On the Solution of the Growth Model with Investment-Specific Technological Change

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Working Paper 2004-39 December 2004

Abstract: Recent work by Greenwood, Hercowitz, and Krusell (1997 and 2000) and Fisher (2003) has emphasized the importance of investment-specific technological change as a main driving force behind long-run growth and the business cycle. This paper shows how the growth model with investment-specific technological change has a closed-form solution if capital fully depreciates. This solution furthers our understanding of the model, and it constitutes a useful benchmark to check the accuracy of numerical procedures to solve dynamic macroeconomic models in cases with several state variables.

JEL classification: E10, E32, D90

Key words: growth model with investment-specific technological change, closed-form solution, long-run growth, business cycle fluctuations

1. Introduction

The recent work of Greenwood, Hercowitz, and Krusell (1997 and 2000) has focused the attention of economists on the role of investment-specific technological change as a main driving force behind economic growth and business cycle fluctuations. Fisher (1999) documents two key empirical observations that support these conclusions. First, the relative price of business equipment in terms of consumption goods has fallen in nearly every year since the 1950s. Second, the fall in the relative price of capital is faster during expansions than during recessions.

Models of investment-specific technological change have also being successfully used to account for the evolution of the skill premium in the U.S. since the Second World War (Krusell et al., 2000) or the cyclical behavior of hours and productivity (Fisher, 2003), among several other applications.

Unfortunately, the standard growth model with investment-specific technological change, as presented in Fisher (2003), does not have a known analytic solution. Therefore, researchers have employed computational methods to solve the model.

In this paper, we show how this standard model has a closed-form solution when there is full depreciation of capital. We derive the exact solution in the case where there is a labor/leisure choice and long-run growth in the economy. The solution has a …