Abstract
The circumstances under which the polynomial distributed lag method can be preferred to the ordinary least squares are discussed in this paper and both stochastic and deterministic restrictions are taken into consideration. The polynomial lag is mainly feasible in small sample situations when the error variance of the model is relatively high and the lag function not too peaked. Two recent Monte Carlo studies, one favouring the Almon lag, the other showing the opposite tendency, are reconsidered and their findings discussed in the light of known analytical results.
Similar content being viewed by others
References
Almon, S.: The distributed lag between capital appropriations and expenditures. Econometrica33, 1965, 178–196.
Amemiya, T., andK. Morimune: Selecting the optimal order of polynomial in the Almon distrib- uted lag. Review of Economics and Statistics56, 1974, 378–386.
Bibby, J., andH. Toutenburg: Prediction and improved estimation in linear models. New York 1977.
Cargill, T., andR.A. Meyer: Some time and frequency domain distributed lag estimators: A comparative Monte Carlo study. Econometrica42, 1974, 1031–1044.
Dhrymes, P.J.: Distributed lags. Problems of estimation and formulation. San Francisco 1971.
Farebrother, R.W.: Partitioned ridge regression. Technometrics20, 1978, 121–122.
Frost, P.A.: Some properties of the Almon lag technique when one searches for degree of polynomial and lag. Journal of the American Statistical Association70, 1975, 606–612.
Hannan, E.J.: The estimation of a lagged regression relation. Biometrica54, 1967, 409–418.
Kuks, J., andV. Olman: Minimaksnaja linejnaja ocenka koefficientov regressii. Eesti NSV teaduste akadeemia toimetised21, 1972, 66–72.
Mouchart, M., andR. Orsi: Polynomial approximations of distributed lags and linear restrictions: A Bayesian approach. Empirical Economics1, 1976, 129–152.
Schmidt, P., andR. Sickles: On the efficiency of the Almon lag technique. International Economic Review16, 1975, 792–795.
Schmidt, P., andR.N. Waud: The Almon lag technique and the monetary versus fiscal policy debate. Journal of the American Statistical Association68, 1973, 11–19.
Shiller, R.J.: A distributed lag estimator derived from smoothness priors. Econometrica41, 1973, 775–788.
Swamy, P.A.V.B., andJ.S. Mehta: A note on minimum average risk estimators for coefficients in linear models. Communications in StatisticsA6, 1977, 1181–1186.
TerÄsvirta, T.: On stepwise regression and economic forecasting. Kansantaloudellinen yhdistys. Helsinki 1970.
—: A comparison of mixed and minimax estimators of linear models. Communications in Statistics (forthcoming), 1980a.
—: Linear restrictions in misspecified linear models and polynomial distributed lag estimation. University of Helsinki, Department of Statistics, Research Report No. 16, 1980b.
—: Some results on improving the least squares estimation of linear models by mixed estimation. Scandinavian Journal of Statistics 8 (forthcoming), 1981.
Theil, H.: Economic Forecasts and Policy, 2nd edition. Amsterdam 1961.
Theil, H., andA.S. Goldberger: On pure and mixed statistical estimation in economics. International Economic Review2, 1961, 65–78.
Theobald, C.M.: Generalizations of the mean square error applied to ridge regression. Journal of the Royal Statistical SocietyB 26, 1974, 103–106.
Thomas, J.J.: Some problems in the use of Almon's technique in the estimation of distributed lags. Empirical Economics2, 1977, 175–193.
Toro-Vizcarrondo, C., andT.D. Wallace: A test of the mean square error criterion for restrictions in linear regression. Journal of the American Statistical Association63, 1968, 558–572.
Trivedi, P.K.: A note on the application of Almon's method of calculating distributed lag coefficients. Metroeconomica22, 1970, 281–286.
Trivedi, P.K., andA.R. Pagan: Polynomial distributed lags: A unified treatment. The Economic Studies Quarterly30, 1979, 37–49.
Wallace, T.D.: Weaker criteria and tests for linear restrictions in regression. Econometrica40, 1972, 689–698.
Yancey, T.A., G.G. Judge andM.E. Bock: A mean square error test when stochastic restrictions are used in regression. Communications in Statistics3, 1974, 755–768.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
TerÄsvirta, T. The polynomial distributed lag revisited. Empirical Economics 5, 69–81 (1980). https://doi.org/10.1007/BF01848044
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01848044