This paper evaluates an empirical model of U.K. money demand developed by Milton Friedman and Anna J. Schwartz in Monetary Trends in the United States and the United Kingdom. Testing reveals misspecification and hence the potential for an improved model. Using recursive procedures on their annual data, we obtain a better-fitting, constant, dynamic error-correction (cointegration) model. Results on exogeneity and encompassing imply that our money demand model is interpretable as a model of money but not of prices, since its constancy holds only conditionally on contemporaneous prices.

[An eight equation dynamic model of aggregate demand in the United Kingdom is estimated by a variety of methods which make different assumptions about, and provide different treatments of, the problems of simultaneity and serial correlation, the latter being both within and between equations. Although the system appears to perform quite well on conventional criteria, the alternative estimators reveal a number of misspecifications and demonstrate the sensitivity of the results to estimators choice. The paper also considers the methodological problems involved in estimating dynamic simultaneous equation models with possibly auto-correlated errors using seasonally unadjusted quarterly data.]

[The finite sample behavior in a dynamic, simultaneous system of least squares and instrumental variables estimators which allow for autoregressive errors is studied by control variable (CV) simulation. To increase simulation precision, the CV's are based on asymptotic approximations to the econometric estimators and so have the same asymptotic distributions, but known finite sample moments. The CV formulae also clarify the properties of the econometric techniques and combined with response surfaces, reduce the specificity of simulation findings. The results confirm the value of asymptotic theory and show that the autoregressive instrumental variables estimator provides a reasonable approach to the simultaneity-autocorrelation-dynamics interaction.]

Macro-economic models are generally designed to achieve a multiplicity of objectives and correspondingly, they have been evaluated using a vast range of statistical, econometric, economic, political and even aesthetic criteria. However, in so far as they claim to represent economic behaviour, empirical macro-economic systems are certainly open to direct evaluation and testing against data information. The last few years have witnessed a substantial growth in the literature on econometric evaluation techniques, but despite important improvements in formalising evaluation procedures and their increased scope, formidable problems confront any investigation of a high dimensional, non-linear, stochastic, dynamic structure. Since system characteristics are the prime concern of economy-wide models, it might be the case that the validity of every individual component is not essential to adequate overall performance. While this viewpoint is debatable it does draw attention to the need for system evaluation procedures, at which point data limitations pose serious constraints on formal tests. Thus a new "limited information" test of forecast encompassing is proposed, based only on forecasts and requiring no other data from a model's proprietors. The derivation, merits and drawbacks of such a test are presented together with some suggestions for testing entailed relationships and inter-equation feedbacks.

Grayham E. Mizon, David F. Hendry; An Empirical Application and Monte Carlo Analysis of Tests of Dynamic Specification, The Review of Economic Studies, Vol

Estimated U.S. M1 demand functions appear unstable, regularly “breaking down,” over 1960–1988 (e.g. missing money, great velocity decline, M1-explosion). We propose a money demand function whose arguments include inflation, real income, long-term bond yield and risk, T-bill interest rates, and learning curve weighted yields on newly introduced instruments in M1 and non-transactions M2. The model is estimated in dynamic error-correction form; it is constant and, with an equation standard error of 0–4%, variance-dominates most previous models. Estimating alternative specifications explains earlier “breakdowns,” showing the model's distinctive features to be important in accounting for the data.

[Definitions are proposed for weak and strong exogeneity in terms of the distribution of observable variables. The objectives of the paper are to clarify the concepts involved, isolate the essential requirements for a variable to be exogenous, and relate them to notions of predeterminedness, strict exogeneity and causality in order to facilitate econometric modelling. Worlds of parameter change are considered and exogeneity is related to structural invariance leading to a definition of super exogeneity. Throughout the paper, illustrative models are used to exposit the analysis.]