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CONRAD – A Maximum Likelihood Program for Estimation of Simultaneous Equations Models that are Non-Linear in the Parameters. (1984). Mellander, Erik ; Jansson, Leif .
In: Working Paper Series.
RePEc:hhs:iuiwop:0131.

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  1. (cf. sec. 2.2.1). The corresponding formula for ~=2 is obtained by mere substitution of 2 and vi for l and y i' respectivelYI and multiplication by -1. - 49 -RarES l ef. Hendry (1971).
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  2. 2 Cf. Haessel (1978). 3 There is a close relationship between the two measures, however, in that they take on identical values when applied to a linear equation with intercept, estimated by OLS.
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  3. 3 I.e. of the Newton type but not requiring evaluation of second order derivatives. See e.g. Quandt (1983, pp. 721-722). 4 An auxiliare routine, MCIIAD, from the same library is also employed.
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  4. 4 ef., however, Durbin (1957).
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  5. 5 The linear search problem is discussed in Quandt (1983, pp. 735-737). For comparisons between Fletcher 's algorithm and the DFP, see Fletcher (1970). 6 Termination may also occur because the prespecified maximum number of function evaluations, MXFN, has been reached.
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  6. 8 The Cholesky factorization is in Theil (1983). An extensive proof of the stated equiva1ence Lau (1978).
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  7. 9 Se Si1vey (1975).
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  8. According to RESF3.DAT (not reprodueed) the number of function evaluations increased by 50 percent, relative to the first estimation. As an indication of the increase in general, this is somewhat on the low side. The increase is seldom higher than 60-70 percent, however. - 69 -REFERERCES Belsley, D.A., 1980, On the Ef:Eicient Computation of the Nonlinear Full-Information MaximumLikelihood Estimator , Journal of Econometric ~, 14, pp. 203-225.
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  9. After having been renarned i t can thus serve as an input file in the next rune This is convenient if, e. g., the optimization algorithm has been stopped before having reached the optimum, due to a too low value having been assigned to MXFN. The search can then continue from the point where it was previously terminated. - 44 -Another conceivable use of the file is to provide starting values when the stochastic specification is changed from the one assuming time-independent residuals to the one allowing them to follow a first order vector autoregression. - 45 -BarES l Cf. Berndt and Khaled (1979, p. 1228). Other generalized measures have been proposed by e.g. Carter and Nagar (1977). The advantage of Berndt's measure is that it is the only cme which is invariant to whether the structural or the reduced form of the system is considered.
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  10. Berndt, E.R. and Khaled, M.S., 1979, Parameter Productivity Measurement and Choice Among Flexible Functional Forms, Journal of Politica ~ E~O~Omy, 81, pp. 1220-1245.

  11. Berndt, E.R. and Savin, N.E., 1977, Conflict Among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model , Econ:. ometrics, 45, pp. 1263-1278.

  12. Berndt, E.R., Hall, B.H., Hall, R.E. and Hausman, J.H., 1974, Estimation and Inference in Nonlinear Structural Models , Annals of Economic and Social Me~sur~!!!~Et, 3, pp. 653-666.

  13. Breusch, T. S., 1979, Conflict .Among Criteria for Testing Hypothesi s: Extensions and Comments , EconC?metrica, 47, pp. 203-207.

  14. Brown, B.W., 1981, Sample Size Requirements in Full Information Maximum Likelihood Estimation , International Economic Review, 22,----_.,-'--_._,-----_._-_._,----pp. 443-460.

  15. Calzolari, G. and panattoni, I.J., 1983, Hessian and Approximated Hessian Matrices in Maximum Likelihood Estimation: A Monte Carlo Study , European Meeting of the Econometric Society, Pisa, Italy.

