*! version 1.1.1

Title

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 by default.

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_Original_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.