Trend breaks and the long-run implications of investment-specific technological progress

ABSTRACT

I update the Greenwood, Hercowitz, and Krusell (1997, GHK) decomposition of U.S. growth into contributions from neutral and investment-specific (IS) technological progress. I allow the decomposition to vary across sub-samples, reflecting the presence of trend breaks in the data. The estimates show strong heterogeneity across periods: while neutral technological progress explained virtually all growth between 1950 and the mid-1970s, IS technological progress accounts for 75% of growth since the 1980s. These results paint a more complex picture of postwar U.S. growth than GHK’s original decomposition and call for a better understanding of the 1970s productivity shifts.

KEYWORDS:

• Neutral technology
• investment-specific technology
• sources of long-run growth
• structural breaks

JEL CLASSIFICATION:

• E13
• O33
• O41
• O47

Acknowledgments

For very helpful comments, I thank the editor (Mark Taylor), three anonymous referees, as well as Fabrice Collard, Martial Dupaigne, Patrick Fève, Pablo Garcia Sanchez, Paolo Guarda, Olivier Pierrard, and BCL colleagues.

This paper should not be reported as representing the views of the Banque centrale du Luxembourg or the Eurosystem.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ To obtain this equation, use the simple property that all variables entering linearly each model equation must grow at the same rate along the balanced growth path. Then, equation (2)(2) $C_t+I_{e,t}+I_{s,t}=Z_t{K}_{e,t-1}^{{\alpha }_e}{K}_{s,t-1}^{{\alpha }_s}{L}_t^{1-{\alpha }_e-{\alpha }_s},$(2) implies $g_y=g_c=g_{i_e}=g_{i_s}=g_z+{\alpha }_e{g}_{k_e}+{\alpha }_s{g}_{k_s}$, equation (3)(3) $K_{e,t}=(1-\delta )K_{e,t-1}+Q_t{I}_{e,t},$(3) implies $g_{k_e}=g_q+g_{i_e}$, and equation (4)(4) $K_{s,t}=(1-\delta )K_{s,t-1}+I_{s,t},$(4) implies $g_{k_s}=g_{i_s}$. Solving this system yields the expression for $g_y$. It also shows that structures grow at the same rate as output in consumption units: $g_y=g_{i_s}=g_{k_s}$.

² Of course, interpreting the relative price as a measure of investment-specific technology requires stringent assumptions related to perfect competition, that are likely to be violated in the data. For instance, time-varying markups and sticky prices would complicate the pass-through of relative technology to relative prices. However, the empirical results from Basu et al. (2011) and Moura (2018) suggest that these wedges are stationary, so that they should not matter much when estimating average growth rates over relatively long samples.

³ I work with log-differentiated variables for two reasons. From an economic perspective, I am interested in breaks in average growth rates, so that looking at log differences makes sense. From a statistical perspective, results from Kim and Perron (2009) tests indicate that it is not possible to reject the null of a unit root in either neutral or IS technology when allowing for a trend break at an unknown time under both the null and alternative hypotheses, so that working with first differences is warranted.

⁴ The Bai-Perron tests also suggest that each series contains only one significant break: the sup $F(1|0)$ statistics reject the null of no break against one break at the 1% level for both neutral and IS technology (exp-Wald statistics of 39.9 and 17.9), while the sup $F(2|1)$ test statistics fail to reject the null of a single break against the alternative of two breaks (exp-Wald statistics of 3.6 and 6.3).