Levinsohn and Petrin's (2003) estimator (LP)

This routine obtains fast estimators of production function coefficients. The routine simplifies LP a bit so it should be useful in large samples (I'll post a benchmark comparison soon). Efficiency of the estimator should be demonstrated.

The section below documents the different stages of the LP estimator (in French so far ...). Then, I suggest a Nonlinear Least Squares approach to LP. Mail me with warm cheers at [email protected] if my presentation below is useful to your work.

Estimation stages in LP

The routine tfp_lp_nlls.do

This repository includes a program that implement Levinsohn and Petrin's (2003) LS estimator in Stata but with a higher execution speed than in levpet and prodest. To achieve higher speed, I implement a nonlinear least squares (NLLS) estimator. The NLLS estimator estimates the capital elasticity and the coefficients of the markov equation simultaneously. Basicaly, steps 4-6 are merged into one Stata command. The routine does not rely on the bootstrap to achieve efficiency of estimated coefficients. Bootstrapping is useful for small samples, whereas this program should be used in large samples of firms and households (millions) as we use e.g. in my research unit @SciencesPo.

As far as I know, the speed of productivity estimation is not very considered as a subject per se. However, when the sample charge is large and unless your computer reaches the speed of a rocket, my routine, goes 6 times faster than the pioneer levpet command by Petrin, A., Poi, B. and Levinsohn, J., 2004, Production function estimation in Stata using inputs to control for unobservables, The Stata Journal, 4, 113-123, or Rovigatti, G. and 3 times faster than prodest by Mollisi, V., 2018, Theory and practice of total-factor productivity estimation: the control function approach using Stata, The Stata Journal, 18, 618-662.

Another advantage is that you don't need to use your own grid search or other optimization algorithm, but instead benefit from the built in algorithms of Stata. Basically, by setting the options in the nl command.

The variables that you must have in your data sheet

I decided not to make a command, for the code is short enough; so, it is more interesting I think for you to copy-paste tfp_lp_nlls.do into your own code. Before, you'll have to rename your variables for firm id, time, added-value, etc. to:

• firm id: siren,
• time: year,
• log of added value: l_v,
• capital stock: l_k,
• log of total hours of work: l_hours,
• log of materials: l_m.

Bon voyage 👍