# Essays in Macroeconometrics

*Mikkel Plagborg-Møller*
Link

Abstract

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 impulseresponse 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.

Smoothness priors sharpen inference (i.e. reduce standard errors) for impulse response functions, since smoother IRFs have fewer effective free parameters. In other words, if you shrink toward a polynomial, that polynomial has fewer parameters than some other complex function you could come up with. It has to look a certain way (like a polynomial), irrespective of the data, which reduces uncertainty. There’s only so many ways to skin a cat, and likewise there’s only so many ways to draw a polynomial of a particular finite order that loosely fits the data. The coefficients of the polynomials effectively define the IRF, so reduced parameter uncertainty is equivalent to reduced IRF uncertainty.

Explicit confirmation that if you have the correct shocks, you can just regress the outcome variable on the shocks directly a la local projections. This is what they do in Origins of Stock Market Fluctuations.

Seems that an inherent drawback of the SVMA approach is that the parameters (which are the impulse response function) are under-identified, so it’s not just that the method makes priors easy and transparent to impose, they *must* be imposed. You could say that this isn’t much of a disadvantage, since in the SVAR setting you often impose the equivalent of priors as well, but in a more obtuse and less direct fashion.