When instruments are weakly correlated with endogenous regressors, conventional methods for instrumental variables estimation and inference become unreliable. A large literature in econometrics develops procedures for detecting weak instruments and constructing robust condence sets, but many of the results in this literature are limited to settings with independent and homoskedastic data, while data encountered in practice frequently violate these assumptions. We review the literature on weak instruments in linear IV regression with an emphasis on results for non-homoskedastic (heteroskedastic, serially correlated, or clustered) data. To assess the practical importance of weak instruments, we also report tabulations and simulations based on a survey of papers published in the American Economic Review from 2014 to 2018 that use instrumental variables. These results suggest that weak instruments remain an important issue for empirical practice, and that there are simple steps researchers can take to better handle weak instruments in applications.
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.
This paper reviews the cost of various interventions that reduce greenhouse gas emissions. As much as possible we focus on actual abatement costs (dollars per ton of carbon dioxide avoided), as measured by 50 economic studies of programs over the past decade, supplemented by our own calculations. We distinguish between static costs, which occur over the lifetime of the project, and dynamic costs, which incorporate spillovers. Interventions or policies that are expensive in a static sense can be inexpensive in a dynamic sense if they induce innovation and learning-by-doing.
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.
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.
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.