Time series data y,=Bo+B Brit ◆1. Basic analysis Economics 20- Prof anderson
Economics 20 - Prof. Anderson 1 Time Series Data yt = b0 + b1 xt1 + . . .+ bk xtk + ut 1. Basic Analysis
Time series vs. Cross sectional Time series data has a ter mporal ordering, unlike cross-section data o 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
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
Examples of Time Series models o A static model relates contemporaneous variables: y,= Bo+ B=+ o A finite distributed lag (FDL) model allows one or more variables to affect y with a lag y=0+C=1+8+82+l o More generally, a finite distributed lag model of order g will include g lags of z Economics 20- Prof anderson
Economics 20 - Prof. Anderson 3 Examples of Time Series Models A static model relates contemporaneous variables: yt = b0 + b1 zt + ut A finite distributed lag (FDL) model allows one or more variables to affect y with a lag: yt = a0 + d0 zt + d1 zt-1 + d2 zt-2 + ut More generally, a finite distributed lag model of order q will include q lags of z
Finite Distributed lag models ◆ We can cal all So the impact propensity -it reflects the immediate change in y For a temporary. 1-period change to its original level in period q+7 y returns ◆ We can call S+,+…+ the long-run propensity (lrp)it reflects the long-run change in y atter a permanent change Economics 20- Prof anderson 4
Economics 20 - Prof. Anderson 4 Finite Distributed Lag Models We can call d0 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 d0 + d1 +…+ dq the long-run propensity (LRP) – it reflects the long-run change in y after a permanent change
Assumptions for unbiasedness o Still assume a model that is linear in parameters:y-Bo+ Bx+...+ Bkxuk+ Still need to make a zero conditional mean assumption: E(uX=0, t=1, 2,...,n e 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 5
Economics 20 - Prof. Anderson 5 Assumptions for Unbiasedness Still assume a model that is linear in parameters: yt = b0 + b1 xt1 + . . .+ bk xtk + ut Still need to make a zero conditional mean assumption: E(ut |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