Publications & Working Papers

Working Paper
Lazarus E, Lewis DJ, Stock JH, Watson MW. HAR Inference: Recommendations for Practice. Working Paper.Abstract

The classic papers by Newey and West (1987) and Andrews (1991) spurred a large body of work on how to improve heteroskedasticity- and autocorrelation-robust (HAR) inference in time series regression. This literature finds that using a larger than usual truncation parameter to estimate the long-run variance, combined with Kiefer-Vogelsang (2002, 2005) fixed-b critical values, can substantially reduce size distortions, at only a modest cost in (size-adjusted) power. Empirical practice, however, has not kept up. This paper therefore draws on the post-Newey West/Andrews literature to make concrete recommendations for HAR inference. We derive truncation parameter rules that choose a point on the size-power tradeoff to minimize a loss function. If Newey-West tests are used, we recommend the truncation parameter rule S = 1.3T1/2 and (nonstandard) fixed-b critical values. For tests of a single restriction, we find advantages to using the equal-weighted cosine (EWC) test, where the long run variance is estimated by projections onto Type II cosines, using ν = 0.4T2/3 cosine terms; for this test, fixed-b critical values are, conveniently, tν or F. We assess these rules using first an ARMA/GARCH Monte Carlo design, then a dynamic factor model design estimated using a 207 quarterly U.S. macroeconomic time series.

Stock JH. Reforming the Renewable Fuel Standard. Working Paper. PDF
Knittel CR, Meiselman BS, Stock JH. The Pass-Through of RIN Prices to Wholesale and Retail Fuels under the Renewable Fuel Standard: Analysis of Post-March 2015 Data. Working Paper. PDF
Coglianese J, Gerarden T, Stock JH. The Effects of Fuel Prices, Regulations, and Other Factors on U.S. Coal Production, 2008-2016. Working Paper. PDF
Lazarus E, Lewis DJ, Stock JH. The Size-Power Tradeoff in HAR Inference. Working Paper :1-60. PDF Supplement
Stock JH, Li J. Cost Pass-Through to Higher Ethanol Blends at the Pump: Evidence from Minnesota Gas Station Data. Working Paper. PDF
Knittel CR, BS M, JH S. The Pass-Through of RIN Prices to Wholesale and Retail Fuels under the Renewable Fuel Standard. Journal of the Association of Environmental and Resource Economists. Forthcoming. PDF
Stock JH, Watson MW. Identification and Estimation of Dynamic Causal Effects in Macroeconomics. Economic Journal. Forthcoming.Abstract
An exciting development in empirical macroeconometrics is the increasing use of external sources of as-if randomness to identify the dynamic causal effects of macroeconomic shocks. This approach – the use of external instruments – is the time series counterpart of the highly successful strategy in microeconometrics of using external as-if randomness to provide instruments that identify causal effects. This lecture provides conditions on instruments and control variables under which external instrument methods produce valid inference on dynamic causal effects, that is, structural impulse response function; these conditions can help guide the search for valid instruments in applications. We consider two methods, a one-step instrumental variables regression and a two-step method that entails estimation of a vector autoregression. Under a restrictive instrument validity condition, the one-step method is valid even if the vector autoregression is not invertible, so comparing the two estimates provides a test of invertibility. Under a less restrictive condition, in which multiple lagged endogenous variables are needed as control variables in the one-step method, the conditions for validity of the two methods are the same.
Stock JH. The Effect of a Higher Ethanol Blend RVP Waiver on RIN Prices. 2017. PDF
Stock JH. Addendum to Comments by James Stock on the Proposed Denial of Petitions for Rulemaking to Change the RFS Point of Obligation. 2017. Comments
Stock JH, Watson MW. Twenty Years of Time Series Econometrics in Ten Pictures. Journal of Economic Perspectives. 2017;31 (2) :59-86. PDF
Fernald JG, Hall RE, Stock JH, Watson MW. The Disappointing Recovery of Output after 2009. Brookings Papers on Economic Activity. 2017;1 :1-89.Abstract

U.S. output expanded only slowly after the recession trough in 2009 even though
the unemployment rate has essentially returned to a pre-crisis, normal level. We use a growthaccounting decomposition to explore explanations for the output shortfall, giving full treatment to cyclical effects that, given the depth of the recession, should have implied unusually fast growth. We find that the growth shortfall has almost entirely reflected two factors: the slow growth of total factor productivity and the decline in labor force participation. Both factors reflect powerful adverse forces largely unrelated to the financial crisis and recession. These forces were in play before the recession.

