Lecture1

Makes statistical sense as it helps to avoid omitted

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makes statistical sense as it helps to avoid omitted variables bias arising from the wrong exclusion of dynamic adjustment processes. Dynamic models are those which contain lagged or leading values of variables, as well as current-dated ones. There are many forms such models can take. For example: Y t = β 1 + β 2 X t + β 3 X t-1 + u t is a distributed lag model (a single distributed lag in X in this case) Y t = β 1 + β 2 X t + β 4 Y t-1 + u t is an autoregressive model (a single autoregressive term in Y in this case) Y t = β 1 + β 2 X t + β 3 X t-1 + β 4 Y t-1 + u t is an autoregressive-distributed lag model (in this case, of order 1 in the autoregressive component and of order 1 in the distributed lag; this is often written as ARDL(1,1), or alternatively ADL(1,1)). Y t = μ + β 0 X t + β 1 X t-1 +... + β q X t-q + χ 1 Y t-1 + ... + χ p Y t-p + u t is an autoregressive-distributed lag model of order p in the autoregressive component and of order q in the distributed lag; this is often written as ARDL(p,q), or alternatively ADL(p,q)). One simple method of accommodating dynamic adjustment processes into our statistical model is to parameterise the model in the form of an error correction model (ECM). Such an approach has proved very fruitful in applied econometric research. (D2) THE ERROR CORRECTION MODEL For simplicity, suppose that the long run (equilibrium) relationship between Y and X is given by Y = β X (3 ) in which we might interpret Y as consumers’ expenditure and X as consumers’ disposable income. However, consumers make 'mistakes' of some kind, or their plans are frustrated, so that they are not always able to attain their target level of consumption. To capture this, redefine the long run relationship as Y * = β X (4) where Y* is interpreted as the target level of consumption, which may or may not be realised in any period. If Y t is actual consumption at time t, and Y* t is target consumption at time t then, if consumers fail to attain their target level of consumption , (Y* - Y) t measures this error. What kind of behaviour might one expect Y to exhibit over time? First of all, you would expect that the level of Y * would change in response to changes in the level of X. Let us write this as: Y = X t t * θ (5) But consumers will not always be in equilibrium. When out of equilibrium in period t, the error will be (Y * - Y) t . In any period when Y * does not equal Y, the observed consumption-income combination will not be an equilibrium one, and may be represented by a point such as 'a' in Figure 1. Figure 1: The Error Correction Mechanism Now suppose that in period (t+1) the consumer corrects a proportion δ of the period t error. That is, in period (t+1) consumption will change by the amount δ (Y * - Y) t , in addition to any change in Y that is due to a change in X. Consider the case where X increases between periods t and t+1 from X t to X t+1 . Moreover, the consumer is in period t out of equilibrium at the point 'a' in Figure 1. We can represent the overall change in Y as the sum of two components (again as shown in Figure 1).

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