Cleaning Up the Kitchen Sink: On the Consequences of the Linearity Assumption for Cross-Country Growth Empirics
Existing work in growth empirics either assumes linearity of the growth function or attempts to capture non-linearities by the addition of a small number of quadratic or multiplicative interaction terms. Under a more generalized failure of linearity or if the functional form taken by the non-linearity is not known ex ante, such an approach is inadequate and will lead to biased and inconsistent OLS and instrumental variables estimators. This paper uses non-parametric and semiparametric methods of estimation to evaluate the relevance of strong non-linearities in commonly used growth data sets. Our tests decisively reject the linearity hypothesis. A preponderance of our tests also rejects the hypothesis that growth is a separable function of its regressors. Absent separability, the approximation error of estimators of the growth function grows in proportion to the number of relevant dimensions, substantially increasing the data requirements necessary to make inferences about the growth effects of regressors. We show that appropriate non-parametric tests are commonly inconclusive as to the effects of policies, institutions and economic structure on growth.