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A common practice in empirical macroeconomics is to examine alternative recursive orderings of the variables in structural vector autogressive (VAR) models. When the implied impulse responses look similar, the estimates are considered trustworthy. When they do not, the estimates are used to bound the true response without directly addressing the identification challenge. A leading example of this practice is the literature on the effects of uncertainty shocks on economic activity. We prove by counterexample that this practice is invalid in general, whether the data generating process is a structural VAR model or a dynamic stochastic general equilibrium model.

Consumers purchase energy in many forms. Sometimes energy goods are consumed directly, for instance, in the form of gasoline used to operate a vehicle, electricity to light a home, or natural gas to heat a home. At other times, the cost of energy is embodied in the prices of goods and services that consumers buy, say when purchasing an airline ticket or when buying online garden furniture made from plastic to be delivered by mail. Previous research has focused on quantifying the pass-through of the price of crude oil or the price of motor gasoline to U.S. inflation. Neither approach accounts for the fact that percent changes in refined product prices need not be proportionate to the percent change in the price of oil, that not all energy is derived from oil, and that the correlation of price shocks across energy markets is far from one. This paper develops a vector autoregressive model that quantifies the joint impact of shocks to several energy prices on headline and core CPI inflation. Our analysis confirms that focusing on gasoline price shocks alone will underestimate the inflationary pressures emanating from the energy sector, but not enough to overturn the conclusion that much of the observed increase in headline inflation in 2021 and 2022 reflected non-energy price shocks.

We propose a new instrument for estimating the price elasticity of gasoline demand that exploits systematic differences across U.S. states in the pass-through of oil price shocks to retail gasoline prices. These differences, which are primarily driven by variation in the cost of producing and distributing gasoline, create cross-sectional dispersion in gasoline price growth in response to an aggregate oil price shock. We find that the elasticity was stable near -0.3 until the end of 2014, but subsequently rose to about -0.2. Our estimates inform the recent debate about gasoline-tax holidays and policies to reduce carbon emissions.

A series of recent articles has called into question the validity of VAR models of the global market for crude oil. These studies seek to replace existing oil market models by structural VAR models of their own based on different data, different identifying assumptions, and a different econometric approach. Their main aim has been to revise the consensus in the literature that oil demand shocks are a more important determinant of oil price fluctuations than oil supply shocks. Substantial progress has been made in recent years in sorting out the pros and cons of the underlying econometric methodologies and data in this debate, and in separating claims that are supported by empirical evidence from claims that are not. The purpose of this paper is to take stock of the VAR literature on global oil markets and to synthesize what we have learned. Combining this evidence with new data and analysis, I make the case that the concerns regarding the existing VAR oil market literature have been overstated and that the results from these models are quite robust to changes in the model specification.

Predictions of oil prices reaching $100 per barrel during the winter of 2021/22 have raised fears of persistently high inflation and rising inflation expectations for years to come. We show that these concerns have been overstated. A $100 oil scenario of the type discussed by many observers, would only briefly raise monthly headline inflation, before fading rather quickly. However, the short-run effects on headline inflation would be sizable. For example, on a yearover- year basis, headline PCE inflation would increase by 1.8 percentage points at the end of 2021 under this scenario, and by 0.4 percentage points at the end of 2022. In contrast, the impact on measures of core inflation such as trimmed mean PCE inflation is only 0.4 and 0.3 percentage points in 2021 and 2022, respectively. These estimates already account for any increases in inflation expectations under the scenario. The peak response of the 1-year household inflation expectation would be 1.2 percentage points, while that of the 5-year expectation would be 0.2 percentage points.

Since the 1970s, exports and imports of manufactured goods have been the engine of international trade and much of that trade relies on container shipping. This paper introduces a new monthly index of the volume of container trade to and from North America. Incorporating this index into a structural macroeconomic VAR model facilitates the identification of shocks to domestic U.S. demand as well as foreign demand for U.S. manufactured goods. We show that, unlike in the Great Recession, the primary determinant of the U.S. economic contraction in early 2020 was a sharp drop in domestic demand. Although detrended data for personal consumption expenditures and manufacturing output suggest that the U.S. economy has recovered to near 90% of pre-pandemic levels as of March 2021, our structural VAR model shows that the component of manufacturing output driven by domestic demand had only recovered to 59% of pre-pandemic levels and that of real personal consumption only to 76%. The difference is mainly accounted for by unexpected reductions in frictions in the container shipping market.

Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identi.ed VAR models may be unintentionally informative about the implied prior for the structural impulse responses. This question is indeed important, but we show that the tools that have been used in the literature to illustrate this potential problem are invalid. Speci.cally, we show that it does not make sense from a Bayesian point of view to characterize the impulse response prior based on the distribution of the impulse responses conditional on the maximum likelihood estimator of the reduced-form parameters, since the the prior does not, in general, depend on the data. We illustrate that this approach tends to produce highly misleading estimates of the impulse response priors. We formally derive the correct impulse response prior distribution and show that there is no evidence that typical sign-identi.ed VAR models estimated using conventional priors tend to imply unintentionally informative priors for the impulse response vector or that the corre- sponding posterior is dominated by the prior. Our evidence suggests that concerns about the Haar prior for the rotation matrix have been greatly overstated and that alternative estimation methods are not required in typical applications. Finally, we demonstrate that the alternative Bayesian approach to estimating sign-identi.ed VAR models proposed by Baumeister and Hamilton (2015) su¤ers from exactly the same conceptual shortcoming as the conventional approach. We illustrate that this alternative approach may imply highly economically implausible impulse response priors.

We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also derive joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse response vector obtained by stacking the impulse responses of interest. We show that such pointwise estimators may imply response function shapes that are incompatible with any possible parameterization of the underlying model. Moreover, conventional pointwise quantile error bands are not a valid measure of the estimation uncertainty about the impulse response vector because they ignore the mutual dependence of the responses. In practice, they tend to understate substantially the estimation uncertainty about the impulse response vector.

This paper examines the advantages and drawbacks of alternative methods of estimating oil supply and oil demand elasticities and of incorporating this information into structural VAR models. I not only summarize the state of the literature, but also draw attention to a number of econometric problems that have been overlooked in this literature. Once these problems are recognized, seemingly conflicting conclusions in the recent literature can be resolved. My analysis reaffirms the conclusion that the one-month oil supply elasticity is close to zero, which implies that oil demand shocks are the dominant driver of the real price of oil. The focus of this paper is not only on correcting some misunderstandings in the recent literature, but on the substantive and methodological insights generated by this exchange, which are of broader interest to applied researchers.

Using a novel dataset, we develop a structural model of the Very Large Crude Carrier (VLCC) market between the Arabian Gulf and the Far East. We study how fluctuations in oil tanker rates, oil exports, shipowner profits, and bunker fuel prices are determined by shocks to the supply and demand for oil tankers, to the utilization of tankers, and to the cost of operating tankers, including bunker fuel costs. Our analysis shows that time charter rates are largely unresponsive to tanker cost shocks. In response to higher costs, voyage profits decline, as cost shocks are only partially passed on to round-trip voyage rates. Oil exports from the Arabian Gulf also decline, reflecting lower demand for VLCCs. Positive utilization shocks are associated with higher profits, a slight increase in time charter rates and lower fuel prices and oil export volumes. Tanker supply and tanker demand shocks have persistent effects on time charter rates, round-trip voyage rates, the volume of oil exports, fuel prices, and profits with the expected sign.

The conventional wisdom that inflation expectations respond to the level of the price of oil (or the price of gasoline) is based on testing the null hypothesis of a zero slope coefficient in a static single-equation regression model fit to aggregate data. Given that the regressor in this model is not stationary, the null distribution of the t-test statistic is nonstandard, invalidating the use of the normal approximation. Once the critical values are adjusted, these regressions provide no support for the conventional wisdom. Using a new structural vector regression model, however, we demonstrate that gasoline price shocks may indeed drive one-year household inflation expectations. The model shows that there have been several such episodes since 1990. In particular, the rise in household inflation expectations between 2009 and 2013 is almost entirely explained by a large increase in gasoline prices. However, on average, gasoline price shocks account for only 39% of the variation in household inflation expectations since 1981.

We study the effects of releases from the U.S. Strategic Petroleum Reserve (SPR) within the context of fully specified models of the global oil market that explicitly allow for storage demand as well as unanticipated changes in the SPR. We show that historically SPR policy interventions, defined as sequences of exogenous SPR shocks during selected periods, have helped stabilize the price of oil. Their effect on the price of oil, however, has been modest. For example, the cumulative effect of the SPR releases after the invasion of Kuwait in 1990 was a reduction of $2/barrel in the real price of oil after 7 months. Whereas emergency drawdowns tend to lower the real price of oil, we find that exchanges tend to raise the real price of oil in the long run. We also provide a detailed analysis of the benefits of the 2018 White House proposal to sell off half of the SPR within the next decade. We show that the expected fiscal benefits of this plan are somewhat higher than the revenue of $16.6 billion dollars projected by the White House.