  16. Derivations based on Pollock I s conventions can be found in Mellander (1984). 3 The solutions for H and X, given below, can also be found in Hendry, op.cit.
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  17. Durbin, J., 1970, Testing for Seria1 Corre1ation in Least Squares Regression When Some of the Regressors Are Lagged Dependent Variables, Econom~tr~ca, 38, pp. 410-421.
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  18. F1etcher, R., 1970, A New Approach to Variable Metric A1gorithms, 13, pp. 31 7- 3 2 2 • Fletcher, R. and Powel1, M.J • D., 1963, A Rapid1y Convergent Descent Method for Minimization, Comp~~u~, pp. 163-168.
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  19. Farebrother, R.W., 1980, The Durbin-Watson Test for Seria1 Corre1ation when There Is No Intercept in the Regression, Ec~nometr:!:.~~, 48, pp. 1553-1563.
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  20. Fischer, F.M., 1966, The__!.dentif!catio~.!,~,!~~~ Eco~~~~, New York, McGraw-Hi11.
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  21. GICOF.DAT <) 1.E-lO <) 78 l 2 7 22 2 22 2 7 - 55 -EXPORT SYSTEM ACC. TO GOLDSTEIN 8< KHAN (1978). ESTIMATlON PERIOD 1960-80. 12 1 2 1 1 O -1.0 1 3 1 0.0 O 1 1.0 1 2 1 4 1 0.0 (> 1 -1. O 1 :3 1 5 1 0.0 <) 1 1.0 1 4 l :3 1 1.0 l -1. (> 1 2: 1 2 <). <) 1 O 1. (I (> 1 1.0 5 1.0 5 7 220 -1.0 2 :3 2 0.0 O 1 1.0 O l -1. O 5 6 1.0 5 7 262 o. O (> l l. (I (I l 1. O 5 7 1.0 5 7 272 0.0 O 1 1.0 (I l -1.0 5 8 1.0 5 7 292 1.0 (I (I 1.0 O 1 1. (I 5 7 l 2 l 0.0 O 1 1. O 1 :3 Notice that LP=Q since the first estimation is to be performed with B=O. Further, MXFN has been set to zero, in order to obtain a printout of the input in RESFl.DAT. As indicated by IFO (first number on the fourth line) the first row of the matrix in DATAM.DAT should be ignored.
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  22. Haessel, W., 1978, Heasuring Goodness of Fi t in Linear and Nonlinear Models , Southern Economic: :.._~~urnal, 44, pp. 648-652.
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  23. Hausman, J .A., 1983, Specification and Estimation of Simultaneous Equations Models, in: Z.Griliches and M.D. Intrilligator (eds.), Handbo~ ok ._.9.;g_~c~no~ics, Vol I, Amsterdam, NorhHolland.
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  24. Hendry, D.F., 1971, Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by aVector Autoregressive Process, Int~~n~~~~!.._~<?.9Eomic ~e~, 12, pp. 257-271.

  25. Hendry, D.F., 1974, Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by aVector Autoregres s i ve Proces s: A Correction , Inte~~~= tional_?conomic Re~iew, IS, p. 260.

  26. Hendry, D.F., 1976, The Structure of Simultaneous Equations Estimators , Journal of Econometrics, 4, pp. 51-78.

  27. Holly, A. and Monfort, A., 1982, Like1ihood Ratio Test, Wa1d Test and KuhnTucker Test in Linear Models with Inequa1ity Constraints on the Regression Parameter II , Econometrica, 50, pp. 63-80. - 71 -Greenberg, E. and Webster, ced Econometrics: A Jr, C.E., 1983, Advanto the Literature New York, John Wiley and Sons.
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  28. It might be remarked that the extremely high value of Berndt's generalized R2 measure~ 0.99999997, is not due to a misprinting of the formula in see. 5.3. Rather, it has been caused by the eombined effees of a short time series and a general tendeney of this measure to lie very elose to unity. fR2 :S of almost the same magnitude are reported in Berndt and Khaled (1979, p.1235)l.
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  29. Jansson, L. and Mellander, E., 1983, under Non-linear Constraints , ters, Il, pp. 343-346.
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  30. Lau, L.J., 1978, Testing and Imposing Monotonicity, Convexity and Quasi-Convexity Constraints , in M. Fuss and D. ~1cFadden (eds.) Production Economics: A Dual Approach to TheorL~nd Applicati0!1s, Vol. I, Amsterdam, North-Hol1and. - 72 -Maddala, G.S., 1978, New York, f\1cGraw-Hill.
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  31. llonnacott, R.J. and Wonnacott, T.H. I 1970, Economet ~ic~, New York, John Wiley and Sons.
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  32. Magnus, ,J.R. and Neudecker, H., 1979, The Commutatation Matrix: Some Properties and Statistical Applications, Ann~!.~~~~~tistics, 7, pp. 381-394.
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  33. Manual, 6:th printing, 1975. 2 Since the double precision has been implemented using the IMPLICIT statement, it can easily be eliminated if deemed unnecessary, however.
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  34. Mellander, E., 1984, Härledning av informationsmatrisen när residualerna genereras aven vektorautoregressiv process och parametrarna lyder under icke-lineära restriktioner (Derivation of the Information matrix when the errors are generated by avector autoregressive process and the parameters obey nonlinear constraints.) Mimeographed.
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  35. Neudecker, H., 1969, Sorne Theorems on Matrix Differentiation with Special Reference to Kronecker Products , Journal of the American Sta-r:..i:.~_Associa_tion, 64, pp. 953-963.
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  36. Optimization Economic LetJudge, G.G., Griffiths, W.E., Hill, R.C. and Lee, T.C., 1980, The_Th~S?Ey__and~~ractice of Econometric~, John Wiley and Sons, New York.
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  37. Pollock, D.S.G., 1979, The~l9:e~r~.2~Econ~me.!Eics Chichester, John Wiley and Sons.
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  38. Quandt, R.E., 1983, Computational Problems and Methods, in: Z. Griliches and M. D. Intrilligator (eds. ) , ~~b0<2~_<?..~_~con~!.ri:.cs, Vol I, Amsterdam, North-Holland.

  39. Rothenberg, T.J., 1971, Identification in Parametric Models , Eco~o~~t~~ca, 39, pp. 577-591.

  40. TheiJ_, H. , 1983, Linear Algebra and Matrix Methods in Econmetrics fl, in: Z. Griliches and M.D. Intril1igator (eds.), Handbook of Econometrics, Vol I, Amsterdam, North-Hol-~--------land.
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