Abstract
“In May of 1972 a meeting of economists and control engineers was arranged at Princeton University by three economists (Edwin Kuh, Gregory Chow and M. Ishaq Nadiri) and a control engineer (Michael Athans). The meeting which was attended by 40 economists and 20 engineers was to explore the possibility that the application of stochastic control techniques, which had been developed in engineering, would be useful in economics as well” (Kendrick, 2002, p. 3). Indeed the application of control theory to economic problems dates back to the mid-to-late fifties (Phillips, 1954, 1958; Holt et al., 1960).1 However, it is only in the seventies, right after the meeting just mentioned, that it gained momentum (Athans and Chow, 1972; Chow, 1975; Fair, 1974; Kendrick, 1976; Turnovsky, 1977). These were the days when the economy was compared to an aircraft and economists were working on an automatic pilot able to drive it through turbulences with the minimum cost. The main problem was ‘fine-tuning’ the economy.
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Notes
See Kendrick (2002) for a lively account of the `birth’ of control methods in economics.
See also Easley and Kiefer (1988) for the general problem of controlling a stochastic process with unknown parameters.
The original references for the KF are Kalman (1960) and Kalman and Bucy (1961).
The term `robust’ is here used in a loose sense and bears no relationship with the concept of `robust control’ used, among the others, in Basar and Bernhard (1995), Bernhard (2002), Hansen et al. (1999), Hansen and Sargent (2001), Tetlow and von zur Muelhen (2001) and Whittle (1990).
See, e.g., Johnston (1984, pp. 415–419) for an introduction to adaptive regression models.
This is due to the fact that most of the econometric theory, both in finite samples and asymptotically, is based on the stationarity assumption and not all results valid for this case hold in the non-stationary case. See, e.g., Van der Meer et al. (1999), Tucci (1995, pp. 251–253), Hamilton (1994, Ch. 13) and the references therein cited. An example of a procedure, based on KF, used to estimate a model with non-stationary parameters can be found in Harvey (1981a, pp. 204–207; 1989, pp. 408–411 ).
Only the coefficients of the exogenous or predetermined variables, or the reduced form parameters, can be assumed to vary stochastically. See, e.g. Tsurumi and Shiba (1982), Swamy (1971) and Raj et al. (1980).
See, e.g., Akerlof and Yellen (1985), Ball et al. (1988), Ball and Romer (1991), Blanchard (1983), Fischer (1977), Mankiw (1985) and Taylor (1979b).
Modeling parameters as TVPs following a `Return to Normality’ boils down to using “a linear regression model with fixed coefficient but serially autocorrelated and heteroscedastic disturbances” (Judge et al., 1985, p. 810). Therefore testing for the presence of this type of parameters reduces to testing for the presence of autocorrelation and heteroscedasticity in the residuals.
See Intriligator (1971, Ch. 11) for a nice introduction to the control problem. As stated there “a functional is a real valued function defined on a set of functions, that is the domain is a set of functions ” (Intriligator, 1971, p. 454 ).
See Pesaran (1989, pp. 88–96) for a nice comparison of the various solution techniques discussed in the literature.
See, e.g., Broze and Szafarz (1991, pp. 40–49) for a nice discussion on uniqueness, parametric non-uniqueness and non-parametric non-uniqueness.
For instance, as will be seen in Ch. 7.2, in the simple Cagan’s (1956) hyper-inflation model the set of infinite ARMA solutions existing when the parameter associated with the future expectation of the endogenous variable is greater than one, in absolute value, is given in terms of one free parameter.
See also Cuthbertson et al. (1992, p. 161).
For a nice introduction to the `general-to-specific’ methodology developed largely by Sargan and his associates at the London School of Economics see Cuthbertson et al. (1992, Ch. 4). A discussion of the implementation of this methodology in a computer code can be found in Krolzig and Hendry (2001).
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Tucci, M.P. (2004). Introduction. In: The Rational Expectation Hypothesis, Time-Varying Parameters and Adaptive Control. Advances in Computational Economics, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4020-2874-8_1
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