We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher's Z ‐transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mrow> <a:mi mathvariant="double-struck">R</a:mi> </a:mrow> <a:mrow> <a:mi>n</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>n</a:mi> <a:mo>−</a:mo> <a:mn>1</a:mn> <a:mo stretchy="false">)</a:mo> <a:mo stretchy="false">/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:msup> </a:math> is provided, and we derive its numerical complexity.

This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our simulation results show that our methods are properly sized under both correct specification and mild to moderate misspecification. We illustrate the method with an application to the model of Acemoglu, Johnson, Robinson, and Yared (2008).

We examine the economic impact of high-yielding crop varieties (HYVs) in developing countries 1960-2000. We use time variation in the development and diffusion of HYVs of 10 major crops, spatial variation in agro-climatically suitability for growing them, and a differences-in-differences strategy to identify the causal effects of adoption. In a sample of 84 counties, we estimate that a 10 percentage points increase in HYV adoption increases GDP per capita by about 15 percent. This effect is fully accounted for by the direct effect on crop yields, factor adjustment, and structural transformation. We also find that HYV adoption reduced both fertility and mortality.