We prove that linear local projections and Vector Autoregressions (VARs) estimate the same impulse response functions. This nonparametric result only requires the lag structures in the two specifications to be unrestricted. We discuss several implications: (i) Local projections and VARs should not be thought of as conceptually separate procedures; instead, they belong to a spectrum of dimension reduction techniques that share the same estimand but have different finite-sample bias-variance properties. (ii) VAR-based structural inference can equivalently be performed using local projections, and vice versa. (iii) Valid structural inference with an external instrument (also known as a proxy variable) can be carried out by ordering the instrument first in a recursive VAR, even if the shock of interest is noninvertible. (iv) Local projections are not more "robust to non-linearities" than VARs.

Macroeconomists often estimate impulse response functions using external instruments (proxy variables) for the shocks of interest. However, existing methods do not answer the key question of how important the shocks are in driving macro aggregates. We provide tools for doing inference on forecast variance decompositions in a general semiparametric moving average model, disciplined only by the availability of external instruments. The share of the forecast variance that can be attributed to a shock is partially identified, albeit with informative bounds. Point identification of most parameters, including historical decompositions, can be achieved under much weaker assumptions than invertibility, a condition imposed in conventional Structural Vector Autoregressive (SVAR) analysis. In fact, external instruments make the invertibility assumption testable. To perform inference, we construct easily computable, partial identification robust confidence intervals. We illustrate our methods using (i) a structural macro model and (ii) an empirical study of the importance of monetary policy shocks.

We document that the U.S. dollar exchange rate drives global trade prices and volumes. Using a newly constructed data set of bilateral price and volume indices for more than 2,500 country pairs, we establish the following facts: 1) Bilateral non-commodities terms of trade are essentially uncorrelated with bilateral exchange rates. 2) The dollar exchange rate quantitatively dominates the bilateral exchange rate in price pass-through and trade elasticity regressions. 3) A 1% U.S. dollar appreciation against all other currencies in the world predicts a 0.6% decline within a year in the volume of total trade between countries in the rest of the world, controlling for the global business cycle. 4) Using a Bayesian semiparametric hierarchical panel data model, we estimate that the importing country's share of imports invoiced in dollars explains 15% of the variance of dollar pass-through across country pairs. Our findings strongly support the dominant currency paradigm as opposed to the traditional Mundell-Fleming pricing paradigms. We then employ a three country model with dollar pricing to demonstrate the asymmetries between the transmission of monetary policy shocks that arise in the U.S. and the rest of the world.

This dissertation consists of three independent chapters on econometric methods for macroeconomic analysis. In the first chapter, I propose to estimate structural impulse response functions from macroeconomic time series by doing Bayesian inference on the Structural Vector Moving Average representation of the data. This approach has two advantages over Structural Vector Autoregression analysis: It imposes prior information directly on the impulse responses in a flexible and transparent manner, and it can handle noninvertible impulse response functions. The second chapter, which is coauthored with B. J. Bates, J. H. Stock, and M. W. Watson, considers the estimation of dynamic factor models when there is temporal instability in the factor loadings. We show that the principal components estimator is robust to empirically large amounts of instability. The robustness carries over to regressions based on estimated factors, but not to estimation of the number of factors. In the third chapter, I develop shrinkage methods for smoothing an estimated impulse response function. I propose a data-dependent criterion for selecting the degree of smoothing to optimally trade off bias and variance, and I devise novel shrinkage confidence sets with valid frequentist coverage.

I propose to estimate structural impulse responses from macroeconomic time series by doing Bayesian inference on the Structural Vector Moving Average representation of the data. This approach has two advantages over Structural Vector Autoregressions. First, it imposes prior information directly on the impulse responses in a flexible and transparent manner. Second, it can handle noninvertible impulse response functions, which are often encountered in applications. Rapid simulation of the posterior distribution of the impulse responses is possible using an algorithm that exploits the Whittle likelihood. The impulse responses are partially identified, and I derive the frequentist asymptotics of the Bayesian procedure to show which features of the prior information are updated by the data. The procedure is used to estimate the effects of technological news shocks on the U.S. business cycle.

Simultaneous confidence bands are versatile tools for visualizing estimation uncertainty for parameter vectors, such as impulse response functions. In linear models, it is known that that the sup-t confidence band is narrower than commonly used alternatives, for example Bonferroni and projection bands. We show that the same ranking applies asymptotically even in general nonlinear models, such as VARs. Moreover, we provide further justification for the sup-t band by showing that it is the optimal default choice when the researcher does not know the audience's preferences. Complementing existing plug-in and bootstrap implementations, we propose a computationally convenient Bayesian sup-t band with exact finite-sample simultaneous credibility. In an application to SVAR impulse response function estimation, the sup-t band - which has been surprisingly overlooked in this setting - is at least 35% narrower than other off-the-shelf simultaneous bands.

We review the main identification strategies and empirical evidence on the role of expectations in the New Keynesian Phillips curve, paying particular attention to the issue of weak identification. Our goal is to provide a clear understanding of the role of expectations that integrates across the different papers and specifications in the literature. We discuss the properties of the various limited-information econometric methods used in the literature and provide explanations of why they produce conflicting results. Using a common dataset and a flexible empirical approach, we find that researchers are faced with substantial specification uncertainty, as different combinations of various a priori reasonable specification choices give rise to a vast set of point estimates. Moreover, given a specification, estimation is subject to considerable sampling uncertainty due to weak identification. We highlight the assumptions that seem to matter most for identification and the configuration of point estimates. We conclude that the literature has reached a limit on how much can be learned about the New Keynesian Phillips curve from aggregate macroeconomic time series. New identification approaches and new datasets are needed to reach an empirical consensus.

This paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings. We characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent and find that these instabilities can be larger than earlier theoretical calculations suggest. We also discuss implications of our results for the robustness of regressions based on the estimated factors and of estimates of the number of factors in the presence of parameter instability. Simulations calibrated to an empirical application indicate that instability in the factor loadings has a limited impact on estimation of the factor space and diffusion index forecasting, whereas estimation of the number of factors is more substantially affected.

When risk averse forecasters are presented with risk neutral proper scoring rules, they report probabilities whose ratios are shaded towards 1. If elicited probabilities are used as inputs to decision-making, naive elicitors may violate first-order stochastic dominance.

Danmarks Nationalbank regularly publishes an index of the development in the strength of the krone, the effective krone-rate index, and an index of the competitiveness of the Danish manufacturing sector, the real effective krone-rate index. Changing trade patterns make it necessary to revise the weights of the currencies in the index from time to time. The 2009 weights are presented below. The most recent revision of the weights is documented in Pedersen (2004).