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

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

Assumptions of the classical Linear Model (Clm) e So far, we know that given the Gauss Markov assumptions, OLS IS BLUE e In order to do classical hypothesis testing we need to add another assumption(beyond the Gauss-Markov assumptions) Assume that u is independent of x,x2…,xk and u is normally distributed with zero mean and variance 0: u- Normal(0, 02) 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

Some Terminology o In the simple linear regression model where y=Bo+ Bx+ u, we typically refer to y as the a Dependent variable, or a Left-Hand Side Variable. or Explained variable, or Regressand

Why study econometrics? Rare in economics(and many other areas without labs! ) to have experimental data Need to use nonexperimental. or observational data to make inferences eImportant to be able to apply economic theory to real world data Economics 20- Prof. Anderson