We propose new methods for estimating the bid-ask spread from observed transaction prices alone. Our methods are based on the empirical characteristic function instead of the sample autocovariance function like the method of Roll (1984). As in Roll (1984), we have a closed form expression for...

We carry out some analysis of the daily data on the number of new cases and number of new deaths by (191) countries as reported to the European CDC. We work with a quadratic time trend model applied to the log of new cases for each country. This seems to accurately describe the trajectory of the...

This paper formulates and estimates multistage production functions for children's cognitive and noncognitive skills. Skills are determined by parental environments and investments at different stages of childhood. We estimate the elasticity of substitution between investments in one period and...