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**Unformatted text preview: **Economics 20 - Prof. Anderson 1 Time Series Data y t = β + β 1 x t1 + . . .+ β k x tk + u t 1. Basic Analysis Economics 20 - Prof. Anderson 2 Time Series vs. Cross Sectional Time series data has a temporal ordering, unlike cross-section data Will need to alter some of our assumptions to take into account that we no longer have a random sample of individuals Instead, we have one realization of a stochastic (i.e. random) process Economics 20 - Prof. Anderson 3 Examples of Time Series Models A static model relates contemporaneous variables: y t = β + β 1 z t + u t A finite distributed lag (FDL) model allows one or more variables to affect y with a lag: y t = α + δ z t + δ 1 z t-1 + δ 2 z t-2 + u t More generally, a finite distributed lag model of order q will include q lags of z Economics 20 - Prof. Anderson 4 Finite Distributed Lag Models We can call δ the impact propensity – it reflects the immediate change in y For a temporary, 1-period change, y returns to its original level in period q +1 We can call δ + δ 1 +…+ δ q the long-run propensity (LRP) – it reflects the long-run change in y after a permanent change Economics 20 - Prof. Anderson 5 Assumptions for Unbiasedness Still assume a model that is linear in parameters: y t = β + β 1 x t1 + . . .+ β k x tk + u t Still need to make a zero conditional mean assumption: E( u t | X ) = 0, t = 1, 2, …, n Note that this implies the error term in any given period is uncorrelated with the explanatory variables in all time periods Economics 20 - Prof. Anderson 6 Assumptions (continued) This zero conditional mean assumption implies the x’s are strictly exogenous An alternative assumption, more parallel to the cross-sectional case, is E( u t | x t ) = 0 This assumption would imply the x’s are contemporaneously exogenous Contemporaneous exogeneity will only be sufficient in large samples Economics 20 - Prof. Anderson 7 Assumptions (continued) Still need to assume that no x is constant, and that there is no perfect collinearity Note we have skipped the assumption of a random sample The key impact of the random sample assumption is that each u i is independent Our strict exogeneity assumption takes care of it in this case Economics 20 - Prof. AndersonEconomics 20 - Prof....

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