Growth Rate Estimation in the presence of Unit Roots
AbstractThis study addresses the issue of the presence of a unit root on the growth rate estimation by the least-squares approach. We argue that when the log of a variable contains a unit root, i.e., it is not stationary then the growth rate estimate from the log-linear trend model is not a valid representation of the actual growth of the series. In fact, under such a situation, we show that the growth of the series is the cumulative impact of a stochastic process. As such the growth estimate from such a model is just a spurious representation of the actual growth of the series, which we refer to as a “pseudo growth rate”. Hence such an estimate should be interpreted with caution. On the other hand, we highlight that the statistical representation of a series as containing a unit root is not easy to separate from an alternative description which represents the series as fundamentally deterministic (no unit root) but containing a structural break. In search of a way around this, our study presents a survey of both the theoretical and empirical literature on unit root tests that takes into account possible structural breaks. We show that when a series is trendstationary with breaks, it is possible to use the log-linear trend model to obtain well defined estimates of growth rates for sub-periods which are valid representations of the actual growth of the series. Finally, to highlight the above issues, we carry out an empirical application whereby we estimate meaningful growth rates of real wages per worker for 51 industries from the organised manufacturing sector in India for the period 1973-2003, which are not only unbiased but also asymptotically efficient. We use these growth rate estimates to highlight the evolving inter-industry wage structure in India.
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Bibliographic InfoPaper provided by Economic Studies, University of Dundee in its series Dundee Discussion Papers in Economics with number 245.
Length: 54 pages
Date of creation: Oct 2010
Date of revision:
Growth Rate; CAGR; AAGR; Unit Root; Trend Stationary; Structural Breaks; Real Wages; Inter-Industry Wage Structure;
Other versions of this item:
- Chatterji, Monojit & Choudhury, Homagni, 2010. "Growth Rate Estimation in the presence of Unit Roots," SIRE Discussion Papers 2010-92, Scottish Institute for Research in Economics (SIRE).
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-11-06 (All new papers)
- NEP-ECM-2010-11-06 (Econometrics)
- NEP-ETS-2010-11-06 (Econometric Time Series)
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