Hypothesis testing If F>F refuse H the restriction(s) imposed by the theory is not valid ( statistically speaking), reject the restricted least squares regression. use the standard ols method If F<F, accept H the given restriction is valid, the rls regression is preferred to ULS
Hypothesis testing: If F>Fc , refuse H0 , the restriction(s) imposed by the theory is not valid （statistically speaking）, reject the restricted least squares regression , use the standard OLS method. If F<Fc , accept H0 , the given restriction is valid, the RLS regression is preferred to ULS
14.2 Dynamic Economic Models Autoregressive and Distributed Lag models ■1。 Definition Dynamic models/ Distributed lag models There is a non-contemporaneous, or lagged, relationship between Y and the x for the effect of a unit change in the value of the explanatory variable is spread over. or distributed over. a number of time periods
14.2 Dynamic Economic Models: Autoregressive and Distributed Lag Models ◼ 1. Definition Dynamic models/ Distributed lag models: －－There is a non-contemporaneous, or lagged, relationship between Y and the Xs , for the effect of a unit change in the value of the explanatory variable is spread over, or distributed over, a number of time periods
The reasons of the dependent variable respond to a unit change in the explanatory variable(s)with a time lag Psychological reasons Technological reasons, such as the purchase of PC, automobile Institutional reasons, such as multiyear contracts
The reasons of the dependent variable respond to a unit change in the explanatory variable(s) with a time lag. · Psychological reasons. · Technological reasons, such as the purchase of PC, automobile · Institutional reasons, such as multiyear contracts
k-period distributed lag model Y=A+B义+B义+B2X2+…+B义tA+ut(1413) Bo>B>B2 The effect of a unit change in the value of the explanatory variable is felt over k periods. B: the short-run /impact multiplier, which means “ the change in the mean value of Y following a un此t change in× in the same period” (B +B ).(B +B, +B,): interim/intermediate multipliers “… in the next, following period” ∑ B,=Bo+B,+B,+.+B, long-run/total multiplier. =n
k-period distributed lag model Yt=A+B0Xt+B1Xt-1+B2Xt-2+…+BkXt-k+ut （14.13） B0＞B1＞B2 The effect of a unit change in the value of the explanatory variable is felt over k periods. ◼ B0 : the short-run /impact multiplier, which means “the change in the mean value of Y following a unit change in X in the same period” ◼ (B0+B1 ),(B0+B1+B2 ):interim/intermediate multipliers. “ ………in the next, following period” long-run/total multiplier. = = + + + + k i n Bi B0 B1 B2 Bk
2. Problems in estimation of distributed Lag Models. The distributed lag model (14.13) does not violate any of the standard assumptions of the classical linear regression model(CLRM), but when we use the ols to estimate. there are some practical problems: (1 Economic theory does not tell us how many lagged values of the explanatory variables should be introduced
◼ 2.Problems in estimation of Distributed Lag Models: The distributed lag model （14.13） does not violate any of the standard assumptions of the classical linear regression model (CLRM), but when we use the OLS to estimate, there are some practical problems: （1）Economic theory does not tell us how many lagged values of the explanatory variables should be introduced