Statistics Question
This assignment is based on the 2019 paper of Arielle Bernhardt, Erica Field, Rohini Pande, and Natalia Rigol (henceforth BFPR) “Household matters: Re-visiting the returns to capital among female microentrepreneurs” published in AER: Insights. In their paper, BFPR make use of different field experiments run in India, Sri Lanka, and Ghana. The data file for this assignment is based on the Indian experiment and drawn from the data used in BFPR. The paper, data file, and answer sheet are now available for download at CANVAS. Before answering the questions, it is strongly recommended that you read the paper thoroughly. Please answer the questions as clearly and concisely as possible, and in accordance to the instructions. At the end of each question, the instructions are written in italics between brackets. Parts of answers that deviate from the requested format, or are difficult to decipher will reduce the grade.
The Indian experiment
BFPR evaluate an experiment among female microentrepreneurs in low-income neighborhoods who all received individual loans that ranged from Rs 4.000 up to Rs 10.000 (which is equivalent to e45 up to e112,5 at the 2023 exchange rate). These female microentrepreneurs were organized in microfinance groups of 5. All these groups had to attend a group-specific repayment meeting, in which repayment conditions were discussed. For the experiment, these groups were randomly assigned to different repayment conditions. One set of microfinance groups received a standard contract in which loan repayment was organized through bi-weekly loan installments starting two weeks after the microentrepreneurs received their loan (control groups). The other set of microfinance groups received a contract with a two-month grace period before they had to start repaying their loan through bi-weekly loan installments (treatment groups). Apart from the grace period, all other contract features were identical. The hypothesis is that microentrepreneurs who receive a grace period in their contract face weaker liquidity constraints and make, as a result of that, better business decision leading up to higher business profits.
As we already mentioned above, these female microentrepreneurs were organized in microfinance groups of 5. The randomization occurred within batches of 20 of such groups. There were in total 9 different batches. This means that treatment assignment is random within each batch (that is, treatment is random conditional upon a full set of batch group indicators).
Question 1
BFPR collected pre-treatment information of the female microentrepreneurs including their age, marital status (marriage 0/1), religion (muslim 0/1), house- hold size, whether they experienced some unexpected household event (house- hold shock 0/1), whether there is water nearby (no drain 0/1), whether they had financial control over their resources (financial control 0/1), years of education, whether they are homeowners (homeowner 0/1), the number of enterprises in the household, and 6 loan amount indicators for having a loan of Rs 4.000, Rs 5.000, Rs 6.000, Rs 8.000, Rs 9.000, and Rs 10.000, respectively. We refer to these pretreatment characteristics as Xihg (where i, h and g stand for female microentrepreneur i in household h in batch group g). In Online Appendix Table A1, BFPR report means and standard deviations for the pretreatment characteristics female microentrepreneurs assigned to the control groups. BFPR make a distinction between households with multiple enterprise owners (column 1) and household where only the female microentrepreneur owns enterprises (column 3).
- Replicate the results of Online Appendix Table A1 (only column 1) and report all the results with 3 decimals for a selected set of pretreatement characteristics in Table A in the answer sheet.1 As example, we have already provided the first entry for the age of female microentrepreneurs 1Note that results expressed with 2 or 4 decimals will give zero points. With results expressed with 3 decimals, we mean the exact four numbers as depicted in the STATA output. If, for example, the output reads 34.02878 we want 34.028 and not 34.029. assigned to the control group in household with multiple enterprise owners, which equals 34.028 with standard deviation 7.322. [Complete Table A column 1 in the answer sheet].
- Provide the STATA output and STATA code needed for generating the results reported in Table A column 1, that is, the means and standard deviations for pre-treatment characteristics of the female microentrepreneurs in families with multiple enterprise owners. [Take a screenshot of the STATA output of column 2, including the STATA command line responsible for the output, and paste it in the answer sheet]. The randomized experiment requires that the female entrepreneurs in treated and control groups are, on average, identical. To test this, BFPR estimate for each pretreatment characteristic in Xihg the following OLS regression Xihg = α0 + α1Gg + δ1Bg + ihg , (1) where Gg is the treatment indicator (which is 1 for those groups who received that grace period contract, and 0 otherwise), and Bg represent a set of dummy indicators for the different batch groups, and ihg is the error term. The coefficient α1 measures the difference between pretreatment characteristics between female entrepreneurs in treated and control groups. The term δ1 is a set of coefficients attached to the different batch group indicators. In this regression it is key to control for the batch group indicators (and not batch group number) because treatment assignment is randomly assigned within each batch group. Recall that the female microentrepreneurs were organized (and treated) in microfinance groups of 5. BFPR have clustered their standard errors at the microentrepreneurial group level. To get the correct standard errors, add the command at the end of your regression command: cluster(group). In Online Appendix Table A1, BFPR report these estimates for α1 in columns 2 and 4. Again, they make a distinction between households with multiple enterprise
owners (column 2) and household where only the female microentrepreneur owns enterprises (column 4). - Replicate the results of Online Appendix Table A1 (only column 2) and report the results with 3 decimals for the same set of pretreatment characteristics in Table A in the answer sheet.2 As example, we have al- ready provided the second entry for the estimated α1 for the age of female 2Note that results expressed with 2 or 4 decimals will give zero points. With results expressed with 3 decimals, we mean the exact four numbers as depicted in the STATA output. If, for example, the output reads 34.02878 we want 34.028 and not 34.029. microentrepreneurs in household with multiple enterprise owners, which equals -1.515 with standard error 0.946. [Complete Table A column 2 in the answer sheet.]
