# **Table 6 Regression of Dummy** **<u>Variable for High School Enrollment on Migrant Share in Village</u>**

|Specification of Instrument|**Non-**<br>**Parame**<br>**tric**|**Dummy**<br>**Variable,**<br>**>3 years**|**Groups of**<br>**Dummy**<br>**Variables**|**Quadratic,**<br>**Years**<br>**Since IDs**<br>**Issued**|**Quartic,**<br>**Years**<br>**Since**<br>**IDs**<br>**Issued**|
|---|---|---|---|---|---|
||**(1)**|**(2)**|**(3)**|**(4)**|**(5)**|
|**IV Estimator, Correcting for Clustering**||||||
|Share of village employed in migrant activities|-0.521|-3.192*|-1.524*|-3.989**|-2.503**|
||(0.576)|(1.780)|(0.793)|(1.872)|(1.061)|
|**IV GMM Estimator (Includes Weighting Matr**|**ix for Effici**|**ency)**||||
|Share of village employed in migrant activities|-0.775|-3.192*|-1.423**|-3.813**|-2.434**|
||(0.532)|(1.780)|(0.789)|(1.838)|(1.040)|
|**Test Statistics**||||||
|Angrist-Pischke F Statistic, instruments|2.168|7.596|3.437|4.132|3.663|
|Hansen J Statistic (overidentification)|29.689||1.723|0.247|1.912|
|p-value, J statistic|0.041||0.886|0.619|0.591|
|Anderson-Rubin F statistic, weak instruments||6.61|6.24|10.59|12.31|
|p-value Anderson-Rubin F statistic||0.010|0.397|0.005|0.015|
|Conditional Likelihood Ratio (CLR) Test|||4.68|10.55|10.98|
|p-value, CLR test|||0.052|0.002|0.002|
|95% Cfid Itl bd CLR Tt|||[-4.52,|[-11.39,|<br>[-6.67,|
|onence nerva, ase on es|||-0.04]|-1.38]|-0.95]|
|**LIML Estimator**||||||
|Share of village employed in migrant activities|-0.648|-3.192*|-1.552*|-4.093**|-2.612**|
||(0.746)|(1.780)|(0.811)|(1.947)|(1.126)|
|**Test Statistics**||||||
|Cluster Corrected F Statistic, instruments|2.168|7.596|3.437|4.132|3.663|
|Hansen J Statistic (overidentification)|29.689||1.723|0.247|1.912|
|p-value, J statistic|0.041||0.886|0.619|0.591|
|Anderson-Rubin F statistic, weak instruments||6.61|6.24|10.59|12.31|
|p-value Anderson-Rubin F statistic||0.010|0.397|0.005|0.015|
|<br>Conditional Likelihood Ratio (CLR) Test|||4.68|10.55|10.98|
|p-value, CLR test|||0.052|0.002|0.002|
||||[-4.55,|[-11.77,|<br>[-7.03,|
|95% Confidence Interval, based on CLR Test|||<br>-0.03]|<br>-1.38]|<br> <br>-0.97]|
|Number of Observations|3160|3160|3160|3160|3160|

Notes: Column 1 corresponds to the instrument as specified in column 2 of Table 2; columns 2-5 correspond to the instrument as specified in columns 1-4 of Table 3. Standard errors clustered at the village-year level, except in the Moreira conditional IV estimator, where they are robust. All regressions control for factors related to village location with village fixed effects, and macroeconomic shocks using province-year fixed effects. To test for weak identification, we use the cluster corrected F statistic. We use the Hansen J statistic to test for overidentification. For weak instrument robust inference, we use two test statistics. The Anderson-Rubin F statistic tests the hypothesis that the instruments and the coefficient on the endogenous variable are jointly zero. Under the assumption of homoscedasticity, the conditional likelihood ratio (CLR) test developed by Moreira (2003) is more powerful, so we also show it and the 95% confidence interval suggested by the CLR test. The Anderson-Rubin and CLR tests are generalized for clustered dependence in error terms using the minimum distance approach by Finlay and Magnusson (2009). The test statistics do not differ whether or not we use the weighting matrix for efficiency with instrumental variables, so we present them once.

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