Structural Change in a Multisector Model of Growth

Economic growth takes place at uneven rates across different sectors of the economy. This paper has two objectives related to this fact: (a) to derive the implications of different sectoral total factor productivity (TFP) growth rates for structural change, the name given to the shifts in industrial employment shares that take place over long periods of time; and (b) to show that even with ongoing structural change, the economy’s aggregate ratios can be constant. We refer to the latter as aggregate balanced growth. The restrictions needed to yield structural change consistent with the facts and aggregate balanced growth are weak restrictions on functional forms that are frequently imposed by macroeconomists in related contexts. We obtain our results in a baseline model of many consumption goods and a single capital good, supplied by a sector that we label manufacturing. Our baseline results are consistent with the existence of intermediate goods and many capital goods under some reasonable restrictions. Production functions in our model are identical in all sectors except for their rates of TFP growth, and each sector produces a differentiated good that enters a constant elasticity of substitution (CES) utility function. We show that a low (below one) elasticity of substitution across final goods leads to shifts of employment shares to sectors with low TFP growth. In the limit, the employment share used to produce consumption goods vanishes from all sectors except for the one with the smallest TFP growth rate, but the employment shares used to produce capital goods and intermediate goods converge to nontrivial stationary values. If the utility function in addition has unit intertemporal elasticity of substitution, during structural change the aggregate capital-output ratio is constant and the aggregate economy is on a balanced growth path. Our results contrast with the results of Cristina Echevarria (1997), John Laitner (2000), Francesco Caselli and Wilbur Coleman II (2001), and Douglas Gollin, Stephen Parente, and Richard Rogerson (2002), who derived structural change in a twoor three-sector economy with nonhomothetic preferences. Our results also contrast with the results of Piyabha Kongsamut, Sergio Rebelo, and Danyang Xie (2001) and Reto Foellmi and Josef Zweimuller (2005), who derived simultaneous constant aggregate growth and structural change. Kongsamut, Rebelo, and Xie (2001) obtain their results by imposing a restriction that maps some of the parameters of their Stone-Geary utility function onto the parameters of the production functions, abandoning one of the most useful conventions of modern macroeconomics, the complete independence of preferences and technologies. Foellmi and Zweimuller (2005) obtain their results by assuming endogenous growth driven by the introduction of new goods into a hierarchic utility function. Our restrictions are quantitative restrictions on a conventional CES utility function that maintains the independence of the parameters of preferences and technologies. Our results confirm William J. Baumol’s (1967) claims about structural change. Baumol divided the economy into two sectors, a “progressive” one that uses new technology and a “stagnant” one that uses labor as the only input. He then claimed that the production costs and prices of the stagnant sector should rise indefinitely, a process known as “Baumol’s cost dis* Ngai: Centre for Economic Performance, London School of Economics and CEPR (e-mail: l.ngai@lse.ac.uk); Pissarides: Centre for Economic Performance, London School of Economics, CEPR, and IZA (e-mail: c.pissarides@lse.ac.uk). We have benefited from comments received at several presentations (the CEPR ESSIM 2004 meetings, the SED 2004 annual conference, the NBER 2004 Summer Institute, the 2004 Canadian Macroeconomic Study Group, and at several universities), and from Fernando Alvarez, Francesco Caselli, Antonio Ciccone, Nobu Kiyotaki, Robert Lucas, Nick Oulton, Danny Quah, Sergio Rebelo, Robert Shimer, Nancy Stokey, Richard Rogerson, Jaume Ventura, and two anonymous referees. Funding from the CEP, a designated ESRC Research Centre, is acknowledged.