The Federal Reserve Bank of Kansas City's Research staff produces a series of working papers presenting results of the department's economic research. These technical papers cover a wide range of economic research topics.

2004

A Simple Model of City Crowdedness

By Jordan Rappaport (RWP 04-12 December 2004)
Population density varies widely across U.S. cities. A calibrated general equilibrium model in which productivity and quality-of-life differ across locations can account for such variation. Individuals derive utility from consumption of a traded good, a nontraded good, leisure, and quality-of-life. The traded and nontraded goods are produced by combining mobile labor, mobile capital, and non-mobile land. An eight-fold increase in population density requires an approximate 50 percent productivity differential or an approximate 20 percent compensating differential. A thirty-two-fold increase in population density requires an approximate 95 percent productivity differential or a 33 percent compensating differential. Empirical evidence suggests productivity and quality-of-life differentials of this magnitude are plausible. The model implies that broad-based technological progress can induce substantial migration to localities with high quality-of-life.

JEL Codes: O400, O510, R110, R120
Keywords: Population Density, Productivity, Quality-of-Life, Compensating Differentials, Economic Growth

Barriers to Network-Specific Innovation

By Antoine Martin and Michael J. Orlando (RWP 04-11 November 2004; Revised September 2005)
We examine incentives for network-specific investment and the implications for network governance. We model an environment in which participants making payments over a network can invest in a technology that reduces the marginal cost of using the network. A network effect results in multiple equilibria; either all agents invest and use of the network is high or no agents invest and use of the network is low. The high-use equilibrium can be implemented where commitment is feasible. Where commitment is infeasible, fixed costs associated with use of the network-specific technology result in a hold-up problem that implements the low-investment equilibrium. As a result, governance structures necessary to achieve commitment will be preferred to those necessary merely to achieve coordination. For example, mutual ownership by network users may emerge where users face risks of ex post renegotiation. Such a governance structure will also be sufficient to avoid the network effect.

JEL Codes: E59, G29, L14, L22
Keywords: Hold-up, Network; Commitment; Payments

Improving Forecast Accuracy by Combining Recursive and Rolling Forecasts

By Todd E. Clark and Michael W. McCracken (RWP 04-10 October 2004)
This paper presents analytical, Monte Carlo, and empirical evidence on the effectiveness of combining recursive and rolling forecasts when linear predictive models are subject to structural change. We first provide a characterization of the bias-variance tradeoff faced when choosing between either the recursive and rolling schemes or a scalar convex combination of the two. From that, we derive pointwise optimal, time-varying and data-dependent observation windows and combining weights designed to minimize mean square forecast error. We then proceed to consider other methods of forecast combination, including Bayesian methods that shrink the rolling forecast to the recursive and Bayesian model averaging. Monte Carlo experiments and several empirical examples indicate that although the recursive scheme is often difficult to beat, when gains can be obtained, some form of shrinkage can often provide improvements in forecast accuracy relative to forecasts made using the recursive scheme or the rolling scheme with a fixed window width.

JEL Codes: C53, C12, C52
Keywords: Structural breaks, forecasting, model averaging

Identification and Normalization in Markov Switching Models of "Business Cycles"

By Penelope A. Smith and Peter M. Summers (RWP 04-09 October 2004)
Recent work by Hamilton, Waggoner and Zha (2004) has demonstrated the importance of identification and normalization in econometric models. In this paper, we use the popular class of two-state Markov switching models to illustrate the consequences of alternative identification schemes for empirical analysis of business cycles. A defining feature of (classical) recessions is that economic activity declines on average. Somewhat surprisingly however, this property has been ignored in most published work that uses Markov switching models to study business cycles. We demonstrate that this matters: inferences from Markov switching models can be dramatically affected by whether or not average growth in the 'low state' is required to be negative, rather than simply below trend. Although such a restriction may not be appropriate in all applications, the difference is crucial if one wants to draw conclusions about 'recessions' based on the estimated model parameters.

JEL Codes: E32, E37, C22
Keywords: Business cycles, Recessions, Markov switching, Beyasian inference, Posterior distribution

Estimating Equilibrium Real Interest Rates in Real Time

By Todd E. Clark and Sharon Kozicki (RWP 04-08 September 2004)
We use a range of simple models and 22 years of real-time data vintages for the U.S. to assess the difficulties of estimating the equilibrium real interest rate in real time. Model specifications differ according to whether the time-varying equilibrium real rate is linked to trend growth, and whether potential output and growth are defined by the CBO's estimates or treated as unobserved variables. Our results reveal a high degree of specification uncertainty, an important one-sided filtering problem, and considerable imprecision due to data uncertainty. Also, the link between trend growth and the equilibrium real rate is shown to be quite weak. Overall, we conclude that statistical estimates of the equilibrium real rate will be difficult to use reliably in practical policy applications.

JEL Codes: C5, E4, C3, E52
Keywords: real-time-data; time-varying parameter; Kalman filter; trend growth.

Aggregate Consumption Wealth Ratio: Does It Work Internationally?

By Paul P.J. Gao and Kevin X.D. Huang (RWP 04-07 August 2004; Last Revised December 2004)
We find that the short-term deviations from long-run consumption-wealth relationship (cay) forecast stock market returns and serve as a conditioning variable in the capital asset pricing model (CAPM) for explaining the cross-section of stock returns for the United Kingdom and Japan. Our cross-sectional regressions using cay as a conditioning variable as opposed to using an alternative variable, tay, constructed using calendar time in place of consumption indicate that it is unlikely to be a spurious variable and provides useful information concerning the economic fundamentals. We show that both a consumption-based capital asset pricing model (CCAPM) and a human-capital-augmented capital asset pricing model (HC-CAPM) in conjunction with this conditioning variable can explain much of the cross-section of stock returns in each of the two countries; yet, in terms of relative performance, our results tend to favor the conditional HC-CAPM over the conditional CCAPM for pricing U.K. and Japanese cross-sectional returns.

