PAC Classification based on PAC Estimates of Label Class Distributions

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect, the better our estimates of the label class distributions, the better the resulting classifier will be. In this paper we make this observation precise by identifying risk bounds of a classifier in terms of the quality of the estimates of the label class distributions. We show how PAC learnability relates to estimates of the distributions that have a PAC guarantee on their $L_1$ distance from the true distribution, and we bound the increase in negative log likelihood risk in terms of PAC bounds on the KL-divergence. We give an inefficient but general-purpose smoothing method for converting an estimated distribution that is good under the $L_1$ metric into a distribution that is good under the KL-divergence.Comment: 14 page

Modeling a Clean Energy Standard for Electricity: Policy Design Implications for Emissions, Supply, Prices, and Regions

The electricity sector is responsible for roughly 40 percent of U.S. carbon dioxide (CO2) emissions, and a shift away from conventional coal-fired generation is an important component of the U.S. strategy to reduce greenhouse gas emissions. Toward that goal, several proposals for a clean energy standard (CES) have been put forth, including one espoused by the Obama administration that calls for 80 percent clean electricty by 2035 phased in from current levels of roughly 40 percent. This paper looks at the effects of such a policy on CO2 emissions from the electricity sector, the mix of technologies used to supply electricity, electricity prices, and regional flows of clean energy credits. The CES leads to a 30 percent reduction in cumulative CO2 emissions between 2013 and 2035 and results in dramatic reductions in generation from conventional coal. The policy also results in fairly modest increases on national electricity prices, but this masks a wide variety of effects across regions.renewables, climate, clean energy standard

Compensation for Electricity Consumers Under a U.S. CO2 Emissions Cap

Policies to cap emissions of carbon dioxide (CO2) in the U.S. economy could pose significant costs on the electricity sector, which contributes roughly 40 percent of total CO2 emissions in the U.S. Using a detailed simulation model of the electricity sector, we evaluate alternative ways that emission allowances can be allocated. Most previous emissions trading programs have allocated the major portion of allowances for free to incumbent firms. In the electricity sector this approach would lead to changes in electricity price that vary by region primarily based primarily on whether prices are market-based or determined by cost-of-service regulation. Allocation to customers, which could be achieved by allocation to local distribution companies (retail utilities) would recover symmetry in the effect of free allocation and lead to signficiantly lower overall electricity prices. However, this form of compensation comes with an efficiency cost that will increase the overall cost of climate policy.emissions trading, allowance allocations, electricity, air pollution, auction, grandfathering, cost-effectiveness, greenhouse gases, climate change, global warming, carbon dioxide, asset value, compensation

A Partial Adjustment Model of U.S. Electricity Demand by Region, Season, and Sector

Identifying the factors that influence electricity demand in the continental United States and mathematically characterizing them are important for developing electricity consumption projections. The price elasticity of demand is especially important, since the electricity price effects of policy implementation can be substantial and the demand response to policy-induced changes in prices can significantly affect the cost of policy compliance. This paper estimates electricity demand functions with particular attention paid to the demand stickiness that is imposed by the capital-intensive nature of electricity consumption and to regional, seasonal, and sectoral variation. The analysis uses a partial adjustment model of electricity demand that is estimated in a fixed-effects OLS framework. This model formulation allows for the price elasticity to be expressed in both its short-run and long-run forms. Price elasticities are found to be broadly consistent with the existing literature, but with important regional, seasonal, and sectoral differences.electricity, demand elasticities, energy demand, partial adjustment

Allowance Allocation in a CO2 Emissions Cap-and-Trade Program for the Electricity Sector in California

The regulation of greenhouse gas emissions from the electricity sector within a cap-and-trade system poses significant policy questions about how to allocate tradable emission allowances. Allocation conveys tremendous value and can have efficiency consequences. This research uses simulation modeling for the electricity sector to examine different approaches to allocation under a cap-and-trade program in California. The decision affects prices and other aspects of the electricity sector, as well as implications for the overall cost of climate policy. An important issue is the opportunity for emission reductions in California to be offset by emission increases in neighboring regions that supply electricity to the state. The amount of emission leakage (i.e. an increase in CO2 emissions outside of California as a result of the program) varies with the regulatory design of the program.cap-and-trade, electricity generation, electricity sector, emissions, regulation, governance, allocation, California

