< Back to STATA Main Page

Stata Command: dkdensity.ado

The "deconvolution" identifies the distribution of X_i even if X_i is not observed, but with two measurements X_1i and X_2i of X_i with measurement errors e_1i = X_1i - X_i and e_2i = X_2i - X_i, respectively. The graph below depicts a deconvolution kernel density estimate for the distribution of total factor productivity (TFP), ω_1982,i, of Chilean firms in the food industry in 1982 along with its 95% uniform confidence band (Kato and Sasaki, 2018). The residuals of production functions in 1982 and 1983 are r_1982,i = ω_1982,i + ε_1982,i. and r_1983,i = ω_1983,i + ε_1983,i = ω_1982,i + η_1983,i + ε_1983,i, where ω denotes productivity, η denotes a productivity shock, and ε denotes an idiosyncratic shock. Therefore, X_1i = r_1982,i and X_2i = r_1983,i serve as repeated measurement for X_i = ω_1982,i with measurement errors, e_1i = ε_1982,i and e_2i = η_1983,i + ε_1983,i, respectively. The graph is automatically produced by the Stata command dkdensity as follows:

Installation:

. ssc install dkdensity

Usage:

. use "example_1982_1983.dta"

. dkdensity resid1982 resid1983, numx(100) domain(4)

Help:

. help dkdensity

Reference: Kato, K. and Y. Sasaki (2018) Uniform Confidence Bands in Deconvolution with Unknown Error Distribution. Journal of Econometrics, 207 (1), pp. 129-161. Paper.