There has been much interest in the relationship between the price of crude oil, the value of the U.S. dollar, and the U.S. interest rate since the 1980s. For example, the sustained surge in the real price of oil in the 2000s is often attributed to the declining real value of the U.S. dollar as well as low U.S. real interest rates, along with a surge in global real economic activity. Quantifying these effects one at a time is difficult not only because of the close relationship between the interest rate and the exchange rate, but also because demand and supply shocks in the oil market in turn may affect the real value of the dollar and real interest rates. We propose a novel identification strategy for disentangling the causal effects of traditional oil demand and oil supply shocks from the effects of exogenous variation in the U.S. real interest rate and in the real value of the U.S. dollar. Our approach exploits a combination of sign and zero restrictions and narrative restrictions motivated by economic theory and extraneous evidence. We empirically evaluate popular views about the role of exogenous real exchange rate shocks in driving the real price of oil, and we examine the extent to which shocks in the global oil market drive the U.S real exchange rate and U.S. real interest rates. Our evidence for the first time provides direct empirical support for theoretical models of the link between these variables.

Shocks to the demand for housing that originate in one region may seem important only for that regional housing market. We provide evidence that such shocks can also affect housing markets in other regions. Our analysis focuses on the response of Canadian housing markets to oil price shocks. Oil price shocks constitute an important source of exogenous regional variation in income in Canada because oil production is highly geographically concentrated. We document that, at the national level, real oil price shocks account for 11% of the variability in real house price growth over time. At the regional level, we find that unexpected increases in the real price of oil raise housing demand and real house prices not only in oil-producing regions, but also in other regions. We develop a theoretical model of the propagation of real oil price shocks across regions that helps understand this finding. The model differentiates between oil-producing and non-oil-producing regions and incorporates multiple sectors, trade between provinces, government redistribution, and consumer spending on fuel. We empirically confirm the model prediction that oil price shocks are propagated to housing markets in non-oil-producing regions by the government redistribution of oil revenue and by increased interprovincial trade.

One of the leading methods of estimating the structural parameters of DSGE models is the VAR-based impulse response matching estimator. The existing asymptotic theory for this estimator does not cover situations in which the number of impulse response parameters exceeds the number of VAR model parameters. Situations in which this order condition is violated arise routinely in applied work. We establish the consistency of the impulse response matching estimator in this situation, we derive its asymptotic distribution, and we show how this distribution can be approximated by bootstrap methods. Our analysis sheds new light on the choice of the weighting matrix and covers both weakly and strongly identified DSGE model parameters. We also show that under our assumptions special care is needed to ensure the asymptotic validity of Bayesian methods of inference. A simulation study suggests that the interval estimators we propose are reasonably accurate in practice. We also show that using these methods may affect the substantive conclusions in empirical work.

It is commonly believed that the response of the price of corn ethanol (and hence of the price of corn) to shifts in biofuel policies operates in part through market expectations and shifts in storage demand, yet to date it has proved difficult to measure these expectations and to empirically evaluate this view. We utilize a recently proposed methodology to estimate the market’s expectations of the prices of ethanol, unfinished motor gasoline and crude oil at horizons from three months to one year. We quantify the extent to which price changes were anticipated by the market, the extent to which they were unanticipated, and how the risk premium in these markets has evolved. We show that the Renewable Fuel Standard (RFS) is likely to have increased ethanol price expectations by as much $1.45 in the year before and in the year after the implementation of the RFS had started. Our analysis of the term structure of expectations provides support for the view that a shift in ethanol storage demand starting in 2005 caused an increase in the price of ethanol. There is no conclusive evidence that the tightening of the RFS in 2008 shifted market expectations, but our analysis suggests that policy uncertainty about how to deal with the blend wall raised the risk premium in the ethanol futures market in mid-2013 by as much as 50 cents at longer horizons. Finally, we present evidence against a tight link from ethanol price expectations to corn price expectations and hence to storage demand for corn in 2005-06.

