A researcher is interested in the impact of microfinance on business out- comes.

Question

A researcher is interested in the impact of microfinance on business out- comes. To evaluate the impact of the program, he runs the following re- gression profitsi = 0 +1microfinancei +i where 0, 1, and 2 are co- efficients, prof itsi are profits for individual i (in dollars), and microf inancei is a variable equal to 1 if individual i got a microfinance loan. The re- searcher gets a dataset from a microfinance bank on 368 borrowers and supplements this information with a survey of 78 other people in the same village that do not get microfinance loans. The researcher runs the regres- sion and gets the following estimates: 0 = 1.36 with a standard error of 0.53, while 1 = 0.51 with a standard error of 0.22. (a) Comment on these results. What are mean profits for people that are not involved in microfinance? What about for people that are involved in microfinance? Is this difference due to microfinance? Why or why not? (b) Worried about omitted variable bias, the researcher also collects in- formation on years of education, and includes this as a control. The new regression coefficients are 0 = 1.20 with a standard error of 0.57, 1 = 0.19 with a standard error of 0.09, and, the coefficient on years of education, 2 = 0.05 with a standard error of 0.02. (Note, education is not a dummy variable (a 0/1 variable); it is years of ed- ucation.) Comment on these results, on any differences between this regression and the previous one (which did not include education) and on whether the effect of microfinance is “big,” in terms of both statistical significance and economic significance. What does it tell us about the potential bias in the previous regression?
A researcher is interested in the impact of microfinance on business out- comes. To evaluate the impact of the program, he runs the following re- gression profitsi = 0 +1microfinancei +i where 0, 1, and 2 are co- efficients, prof itsi are profits for individual i (in dollars), and microf inancei is a variable equal to 1 if individual i got a microfinance loan. The re- searcher gets a dataset from a microfinance bank on 368 borrowers and supplements this information with a survey of 78 other people in the same village that do not get microfinance loans. The researcher runs the regres- sion and gets the following estimates: 0 = 1.36 with a standard error of 0.53, while 1 = 0.51 with a standard error of 0.22. (a) Comment on these results. What are mean profits for people that are not involved in microfinance? What about for people that are involved in microfinance? Is this difference due to microfinance? Why or why not? (b) Worried about omitted variable bias, the researcher also collects in- formation on years of education, and includes this as a control. The new regression coefficients are 0 = 1.20 with a standard error of 0.57, 1 = 0.19 with a standard error of 0.09, and, the coefficient on years of education, 2 = 0.05 with a standard error of 0.02. (Note, education is not a dummy variable (a 0/1 variable); it is years of ed- ucation.) Comment on these results, on any differences between this regression and the previous one (which did not include education) and on whether the effect of microfinance is “big,” in terms of both statistical significance and economic significance. What does it tell us about the potential bias in the previous regression?
A researcher is interested in the impact of microfinance on business out- comes. To evaluate the impact of the program, he runs the following re- gression profitsi = 0 +1microfinancei +i where 0, 1, and 2 are co- efficients, prof itsi are profits for individual i (in dollars), and microf inancei is a variable equal to 1 if individual i got a microfinance loan. The re- searcher gets a dataset from a microfinance bank on 368 borrowers and supplements this information with a survey of 78 other people in the same village that do not get microfinance loans. The researcher runs the regres- sion and gets the following estimates: 0 = 1.36 with a standard error of 0.53, while 1 = 0.51 with a standard error of 0.22. (a) Comment on these results. What are mean profits for people that are not involved in microfinance? What about for people that are involved in microfinance? Is this difference due to microfinance? Why or why not? (b) Worried about omitted variable bias, the researcher also collects in- formation on years of education, and includes this as a control. The new regression coefficients are 0 = 1.20 with a standard error of 0.57, 1 = 0.19 with a standard error of 0.09, and, the coefficient on years of education, 2 = 0.05 with a standard error of 0.02. (Note, education is not a dummy variable (a 0/1 variable); it is years of ed- ucation.) Comment on these results, on any differences between this regression and the previous one (which did not include education) and on whether the effect of microfinance is “big,” in terms of both statistical significance and economic significance. What does it tell us about the potential bias in the previous regression?

Explanation / Answer

(a) The variable microfinance is significant at 5% level. Since the t-stat for the slope i.e. coefficient for microfinance is = coeff/SE = 0.51/.22

Also, the profit in case of microfinance is 0.51 dollar more than that in case of non-microfinance.

The mean profit in dollar for:

1) Microfinance = 1.36 +0.51 =1.87

2) Microfinance = 1.36 +0=1.36

Yes, there is difference in profit values due to the significant slope value in equation.

(b) The new regression equation carrying more variables (explanatory) will have better fit (R-sq). However, we need to again test for significant of both the variables based on t-stat:

Formula:

Since t-critical at 95% confidence is 1.97

So both the variables are significant.

Also more the years of education more the profit. Still, microfinance yields more profit of 0.19 dollars as compared to non-microfinance.

microfinance 2.111111 education years 2.5

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