NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Richard Startz

Department of Economics,
University of California
Santa Barbara, CA 93106
Tel: 206-543-8172

E-Mail: EmailAddress: hidden: you can email any NBER-related person as first underscore last at nber dot org

NBER Working Papers and Publications

1989A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market
with Christopher M. Turner, Charles R. Nelson: w2818
Risk premia in the stock market are assumed to move with time varying risk. We present a model in which the variance of time excess return of a portfolio depends on a state variable generated by a first-order Markov process. A model in which the realization of the state is known to economic agents, but unknown to the econometrician. is estimated. The parameter estimates are found to imply that time risk premium declines as time variance of returns rises. We then extend the model to allow agents to be uncertain about time state. Agents make their decisions in period t using a prior distribution of time state based only on past realizations of the excess return through period t-1 plus knowledge of the structure of the model. These parameter estimates from this model are consistent with asset...

Published: Journal of Financial Economics, April 1990. citation courtesy of

December 1988Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence
with Myung Jig Kim, Charles R. Nelson: w2795
Recent research based on variance ratios and multiperiod-return autocorrelations concludes that the stock market exhibits mean reversion in the sense that a return in excess of the average tends to be followed by partially offsetting returns in the opposite direction. Dividing history into pre-1926, 1926-46, and post-1946 subperiods, we find that the mean-reversion phenomenon is a feature of the 1926-46 period, but not of the post-1946 period which instead exhibits persistence of returns. Evidence for pre-1926 data is mixed. The statistical significance of test statistics is assessed by estimating their distribution using stratified randomization. Autocorrelations of multiperiod returns imply a forecast of future returns, which is presented for post-war three-year returns using 1926-46, fu...

Published: Review of Economic Studies, Vol. 58, No. 195, pp. 515-528, (May 1991). citation courtesy of

September 1988Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator
with Charles R. Nelson: t0068
New results on the exact small sample distribution of the instrumental variable estimator are presented by studying an important special case. The exact closed forms for the probability density and cumulative distribution functions are given. There are a number of surprising findings. The small sample distribution is bimodal. with a point of zero probability mass. As the asymptotic variance grows large, the true distribution becomes concentrated around this point of zero mass. The central tendency of the estimator may be closer to the biased least squares estimator than it is to the true parameter value. The first and second moments of the IV estimator are both infinite. In the case in which least squares is biased upwards, and most of the mass of the IV estimator lies to the right of the ...

Published: Journal of Business, January 1990.

The Distribution of the Instrumental Variables Estimator and Its t-RatioWhen the Instrument is a Poor One
with Charles R. Nelson: t0069
When the instrumental variable is a poor one, in the sense of being weakly correlated with the variable it proxies, the small sample distribution of the IV estimator is concentrated around a value that is inversely related to the feedback in the system and which is often further from the true value than is the plim of OLS. The sample variance of residuals similarly becomes concentrated around a value which reflects feedback and not the variance of the disturbance. The distribution of the t-ratio reflects both of these effects, stronger feedback producing larger t-ratios. Thus, in situations where OLS is badly biased, a poor instrument will lead to spurious inferences under IV estimation with high probability, and generally perform worse than OLS.

Published: Econometrica, April 1990.

 
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