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.

### 1995

**Small Sample Properties of Estimators of Nonlinear Models of Covariance Structure**By Todd E. Clark (RWP 95-01 March 1995)

This study examines the small sample properties of GMM and ML estimators of non-linear models of covariance structure. The study focuses on the properties of parameter estimates and the Hansen (1982) and Newey (1985) model specification test. It use Monte Carlo simulations to consider the properties of estimates for some simple factor models, the Hall and Mishkin (1982) model of consumption and income changes, and a simple Bernanke (1986) decomposition model. This analysis establishes and seeks to explain a number of results. Most importantly, optimally weighted GMM estimation yields some biased parameter estimates, and GMM estimation yields a model specification test with size substantially greater than the asymptotic size.

Keywords: GMM, ML, covariance structure, Monte Carlo

**How Reliable Are Adverse Selection Models of the Bid-ask Spread?**By Robert Neal and Simon Wheatley (RWP 95-02 March 1995)

Theoretical models of the adverse selection component of bid-asked spreads predict the component arises from asymmetric information about a firm's fundamental value. We test this prediction using two well known models [Glosten and Harris (1988) and George, Kaul, and Nimalendran (1991)] to estimate the adverse selection component for closed-end funds. Closed-end funds hold diversified portfolios and report their net asset values on a weekly basis. Thus, there should be little uncertainty about their fundamental values and their adverse selection components should be minimal. Estimates of the component from the two models, however, average 19 and 52 percent of the spread. These estimates, while smaller than corresponding estimates from common stocks, are large enough to raise doubts about the reliability of these models.

**Direct Tests of Index Arbitrage Models**By Robert Neal (RWP 95-03 March 1995)

Previous tests of stock index arbitrage models have rejected the no-arbitrage constraint imposed by these models. This paper provides a detailed analysis of actual S&P 500 arbitrage trades and directly relates these trades to the predictions of index arbitrage models. An analysis of arbitrage trades suggests that (i) short sale rules are unlikely to restrict arbitrage, (ii) the opportunity cost of arbitrage funds exceeds the Treasury Bill rate, and (iii) the average price discrepancy captured by arbitrage trades is small. Tests of the models provide some support for a version of the arbitrage model that incorporates an early liquidation option. The ability of these models to explain arbitrage trades, however, is relatively low.

**Central Bank Intervention and the Volatility of Foreign Exchange Rates: Evidence from the Options Market**By Catherine Bonser-Neal and Glenn Tanner (RWP 95-04 April 1995)

This paper tests the effects of central bank intervention on the ex ante volatility of $/DM and $/Yen exchange rates. In contrast to previous research which employed GARCH estimates of conditional volatility, we estimate ex ante volatility using the implied volatilities of currency options prices. We also control for the effects of other macroeconomic announcements. We find little support for the hypothesis that central bank intervention decreased expected exchange rate volatility between 1985 and 1991. Federal Reserve intervention was generally associated with a positive change in exante $/DM and $/Yen volatility, or with no change. Perceived Bundesbank intervention did not alter $/DM ex ante volatility in any of the periods, while perceived Bank of Japan intervention was associated with positive changes in ex ante $/Yen volatility during the 1985-91 period as a whole and during the February 1987 to December 1989 post-Louvre Accord subperiod.

**Money Is What Money Predicts: The M* Model of the Price Level**By Gregory D. Hess and Charles S. Morris (RWP 95-05 June 1995)

Over the past twenty years, the monetary aggregates used by the Federal Reserve as indicators of economic activity and inflation have changed several times. Each of the changes in the measures of money was sparked by a breakdown in the fit of empirical money demand functions. The Federal Reserve's strategy following these breakdowns has been to redefine money by simply adding new assets to the old definitions. The criterion in each case was whether adding the new assets produced an empirically stable money demand function. Unfortunately, while a stable demand for money is a worthwhile ultimate goal, history has demonstrated that it is also an elusive one.

In this paper, we propose an alternative objective for identifying a useful monetary aggregate--the price level. Our monetary aggregate is a weighted-sum aggregate where the weights on the component assets vary across assets and over time such that the aggregate is the best predictor of the price level. The only assumption made in choosing the weights is that the Quantity Theory of Money holds in the long run. We find that the new monetary aggregate, M*, has a stable velocity in the long run and that it predicts the long-run price level and rate of inflation better than M2.