Why Use Instrumental Variables? e Instrumental Variables(IV)estimation is used when your model has endogenous xs That is, whenever Cov(x,l)≠0 Thus. i can be used to address the problem of omitted variable bias 2 Additionally iv can be used to solve the classic errors-in-variables problem Economics 20- Prof anderson

Fixed Effects estimation When there is an observed fixed effect. an alternative to first differences is fixed effects estimation Consider the average over time of y Bx1+…+Bxik+a1+l The average of a, will be ai so if you subtract the mean. a will be differenced out just as when doing first differences Economics 20- Prof anderson

A True panel vs a Pooled cross section Often loosely use the term panel data to refer to any data set that has both a cross sectional dimension and a time-series dimension More precisely it's only data following the same cross-section units over time Otherwise it's a pooled cross-section Economics 20- Prof anderson

Testing for AR(IS eria Correlation Want to be able to test for whether the errors are serially correlated or not Want to test the null thatp=0 in u,=pu, 1 +et=2.. where u is the model error

Stationary Stochastic Process e A stochastic process is stationary if for every collection of time indices 11 e Thus, stationarity implies that the x,'s are dentically distributed and that the nature of any correlation between adjacent terms is

Time series vs Cross sectional e 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

Functional form e We' ve seen that a linear regression can really fit nonlinear relationships 2 Can use logs on RHS, LHS or both Can use quadratic forms ofx's Can use interactions ofx's e How do we know if we've gotten the right functional form for our model? Economics 20- Prof anderson

What is Heteroskedasticity Recall the assumption of homoskedastic implied that conditional on the explanator variables the variance of the unobserved error u was constant If this is not true that is if the variance of u is different for different values of thex's. then the errors are heteroskedastic

Dummy variables a dummy variable is a variable that takes on the value l or o Examples: male(= 1 if are male, O otherwise), south(=l if in the south, 0 otherwise), etc dummy variables are also called binar variables. for obvious reasons Economics 20- Prof anderson

Redefining variables Changing the scale of the y variable will lead to a corresponding change in the scale of the coefficients and standard errors. so no change in the significance or interpretation Changing the scale of one x variable will lead to a change in the scale of that coefficient and standard error, so no change in the significance or interpretation Economics 20- Prof anderson