Dynamic Econometrics
Dynamic Econometrics provides a systematic framework for empirical modelling of economic data, focusing on economic time series. Drawing on a likelihood approach, this book lays out the economic and statistical underpinnings for empirical modelling, develops a typology of dynamic models, and ties the statistical theory of reduction to exogeneity, model evaluation, diagnostic testing, encompassing, and model design.
The concept of a data generation process (DGP) is central to the theory of reduction, which implies that empirical models are derived from that DGP, rather than being autonomous constructs. This framework also allows a direct and unified analysis of many traditionally ad hoc “problems” in econometrics, such as residual autocorrelation and het- eroscedasticity, simultaneity, measurement errors, data mining, misspecification, nonsense regressions, causality, expectations, structural breaks, and the Lucas critique. Constructively, Hendry (1995) provides a progressive research strategy for empirical econometric modelling that embodies both economic theory and data features, explicitly allowing for evolution in the data's structure and in economic theory itself. The empirical studies in Section 5 exemplify that progressive research strategy, and Hendry and Nielsen (2007) further develop the likelihood basis for this approach.David's education set the stage for Dynamic Econometrics. He was motivated to study economics in Aberdeen and then in London because he saw unemployment, living standards, and equity as important issues. A scientific approach to their understanding required quantification, however, which led him to econometrics—and thence to econometric methodology—to determine what could be learnt from non-experimental empirical evidence. In David's view, if econometrics could develop good models of economic reality, economic policy decisions could be significantly improved.
Since policy requires causal links, economic theory plays a central role in model formulation. However, being highly abstract and simplified, economic theory could not be the sole basis for model formulation. Data and their analysis are crucial, with much variation in the data being due not to economic factors but to “special events” such as wars and major changes in policy, institutions, and legislation. Failure to account for these special events can obfuscate the role of economic forces in an empirical model.Then, as now, the “conventional” approach to modelling was to write down the economic theory, collect variables with the same names (such as consumers' expenditure for consumption), develop mappings between the theory constructs and the observations, and then estimate the resulting equations. That approach often ignored institutional aspects and inter-agent heterogeneity, as well as inherent conflicts of interest between agents on different sides of the market. Nevertheless, economists often believed their theories to such an extent that they retained them, even when the theories were strongly rejected by the data.
David had learned that the conventional approach did not work well empirically and that the straitjacket of that approach meant that one understood neither the data nor economic behaviour. Instead, David tried a more data-based approach, in which economic theory provided guidance rather than a complete structure—but that approach required developing concepts of model design and modelling strategy.
David's approach has four basic stages, beginning with an economic analysis to delineate key economic factors. The next stage embeds those factors in a general empirical model that also allows for other potential determinants and relevant special features. Then, the congruence of that general model is tested. Finally, the general model is simplified to a parsimonious undominated congruent final selection that encompasses the original model, thereby ensuring that all reductions (aka simplifications) are valid.
Chris Gilbert (1986) contrasted the conventional approach and David's approach, nicknaming the two as the “Average Economic Regression” (AER) and “Professor Hendry's Econometric Methodology”. While the latter is often known as the “LSE” or “Hendry” approach, David is the first to acknowledge that many other individuals have also contributed to it and that not all of those individuals have been at LSE. Moreover, David himself has now spent most of his professional career at the University of Oxford, not LSE.
When David began developing his approach, the first tractable cases for general-to-specific modelling were linear dynamic single equations, where a key issue was choice of appropriate lag length. That said, the general-to- specific principle applies to all econometric modelling, albeit with some complications for nonlinear settings; see Trivedi (1970), Mizon (1977) and Hendry (1984a) for early empirical and theoretical contributions. Many other aspects followed, such as developing a taxonomy for model evaluation, orthogonalising variables, and recommencing an analysis at the general model if a rejection occurs. Additional developments expanded this approach to system modelling, in which several (or even all) variables are treated as endogenous; see Hendry, Pagan and Sargan (1984). Cointegration is easily analysed as a reduction in this framework. So is encompassing of the VAR and determining whether a conditional model entails a valid reduction; cf. Mizon (1995) and Hendry (1997). David's empirical research embodies these features of model construction, as Section 5 details. Sections 2.3 and 3 discuss how his approach could be and was automated with machine learning, resulting in the Autometrics feature of his and Jurgen Doornik's econometrics software package OxMetrics.
