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...

Previous work has analyzed whether luminosity data contain useful information for estimating economic output and concluded that there was significant promise for regions with poor quality economic statistics. The present paper examines alternative measures of the precision of the estimates using...