- Provide the STATA output and STATA code needed for generating the results reported in Table A column 2 for the pretreatment characteristic years of education. [Take a screenshot of the STATA output of column 2, including the STATA command line responsible for the output, and paste it in the answer sheet].
- The estimate attached to the Rs. 10.000 loan indicator is statistically significant, which suggests that female entrepreneurs in the treatment groups more often loaned the highest amount than female entrepreneurs in the control groups. Is this a concern? [Circle the correct answer in the answer
sheet].
Question 2
BFPR estimate the effect of the grace period treatment on enterprise profits by OLS, estimating the following equation: Yihg = β0 + β1Gg + θ1Bg + γ1Xihg + μihg , (2) where Yihg are the weekly enterprise profits of female enterpreneur i in household h in batch group g. The variables Gg , Bg , Xihg are as defined earlier and μihg is the error term. The coefficient β1 is the average treatment effect of being assigned to the grace period contract. The coefficients θ1 and γ1 are attached the different batch group indicators and pretreatment characteristics. In Table 2, BFPR report the β1 estimates for female enterprise profits (column 1) and all household enterprise profits (column 2). In the notes of Table 2, BFGR indicate that they want to estimate their regressions on the largest sample possible. They therefore include all controls in Xihg (we list these characteristics in Question 1). In cases where a control variable (in Xihg ) is missing, they set its value to
zero and include a dummy for whether the variable is missing.
- Replicate the main estimation results of Table 2 (columns 1 and 2) and report all the β1 estimates in 3 decimals in Table B in the answer sheet (together with the standard error). Do not forget to control for the dummies for whether the control variables are missing. As before, BFPR have clustered their standard errors at the microentrepreneurial group level. To get the correct standard errors, add the command at the end of your regression command: cluster(group). [Complete Table B in the answer sheet].
- Provide the STATA output and STATA code needed for the average treatment effect estimates presented in columns 1. [Take a screenshot of the STATA regression results using the specification of column 1, including the STATA command line responsible for the output, and paste it in the answer sheet].
Question 3
In their experiment, BFGR measure pre-treatment characteristics in the baseline survey and profit measures in the follow-up survey. In between surveys, some of the enterprises under study got bankrupt. BFGR keep these enterprises in the analysis and code their profits as zero. Bankruptcy itself, however, is a relevant and interesting outcome to consider when estimating the effect of grace period treatment.
- If you would focus on households where only the female microentrepreneur owns enterprises, what is the share of female enterprises that went bankrupt? [Report the bankruptcy share in 3 decimals in Table C in the answer sheet.]
- What happens to the treatment effect estimate reported in Table 2 column 1 when you switch the left-hand side variables in (2) to a bankruptcy indicator and estimate the effect of the grace period treatment on enterprise bankruptcy by OLS?[Construct the bankruptcy indicator yourself based on female enterprise profits. Report the treatment effects estimate together with the standard error in 3 decimals in Table C in the answer sheet. Use the same right hand side specification as the one you used to replicate the estimation results of Table 2 (columns 1).]
- Apart from liquidity constraints, female microentrepreneurs may experience difficulties running their enterprise when they have young children (under 6). Report the treatment effect estimates for bankruptcy (together with the standard error) with 3 decimals for female microentrepreneurs with and without young children (under 6). [Report the corresponding treatment effect estimates in Table C columns 2 and 3 in the answer sheet.]
- According to these regression results, are female microentrepreneurs with young children more, less, or equally responsive to the grace period con- tract than female microentrepreneurs without young children. [Circle the correct answer in the answer sheet].
