Estimating a common deterministic time trend break in large panels with cross sectional dependence

• Published in: Journal of econometrics Vol. 164; no. 2; pp. 310 - 330
• Main Author: Kim, Dukpa
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2011; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Acceleration of convergence; Applications; Correlation; Correlation analysis; Deterministic trend; Distribution theory; Econometrics; equations; Estimating techniques; Estimation; Exact sciences and technology; Insurance, economics, finance; Limit theorems; Mathematics; Monte Carlo simulation; Numerical analysis; Numerical analysis. Scientific computation; Panel data; prices; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Structural break; Structural break Deterministic trend Panel data; Structural change; Studies; Time series; Unit root; United States; United States > US; United States; C33; Panel data; Deterministic trend; Structural break; Statistical distribution; Error estimation; Error rate; Serial correlation; Dependent variable; Stochastic method; Unit root; Limit distribution; Cross sectional study; Convergence rate; Approximation theory; Monte Carlo method; Data analysis; Convergence acceleration; Price index; Statistical estimation; Statistical method; Numerical analysis; Correlation analysis; Trend analysis; Cross correlation; Econometrics
• DOI: 10.1016/j.jeconom.2011.06.018
• ISSN: 0304-4076

This paper develops an estimation procedure for a common deterministic time trend break in large panels. The dependent variable in each equation consists of a deterministic trend and an error term. The deterministic trend is subject to a change in the intercept, slope or both, and the break date is common for all equations. The estimation method is simply minimizing the sum of squared residuals for all possible break dates. Both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate. The rate of convergence is faster when the errors are stationary than when they have a unit root. When there is no cross sectional dependence among the errors, the rate of convergence depends on the number of equations and thus is faster than the univariate case. When the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters, the rate of convergence does not depend on the number of equations and thus reduces to the univariate case. The limiting distribution of the break date estimate is also provided. Some Monte Carlo experiments are performed to assess the adequacy of the asymptotic results. A brief empirical example using the US GDP price index is offered.