It has been forty years since the oil crisis of 1973/74. This crisis has been one of the defining economic events of the 1970s and has shaped how many economists think about oil price shocks. In recent years, a large literature on the economic determinants of oil price fluctuations has emerged. Drawing on this literature, we first provide an overview of the causes of all major oil price fluctuations between 1973 and 2014. We then discuss why oil price fluctuations remain difficult to predict, despite economists’ improved understanding of oil markets. Unexpected oil price fluctuations are commonly referred to as oil price shocks. We document that, in practice, consumers, policymakers, financial market participants and economists may have different oil price expectations, and that, what may be surprising to some, need not be equally surprising to others.

Traditional least squares estimates of the responsiveness of gasoline consumption to changes in gasoline prices are biased toward zero, given the endogeneity of gasoline prices. A seemingly natural solution to this problem is to instrument for gasoline prices using gasoline taxes, but this approach tends to yield implausibly large price elasticities. We demonstrate that anticipatory behavior provides an important explanation for this result. We provide evidence that gasoline buyers increase gasoline purchases before tax increases and delay gasoline purchases before tax decreases. This intertemporal substitution renders the tax instrument endogenous, invalidating conventional IV analysis. We show that including suitable leads and lags in the regression restores the validity of the IV estimator, resulting in much lower and more plausible elasticity estimates. Our analysis has implications more broadly for the IV analysis of markets in which buyers may store purchases for future consumption.

Some observers have conjectured that oil supply shocks in the United States and in other countries are behind the plunge in the price of oil since June 2014. Others have suggested that a major shock to oil price expectations occurred when in late November 2014 OPEC announced that it would maintain current production levels despite the steady increase in non-OPEC oil production. Both conjectures are perfectly reasonable ex ante, yet we provide quantitative evidence that neither explanation appears supported by the data. We show that more than half of the decline in the price of oil was predictable in real time as of June 2014 and therefore must have reflected the cumulative effects of earlier oil demand and supply shocks. Among the shocks that occurred after June 2014, the most influential shock resembles a negative shock to the demand for oil associated with a weakening economy in December 2014. In contrast, there is no evidence of any large positive oil supply shocks between June and December. We conclude that the difference in the evolution of the price of oil, which declined by 44% over this period, compared with other commodity prices, which on average only declined by about 5%-15%, reflects oil-market specific developments that took place prior to June 2014.

Although there is much interest in the future retail price of gasoline among consumers, industry analysts, and policymakers, it is widely believed that changes in the price of gasoline are essentially unforecastable given publicly available information. We explore a range of new forecasting approaches for the retail price of gasoline and compare their accuracy with the no-change forecast. Our key finding is that substantial reductions in the mean-squared prediction error (MSPE) of gasoline price forecasts are feasible in real time at horizons up to two years, as are substantial increases in directional accuracy. The most accurate individual model is a VAR(1) model for real retail gasoline and Brent crude oil prices. Even greater reductions in MSPEs are possible by constructing a pooled forecast that assigns equal weight to five of the most successful forecasting models. Pooled forecasts have lower MSPE than the EIA gasoline price forecasts and the gasoline price expectations in the Michigan Survey of Consumers. We also show that as much as 39% of the decline in gas prices between June and December 2014 was predictable.

One of the leading methods of estimating the structural parameters of DSGE models is the VAR-based impulse response matching estimator. The existing asympotic theory for this estimator does not cover situations in which the number of impulse response parameters exceeds the number of VAR model parameters. Situations in which this order condition is violated arise routinely in applied work. We establish the consistency of the impulse response matching estimator in this situation, we derive its asymptotic distribution, and we show how this distribution can be approximated by bootstrap methods. Our methods of inference remain asymptotically valid when the order condition is satisfied, regardless of whether the usual rank condition for the application of the delta method holds. Our analysis sheds new light on the choice of the weighting matrix and covers both weakly and strongly identified DSGE model parameters. We also show that under our assumptions special care is needed to ensure the asymptotic validity of Bayesian methods of inference. A simulation study suggests that the frequentist and Bayesian point and interval estimators we propose are reasonably accurate in finite samples. We also show that using these methods may affect the substantive conclusions in empirical work.

