The essay entails a paper on the Total factor productivity of a country level production function. Total factor productivity makes sure that the production of both the machinery and the labour is in the best way condition.

## Total factor productivity country level production function

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. 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. Could you use the regression results from part a) to measure differences in TFP across countries? If so, briefly explain how. You have learned from an economist that the measurement of the capital stock can be quite noisy because its hard to measure in general. What concern could this give rise to in the estimation that you describe in part a)? Be as formal as possible in your answer. A friend tells you that rich countries save more because they are rich and, hence, accumulate more capital. If this is true, would that give rise to any concerns for your estimation in a)?

Can you think of a way to address the concerns in c) and d) with a statistical technique we have learned so far in the course? What would be the advantage of the technique relative to your estimation in a)? What would be the conditions that need to hold true for this technique to yield a valid estimate of α? Can you come up with a tentative but concrete example?

### Question 2

Google Foundation has hired you as part of their impact evaluation team. Your first assignment is to evaluate a Randomized Control Trial that they have implemented before you arrived. Two years before you arrive, they have installed free broadband internet access to 100 Indian villages, which they randomly selected from a list of 200 villages that all had expressed their interest in participating in the project. All 200 villages are very close to one another in the same small and densely populated region within one Indian subdistrict.

The board asks you to estimate the Average Treatment Effect of their intervention on village-level. GDP per capita. What data (which variables) do you require from their project team to answer this question? Which regression equation would you want to use these data for? Describe each variable and subscripts and explain the interpretation of the regression coefficients. What potential concerns would you raise to the board about interpreting your findings fromas the Average Treatment Effect of the program? Discuss at least 3 and be specific about each concern.