Kernel Regression in Empirical Microeconomics

Financial dependence and growth: Diminishing returns to improvement in financial development

“…where η is defined by the instrumental variable equation F inDev = Instrument * π + η and E(v|ExtF inDep * F inDev, η, z) = 0 (See Blundell and Duncan (1998) and Newey, Powell, and Vella (1999)). After estimating η from an OLS regression, equation (6) is estimated using differencing.…”

Regression Discontinuity Designs in Economics

“…In the context of the graph discussed here, the only modification to the cross-validation function is that the predicted value Y � (X i ) is based only on a regression with a constant term, which means Y � (X i ) is the average value of Y among all observations in the bin (excluding observation i). Note that this is slightly different from the standard cross-validation procedure in kernel regressions where the left-out observation is in the middle instead of the edge of the bin (see, for example, Blundell and Duncan (1998) Another test is based on the idea that if the bins are "narrow enough", then there should not be a sys- and 7c. In all cases, we also show the fitted values from a quartic regression model estimated separately on each side of the cutoff point.…”

“…Note that two of the dummies are excluded because of collinearity with the constant and the treatment dummy, D. 32 In terms of specification choice 31 See Blundell and Duncan (1998) for a more general discussion of series estimators. 32 While excluding dummies for the two bins next to the cutoff point yields more interpretable results (τ remains the treatment effect), the test is invariant to the excluded bin dummies, provided that one excluded dummy is on the left of the cutoff point and procedure, the idea is to add a higher order term to the polynomial until the bin dummies are no longer jointly significant.…”

Differences in the distribution of high school achievement: The role of class-size and time-in-term

“…The kernel density estimator has been discussed in several papers (DiNardo, Fortin and Lemieux, 1996;Blundell and Duncan, 1998;Yatchew, 1998;DiNardo and Tobias (2001)). Here θ i is the sample weight, normalized to sum to one.…”