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Estimation of Polynomial Distributed Lags and Leads with End Point Constraints

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  • Donald W.K. Andrews
  • Ray C. Fair

Abstract

This paper considers the use of the polynomial distributed lag (PDL) technique when the lag length is estimated rather than fixed. We focus on the case where the degree of the polynomial is fixed, the polynomial is constrained to be zero at a certain lag length q, and q is estimated along with the other parameters. We extend the traditional PDL setup by allowing q to be real-valued rather than integer-valued, and we derive the asymptotic covariance matrix of all the parameter estimates, including the estimate of q. The paper also considers the estimation of distributed leads rather than lags, a case that can arise if expectations are assumed to be rational.

Suggested Citation

  • Donald W.K. Andrews & Ray C. Fair, 1989. "Estimation of Polynomial Distributed Lags and Leads with End Point Constraints," NBER Technical Working Papers 0079, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0079
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    1. Hendry, David F. & Pagan, Adrian R. & Sargan, J.Denis, 1984. "Dynamic specification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 18, pages 1023-1100, Elsevier.
    2. Cumby, Robert E. & Huizinga, John & Obstfeld, Maurice, 1983. "Two-step two-stage least squares estimation in models with rational expectations," Journal of Econometrics, Elsevier, vol. 21(3), pages 333-355, April.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Schmidt, Peter, 1973. "On the Difference Between Conditional and Unconditional Asymptotic Distributions of Estimates in Distributed Lag Models with Integer-Valued Parameters," Econometrica, Econometric Society, vol. 41(1), pages 165-169, January.
    5. Fair, Ray C, 1993. "Inflationary Expectations and Price Setting Behavior," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 8-18, February.
    6. Harper, Charles P, 1977. "Testing for the Existence of a Lagged Relationship within Almon's Method," The Review of Economics and Statistics, MIT Press, vol. 59(2), pages 204-210, May.
    7. Pagano, Marcello & Hartley, Michael J., 1981. "On fitting distributed lag models subject to polynomial restrictions," Journal of Econometrics, Elsevier, vol. 16(2), pages 171-198, June.
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    Cited by:

    1. Fair, Ray C, 1993. "Inflationary Expectations and Price Setting Behavior," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 8-18, February.
    2. Rucker C. Johnson & Steven Raphael, 2009. "The Effects of Male Incarceration Dynamics on Acquired Immune Deficiency Syndrome Infection Rates among African American Women and Men," Journal of Law and Economics, University of Chicago Press, vol. 52(2), pages 251-293, May.
    3. Townsend, Rob F. & van Zyl, Johan & Thirtle, Colin G., 1997. "Assessing the benefits of research expenditures on maize production in South Africa," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 36(4), pages 1-13, December.
    4. Alessandro Magrini & Fabio Bartolini & Alessandra Coli & Barbara Pacini, 2019. "A structural equation model to assess the impact of agricultural research expenditure on multiple dimensions," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 2063-2080, July.

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