Simultaneous confidence bands are used in applied work to visualize estimation uncertainty for vector-valued parameters. Although many confidence bands have been proposed - e.g., Bonferroni, projection, and sup-t bands - theoretical comparisons and practical recommendations are lacking outside the linear regression model. In a general nonlinear setting, we show that commonly reported confidence bands have the same form, asymptotically: a consistent point estimator for the parameter of interest plus/minus c times the vector of coordinate-wise standard errors. The sup-t band is known to be the narrowest band inside this one-parameter family that achieves simultaneous coverage. We show that, additionally, the sup-t band uniquely minimizes "worst case" regret among all translation equivariant bands, where the worst case is taken over possible loss functions in coordinate-wise lengths. Hence, the sup-t band is a good default choice when the researcher does not know the audience's preferences. We propose a simple Bayesian implementation of the sup-t band, which has exact finite-sample simultaneous credibility and is often asymptotically equivalent with standard plug-in or bootstrap implementations. We apply the sup-t band to two settings where it has been overlooked: impulse response function estimation and sensitivity analysis in linear regression. In our applications, the sup-t band is at least 15-35% narrower than other simultaneous bands.

We document that it is not bilateral exchange rates but the dollar exchange rate that 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) The dollar exchange rate quantitatively dominates the bilateral exchange rate in price pass-through and trade elasticity regressions. U.S. monetary policy induced dollar fluctuations have high pass-through into bilateral import prices. 2) Bilateral non-commodities terms of trade are essentially uncorrelated with bilateral exchange rates. 3) The cross-sectional heterogeneity in pass-through/elasticity across country pairs is related to the share of imports invoiced in dollars. Our results derive from fixed effects panel regressions as well as a Bayesian semiparametric hierarchical panel data model. Unlike standard panel regressions, the Bayesian approach allows us to quantify the cross-sectional heterogeneity of exchange rate pass-through/elasticities and the relation of this heterogeneity to dollar invoicing. Our findings strongly support the dominant currency paradigm as opposed to the traditional Mundell-Fleming pricing paradigms.

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.

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).