Stata Command: robustpf
Stata Command: robustpf.ado
The STATA output displayed below shows an estimate of a net-output production function with robustness against errors in proxy variables based on Hu, Huang and Sasaki (2020). Errors in proxies pave the way for functional independence to overcome the problem of an identification failure by traditional production function estimators as pointed out by Ackerberg, Caves and Fraser (2015). The estimates are the coefficients of capital (k), skilled labor (ls), and unskilled labor (lu). These results can be automatically produced by the Stata command robustpf as follows.
Installation:
. ssc install robustpf
Usage:
. use "example_Chile.dta"
. xtset id year
. robustpf y, capital(k) free(ls lu) proxy(m)
Help:
. help robustpf
Reference: Hu, Y., G. Huang, and Y. Sasaki (2020) Estimating Production Functions with Robustness Against Errors in the Proxy Variables. Journal of Econometrics, 215 (2), pp. 375-398. Paper.
The table below compares estimates by Levinson and Petrin (LP), Wooldridge (W), Ackerberg, Caves, and Fraser (ACF), and Hu, Huang, and Sasaki (HHS) for Chilean firms in the food production industry between 1981 and 1983. Estimates of the labor coefficients are small for LP and W. They become larger when the ACF correction is applied. However, the ACF estimates imply increasing returns to scale. HHS estimates are similar to ACF in the labor coefficients, but exhibit constant returns to scale.
robustpf -- Executes estimation of production functions robustly against errors in proxy variables.
Syntax
robustpf y k l1 ... lJ [if] [in] [, proxy(varname) m1(varname) ... m5(varname) onestep init_k(real) init_l(real) init_m(real)]
Description
robustpf estimates production functions robustly against errors in proxy variables, based on the identification and estimation theories developed in Hu, Huang, and Sasaki (2020). The command takes as input an output variable y, a capital variable k, and J types of labor variables l1...lJ. In addition, for estimation of a gross-output production function, a user can set up to five intermediate input variables as options m1()...m5(). A user must set a proxy variable by calling the option proxy(), which often takes one of the intermediate input variables or an investment variable. Displayed results consist of returns to scale and coefficients of each input variable.
Options
proxy(varname) takes the proxy variable used for estimation of the production function. Receiving no input for this option, the command produces no estimation results.
m1(varname)...m5(varname) take up to five intermediate input variables for estimation of the gross-output production function. Receiving no input for any of these options, the command estimates the net-output production function.
onestep sets an indicator for implementing just one step of the GMM estimation. Not calling this option will lead to the two-step efficient GMM estimation by default.
init_capital(real) sets the initial value of the capital coefficient for an optimization routine of the GMM estimation. The default value is init_capital(0.0).
init_free(real) sets the initial value(s) of the labor coefficient(s) for an optimization routine of the GMM estimation. The default value is init_free(0.0).
init_m(real) sets the initial value(s) of the intermediate input coefficient(s) for an optimization routine of the GMM estimation. The default value is init_m(0.5).
(The moment function for GMM estimation is nonlinear, and hence it is recommended to try multiple initial values to improve the possibility of attaining the globally optimal solution.)
Examples
(Variables: id ID, year year, y output, k capital, ls skilled labor, lu unskilled labor, m material, e electricity) Estimation of net-output production function with material as a proxy:
. use "example_Chile.dta" . xtset id year . robustpf y, capital(k) free(ls lu) proxy(m)
Estimation of gross-output production function with material as a proxy:
. use "example_Chile.dta" . xtset id year . robustpf y, capital(k) free(ls lu) m(m e) proxy(m)
Stored results
robustpf stores the following in e():
Scalars e(N) observations e(T) time periods e(minT) first time period e(maxT) last time period e(objective) value of the GMM objective
Macros e(cmd) robustpf e(properties) b V
Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators e(br) returns to scale (RTS) e(Vr) variance of the RTS estimator
Functions e(sample) marks estimation sample
Reference
Hu, Y., G. Huang, and Y. Sasaki. 2020. Estimating Production Functions with Robustness Against Errors in the Proxy Variables. Journal of Econometrics, 215 (2), pp. 375-398. Link to Paper
Authors
Yingyao Hu, Johns Hopkins University, Baltimore, MD. Guofang Huang, Purdue University, West Lafayette, IN. Yuya Sasaki, Vanderbilt University, Nashville, TN.