Estimation of a non-invertible moving average process: The case of overdifferencing

The effect of differencing all of the variables in a properly specified regression equation is examined. Excessive use of the difference transformation induces a non-invertible moving average (MA) process in the disturbances of the transformed regression. Monte Carlo techniques are used to examine the effects of overdifferencing on the efficiency of regression parameter estimates, inferences based on these estimates, and tests for overdifferenccing based on the estimator of the MA parameter for the disturbances of the differences regression. Overall, the problem of overdifferencing is not serious if careful attention is paid to the properties of the disturbances of regression equations.     

Margin requirements and stock volatility

Since 1934 the Federal Reserve Board has had the power to set separate limits on the amount of credit that can be extended to purchasers of common stock. There has been much recent debate about the efficacy of these margin regulations. This article argues that the Fed has responded to increases in stock prices by raising margin requirements. The increase in prices has been associated with a decrease in volatility. There is no evidence that changes in margin requirements reduce subsequent stock return volatility. Also, trading halts have not had much effect on volatility in the past. Trading halts that were associated with banking panics were associated with high stock return volatility, but halts without bank panics were not associated with high levels of volatility.This article summarizes discussion that was presented at the Columbia Center for the Study of Futures Markets Conference on Regulatory Reform of Stock and Futures Markets, May 12, 1989.     

Money,income, and sunspots: Measuring economic relationships and the effects of differencing

This paper discusses the question of whether economic time series regression models should be estimated between the levels or the changes of the variables of interest. We argue that many economic models should be estimated between the changes of the variables, rather than the levels of the variables. In addition, comparisons of the levels and changes regressions can be used as a crude test of model specification. These issues are illustrated with examples from Friedman and Meiselman's (1963) study of annual income and consumption and with data on sunspot activity from 1897–1958.     

Asset returns and inflation

We estimate the extent to which various assets were hedges against the expected and unexpected components of the inflation rate during the 1953–1971 period. We find that U.S. government bonds and bills were a complete hedge against expected inflation, and private residential real estate was a complete hedge against both expected and unexpected inflation. Labor income showed little short-term relationship with either expected or unexpected inflation. The most anomalous result is that common stock returns were negatively related to the expected component of the inflation rate, and probably also to the unexpected component.     

Stock exchange seats as capital assets

Stock exchange seats are important assets for securities brokers since they provide access to centralized secondary trading markets for corporate securities at a reduced cost. This paper provides empirical evidence on the dynamic behavior of monthly New York and American Stock Exchange seat prices over the 1926–1972 period. Specifically, evidence is presented which: (a) is consistent with a multiplicative random walk model for seat prices; (b) indicates that unexpected changes in the prices of exchange-listed stocks or in the volume of shares traded on the exchange are important new information about the value of seats in each month; and (c) indicates that the market for seats is efficient in assimilating new information and quickly incorporates new information into the prices of seats. In addition, we examine the effect of the infrequent trading of seats on the statistical properties of the models.