Nonlinear Models of Convergence
A significant issue in studies of economic development is whether economies (countries, regions of a country, etc.) converge to one another in terms of per capita income. In this paper, nonlinear asymptotically subsiding trends of the income gap in a pair
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Novosibirsk State University, Novosibirsk, Russia [email protected] Institute of Economics and Industrial Engineering of the SB RAS, Novosibirsk, Russia
Abstract. A significant issue in studies of economic development is whether economies (countries, regions of a country, etc.) converge to one another in terms of per capita income. In this paper, nonlinear asymptotically subsiding trends of the income gap in a pair of economies model the convergence process. A few specific forms of such trends are proposed: log-exponential trend, exponential trend, and fractional trend. A pair of economies is deemed converging if time series of their income gap is stationary about any of these trends. To test for stationarity, standard unit root tests are applied with non-standard test statistics that are estimated for each kind of trends. Keywords: Income convergence Time series econometrics Nonlinear timeseries model Unit root
1 Introduction A significant issue in studies of economic development is whether economies (countries, regions of a country, cities, etc.) converge to one another in terms of per capita income. There are a number of methodologies to test for the convergence hypothesis. The most widespread one in the literature is the analysis of a negative cross-section correlation between initial per capita income and its growth, the so-called betaconvergence (see, e.g., [1]). An alternative methodology is the distribution dynamics analysis that explores the evolution of cross-economy income distribution [2]. Both approaches provide only an aggregated characterization of convergence. If the whole set of economies under consideration is found to converge, it is not possible to reveal economies with a deviant behavior (e.g., diverging or randomly walking). On the other hand, if the convergence hypothesis is rejected, it is not able to detect a subset (or subsets) of converging economies. Methodologies based on time-series analysis make it possible to overcome this problem. They consider time series of the income gap, i.e., the difference of logarithms of per capita incomes in a pair of economies r and s, yrst = yrt – yst = ln(Yrt/Yst), t denoting time. To discriminate between logarithmic and real (e.g., percentage) terms, Yrt/Yst – 1 is called income disparity. One element of the pair can be an aggregate, for instance, the national economy when economies under consideration are the country’s regions.
© Springer Nature Switzerland AG 2020 Y. Kochetov et al. (Eds.): MOTOR 2020, CCIS 1275, pp. 207–215, 2020. https://doi.org/10.1007/978-3-030-58657-7_18
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K. Gluschenko
Bernard and Durlauf [3] have put forward a formal definition of convergence: economies r and s converge if the long-term forecasts of per capita income (conditionally on information available by the moment of the forecast, I) for both economies are equal, that is limt!1 Eðyrst jI Þ ¼ 0:
ð1Þ
Despite this definition of convergence is general, procedures of testing for convergence applied in [3] in fact detect only a particular class of processes satisfying (
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