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American Economic Review Papers Proceedings 2008 98 2 251 255 http www aeaweb org articles php doi 10 1257 aer 98 2 251 Allowing the Data to Speak Freely The Macroeconometrics of the Cointegrated Vector Autoregression By Kevin D Hoover S ren Johansen and Katarina Juselius an initial condition 1the height of the tower2 determines the distance the ball falls for each time in theory Of course no object conforms perfectly to the gravity law If one had a generous enough notion of approximation if the ball were steel and the initial height were not too high then tight bounds of approximation would work but not if the ball were styrofoam Now there are three choices A2 declare that theory is no good B2 modify the original theory to account for the factors such as air resistance or C2 attempt to assess empirically the combined forces that must be used to adjust the gravity law to its application in the particular case In economics as in physics the difficulty is that our theory holds ceteris paribus When other things are not equal there is always some residual left unexplained which if large may render the theory empirically irrelevant As scientists we can either attempt to elaborate the theory in such a way that fewer and fewer ceteris paribus conditions are invoked B2 or we can attempt to provide an adequate empirical characterization of the factors that determine the initial gap between theory and data 1C2 Strategy C can be seen as the passive analogue to a controlled experiment 1 cf Haavelmo 1944 esp chaps 1 and 22 It has an advantage over B in the sense of providing clues as to how the theory needs to be developed clues that would be helpful in strategy B but for which strategy B itself offers no internal resources What is more strategy C gives some hope of actually isolating the action of the gravity law and therefore in fact testing whether it is a contributing factor to a successful account of the data It is only when we can control for enough of the complicating factors that the underlying quadratic relationship of the gravity law can be detected The extreme limit of strategy B is what Milton Friedman has called the Walrasian methodology by which he refers not to general equilibrium theory per se but to the idea that one must have a complete detailed theoretical All economists agree that reality is complex and that the tools with which we confront it are far simpler Theorists sometimes deal with this gap by asking very little of the data Start with the stylized facts and develop relatively simply theories to account for them Unfortunately stylized facts are often too stylized to discriminate among plausible candidate theories or to provide a basis for accurate quantification Alternative approaches start from the other end and ask much of the data One European tradition which derives from Trygve Haavelmo s The Probability Approach in Econometrics 119442 focuses on obtaining good characterizations of data before testing and on drawing out the implications of data that ought to constrain economic theorizing The application of the cointegrated vector autoregression 1CVAR2 recounted for example in Katarina Juselius s 120062 textbook and facilitated by the CATS in RATS econometric software 1Jonathan G Dennis et al 20062 is a special macroeconometric case of the Probability Approach The message of the Probability Approach and the CVAR approach can be summarized in the slogan facts not stylized facts I Between Data and Theory All econometrics aims ultimately to confront theory and data Different approaches differ in how they conceive the relationship and the problems that it poses To start think of an ideal case such as one might find in a physics textbook The law of gravity is applied to the dropping of a ball from a tower The law together with Hoover Department of Economics Duke University Box 90097 Durham NC 27278 e mail kd hoover duke edu Johansen Department of Economics University of Copenhagen Studiestr de 6 1455 K benhavn K Denmark e mail soren johansen econ ku dk Juselius Department of Economics University of Copenhagen Studiestr de 6 1455 K benhavn K Denmark e mail katarina juselius econ ku dk 251 252 MAY 2008 AEA PAPERS AND PROCEEDINGS account in order to say anything useful about the economy at all 1 see Hoover 20062 The extreme limit of strategy C is a completely atheoretical analysis of data Both extremes are hopeless strategy B because we lack the cognitive capacity to elaborate a complete theory from first principles strategy C because without some prior conceptual notion we would never find a starting place for any investigation Still the Probability Approach leans toward strategy C the weight of the analysis is on characterizing the data and on using the data to criticize and guide theorizing In Friedman s terms the approach is Marshallian or as Hoover 120062 puts it archaeological we learn about the economy a piece at a time by removing the overlay of detritus to uncover the underlying structure guided by our theoretical conception of what we are looking for which is tested and enriched by each new discovery II Models of Theory Models of Data The CVAR approach builds on Haavelmo s 119442 great insight that the gap between theory and data need not be treated as an unstructured residual of approximation but could itself be modeled statistically using the theory of probability The cost is that we now need another level of modeling in addition to theory a statistical model constructed in such a way that a 2 theory has implications interpretable in its terms and b2 data are described fully enough that its only residuals are identically independent random errors that is unsystematic noise The payoff is that such a statistical model warrants the use of likelihood methods and provides a firm basis for deductions about the implications for theory The CVAR approach sees the world as a highly complex dynamic system the properties of which must be inferred from data reflecting a single 1nonreplicable 2 realization of a multivariate path dependent process Naturally this data generating process must be approximated by simpler relationships which characterize the data accurately enough for our particular purposes The statistical model ties economic theory to the data when it nests both the data generating process and the theoretical model Then the parameters of the theoretical model can be read as assertions about parameters of the statistical model which can be tested against the