Harald Uhlig

On adjusting the Hodrick-Prescott filter for the frequency of observations

This paper studies how the Hodrick-Prescott filter should be adjusted when changing the frequency of observations. It complements the results of Baxter and King (1999) with an analytical analysis, demonstrating that the filter parameter should be adjusted by multiplying it with the fourth power of the observation frequency ratios. This yields an HP parameter value of 6.25 for annual data given a value of 1600 for quarterly data. The relevance of the suggestion is illustrated empirically.

On Adjusting the HP-Filter for the Frequency of Observations

This paper studies how the HP-Filter should be adjusted, when changing the frequency of observations. It complements the results of Baxter and King (1999) with an analytical analysis, demonstrating that the filter parameter should be adjusted by multiplying it with the fourth power of the observations frequency ratios. This yields an HP parameter value of 6.25 for annual data given a value of 1600 for quarterly data. The relevance of the suggestion is illustrated empirically.

Understanding Unit Rooters: A Helicopter Tour

For the first-order univariate autoregression without constant term, the joint density (corresponding to a flat prior) for the true coefficient and its least squares estimate is estimated by Monte Carlo and graphically displayed. The graphs show how a symmetric distribution for the coefficient conditional on the estimate coexists with an asymmetric distribution for the estimate conditional on the coefficient. Prior densities implicit in treating classical significance levels as if they were Bayesian posterior probabilities are calculated. They are shown to depend sensitively on the estimated coefficient and to put substantial probability on values of the coefficient above one. Copyright 1991 by The Econometric Society.

Solving Nonlinear Stochastic Growth Models: a Comparison of Alternative Solution Methods

The purpose of this article is to report on a comparison of several alternative numerical solution techniques for nonlinear rational-expectations models. The comparison was made by asking individual researchers to apply their different solution techniques to a simple representative-agent, optimal, stochastic growth model. Decision rules as well as simulated time series are compared. The differences among the methods turned out to be quite substantial for certain aspects of the growth model. Therefore, researchers might want to be careful not to rely blindly on the results of any chosen numerical solution method in applied work.

An Analysis of the Stability and Growth Pact

We use a stylised model to analyse the Stability and Growth Pact for countries that have formed the European Monetary Union (EMU). In our model, shortsighted governments fail to internalise the consequences of their debt policies for the common inflation rate fully. Therefore, while governments have no incentive to sign a stability pact in the absence of a monetary union, they do so with monetary union to restrain this externality. With uncertainty, a monetary union combined with an appropriately designed pact will be strictly preferred to autonomy. With differences in initial conditions, conflicts of interest arise. We study the Nash bargaining solution.

How Far Are We from the Slippery Slope? The Laffer Curve Revisited

The goal of this paper is to examine the shape of the Laffer curve quantitatively in a simple neoclassical growth model calibrated to the US as well as to the EU-15 economy. We show that the US and the EU-15 area are located on the left side of their labor and capital tax Laffer curves, but the EU-15 economy being much closer to the slippery slopes than the US. Our results indicate that since 1975 the EU-15 area has moved considerably closer to the peaks of their Laffer curves. We find that the slope of the Laffer curve in the EU-15 economy is much flatter than in the US which documents a much higher degree of distortions in the EU-15 area. A dynamic scoring analysis shows that more than one half of a labor tax cut and more than four fifth of a capital tax cut are self-financing in the EU-15 economy.

A law of large numbers for large economies

SummaryLetX(i),iε[0; 1] be a collection of identically distributed and pairwise uncorrelated random variables with common finite meanμ and variance σ2. This paper shows the law of large numbers, i.e. the fact that ∝01X(i)di=μ. It does so by interpreting the integral as a Pettis-integral. Studying Riemann sums, the paper first provides a simple proof involving no more than the calculation of variances, and demonstrates, that the measurability problem pointed out by Judd (1985) is avoided by requiring convergence in mean square rather than convergence almost everywhere. We raise the issue of when a random continuum economy is a good abstraction for a large finite economy and give an example in which it is not.

Increasing the capital income tax may lead to faster growth

This paper shows that under rather mild conditions, higher capital income taxes lead to faster growth in an overlapping generations economy with endogenous growth. Government expenditures are financed with labor income taxes as well as capital income taxes. Since capital income accrues to the old, taxing it reliefs the tax burden on the young and leaves them with more income out of which to save. We argue that savings are sufficiently interest inelastic so that higher savings and therefore higher growth result. The basic argument is not seriously challenged by a grandfather clause for initial capital or by the old receiving some labor income as well.

Fiscal Stimulus and Distortionary Taxation

We quantify the fiscal multipliers in response to the American Recovery and Reinvestment Act (ARRA) of 2009. We extend the benchmark Smets-Wouters (Smets and Wouters, 2007) New Keynesian model, allowing for credit-constrained households, the zero lower bound, government capital and distortionary taxation. The posterior yields modestly positive short-run multipliers around 0.52 and modestly negative long-run multipliers around -0.42. The multiplier is sensitive to the fraction of transfers given to credit-constrained households, the duration of the zero lower bound and the capital. The stimulus results in negative welfare effects for unconstrained agents. The constrained agents gain, if they discount the future substantially.

Reasonable extreme bounds analysis

Abstract Leamer (1983) has given bounds for a parameter of a model estimated by ordinary least squares for all possible specifications with a given group of explanatory variables. However, some of these specifications will have low R2 specification and these can lead to wide bounds. In this paper, bounds are derived for all specifications with R2 values a given percentage of the maximum R2 value. These exact bounds can be found from calculating only two regressions. The techniques are applied to a study of the velocity of money.