# ECO £404 – Assignment £

## 1 Estimatimg Productiom Fumctiom

Download the data “data-olley-pakes”. There are †3fi firms and 6 years of data. Each row refers to one firm in one year. The variables are as follows: firm, year, output, age, capital, labor, and investment. If a firm‘s values are zero in a given year, that means that the firm does not exist in that year, it has either exited already or not yet entered.

You can answer the questions using either STATA or MATLAB, although I would suggest you to implement the Olley and Pakes (OP) estimator in MAT- LAB to have a better understanding of the method. If you are using STATA,  do not forget to change the zeros into dots so that STATA understands that the variables are missing¡ otherwise it will consider the zeros as observations. Make sure you put the data in logs before estimating the model.

## 1.1 Model

Assume the firms have a Cobb-Douglas production function (let‘s ignore firm‘s age in the exercise, but you can include it if you want to):

yst = Ø0 ‡ Ø11st ‡ Øhhst ‡ cst ‡ ost, (fi)

where yst is the log of output¡ 1st is the log of labor¡ hst is the log of capital¡ the term cst represents “productivity shocks” that are observed or predictable by the firms before making their input decisions at t¡ and ost represents both i.i.d. shocks to production that are not predicted by the firms and measurement errors in the observed variables. The endogeneity problem in estimating (fi)  comes from the correlation between the inputs and cst.

## 1.2 Øuestiom

fi. Estimate the production function using pooled OLS for both the unbal- anced and for the balanced panel data. What do you find? Are the estimates significant? Are they economically reasonable? Why would you expect them to be biased?

£. Assume cst = cs, i.e., it is a time-invariant fixed-effect. Estimate the production function using the fixed-effect estimator. What do you find? Are the estimates significant? Are they economically reasonable?

3. Assume cst = gcst—fi ‡ Øst, where |g| c fi and Øst is i.i.d. Add the fixed- effect as in the unobservables. Estimate the production function using the SYS GMM estimator proposed by Blundell and Bond. What do you find? Are the estimates significant? Are they economically reasonable?

4. Return to the original model (fi) and assume the model satisfies the OP assumptions. Estimate the model using investments as a proxy for cst.