Balanced Growth with Structural Change

We study the interactions between aggregate growth and structural change. Our economy has many sectors characterized by different rates of total factor productivity growth and producing differentiated products. All sectors produce consumption goods but one sector, labelled manufacturing, also produces capital goods. We derive sufficient conditions for the coexistence of a balanced aggregate growth path, with all aggregates growing at the same rate, and structural change, characterized by sectoral labor reallocation. We show that the conditions needed for these outcomes are weak restrictions on the utility function: the intertemporal elasticity of substitution needs to be equal to one and the elasticity of substitution across consumption goods needs to be different from one. When these conditions are met the aggregate growth rate of our many-sector economy is the same as the labor-augmenting growth rate of the manufacturing sector (with all aggregates defined in value terms in terms of manufacturing which is used as the numeraire). We present evidence from sectoral US data that is consistent our conclusions, provided the cross-sectional consumption elasticity is less than one, i.e., provided the final products of our sectors are poor substitutes. We show that when this condition is met the sectors with high TFP growth shrink and the ones with low TFP growth expand, at least initially, but eventually, all sectors vanish except for the sector with the lowest TFP growth and manufacturing. The model makes strong predictions about the convergence paths for each sector and in the final part of the paper we use he model to study the dynamic adjustment paths for a three-sector economy, with agriculture, a consumption sector with high TFP growth, manufacturing, a sector that produces both consumption and capital goods and characterized by medium TFP growth, and services, a consumption-goods sector with low productivity growth. We show that our model captures well the shrinking of agricultural employment, the initial (mild) expansion and subsequent contraction of manufacturing employment and the expansion of services employment