A study of the approximation and estimation of CES production functions
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The purpose of the dissertation is to propose and explore an empirical procedure to test if a CES production function is appropriate to describe a given dataset and inform on which nested structure should be adopted when there are more than two inputs. This is particularly useful for the estimation of elasticities of substitution. The ﬁrst chapter reviews the applied literature on the estimation of these elasticities and shows that Translog functions are the most popular as they are ﬂexible enough to be adopted in various empirical applications. Conversely, Constant Elasticities of Substitution (CES) production functions are rarely employed, mostly in the computable general equilibrium (CGE) framework. Indeed, the CES production functions are based on maintained hypotheses (i.e. homogeneity, separability, and constant elasticities) which are seldom satisﬁed empirically. In the second chapter, we show how these assumptions can be tested, exploiting the link between the Translog and CES functions: the former can be seen as a second-order Taylor expansion of the latter. In particular, we provide the necessary and suﬃcient constraints on the Translog coeﬃcients for all the feasible three-input and four-input cases. Given this information, the third chapter illustrates an empirical procedure that can be used to test whether an available dataset is consistent with a CES production technology, and, if that is the case, to determine which nested structure describes it more accurately. Finally, in the last chapter, we apply this procedure to the EU-KLEM dataset, to obtain constant elasticities of substitution for the United Kingdom.