A simple model of productivity slowdown

Abstract

This article demonstrates a simple mechanism of productivity slowdown. There are two types of technological change: exogenous and endogenous. After news arrives that there will be an acceleration of exogenous technological progress in the future, endogenous technological progress may slow down.

Notes

¹ All the numbers in this section are taken from Nordhaus (2005, Table 3). Nordhaus shows that the same pattern can be found using other measures of productivity.

² Another related literature is the one that focuses on the role of the general purpose technologies (GPTs). Helpman and Trajtenberg's (1998) model exhibits a slowdown in output after the arrival of a new GPT due to the increase in the resources devoted to R&D investment. Aghion and Howitt (1998a) emphasize the role of social learning in creating a delayed slump in aggregate output after the arrival of a new GPT.

³ This includes not only the measured R&D but also any productivity-enhancing expenditures, such as expenditures for learning and reorganization. The data shows that the measured R&D/GDP ratio declined starting in the late 1960s until the end of the 1970s, and then somewhat recovered (Aghion and Howitt 1998b, Figure 12.3).

⁴ Alternatively, one can model the endogenous technological change as in the recent endogenous growth literature–e.g. Romer (1990) Grossman and Helpman (1991) and Aghion and Howitt (1992).

⁵ Since we do not have capital stock and there is no population growth, this also corresponds to the growth rate of labour productivity.

⁶ In general, the diffusion of a new technology is not immediate. See Mukoyama (2004) and reference therein for studies of diffusion of new technologies.

⁷ Case II is less plausible than Case I, since it implies that if the new regime arrives at the same time as the news (t ₁ = t ₀), the consumption level jumps down. Later we will show that with reasonable parameter values, Case I realizes.

Fig. 1 Case I

Fig. 2 Case II

⁸ The numerical solutions are computed using forward- and backward-shooting methods. See Judd (1998, Chapter 10).

Fig. 3 Time series of γ_TFP