Supply Curves for Conserved Electricity

In this paper, we introduce a new top-down approach to modeling the effects of publicly financed energy-efficiency programs on electricity consumption and carbon dioxide emissions. The approach draws on a partial-adjustment econometric model of electricity demand and represents the results of a reverse auction for electricity savings from different levels of public investment. The model is calibrated to recent estimates of the cost-effectiveness of rate payer–funded efficiency programs at reducing electricity consumption. The results suggest that supply curves for conserved electricity are upward sloping, convex, and dependent on policy design and electricity prices. Under the scenarios modeled, electricity savings of between 1 and 3 percent are achievable at a marginal cost of $50 per megawatt hour (MWh) and a corresponding average cost of$25–$35/MWh.energy efficiency, climate change

The Effect on Asset Values of the Allocation of Carbon Dioxide Emission Allowances

Paradoxically, owners of existing generation assets may be better off paying for carbon dioxide emission allowances than having them distributed for free. This analysis shows that it takes just 7.5% of the revenue raised under an auction to preserve the asset values of existing generators.carbon dioxide, emission allowance trading, allocation, electricity, restructuring, air pollution, auction, grandfathering, generation performance standard, outputbased allocation, cost-effectiveness

Estimating structural mean models with multiple instrumental variables using the generalised method of moments

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypical variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semi-parametric models that use instrumental variables to identify causal parameters, but there has been little work on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper, we show how additive, multiplicative and logistic SMMs with multiple discrete instrumental variables can be estimated efficiently using the generalised method of moments (GMM) estimator, how the Hansen J-test can be used to test for model mis-specification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension, but no evidence of unobserved confounding.

Restructuring and Cost of Reducing NOx Emissions in Electricity Generation

The U.S. electric power sector is in the midst of two major regulatory changes. One is the change from cost-of-service regulation to competition as a means of disciplining electricity prices, often referred to as “electricity restructuring.” The other is the apparently increasing scope and stringency of environmental regulation; proposed tighter restrictions on nitrogen oxide (NOx) emissions from existing generators are one recent example. We look at the effects of restructuring on three issues: (a) economic surplus and environmental quality, (b) the cost of NOx control policies and who bears the costs, and (c) the cost-effectiveness of a seasonal and an annual NOx cap in the SIP Call region. We find that without the NOx cap, nationwide restructuring leads to higher NOx and carbon emissions from the electricity sector. Adding either a seasonal or an annual NOx cap-and-trade regime in the eastern United States mitigates the increase in NOx emissions but has a much smaller effect on carbon emissions. The out-of-pocket compliance cost associated with achieving a seasonal or an annual NOx cap is moderately higher with nationwide restructuring than without, but the changes in economic surplus are significantly higher. For a seasonal policy, most of the costs are borne by electricity consumers. For an annual policy, most of the incremental costs beyond those with seasonal controls are borne by producers. However, the economic benefits of nationwide restructuring more than offset the higher costs of controlling NOx emissions in a more competitive environment. The foregone economic surplus is compared with the benefits resulting from NOx emission reductions using an integrated assessment model of atmospheric transport and valuation of human health effects. We find an annual policy dominates a seasonal policy from a cost effectiveness perspective under limited restructuring, and even more strongly under nationwide restructuring.electricity, restructuring, deregulation, competition, emissions trading, particulates, nitrogen oxides, NO x, health benefits, cost effectiveness

Estimating Structural Mean Models with Multiple Instrumental Variables using the Generalised Method of Moments

Instrumental variables analysis using genetic markers as instruments is now a widely used technique in epidemiology and biostatistics. As single markers tend to explain only a small proportion of phenotypical variation, there is increasing interest in using multiple genetic markers to obtain more precise estimates of causal parameters. Structural mean models (SMMs) are semi-parametric models that use instrumental variables to identify causal parameters, but there has been little work on using these models with multiple instruments, particularly for multiplicative and logistic SMMs. In this paper, we show how additive, multiplicative and logistic SMMs with multiple discrete instrumental variables can be estimated efficiently using the generalised method of moments (GMM) estimator, how the Hansen J-test can be used to test for model mis-specification, and how standard GMM software routines can be used to fit SMMs. We further show that multiplicative SMMs, like the additive SMM, identify a weighted average of local causal effects if selection is monotonic. We use these methods to reanalyse a study of the relationship between adiposity and hypertension using SMMs with two genetic markers as instruments for adiposity. We find strong effects of adiposity on hypertension, but no evidence of unobserved confounding.Structural Mean Models, Multiple Instrumental Variables, Generalised Method of Moments, Mendelian Randomisation, Local Average Treatment Effects