This article examines how the shale oil revolution has shaped the evolution of U.S. crude oil and gasoline prices. It puts the evolution of shale oil production into historical perspective, highlights uncertainties about future shale oil production, and cautions against the view that the U.S. may become the next Saudi Arabia. It then reviews the role of the ban on U.S. crude oil exports, of capacity constraints in refining and transporting crude oil, of differences in the quality of conventional and unconventional crude oil, and of the recent regional fragmentation of the global market for crude oil for the determination of U.S. oil and gasoline prices. It discusses the reasons for the persistent wedge between U.S. crude oil prices and global crude oil prices in recent years and for the fact that domestic oil prices below global levels need not translate to lower U.S. gasoline prices. It explains why the shale oil revolution unlike the shale gas revolution is unlikely to stimulate a boom in oil-intensive manufacturing industries. It also explores the implications of shale oil production for the transmission of oil price shocks to the U.S. economy.

Futures markets are a potentially valuable source of information about market expectations. Exploiting this information has proved difficult in practice, because the presence of a time-varying risk premium often renders the futures price a poor measure of the market expectation of the price of the underlying asset. Even though the expectation in principle may be recovered by adjusting the futures price by the estimated risk premium, a common problem in applied work is that there are as many measures of market expectations as there are estimates of the risk premium. We propose a general solution to this problem that allows us to uniquely pin down the best possible estimate of the market expectation for any set of risk premium estimates. We illustrate this approach by solving the long-standing problem of how to recover the market expectation of the price of crude oil. We provide a new measure of oil price expectations that is considerably more accurate than the alternatives and more economically plausible. We discuss implications of our analysis for the estimation of economic models of energy-intensive durables, for the debate on speculation in oil markets, and for oil price forecasting.

Although oil price shocks have long been viewed as one of the leading candidates for explaining U.S. recessions, surprisingly little is known about the extent to which oil price shocks explain recessions. We provide the first formal analysis of this question with special attention to the possible role of net oil price increases in amplifying the transmission of oil price shocks. We quantify the conditional recessionary effect of oil price shocks in the net oil price increase model for all episodes of net oil price increases since the mid-1970s. Compared to the linear model, the cumulative effect of oil price shocks over course of the next two years is much larger in the net oil price increase model. For example, oil price shocks explain a 3% cumulative reduction in U.S. real GDP in the late 1970s and early 1980s and a 5% cumulative reduction during the financial crisis. An obvious concern is that some of these estimates are an artifact of net oil price increases being correlated with other variables that explain recessions. We show that the explanatory power of oil price shocks largely persists even after augmenting the nonlinear model with a measure of credit supply conditions, of the monetary policy stance and of consumer confidence. There is evidence, however, that the conditional fit of the net oil price increase model is worse on average than the fit of the corresponding linear model, suggesting much smaller cumulative effects of oil price shocks for these episodes of at most 1%.

The substantial variation in the real price of oil since 2003 has renewed interest in the question of how to forecast monthly and quarterly oil prices. There also has been increased interest in the link between financial markets and oil markets, including the question of whether financial market information helps forecast the real price of oil in physical markets. An obvious advantage of financial data in forecasting oil prices is their availability in real time on a daily or weekly basis. We investigate whether mixed-frequency models may be used to take advantage of these rich data sets. We show that, among a range of alternative high-frequency predictors, especially changes in U.S. crude oil inventories produce substantial and statistically significant real-time improvements in forecast accuracy. The preferred MIDAS model reduces the MSPE by as much as 16 percent compared with the no-change forecast and has statistically significant directional accuracy as high as 82 percent. This MIDAS forecast also is more accurate than a mixed-frequency realtime VAR forecast, but not systematically more accurate than the corresponding forecast based on monthly inventories. We conclude that typically not much is lost by ignoring high-frequency financial data in forecasting the monthly real price of oil.

The U.S. Energy Information Administration (EIA) regularly publishes monthly and quarterly forecasts of the price of crude oil for horizons up to two years, which are widely used by practitioners. Traditionally, such out-of-sample forecasts have been largely judgmental, making them difficult to replicate and justify. An alternative is the use of real-time econometric oil price forecasting models. We investigate the merits of constructing combinations of six such models. Forecast combinations have received little attention in the oil price forecasting literature to date. We demonstrate that over the last 20 years suitably constructed real-time forecast combinations would have been systematically more accurate than the no-change forecast at horizons up to 6 quarters or 18 months. MSPE reduction may be as high as 12% and directional accuracy as high as 72%. The gains in accuracy are robust over time. In contrast, the EIA oil price forecasts not only tend to be less accurate than no-change forecasts, but are much less accurate than our preferred forecast combination. Moreover, including EIA forecasts in the forecast combination systematically lowers the accuracy of the combination forecast. We conclude that suitably constructed forecast combinations should replace traditional judgmental forecasts of the price of oil.

