Peter von zur Muehlen

Robust monetary policy with misspecified models: Does model uncertainty always call for attenuated policy?

We explore Knightian model uncertainty as an explanation for the observed excess persistence and attenuation in estimated interest-rate reaction functions for the United States, relative to what optimal feedback rules would suggest. Two types of uncertainty are identified: (i) unstructured model uncertainty captured in additive shock error processes that result from omitted-variable misspecifications, and (ii) structured model uncertainty, where one or more parameters are posited as the source of misspecification. We estimate a forward-looking model of the U.S. economy, and find that rules for this model that are robust against unstructured model uncertainty, or against one-time parametric shifts, are more aggressive than the optimal linear quadratic rule. However, policies designed to protect the economy against the worst-case consequences of misspecified dynamics are less aggressive and good approximations of the estimated rule. Some drawbacks of robust policies are discussed. Finally, a connection between the degree of structure an authority ascribes to the uncertainty it faces and the extent and likelihood of policy attenuation in response to that uncertainty is explored.

Further thoughts on testing for causality with econometric models

Abstract The ontological basis for causality testing must be some empirically interpretable system leading one to specify a logically valid a priori law that can be shown to exist. Such paradigms as conventional, linear and non-linear models, be they structural or time series, tend to embody contradictory assumptions that, unfortunately, make causal interpretability problematic. The paper demonstrates how these difficulties can be avoided using a stochastic-coefficient approach. The final part of this article is devoted to a discussion of probabilistic logic as a valid tool for scientific analysis and interpretation of causal relationships.

Monopolistic competition and sequential search

Abstract In models describing sequential search as an optimal mode of behavior for buyers seeking the lowest price, it is often implicitly assumed that price dispersion actually exists. To evaluate the existence of equilibrium price distributions under sequential search, this paper presents two variants of a model of monopolistic competition. It is shown that under reasonable assumptions in a finite market, Nash competitive behavior is not consistent with price dispersion in equilibrium. However, in a continuous atomistic market, a price distribution can arise as a mapping from the distribution over search costs among consumers.

Comparing forecasts from fixed and variable coefficient models: The case of money demand *

In this paper we introduce a class of tentatively plausible, fixed-coefficient models of money demand and evaluate their forecast performance. When these models are reestimated allowing all coefficients to vary over time, the forecasting performance improves dramatically. Aside from offering insights about improved methods of analyzing time series data, the most promising direct use for point estimates derived from time-varying coefficients is as an aid in calibrating proposed models of the kind discussed here.

The effect of past and future economic fundamentals on spending and pricing behavior in the FRB/US macroeconomic model

This paper derives and presents mean leads and lags as well as patterns of relative importance weights implied by the PAC (polynomial-adjustment-cost) error-correction equations which form the core of the FRB/US model at the Federal Reserve Board. Relative importance weights measure the contributions of past and future expected changes in fundamentals on current decisions. These and the associated mean lags and leads can be considered summary measures of key dynamic properties of FRB/US. The spending equations are those for total consumption, durable consumption, business equipment, residential housing, and private inventories. The pricing equations are those for the price level and wage growth. In addition FRB/US has one PAC equation for dividends and one for labor hours.

Optimal price adjustment: Tests of a price equation in U. S. manufacturing

The following description and analysis of a firm in atomistic competition is motivated by the need to specify a dynamic equation of price behavior to be tested on U.S. manufacturing time-series data. It will be shown that uncertainty of price information in a market composed of many competing firms leads to a model which is more or less in the Evans tradition of dynamic monopoly theory.3 The key dynamic element is the firms reaction to customer behavior in an uncertain price situation. Price uncertainty forces newcomers to the market to search for an acceptable price which is less than the marginal utility of the good. Old customers may decide to search after a price increase, if the expected difference in search costs and price is less than the recently experienced price change. The implications of the theory are examined using a phase diagram analysis. Of particular interest for empirical study are the effects of changes in model parameters on the time path of the optimal price control equation. In line with the conclusions of the theoretical model the estimation results seem to suggest that price adjusts to a moving equilibrium path in a variable manner determined by cyclical factors in the economy.

The 'flexible accelerator' and optimization with a finite horizon

Abstract So-called ‘flexible accelerator’ or partial adjustment models can be derived from dynamic optimization under convex adjustment costs. However, even with time-invariant adjustment costs and constant discount rate, constancy of the speed of adjustment requires infinite horizon planning. Using a simple production model, it is shown here that for finite horizons, the adjustment may nevertheless be approximately constant for much of the time if the discount rate is high enough and if the marginal adjustment cost is sufficiently small.

Price dispersion in atomistic competition

Abstract This note presents necessary conditions for non-degenerate price dispersion in a continuous atomistic market where buyers with price-elastic demand search sequentially for the lowest price, and firms maximize profit subject to a variable average cost function.