Effects in Different Sub-Samples

Dividing the full sample into collectively exhaustive sub-samples shows the effect of teacher test scores on student achievement in different settings (see Table 3-7).

Table 3-7. Regression Results for Sub-Samples

Sample Beta Rob. S.E. N Beta Rob. S.E. N

All 0.0371 (0.0125) 6819 0.0446 (0.0135) 4302 Urban Area 0.0314 (0.0162) 4666 0.0397 (0.0194) 2295 Rural Area 0.0482 (0.0182) 2153 0.0504 (0.0184) 2007 Public School 0.0373 (0.0120) 6054 0.0500 (0.0135) 3728 Private School 0.0377 (0.0580) 765 0.0024 (0.0498) 574 Multigrade School 0.0426 (0.0219) 2149 0.0523 (0.0217) 2003 Complete School 0.0334 (0.0153) 4670 0.0384 (0.0177) 2299 Student 1st Language: Spanish 0.0331 (0.0133) 6121 0.0400 (0.0147) 3735 Student 1st Language: Native 0.0714 (0.0356) 652 0.0777 (0.0370) 537 Male Student 0.0274 (0.0150) 3471 0.0395 (0.0169) 2232 Female Student 0.0415 (0.0169) 3348 0.0485 (0.0186) 2070 Male Teacher 0.0239 (0.0196) 2791 0.0185 (0.0217) 1942 Female Teacher 0.0339 (0.0176) 3623 0.0461 (0.0188) 2115 Student-Teacher Same Gender 0.0595 (0.0172) 3294 0.0724 (0.0187) 2022 Student-Teacher Diff. Gender 0.0138 (0.0162) 3120 0.0198 (0.0182) 2035 Teacher 1 Year with Class 0.0482 (0.0217) 2069 0.0655 (0.0236) 1478 Teacher 2 Years with Class 0.0541 (0.0219) 2355 0.0357 (0.0234) 1442 Teacher 3-6 Years with Class 0.0532 (0.0269) 1651 0.0953 (0.0303) 886 Teacher Degree: University 0.0399 (0.0221) 1810 0.0250 (0.0210) 1182 Teacher Degree: Institute 0.0370 (0.0155) 4787 0.0606 (0.0175) 2982

Same-teacher, one-classroom (STOC) Same-teacher

Note: Robust standard errors in brackets, observations clustered at teacher level.. Regression results for specification without control variables. Measurement error correction with reliability factor of 0.62

Even though the sample size reduces considerably in the different sub-groups, a positive, statistically and economically significant effect appears in almost all sub-samples. In the same teacher sample (left panel) it mostly varies between about 0.03 and 0.04, in the STOC sample (right panel) between about 0.04 and 0.05 when measurement error is not corrected for. The effect is small and statistically weak or insignificant in private schools, for student-teacher different gender pairs, male teachers and teachers with university degree.

We cannot reject the hypothesis that there is no effect of teacher test scores in private schools. Possible reasons are the small sample size of private school students, different learning transmission mechanisms in private than public schools or non- linearities in the teacher test score effect as private student tend to be in the high range of test scores in both subjects.

Comparing the results for students whose mother tongue is Spanish and native the point estimates suggest that there may be a bigger effect for native (0.071) than Spanish (0.033) students.

The most drastic difference between the effect estimate for two categories is between student teacher pairs of the same gender and those with different genders. While for the same-gender case the effect is estimated to be 0.073 and highly significant, the effect is 0.02 and insignificant for the different-gender case in the STOC sample. Only in this case can the effect in two mutually exclusive subsets be statistically distinguished.32

This finding may suggest that in order for the teacher to transmit knowledge to students there must be some connection between the two which may be facilitated by sharing the same gender.

Extended results are presented in the appendices 1, 2 and 3. We estimate and discuss results which allow for subject-specific impacts of teacher knowledge (Appendix 3.1). We conclude that teacher test score effects cannot be consistently estimated without the assumption that effects do not vary between subjects. We also consider a possible non-linearity of effects by estimating quantile regressions (Appendix 3.2). Overall, the evidence from OLS regressions in different sub-samples and quantile regressions is not suggestive of the fact that there are strong non-linearities in the impact of teacher subject knowledge on student subject knowledge. Furthermore, we discuss the generalizability of results to the Peruvian student population at large (Appendix 3.3). Even though the same- teacher sample on which the main estimations are performed is not a representative sub- sample of the Peruvian student population, the results from a matching procedure indicate that the estimated teacher test score effects hold for the Peruvian student population at large.

3.5

Conclusion

We believe that this paper has presented a well-identified estimate of teacher academic skills on student achievement by exploiting within-teacher within-student

32 _{Equality of coefficients was tested by regressing the difference in student test scores on dummy variables for}

the sub-sample (e.g., urban and rural) and interaction effects between sub-sample dummy variables and teacher test score difference. Afterwards, a t-test was conducted to test the equality of interaction effects.

variation in test scores. We find that a one standard deviation increase in teacher subject knowledge increases student achievement by around 4 percent of a standard deviation, and by more when correcting for measurement error attenuation. This effect is robust to most sub-samples of the data and representative for the Peruvian 6th _{grade population at}

large. It should be interpreted as an effect in a developing country setting of low academic standards overall.

Unfortunately, the data does not permit to calculate a credible output-based total teacher quality distribution. Thus we cannot answer the question what share of the total teacher quality effect is due to teachers’ subject knowledge.

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