Using a normalized CES function with factor-augmenting technical progress, we estimate a supply-side system of the U.S. economy from 1953 to 1998. Avoiding potential estimation biases that may have occurred in earlier studies and putting a high emphasis on data consistency, we obtain robust results not only for the aggregate elasticity of substitution but also for the parameters of labor and capital augmenting technical change. We find that the elasticity of substitution is significantly below unity and that technical progress shows an asymmetrical pattern where the growth of labor-augmenting technical progress is exponential, while that of capital is hyperbolic or logarithmic. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

4Non-technical summary 5

The elasticity of substitution between capital and labor and, in turn, the direction of technical change are critical parameters in many fields of economics. Until recently, though, the application of production functions with specifically non‐unitary substitution elasticities (i.e., non‐Cobb–Douglas) was hampered by empirical and theoretical uncertainties. As recently revealed, ‘normalization’ of production‐technology systems holds out the promise of resolving many of those uncertainties. We survey and assess the intrinsic links between production (as conceptualized in a production function), factor substitution (as made most explicit in Constant Elasticity of Substitution functions) and normalization (defined by the fixing of baseline values for relevant variables). First, we recall how the normalized Constant Elasticity of Substitution function came into existence and what normalization implies for its formal properties. Then we deal with the key role of normalization in recent advances in the theory of business cycles and of economic growth. Next, we discuss the benefits normalization brings for empirical estimation and empirical growth research. Finally, we identify promising areas of future research.

We develop a framework for measuring and analyzing medium-run departures from balanced growth, and apply it to developments in the euro area. A time-varying factor-augmenting production function (mimicking directed technical change) with below-unitary substitution elasticity is shown to account for the observed dynamics of factor incomes shares, TFP growth, and its components. Based on careful data accounting, we also identify a rising markup and the importance of financial-market regulations in the 1970s. The balanced growth path emerges as a special (and testable) case of our framework, as do existing strands of medium-run debates.

4Non-technical summary 5

In this paper, we seek to re-establish the link between the CES production function and neoclassical growth theory. We did so in three dimensions. First, we reviewed the increasing importance of the CES technology in modern dynamic macroeconomics, in expanding not only theory but also in addressing important policy questions. Second, we argued that the importance of the CES function in growth theory is intimately linked to 'normalization'. Finally, we examined the data congruence between CES functions and recent growth patterns in US and euro-area economies, where we apply CES functions with factor-augmenting and time-varying technical progress.

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Capital-labor substitution and TFP estimates are essential features of many economic models. Such models typically embody a balanced growth path. This often leads researchers to estimate models imposing stringent prior choices on technical change. We demonstrate that estimation of the substitution elasticity and TFP growth can be substantially biased if technical progress is thereby mis-specified. We obtain analytical and simulation results in the context of a model consistent with balanced and near-balanced growth (i.e., departures from balanced growth but broadly stable factor shares). Given this evidence, a Constant Elasticity of Substitution production function system is then estimated for the US economy. Results show that the estimated substitution elasticity tends to be significantly lower using a factor-augmenting specification (well below one). We are also able to reject conventional neutrality forms in favor of general factor augmentation with a non-negligible capital-augmenting component. Our work thus provides insights into production and supply-side estimation in balanced-growth frameworks.