U.S. retail food price increases in recent years may seem large in nominal terms, but after adjusting for inflation have been quite modest even after the change in U.S. biofuel policies in 2006. In contrast, increases in the real prices of corn, soybeans, wheat and rice received by U.S. farmers have been more substantial and can be linked in part to increases in the real price of oil. That link, however, appears largely driven by common macroeconomic determinants of the prices of oil and agricultural commodities rather than the pass-through from higher oil prices. We show that there is no evidence that corn ethanol mandates have created a tight link between oil and agricultural markets. Rather increases in food commodity prices not associated with changes in global real activity appear to reflect a wide range of idiosyncratic shocks ranging from changes in biofuel policies to poor harvests. Increases in agricultural commodity prices in turn contribute little to U.S. retail food price increases, because of the small cost share of agricultural products in food prices. There is no evidence that oil price shocks have caused more than a negligible increase in retail food prices in recent years. Nor is there evidence for the prevailing wisdom that oil-price driven increases in the cost of food processing, packaging, transportation and distribution are responsible for higher retail food prices. Finally, there is no evidence that oil-market specific events or for that matter U.S. biofuel policies help explain the evolution of the real price of rice, which is perhaps the single most important food commodity for many developing countries.

Notwithstanding a resurgence in research on out-of-sample forecasts of the price of oil in recent years, there is one important approach to forecasting the real price of oil which has not been studied systematically to date. This approach is based on the premise that demand for crude oil derives from the demand for refined products such as gasoline or heating oil. Oil industry analysts such as Philip Verleger and financial analysts widely believe that there is predictive power in the product spread, defined as the difference between suitably weighted refined product market prices and the price of crude oil. Our objective is to evaluate this proposition. We derive from first principles a number of alternative forecasting model specifications involving product spreads and compare these models to the no-change forecast of the real price of oil. We show that not all product spread models are useful for out-of-sample forecasting, but some models are, even at horizons between one and two years. The most accurate model is a time-varying parameter model of gasoline and heating oil spot spreads that allows the marginal product market to change over time. We document MSPE reductions as high as 20% and directional accuracy as high as 63% at the two-year horizon, making product spread models a good complement to forecasting models based on economic fundamentals, which work best at short horizons.

We propose an exchange rate model that can explain both the observed volatility and the persistence of real and nominal exchange rate movements and thus in some measure resolves Rogoff’s (1996) purchasing power parity puzzle. Our analysis reconciles the well-known difficulties in beating the random walk forecast model with the statistical evidence of nonlinear mean reversion in deviations from fundamentals. Our analysis also provides a compelling rationale for the long-horizon predictability of exchange rates. We find strong empirical support for long-horizon predictability, and we explain why it is difficult to exploit this predictability in real-time forecasts. Our results not only lend support to economists’ beliefs that the exchange rate is inherently predictable, but they also help us to understand the reluctance of applied forecasters to abandon chartist methods in favor of models based on economic fundamentals.

The statistical reliability of estimated VAR impulse responses is an important concern in applied work, because economic time series tend to be short. I show that the small-sample distribution of impulse response estimates can be extremely biased and skewed. This fact has been largely ignored by existing methods for the construction of impulse response confidence intervals. I propose a bias-corrected bootstrap confidence interval for impulse response estimates that explicitly accounts for the bias and skewness of the small-sample distribution, while retaining asymptotic validity in stationary autoregressions. Monte Carlo simulations for a wide range of bivariate models with normal innovations and known lag order show that in small samples the bias-corrected bootstrap interval tends to be more accurate than traditional confidence intervals. I also analyze the effects of departures from normality and the role of parametric assumptions for the construction of impulse response confidence intervals. Empirical examples illustrate the conclusions of the Monte Carlo study. In addition, I study the impact of lag order uncertainty on inference in VAR models. I establish that for impulse response analysis the Akaike information criterion is an asymptotically valid lag order selection criterion with superior small-sample properties, and I generalize the bias-corrected bootstrap interval to account for lag order estimation uncertainty. A Monte Carlo study shows that this interval is more accurate than standard intervals that condition on the estimated lag order as though it were the true lag order.