Dynamic Econometrics is the largest single project in David's professional career, and it had several false starts. In 1972, the large Italian public holding company IRI invited David and his former LSE classmate Pravin Trivedi to publish (in Italian) a set of lectures on dynamic modelling.
In preparing those lectures, David and Pravin became concerned that conventional econometric approaches camouflaged misspecification. Rather than resulting directly in a book, that process laid out a research agenda that included a general analysis of misspecification, as in Hendry (1973, 1975); the unified treatment of econometric estimators, in Hendry (1976); and empirical model design, systematised in Hendry and Richard (1982, 1983) and Hendry (1983, 1987a).In the 1980s, David visited Duke University on a regular basis and again attempted to write the book—this time with Bob Marshall and Jean-Franςois Richard. Common factors, the theory of reduction, equilibrium correction, cointegration, encompassing, and exogeneity had already clarified the empirical analysis of individual equations; and powerful software with recursive estimators implemented the ideas.
Modelling complete systems raised new econometric and operational issues, so David and colleagues wrote the software package PcFiml, now part of OxMetrics; see Section 3. PcFiml ensures that system modelling begins with the unrestricted system, which is first checked for congruence. Modelling then reduces that system to a specific model thereof, tests over-identification, and encompasses the VAR; see Hendry, Neale and Srba (1988), Hendry and Mizon (1993), and Doornik and Hendry (1994). This work paralleled and drew on concurrent developments in system cointegration by S0ren Johansen, Katarina Juselius, and others in Copenhagen; see Johansen (1988, 1995), Johansen and Juselius (1990), and Juselius (2006). A daunting list of topics still remained, including general-to-specific modelling and diagnostic testing in systems, model reliability, and the role of inter-temporal optimisation theory. Bob and Jean-Franςois became more interested in auctions and experimental economics, so their co-authorship lapsed.
In the late 1980s, David circulated a first full draft of Dynamic Econometrics for comments, drawing extensively on help from Duo Qin and Carlo Favero.
In Oxford, Duo had transcribed David's course lectures, themselves based on earlier draft chapters, and Carlo had drafted answers for the solved exercises. The final manuscript still took years more to complete.As published, Dynamic Econometrics systematically covers a vast array of topics in econometric modelling and is almost 1000 pages long, 6 cm thick, and heavy—which David has jokingly remarked makes it useful as a doorstop. David dedicated the book to his wife Evelyn and their daughter Vivien. The dedication was much more than perfunctory. Evelyn and Vivien not only facilitated time to work on ideas and visit collaborators, tolerated numerous discussions on econometrics, and corrected grammar; Vivien—a professional economist in her own right—worked through analyses and helped debug the software.
Dynamic Econometrics notably and deliberately omitted several major strands of David's research, as they were being published elsewhere. Those strands include Monte Carlo methodology, in Hendry (1984b) and Hendry, Neale and Ericsson (1990); numerical issues and econometric software, in Hendry (1976), Hendry and Srba (1977, 1980), and Doornik and Hendry (1992, 1994); the history of econometrics, in Hendry and Morgan (1995); forecasting, in Clements and Hendry (1994, 1998a, b, 1999a, 2002a); and cointegration in Hendry (1986a), Banerjee and Hendry (1992a), and Banerjee, Dolado, Galbraith and Hendry (1993). On the last, Dynamic Econometrics lacks an extensive discussion of cointegration—a surprising omission, given David's interest in and major contributions to cointegration and equilibrium correction. However, because (co) integrated series can be reduced to stationarity, much of Dynamic Econometrics assumes stationarity, allowing Dynamic Econometrics to focus on modelling per se. Fittingly, the next subsection turns to cointegration.
2.2