Broken trend stationarity of hours worked

Abstract

The estimated impact of a technology shock on hours worked using Structural Vector Autoregressions (SVARs) depends to a great extent on whether or not hours worked is considered to be integrated of first order. It is shown in this article that the widely analysed time series of hours worked per capita in the US business sector evolves around a broken linear trend. When this fact is taken into account, the unit root null is rejected by recently proposed tests. Therefore, it can be stated that empirical specifications with hours in first differences are not recommended. It seems more appropriate to control for the presence of this shift in the deterministic component. We also draw this conclusion from a bivariate model for both productivity growth and hours worked. Our results suggest that technology improvements have a negative but nonsignificant effect on hours only in the very short run. This impact later becomes positive and statistically significant after five periods.

Keywords:

• structural change
• unit roots
• technology shocks
• SVAR

JEL Classification::

• C12
• C22
• E00

Notes

¹ This information can be found in http://research.stlouisfed.Org//fred2/series/CNP16OV.

² This is the most general case. Perron and Yabu (2009) also consider more restrictive specifications with only a structural change in the intercept (Model I) or in the slope (Model II) parameters.

³ The noncentrality parameter has been set to −18.5.

⁴ Appendix B, p. 95.

⁵ This author suggested that these changes implied a high-low-high pattern in the productivity growth time series. This evolution is supposed to be related to unusual historical events with persistent and nonpermanent effects like steam power, electricity, the interstate highway system or information technologies. Another interpretation, given by Francis and Ramey (2009), is that they reflect the entry of the baby boom generation into the labour market.

⁶ The identification strategy proposed by Galí (1999) hinges on the presence of a unit root in productivity. This author provided evidence supporting this assumption. Nonetheless, there is a wide consensus in the related literature that productivity growth is a stationary process.

⁷ Although this approach has been criticized by Chari et al. (2008), its usefulness in identifying technological shocks and relating the empirical evidence to the RBC and NK paradigms has been corroborated by Erceg et al. (2005) and Francis and Ramey (2005).

⁸ The same analysis has been carried out for the first-differenced and level specifications of hours and neglecting the presence of deterministic shifts with our updated sample period. As could be expected, the first-differenced specification leads us to conclude that hours decrease after a positive technology shock while the level specification suggests that the response is positive.