6 the model should be able to encompass a range of

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(6) THE MODEL SHOULD BE ABLE TO ENCOMPASS A RANGE OF ALTERNATIVE MODELS. Do not worry if these some of these concepts appear incomprehensible at the moment; they should not do so later. After reading these notes, you may like to turn for more explanation and discussion to Gilbert (1986) [easy], and Hendry and Richard (1982,1983) [quite technical]. Time series modelling usually involves a search to find a satisfactory model. This search involves going through a variety of steps. The criteria of an adequate model listed above apply primarily to any model which we deem to be the final outcome of our empirical search. If any of these conditions is not met in our final model, we cannot regard the model as satisfactory. However, with some exceptions to be explained later, criteria (1), (3), (4) and (5) apply at every point of the empirical investigation, and so any 'interim' model obtained during a search procedure should satisfy these conditions. If it does not, it is not a valid basis for subsequent statistical inference [C] ECONOMIC THEORY Criterion (2) requires that our model be consistent with some economic theory - any results we obtain must be explicable in terms of some economic model. Statistical adequacy alone is not enough. We will focus, by way of example, on a data set that is (we hope) consistent with the theory of consumers’ expenditure. Let us assume that economic theory suggests a long run equilibrium relationship of the form C = AW Y α β ( 1) where C is real (constant price) total consumers' expenditure, W is the real value of consumers; gross wealth Y is real personal disposable income α , β and A are constant parameters. Taking logs of (1) we obtain the following long run relationship which is linear in both parameters and (transformed) variables: c = a + w + y α β (1b) where lower case letters denote natural logarithm transformations of the corresponding upper case variables. INTERPRETATION OF PARAMETERS Parameters are partial derivatives, and therefore show the effect on the dependent variable of a unit change in the value of one explanatory variable, given that other explanatory variables remain constant. Thus, in equation (1b), β = c/ y, and so gives the impact on c of a unit change in y. As c and y are in logarithms, it follows that β = ( C/C)/( Y/Y) where C and Y are the untransformed variables (not in logarithms). So β , is the elasticity of C with respect to Y. In all models in which variables are in natural log form, parameters can be interpreted as elasticities in this way. D ECONOMETRIC ANALYSIS D1: STATICS AND DYNAMICS: EQUILIBRIUM AND ADJUSTMENTS TO EQUILIBRIUM Suppose that we have time series data on Y t and X t , t=1,...,T and that we write the regression model counterpart to (0) as Y = + X + u t = 1,...,T t t t β β 1 2 ( 2) Equation (2) is an example of a static econometric model. Only current-dated values of any variable enter the 2
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model; it contained no lagged or lead values of variables. It will usually be a poor starting point for applied work, as it embodies no information about the behaviour of agents outside equilibrium. Since disequilibrium states are likely in many economic processes, we should allow for these in our modelling exercise. This also
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