Co-integration, Error Correction, and the Econometric Analysis of Non-stationary Data
David's early exposure to and understanding of error correction models— what are now called equilibrium correction models—lay the foundation for his contributions to cointegration, including the book by Banerjee, Dolado, Galbraith and Hendry (1993) titled Co-integration, Error Correction, and the Econometric Analysis of Non-stationary Data.
In the late 1960s and early 1970s, David had learned from the equilibrium correction models in Sargan (1964) how to model in differences and in levels of economic variables. A decade prior to Sargan's paper, Bill Phillips (1954)—of Phillips curve fame and also at LSE—had analysed integral, proportional, and derivative control in formulating economic policy. Phillips's framework was also equilibrium correction; see in addition Smith (1926) and Mills (2011).In the early 1970s, David, with James Davidson, began modelling UK consumers' expenditure in an equilibrium correction framework, eventually published as Davidson, Hendry, Srba and Yeo (1978). At the same time, David and Gordon Anderson were modelling building societies, which are the British analogue of the US savings and loans associations. David discussed that work in his invited presentation at the August 1975 Toronto Econometric Society World Congress, showing that a system of equilibrium corrections could offset non-stationarity; see Hendry and Anderson (1977).
A major turning point came shortly thereafter during David's sabbatical in the USA. In November 1975, Chris Sims and the Minneapolis Fed sponsored a conference “New Methods in Business Cycle Research”. In a presentation at the conference, Clive Granger critiqued the then common poor econometrics of static regressions involving trending data, showing in particular that a high R2 and a low Durbin-Watson statistic were diagnostic of misspecification and indicative of a nonsense regression in the sense of Yule (1926).
As an alternative, Clive proposed modelling differences of the variables, as advocated by Box and Jenkins (1970).David was a discussant for Clive's presentation. While sympathetic to Clive's critique, David thought that the common factor interpretation of error autocorrelation—in combination with equilibrium correction models— resolved the problem of nonsense regressions better than did differencing. Moreover, equilibrium correction models retained the economics. Clive's and David's presentations were subsequently published in the conference volume as Granger and Newbold (1977) and Hendry (1977).
At the conference, Clive was sceptical about relating differences to lagged levels, as in an equilibrium correction framework, and he doubted that the correction in levels could be stationary. Differences of the data did not have a unit root, whereas their lagged levels did. Investigating that issue helped Clive discover cointegration, with results published initially in Granger (1981, 1986), Granger and Weiss (1983), and Engle and Granger (1987). In his Nobel Prize Lecture, Clive gives an amusing account of his interchange with David at the Minneapolis conference:
A colleague, David Hendry, stated that the difference between a pair of integrated series could be stationary. My response was that it could be proved that he was wrong, but in attempting to do so, I showed that he was correct, and generalized it to cointegration, and proved the consequences such as the errorcorrection representation... (Granger 2004: 363).
Clive's development of cointegration also resolved the debate between modelling in levels and modelling in differences, as David discussed in Hendry (2004).
In mid-1983, David visited Rob Engle and Clive Granger in San Diego and returned to Oxford all enthused about testing for cointegration. That rapidly resulted in one of the very first empirical applications of the Engle- Granger test for cointegration—Hendry and Ericsson (1983), later published as Hendry and Ericsson (1991a); see Section 5.3.
David's interest in cointegration led to an explosion of research activity: two special issues on cointegration for the Oxford Bulletin of Economics and Statistics, published as Hendry (1986a) and Banerjee and Hendry (1992a); a number of papers, including Banerjee, Dolado, Hendry and Smith (1986), Hendry (1986b), Hendry and Neale (1988, 1991), Banerjee and Hendry (1992b), and Campos, Ericsson and Hendry (1996); and the book by Banerjee, Dolado, Galbraith and Hendry (1993). The last was prompted in part by innovative mathematical statistics that use Wiener processes to help describe the limiting distributions of unit-root processes, as developed by Phillips (1986, 1987), Stock (1987), Johansen (1988), Chan and Wei (1988), and others. David felt that the power and generality of that new approach would dominate the future of econometrics, especially since some proofs became easier, as with the forecast-error distributions in Clements and Hendry (1996a, b).
The key insight with cointegration, though, was conceptual. In the Granger representation theorem in Engle and Granger (1987), the data are integrated and cointegrated because the number of distinct equilibrium correction terms is less than the number of decision variables. Johansen (1988) formalised that property as reduced-rank feedbacks of combinations of levels onto growth rates. Cointegration also explained and helped reinterpret many earlier results.
For instance, in Sargan (1964), the equilibrium relationship involved real wages relative to productivity, with the measured disequilibrium determining future wage rates, given current inflation rates. Likewise, in Davidson, Hendry, Srba and Yeo (1978), disequilibrium between consumers’ expenditure and income affected future growth in expenditure; and Hendry (1980) showed that “nonsense regressions” could be both created and detected.
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