MSE-improvement of the least squares estimator by dropping variables

It is well known that dropping variables in regression analysis decreases the variance of the least squares (LS) estimator of the remaining parameters. However, after elimination estimates of these parameters are biased, if the full model is correct. In his recent paper, Boscher (1991) showed that the LS-estimator in the special case of a mean shift model (cf. Cook and Weisberg, 1982) which assumes no “outliers” can be considered in the framework of a linear regression model where some variables are deleted. He derived conditions under which this estimator outperforms the LS-estimator of the full model in terms of the mean squared error (MSE)-matrix criterion. We demonstrate that this approach can be extended to the general set-up of dropping variables. Necessary and sufficient conditions for the MSE-matrix superiority of the LS-estimator in the reduced model over that in the full model are derived. We also provide a uniformly most powerful F-statistic for testing the MSE-improvement.     

Green Tax Reform and Competitiveness

This paper studies a revenue-neutral green tax reform that substitutes energy for wage taxes in an open economy with unemployment. As long as the labour tax rate exceeds the energy tax rate, such a reform will increase employment, reduce the domestic firms' unit cost of production and hence increase international competitiveness and output of the economy. The driving force behind these results is the technological substitution process that a green tax reform will bring about. The resulting reduction in unemployment is welfare increasing since energy, which the country has to buy at its true national opportunity cost, is replaced with labour, whose price is above its social opportunity cost.     

Royalty reform and illegal reporting of harvest volumes under alternative penalty schemes

We study royalty reform in a timber concessions framework. Illegal logging in the form of underreporting of harvesting is modeled. Harvesters can be either risk neutral or risk averse. Detection of illegal logging by the government is imperfect and costly. We focus on the government’s policy problem, solving first for socially optimal royalty and auditing levels, and then examining a revenue-neutral reform toward this benchmark. We find that higher royalty progression will always decrease actual harvest volume regardless of risk preferences for the harvester, but the effect of a reform on reported harvest volume is sensitive to the penalty scheme imposed by the government. If the fine is levied on evaded royalty payments, then higher royalty progression may increase reported harvest volume. But when the fine is levied on undeclared harvest volume, the reverse happens. Higher royalty regression increases actual harvest volume under both penalty schemes, but it may decrease reported harvest volume. Higher regression will increase undeclared harvest volume when the fine is levied on evaded royalty payments.      

On Pollution Permit Banking and Market Power

We consider a pollution permit market with a large firm and fringe of competitive firms. To smooth compliance towards a long-run emissions goal, firms are initially allocated a stock (i.e., bank) of permits that can be gradually consumed. We first show how the large firm can credibly manipulate the spot market in subgame-perfect equilibrium. Motivated by features observed in the US market for sulfur dioxide emissions, we then show that the introduction of stock transactions has no effects on market power, but that forward trading and incomplete observability of stock holdings do have pro-competitive effects. Both authors are also Research Associates at the MIT Center for Energy and Environmental Policy Research.