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Dynamic Adjustment of Internal Prices to External Price Changes, Federal Republic of Germany, 1958–1979

An Application of Rank-Reduced Distributed-Lag Estimation by Spline Functions
  • John S. Chipman
Conference paper

Abstract

This paper presents a method for estimating lag distributions in a large-scale dynamic model in which import and export prices are treated as the explanatory variables explaining internal prices. The model is applied to monthly data on import prices, export prices, and domestic producer prices of industrial products in the Federal Republic of Germany, covering the 22-year period 1958–1979. The basic data set consists of monthly price indices (multiplied by their weights) for 34 import categories, 32 export categories, and 34 domestic categories of commodities, as indicated in Table 1.

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References

  1. Aimon, Sh.: The Distributed Lag between Capital Appropriations and Expenditures. Econometrica 33, 1965, 178–196, .CrossRefGoogle Scholar
  2. Bacon, R.W., and J.A. Hausman: The Relationship between Ridge Regression and the Minimum Mean Square Error Estimator of Chipman. Oxford Bulletin of Economics and Statistics 36, 1974, 115–124.Google Scholar
  3. Chipman, J.S.: On Least Squares with Insufficient Observations. Journal of the American Statistical Association 59, 1964, 1078–1111, .CrossRefGoogle Scholar
  4. Chipman, J.S.: Statistical Problems Arising in the Theory of Aggregation. Applications of Statistics. Ed. by P.R. Krishnaiah. Amsterdam 1977, 123–140.Google Scholar
  5. Chipman, J.S.: Towards the Construction of an Optimal Aggregative Model of International Trade: West Germany, 1963–1975. Annals of Economic and Social Measurement 6, 1978, 535–554.Google Scholar
  6. Chipman, J.S.: Efficiency of Least-Squares Estimation of Linear Trend when Residuals are Auto correlated. Econometrica 47, 1979, 115–128, .CrossRefGoogle Scholar
  7. Chipman, J.S.: Exchange-Rate Flexibility and Resource Allocation. Flexible Exchange Rates and the Balance of Payments: Essays in Memory of Egon Sohmen. Ed. by J. S. Chipman and Ch.R. Kindleberger. Amsterdam 1980, 159–209.Google Scholar
  8. Chipman, J.S., and M. M. Rao: The Treatment of Linear Restrictions in Regression Analysis. Econometrica 32, 1964a, 198–209.CrossRefGoogle Scholar
  9. Chipman, J.S., : Projections, Generalized Inverses, and Quadratic Forms. Journal of Mathematical Analysis and Applications 9, 1964b, 1–11.CrossRefGoogle Scholar
  10. Corradi, C., and G. Gambetta: The Estimation of Distributed Lags by Spline Functions. Empirical Economics 1 (1), 1975, 41–51.CrossRefGoogle Scholar
  11. Eckart, C., and G. Young: The Approximation of One Matrix by Another of Lower Rank. Psychometrika 1, 1936, 211–218, .CrossRefGoogle Scholar
  12. Eckart, C., : A Principal Axis Transformation for Non-Hermitian Matrices. Bulletin of the American Mathematical Society 45, 1939, 118–121.CrossRefGoogle Scholar
  13. Goldstein, M., and A. F. M. Smith: Ridge-Type Estimators for Regression Analysis. Journal of the Royal Statistical Society [B], 36 (2), 1974, 284–291.Google Scholar
  14. Golub, G., and W. Kahan: Calculating the Singular Values and Pseudo-Inverse of a Matrix. Journal of the Society for Industrial and Applied Mathematics, Series B (Numerical Analysis) 2 (2), 1965, 205–224.Google Scholar
  15. Golub, G.H., and C. Reinsch: Singular Value Decomposition and Least Squares Solutions. Numerische Mathematik 14, 1970, 403–420.CrossRefGoogle Scholar
  16. Greville, T.N.E.: Data Fitting by Spline Functions. Mathematics Research Center, United States Army, University of Wisconsin, Madison, MRC Technical Summary Report No. 893, 1968, (mimeographed).Google Scholar
