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Cobb-Douglas production function revisited, VAR and VECM analysis and a note on Fischer/Cobb-Douglass paradox

Josheski, Dushko and Lazarov, Darko and Koteski, Cane (2011): Cobb-Douglas production function revisited, VAR and VECM analysis and a note on Fischer/Cobb-Douglass paradox.

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Abstract

Cobb-Douglas production function is a basic function in growth models. The modeling in this paper showed that VAR is stable; KPSS test showed that output, capital and labor are not trend stationary. Johansen’s co-integration test showed that a requirement for Fischer/Cobb-Douglass paradox to work is met at 3 lags, there factor shares are I(0). The Fisher/Cobb-Douglas Paradox is based on constant factor shares. (In terms of time-series analysis, such constancy is equivalent to factor shares being I(0). The Fisher/Cobb-Douglas Paradox is thus why the estimated σ equals unity independent of the underlying production technologies generating the simulated data.At 4 lags however these variables are I(1) variables i.e. Cobb-Douglass is not CES function anymore. ADF test for factors of production showed that natural logarithm of capital is stationary variable, while log of labor is not-stationary except at 10% level of significance. Adjustment parameters showed that labour responds more / faster than loutput (log of GDP) and lcapital on if there is change / shock in the system.VECM model failed the stability eingevalues test.

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