Question 1:
Imagine you knew that the true country-level production function was: , where Y is PPP-adjusted GDP, K is the PPP-adjusted value of the capital stock, L is the number of workers in the workforce, A is total factor productivity (TFP), and α and β are production function parameters.
Imagine also that you had a dataset with one cross-section of countries in 2011 containing information on nominal GDP in local currency, the nominal exchange rate vis-à-vis the dollar, an index of the level of prices relative to the US, the nominal value of the capital stock in local currency, and data on L.
a) How could you use this dataset to empirically estimate the parameters α and β using an OLS regression. Be specific about each step of this analysis.
b) Briefly interpret what the point estimates of the α and β coefficients would mean. Also explain how these estimates could be informative to verify whether the country-level production function has constant returns to scale.
c) Could you obtain an estimate of country-level TFP even though it is not a variable in your dataset? If so, be specific about each step of the analysis. Also write a sentence to interpret what exactly your measure of TFP would represent/capture in the data.
d) Do you think your OLS estimates of α and β are likely unbiased? Briefly write down the potential biases and be as formal as possible in defining each of them.
Question 2:
The director of an NGO is once again desperate: She proudly presented to her donors the statistically significant and positive effects of their village-level intervention from an RCT impact evaluation that their NGO had conducted. She said that this time they had learnt their lessons so that the randomization had worked perfectly. She then presented the donors the difference in the mean of the outcomes after the intervention between treatment and control villages, and these mean outcomes were all much better for the villages that had received the program intervention relative to the villages that had not received the treatment, and in a statistically significant way.
She tells you that she does not understand the remaining skepticism of the donors: they walked away unconvinced after she mentioned that the take-up rate of the program intervention was substantially less than 100% in the treatment group --which she thinks of as perfectly normal given the experience of her NGO.
1
a) Use the potential outcomes framework to explain to the director what the donors' concern may be based on.
b) Given this concern, would you think that the treatment effect of the program is likely upward biased or downward biased? Refer to the potential outcomes framework to be specific.
c) Is there a solution that the director could use to convince the donors? Use the potential outcomes framework to explain her how to do it.