Stata Command: xtusreg
Stata Command: xtusreg.ado
The Stata output displayed below shows an estimate of the autoregressive coefficient of earnings using NLS Original Cohorts: Old Men, a panel data with unequal time spacing, starting with 1965, 1966, 1968, and so on. Traditional methods, such as xtabond, of estimation of dynamic panel models usually require three consecutive time periods or two pairs of two consecutive time periods. On the other hand, the identification and estimation theories developed by Sasaki and Xin (2017) apply to panel data with irregularly unequal time spacing, as is the case with NLS Original Cohorts: Old Men. This output can be produced by the Stata command xtusreg as follows.
Installation:
. ssc install xtusreg
Usage:
. use "NLS_Originl_Cohort.dta"
. xtset id year
. xtusreg logincome
Help:
. help xtusreg
Reference: Sasaki, Y. and Y. Xin (2017) Unequal Spacing in Dynamic Panel Data: Identification and Estimation. Journal of Econometrics, 196 (2), pp. 320-330. Paper.
Download the manuscript and package forthcoming in The Stata Journal
xtusreg -- Executes estimation and inference for fixed-effect dynamic panel data models when panel data consist of unequally spaced time periods.
Syntax
xtusreg depvar [indepvars] [if] [in] [, twostep nonormalization gamma(real) beta(real)]
Description
xtusreg estimates coefficients of fixed-effect linear dynamic panel models under unequal spacing of time periods in data, based on the identification and estimation theories developed in Sasaki and Xin (2017). The admissible pattern of unequal spacing is the US Spacing -- see Definition 2 and Example 2 in Sasaki and Xin (2017). This spacing pattern is characterized by the availability of two pairs of two consecutive time gaps. For example, a data set that includes observations from surveys in years 1966, 1967, and 1970 is unequally spaced. However, it exhibits the US Spacing with two pairs, (0,1) and (3,4), of two consecutive time gaps, as there are 0-year gap between 1966 and 1966, 1-year gap between 1966 and 1967, 3-year gap between 1967 and 1970, and 4-year gap between 1966 and 1970. One may simply run the fixed-effect dynamic panel autoregression of the dependent variable alone. Alternatively, one may run the fixed-effect dynamic panel autoregression with time-varying covariate(s). The estimator is based on the normalization (see Sasaki and Xin, 2017, Appendix C.1) for robustness.
Options
twostep sets an indicator for the two-step GMM estimation. Not calling this option leads to a one-step GMM estimation. This option will not make a difference in the results if parameters are just identified.
nonormalization sets an indicator for not executing the location-scale normalization. Not calling this option leads to an implementation of the location-scale normalization by default. Appendix C.1 of Sasaki and Xin (2017) recommends to implement the location-scale normalization.
gamma(real) sets the initial value of the autoregressive coefficient for a numerical optimization in the GMM estimation. The default value is gamma(0).
beta(real) sets the initial value of the regression coefficients for a numerical optimization in the GMM estimation. The default value is beta(0).
Examples
Loading the NLS Original Cohorts: Older Men:
. use "NLS_Originl_Cohort.dta"
Set i and t variables:
. xtset id year
Estimation of the AR(1) coefficient of logincome:
. xtusreg logincome
Estimation of the AR(1) coefficient of logincome along with the regression coefficient of age:
. xtusreg logincome age
Time-invariant variables cannot be included for fixed-effect panel regressions. To account for heterogeneity across time-invariant variables, one can run a regression for each category as:
. xtusreg logincome if !white . xtusreg logincome if white
Stored results
robustpf stores the following in e():
Scalars e(NT) observations e(N) cross sectional units e(T) time periods e(objective) value of the GMM objective
Macros e(cmd) xtusreg e(steps) number of GMM steps: one or two e(properties) b V
Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators e(tlist) list of time periods
Functions e(sample) marks estimation sample
Reference
Sasaki, Y. and Y. Xin 2017. Unequal Spacing in Dynamic Panel Data: Identification and Estimation. Journal of Econometrics, 196 (2), pp. 320-330. Link to Paper
Authors
Yuya Sasaki, Vanderbilt University, Nashville, TN. Yi Xin, California Institute of Technology, Pasadena, CA.