**Growth rate estimation in the presence of unit roots.** / Chatterji, Monojit; Choudhury, Homagni.

Research output: Working paper › Discussion paper

Chatterji, M & Choudhury, H 2010 'Growth rate estimation in the presence of unit roots' Dundee Discussion Papers in Economics, no. 1520, University of Dundee.

Chatterji, M., & Choudhury, H. (2010). *Growth rate estimation in the presence of unit roots*. (Dundee Discussion Papers in Economics; No. 1520). University of Dundee.

Chatterji M, Choudhury H. Growth rate estimation in the presence of unit roots. University of Dundee. 2010, (Dundee Discussion Papers in Economics; 1520).

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title = "Growth rate estimation in the presence of unit roots",

keywords = "Growth rate, CAGR, AAGR, Unit roots, Trend stationary, Structural breaks, Real wages, Inter-industry wage structure, Average Annual Growth Rate (AAGR), Compound Annual Growth Rate (CAGR)",

publisher = "University of Dundee",

author = "Monojit Chatterji and Homagni Choudhury",

year = "2010",

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series = "Dundee Discussion Papers in Economics",

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TY - UNPB

T1 - Growth rate estimation in the presence of unit roots

A1 - Chatterji,Monojit

A1 - Choudhury,Homagni

AU - Chatterji,Monojit

AU - Choudhury,Homagni

PB - University of Dundee

PY - 2010

Y1 - 2010

N2 - This 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.

AB - This 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.

KW - Growth rate

KW - CAGR

KW - AAGR

KW - Unit roots

KW - Trend stationary

KW - Structural breaks

KW - Real wages

KW - Inter-industry wage structure

KW - Average Annual Growth Rate (AAGR)

KW - Compound Annual Growth Rate (CAGR)

M1 - Discussion paper

BT - Growth rate estimation in the presence of unit roots

T3 - Dundee Discussion Papers in Economics

T3 - en_GB

ER -

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