JEL Codes: E21, G12, G14
Keywords: Asset Pricing Models, Conditional Asset Pricing Models, CAY

Specific Factors Meet Intermediate Inputs: Implications for Strategic Complementarities and Persistence

By Kevin X.D. Huang (RWP 04-06 June 2004; Last Revised February 2005)
A central challenge to monetary business-cycle theory is to find a solution to the problem of persistence and delay in the real effects of monetary shocks. Previous research has identified separately specific factors and intermediate inputs as two promising mechanisms for generating the persistence and delay in a staggered price-setting framework. Models based on either of these two mechanisms have also been used in the design of optimal monetary policy. By examining a staggered price model that features both specific factors and intermediate inputs, the author finds an offsetting interaction between the two individually promising mechanisms, which leads to a cancellation of much of the impact of each in propagating monetary shocks. This finding posits a challenge to the search for robust monetary transmission mechanism and design of optimal monetary policy.

JEL Codes: E24, E32, E52
Keywords: Specific factors; Intermediate inputs; Strategic complementarities; Persistence; Hump-shape

Multiple Stages of Processing and the Quantity Anomaly in International Business Cycle Models

By Kevin X.D. Huang and Zheng Liu (RWP 04-05 June 2004)
We construct a two-country DSGE model with multiple stages of processing and local currency staggered price-setting to study cross-country quantity correlations driven by monetary shocks. The model embodies a mechanism that propagates a monetary surprise in the home country to lower the foreign price level while restraining the home price level from rising too quickly; and, it does so through reducing material costs in terms of the foreign currency unit while dampening the upward movements in the costs in terms of the home currency unit, both in absolute terms and relative to the costs of primary factors. We show that, through this mechanism and a resulting factor substitution effect, the model is able to generate significant cross-country quantity correlations, with correlations in consumption considerably lower than correlations in output, as in the data.

JEL Codes: E32, F31, F41
Keywords: Stages of processing; Monopolistic competition; Local currency pricing; Welfare

Production Interdependence and Welfare

By Kevin X.D. Huang and Zheng Liu (RWP 04-04 June 2004)
The international welfare effects of a country’s monetary policy shocks have been controversial in the literature. While a unilateral monetary expansion increases the production efficiency in each country, it affects terms of trade in favor of one country against another depending on the currencies of price setting. We show that the increased world production interdependence magnifies the efficiency-improvement effect while dampening the terms-of-trade effect. As a consequence, a unilateral monetary expansion can be mutually beneficial and thus Pareto improving regardless of in which currency unit prices are set. In this sense, international monetary policy transmission may not be a source of potential conflict in a world with production interdependence.

JEL Codes: E32, F31, F41
Keywords: Stages of processing; Monopolistic competition; Local currency pricing; Welfare

Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference Hypothesis

By Todd E. Clark and Kenneth D. West (RWP 04-03 May 2004)
We consider using out of sample mean squared prediction errors (MSPEs) to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable. Under the null of zero predictability, the population MSPE of the null “no change” model equals that of the linear alternative. We show analytically and via simulations that despite this equality, the alternative model’s sample MSPE is expected to be greater than the null’s. We propose and evaluate an asymptotically normal test that properly accounts for the upward shift of the sample MSPE of the alternative model. Our simulations indicate that our proposed procedure works well.

JEL Codes: C52, C53, C12, F31
Keywords: Forecast evaluation, causality, exchange rates

Financial Intermediaries, Markets, and Growth

By Falko Fecht, Kevin Huang, and Antoine Martin (RWP 04-02 April 2004; Last Revised May 2004)
In many models of financial intermediation, markets reduce welfare because they limit the amount of risk-sharing intermediaries can offer. In this paper we study a model in which markets also promote investment in a productive technology. A trade-off between risk sharing and growth arises endogenously. In the model, financial intermediaries provide insurance to households against a liquidity shock. Households can also invest directly on a financial market if they pay a cost. In equilibrium, the ability of intermediaries to share risk is constrained by the market. This can be beneficial because intermediaries invest less in the productive technology when they provide more risk-sharing. We show the mix of intermediaries and market that maximizes welfare depend on parameter values. We also show the optimal mix of two very similar economies can be very different.

JEL Codes: E44, G10, G20
Keywords: Financial intermediaries; Financial Markets; Risk-sharing; Growth

Heterogeneity, Redistribution, and the Friedman Rule

By Joydeep Bhattacharya, Joseph H. Haslag, and Antoine Martin (RWP 04-01 February 2004; Last Revised September 2004)
We study monetary models with non-degenerate stationary distribution of money holdings. We find that the Friedman rule does not typically maximize ex-post social welfare. An increase in the rate of growth of the money supply has two effects: the standard distortionary, or rate-of-return, effect makes money a less desirable asset for all moneyholders. A second, redistributive effect, creates a transfer from one type of agent to the other. An increase in the rate of growth on money away from the Friedman rule can produce a rate-of-return effect that dominates the standard effect.

JEL Codes: E31, E52, H23
Keywords: Friedman rule, monetary policy, redistribution, heterogeneity