Stock JH. Proposed Denial of Petitions for Rulemaking to Change the RFS Point of Obligation: Docket ID No. EPA-OAR–2016–0544. 2017. Comments
Stock JH, Pouliot S, Smith A. RIN Pass-Through at Gasoline Terminals. 2017. PDF
Coglianese J, Davis LW, Kilian L, Stock JH. Anticipation, Tax Avoidance, and the Price Elasticity of Gasoline Demand. Journal of Applied Econometrics. 2017;32 (1) :1-15. PDF
Metcalf GE, Stock J. Integrated Assessment Models and the Social Cost of Carbon: A Review and Assessment of U.S. Experience. Review of Environmental Economics and Policy . 2017;11 (1) :80-99. PDF
Gillingham KT, Stock JH. Federal Minerals Leasing Reform and Climate Policy. The Hamilton Project [Internet]. 2016. Publisher's VersionAbstract


Through its minerals leasing program, the U.S. government plays a large role in the extraction of oil, natural gas, and coal. This footprint is the largest for coal: 41 percent of U.S. coal is mined under federal leases, and burning this coal accounts for 13 percent of U.S. energy-related carbon dioxide (CO2) emissions. Currently, producers and consumers of this coal do not bear the full social costs associated with its use. At the same time, the threat of climate change has led the international community, including the United States, to pledge significant reductions in CO2 emissions. Over the past two decades Democratic and Republican administrations have taken steps to reduce U.S. CO2 emissions by reducing use of fossil fuels. Despite growing public attention to the climate consequences of fossil fuel extraction, U.S. climate policy so far has not extended to the government’s role as a major source of fossil fuels. We propose to incorporate climate considerations into federal coal leasing by placing a royalty adder on federal coal that is linked to the climate damages from its combustion. The magnitude of the royalty adder should be chosen to recognize both the substitution of nonfederal for federal coal, and the interaction of the royalty adder with other climate policies. A royalty adder set to 20 percent of the social cost of carbon would reduce total power sector emissions, raise the price of federal coal to align with coal mined on private land, increase coal mining employment in Appalachia and the Midwest, and provide additional government revenues to help coal communities. This proposal strikes a middle path between calling for a stop to all federal fossil fuel leasing on the one hand, and relying entirely on imperfect downstream regulation on the other.


Gillingham K, Bushnell J, Fowlie M, Greenstone M, Kolstad C, Krupnick A, Morris A, Schmalensee R, Stock JH. Reforming the U.S. Coal Leasing Program. Science [Internet]. 2016;354 (6316) :1096-1098. Publisher's Version
Gerarden T, Reeder WS, Stock JH. Federal Coal Program Reform, the Clean Power Plan, and the Interaction of Upstream and Downstream Climate Policies. NBER WP 22214. 2016.Abstract

Coal mined on federally managed lands accounts for approximately 40% of U.S. coal consumption and 13% of total U.S. energy-related CO2 emissions. The U.S. Department of the Interior is undertaking a programmatic review of federal coal leasing, including the climate effects of burning federal coal. This paper studies the interaction between a specific upstream policy, incorporating a carbon adder into federal coal royalties, and downstream emissions regulation under the Clean Power Plan (CPP). After providing some comparative statics, we
present quantitative results from a detailed dynamic model of the power sector, the Integrated Planning Model (IPM). The IPM analysis indicates that, in the absence of the CPP, a royalty adder equal to the social cost of carbon could reduce emissions by roughly ¾ of the emissions reduction that the CPP is projected to achieve. If instead the CPP is binding, the royalty adder would: reduce the price of tradeable emissions allowances, produce some additional emissions reductions by reducing leakage, and reduce wholesale power prices under a mass-based CPP but increase them under a rate-based CPP. A federal royalty adder increases mining of non-federal coal, but this substitution is limited by a shift to electricity generation by gas and renewables.

Key words: extraction royalties, social cost of carbon
JEL codes: Q54, Q58, Q38

Stock JH, Watson MW. Factor Models and Structural Vector Autoregressions in Macroeconomics. 2016. stock_watson_dfm_hom_030916.pdf