Fractional integration in total factor productivity: evidence from US data

Abstract

This study examines the stochastic properties of different measures of Total Factor Productivity (TFP) in the USA and their components using fractional integration. The results show that its structure is more complicated than expected, formed by the interaction of various seasonal and non-seasonal unit (or fractional) processes. Thus, output (measured in terms of the GDP or the business sector value added) may be modelled as a unit root; the order of integration of capital is much higher than 1 and it may be specified even as an I(2) process, while labour contains a seasonal unit root. However, in all these cases, fractional degrees of integration may be even better characterizations for these series. As a result, the TFP series appear to be seasonally fractionally integrated, with d constrained between 0.5 and 1. A deeper investigation of the orders of integration at each of the frequencies shows that the order of integration at zero plays a much more important role that the seasonal frequencies, a result that is explained by the different stochastic nature of the components underlying the TFP.

Acknowledgement

Financial support from Gobierno de Navarra is gratefully acknowledged. All errors are our own.

Notes

¹ For an alternative definition of fractionally integrated process (the type I class), see Marinucci and Robinson (1999).

² See also Baillie (1996) for an interesting review of I(d) models.

³ These conditions are very mild, regarding technical assumptions in ψ(λ) that are satisfied by the model in Equations 1 and 6.

⁴ Applied articles using this version of Robinson's (1994) tests can be found in Gil-Alana (2001, 2004b).

⁵ An empirical application of the Bloomfield model with fractional integration in Macroeconomics time series is Gil-Alana (2003).