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

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

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

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

Consistency e Under the Gauss-Markov assumptionS OLS IS BLUE, but in other cases it wont always be possible to find unbiased estimators o In those cases, we may settle for estimators that are consistent, meaning as n→>∞,the distribution of the estimator collapses to the parameter value Economics 20- Prof anderson

Parallels with Simple regression Bo is still the intercept B, to Bk all called slope parameters u is still the error term(or disturbance) Still need to make a zero conditional mean assumption, so now assume that E(lx,x2…,x)=0 Still minimizing the sum of squared residuals. so have k+l first order conditions Economics 20- Prof anderson

Ch.8 Nonspherical Disturbance This chapter will assume that the full ideal conditions hold except that the covari- ance matrix of the disturbance, i.e. E(EE)=02Q2, where Q is not the identity matrix. In particular, Q may be nondiagonal and / or have unequal diagonal ele- ments Two cases we shall consider in details are heteroscedasticity and auto-