting the minimum wage.
- Coordinate income policies with tax and social security reforms to avoid encouraging non-regular work and to mobilize more female labor into regular jobs (e.g., reconsider spousal tax deduction and social insurance thresholds).

*Source: IMF Staff calculations and analysis in _wp16232 (Period: 1997–2014; Ministry of Health, Labour and Welfare data).*

### 1. Average Total Wages Regression:

### 1. Average Total Wages Regression

### First-stage regression results and diagnostics
- Table A.1 first-stage summary:
  - Real Minimum Wage (in log)
  - R-squared: 0.7478
  - Adjusted R-sq: 0.7409
  - Partial R-Sq: 0.2027
  - F (2,365): 30.9384
  - Prob > F: 0.0000

- Critical values (Number of Endogenous regressors: 1; Number of Excluded instruments: 3)
  - 2SLS relative bias 5% 10% 20% 30%: 13.91 9.08 9.54 5.39
  - 2SLS Size of nominal 5% Wald Test 10% 15% 20% 25%: 22.30 12.83 9.54 7.80

- Interpretation and inference:
  - The F-statistic is 30.94, which exceeds Stock, Wright and Yogo’s (2002) recommended F-statistic value for inference (F=10) for a 2SLS estimator to be reliable.
  - The test statistic exceeds the critical values for the “2SLS relative bias test” at 5%, 10%, 20% and 30% (30.94 > 13.9).
  - The test statistic exceeds the “2SLS Size of nominal 5% Wald Test” critical value at the 10%, 15%, 20% and 25% levels (30.93 > 22.30).
  - Conclusion: instruments satisfy Stock and Yogo (2005)’s two conditions for an instrument to not be weak.

### Over-identifying restrictions tests
- Table A.2 Test of Over-Identifying Restrictions:
  - Sargan (score) chi2(1) = 7.3 p= 0.0069
  - Basmann chi2(1) = 7.24 p= 0.0071
  - Wooldridge (score) chi2(2) = 8.25 p = 0.0161

- Interpretation:
  - Based on the Wooldridge score test, we do not reject the null hypothesis that our instruments are valid at the 1% significance level.
  - We reject the null hypothesis that our instruments are valid at the 5% significance level.

---

### 2. Average Male Wages Regression

### First-stage regression results and diagnostics
- Table A.3 first-stage summary:
  - Real Minimum Wage (in log)
  - R-squared: 0.7445
  - Adjusted R-sq: 0.7382
  - Partial R-Sq: 0.2375
  - F (2,365): 37.9969
  - Prob > F: 0.0000

- Critical values (Number of Endogenous regressors: 1; Number of Excluded instruments: 3)
  - 2SLS relative bias 5% 10% 20% 30%: 13.91 9.08 6.46 5.39
  - 2SLS Size of nominal 5% Wald Test 10% 15% 20% 25%: 22.30 12.83 9.54 7.80

- Interpretation and inference:
  - The F-statistic is equal to 37.99, exceeding Stock, Wright and Yogo’s (2002) recommended F-statistic value for inference (F=10) for a 2SLS estimator to be reliable.
  - The F-statistic also passes the tests for 2SLS relative bias, and the 2SLS Size of nominal 5% Wald Test.

### Over-identifying restrictions tests
- Table A.4 Test of Over-Identifying Restrictions:
  - Sargan (score) chi2(2) = 4.36 p= 0.1131
  - Basmann chi2(1) = 4.293 p= 00.1169
  - Wooldridge (score) chi2(2) = 5.00398 p = 0.0819

- Interpretation:
  - Based on the Sargan and Basmann score tests, we do not reject the null hypothesis that our instruments are valid at the 1%, 5% and 10% significance level.
  - With the Wooldridge score test, we reject the null hypothesis that our instruments are valid at the 10% significance level.

---

### 3. Average Female Wages Regression

### First-stage regression results and diagnostics
- Table A.5 first-stage summary:
  - Real Minimum Wage (in log)
  - R-squared: 0.7477
  - Adjusted R-sq: 0.7415
  - Partial R-Sq: 0.2320
  - F (2,366): 36.8583
  - Prob > F: 0.0000

- Critical values (Number of Endogenous regressors: 1; Number of Excluded instruments: 3)
  - 2SLS relative bias 5% 10% 20% 30%: 13.91 9.08 6.46 5.39
  - 2SLS Size of nominal 5% Wald Test 10% 15% 20% 25%: 22.30 12.83 9.54 7.80

- Interpretation and inference:
  - The F-statistic is equal to 36.85, exceeding Stock, Wright and Yogo’s (2002) recommended F-statistic value for inference (F=10) for a 2SLS estimator to be reliable.
  - The F-statistic also passes the tests for 2SLS relative bias, and the 2SLS Size of nominal 5% Wald Test.

### Over-identifying restrictions tests
- Table A.6 Test of Over-Identifying Restrictions:
  - Sargan (score) chi2(2) = 0.85916 p= 0.6508
  - Basmann chi2(1) = 0.83225 p= 0.6576
  - Wooldridge (score) chi2(2) = 0.897377 p = 0.6385

- Interpretation:
  - Based on the Sargan, Basmann, and Wooldridge score tests, we do not reject the null hypothesis that our instruments are valid at the 1%, 5% and 10% significance level.

*Source: _wp16232 - 1. Average Total Wages Regression*

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