Overview
Harald Uhlig is a macroeconomist and econometrician, at the time of the 1997 paper affiliated with CentER at Tilburg University (later Princeton and the University of Chicago). His work spans Bayesian econometrics, unit root theory, and structural VAR identification. His 1997 Econometrica paper introduced the BVAR with multiplicative Wishart stochastic volatility; his 2005 Journal of Monetary Economics paper introduced sign-restriction identification for structural VARs.
Key Contributions / Features
- BVAR with stochastic volatility (1997): Extended the conjugate BVAR framework to allow a time-varying m×m error precision matrix Ht evolving via a multiplicative Wishart (multivariate Beta) random walk. Showed that the matrix-normal inverse-Wishart posterior family is preserved at each time step, giving exact Kalman-filter-like recursions without MCMC.
- Sign restrictions for structural VARs (2005): Proposed an agnostic identification strategy for monetary policy shocks: require only that a contractionary shock not raise prices, not raise nonborrowed reserves, and not lower the federal funds rate — leaving the output response completely unrestricted. Showed that GDP ambiguity is the data-honest result; Cholesky's large negative output effects are an artifact of its implicit zero contemporaneous restriction on GDP, not evidence in the data. See Sign Restriction Identification.
- Unit roots: Bayesian perspective (1994a): Argued that from a Bayesian standpoint, macroeconomists should be largely agnostic about whether macro variables have exact unit roots — the posterior probability of a unit root is sensitive to the prior and may not concentrate at 1 even with large samples.
- Singular Wishart distributions (1994b): Established distributional results for singular Wishart and multivariate Beta distributions needed for the BVAR-SV conjugate updating theorems.
- Sims-Uhlig (1991): "Understanding Unit Rooters: A Helicopter Tour," Econometrica 59(6): 1591–1599. Co-authored with Christopher Sims. Showed that the likelihood function in AR(1) models is Gaussian-symmetric around ρ^ regardless of whether ρ=1, while the classical sampling distribution of ρ^ is asymmetric (Dickey-Fuller). Using DF p-values as posterior probabilities implicitly imposes an irrational, data-dependent prior that favors explosive values of ρ. Recommended reporting conventional t and F statistics as the natural summary of the likelihood shape. See Unit Root Inference.
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