Abstract: Instrumental variable (IV) estimation is widely used to address endogeneity when ordinary least squares (OLS) would produce biased estimates. In the presence of endogeneity: OLS is inconsistent yet more efficient than IV, while IV is consistent but less efficient than OLS. A specification test by Hausman is commonly applied to select between IV and OLS estimators when the presence or strength of endogeneity is uncertain. We study three versions of hybrid estimators that combine OLS and IV rather than selecting one or the other: 1) a hybrid estimator, which is a convex combination of OLS and IV; 2) a shrunken hybrid estimator, which is a convex combination of the hybrid estimator and 0; and 3) a double hybrid estimator, which is a non-convex combination of OLS and IV. We derive optimal weights for each estimator by minimizing its mean-squared error (MSE)—which combines accuracy and precision to minimize the risk of policy errors—and we use the plug-in principle to develop feasible versions of each estimator. Following Hansen (2017), we use Monte Carlo simulations to compare the MSE performance of the hybrid estimators to the conventional Hausman-pretest estimator under a wide range of data conditions. We find that at least one hybrid estimator outperforms the Hausman pretest estimator under a given level of endogeneity, instrument strength and sample size. This helps give more options of estimating techniques to minimize the risk of policy errors.
Abstract: Researching electricity consumption, has been of interest for various reasons in the literature, to name a few; designing of pricing structure, facilitation of energy conservation and planning the infrastructure roll-out. The national surveys while, are representative of the population, however, lack the detailed monthly electricity consumption patterns of households along with appliance holdings and outages. This paper uses the PRECON dataset (minute-interval dataset covering 42 households in Lahore for the year June 2018 to June 2019). It uses sharp regression discontinuity design to study the local effect, if any, on the electricity consumption of the household, while transitioning from off-peak price to the peak-hours price on a daily basis. This diagnosis is important to see whether the price signal results in any change in consumption. This study finds that only for months, when the consumption is highest, resulting in higher electricity bills, are consumers more responsive to the change in price from off-peak to peak-hours daily. They seem to lower their average consumption in June to August for 30 minutes after the peak price starts, saving a 3.36 percent of their average monthly peak hour consumption.