  17. Greville, T.N.E.: Introduction to Spline Functions. Theory and Application of Spline Functions. Ed. by T.N.E. Greville. New York 1969, 1–35.Google Scholar
  18. Guckes, S.: Zur Neuberechnung der Preisindices auf Basis 1970. Wirtschaft und Statistik, 1973, 691–693. English translation: A New Computation of the Price Indices on Base 1970. Studies on Statistics (28), 1974.Google Scholar
  19. Hamlen, S.S., and W. A. Hamlen: Harmonic Alternatives to the Almon Polynomial Technique. Journal of Econometrics 7, 1978, 57–66, .CrossRefGoogle Scholar
  20. Ho, D.S.: An Econometric Study of the Relationship between International and Domestic Prices in the Japanese Economy. Ph.D. thesis, University of Minnesota, Minneapolis 1977.Google Scholar
  21. Hoerl, A.E., and R.W. Kennard: Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics 12, 1970a, 55–67.CrossRefGoogle Scholar
  22. Hoerl, A.E., : Ridge Regression: Application to Nonorthogonal Problems. Technometrics 12, 1970b, 69–82.CrossRefGoogle Scholar
  23. Kravis, L.B., and R.E. Lipsey: Price Competitiveness in World Trade. New York 1971.Google Scholar
  24. Learner, E.E.: Multicollinearity: A Bayesian Interpretation. Review of Economics and Statistics 55, 1973, 371–380.CrossRefGoogle Scholar
  25. Lucas, R.E., Jr.: Econometric Testing of the Natural Rate Hypothesis. The Econometrics of Price Determination. Proceedings of a Conference held on October 30–31; 1970. Washington, D.C., 1970.Google Scholar
  26. Marquardt, D. W.: Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation. Technometrics 12, 1970, 591–612, .CrossRefGoogle Scholar
  27. Ouanes, A.: Econometric Study of the International Transmission of Inflation: The Case of West Germany. Ph.D. thesis, University of Minnesota, Minneapolis 1979.Google Scholar
  28. Rostin, W.: Die Indices der Außenhandelspreise auf Basis 1970. Wirtschaft und Statistik, 1974, 387–394. English translation: Indices of Foreign Trade Prices, Base 1970. Studies on Statistics (30), 1974.Google Scholar
  29. Samuelson, P.A.: Prices of Factors and Goods in General Equilibrium. Review of Economic Studies 21, 1953, 1–20.CrossRefGoogle Scholar
  30. Shephard, R.W.: Cost and Production Functions. Princeton, N.J., 1953.Google Scholar
  31. Shiller, R.J.: A Distributed Lag Estimator Derived from Smoothness Priors. Econometrica 41, 1973, 775–788.CrossRefGoogle Scholar
  32. Sims, Ch. A.: Money, Income and Causality. American Economic Review 62, 1972, 540–552.Google Scholar
  33. Sims, Ch.A.: Distributed Lags. Frontiers of Quantitative Economics, Vol. II. Ed. by M. D. Intrilligator and D. A. Kendrick. Amsterdam 1974, 289–332.Google Scholar
  34. Statistisches Bundesamt, Wiesbaden: Fachserie M, Preise, Löhne, Wirtschaftsrechnungen: Reihe 1, Preise und Preisindizes für Außenhandelsgüter; Reihe 3, Preise und Preisindizes für industrielle Produkte (Erzeugerpreise). Mainz 1958–1976.Google Scholar
  35. Fachserie 17, Preise: Reihe 8, Preise und Preisindizes für die Ein- und Ausfuhr; Reihe 2, Preise und Preisindizes für industrielle Produkte (Erzeugerpreise). Mainz 1977–1979.Google Scholar
  36. Sims, Ch.A.: Systematisches Warenverzeichnis für die Industriestatistik, Ausgabe 1970. Mainz 1970.Google Scholar
  37. Wedin, P.-Ä.: On the Almost Rank Deficient Case of the Least Squares Problem. BIT Nordisk Tidskrift for Informationsbehandling 13 (3), 1973, 344–354.Google Scholar
  38. Zellner, A.C.: An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias. Journal of the American Statistical Association 57, 1962, 348–368.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • John S. Chipman

There are no affiliations available

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