Econometrics Final

panel data

contains observations on multiple entities where each entity is observed at two or more points in time; solves OVB

Why is panel data useful?

we can control for factors that (1) vary across entities but to not vary over time and (2) could cause OVB

entity fixed variables (Z_i)

omitted variables that vary across entities but do not change over time; n different intercepts; 1 slope for all entities

time fixed variables

an omitted variable might vary over time but not across entities; intercepts change over time

entity and time fixed effects together

use entity demeaning and (T - 1) dummies

clustered standard errors

needed because observations for the same entity are not independent because it’s the same entity; allows for errors to be correlated within clusters (entities)

linear probability model (LPM)

predicted value is a probability; coefficients is the difference in probability

probit model

models probability that Y=1 using the cumulative standard normal distribution function

logit model

models probability of Y=1 using the cumulative standard logistic distribution function

maximum likelihood estimator (MLE)

value of B0 and B1 that maximize the likelihood function

measures of fit for binary dependent variables

(1) fraction correctly predicted (2) pseudo-R²

pseudo-R²

measures fit using likelihood function; measures improvement in value of log likelihood, relative to having no X’s

instrumental variables solve

(1) OVB (2) simultaneously causality bias (3) error-in-variables (4) sample selection bias

identification (for IV)

a parameter is said to me identified if different values of the parameter would produce different distributions of the data; depends on number of instruments (m) and number of endogenous regressors (k)

overidentified

m > k

underidentified

m < k

how to test for relevance of IV

F-test; weak if first stage coefficients are zero or nearly zero; weak if first stage F-statistic < 10

how to test for exogeneity of IV

J-test

J-test

(1) estimate equation of interest using TSLS and all m instruments; compute predicted values Y using X to estimate the second stage (2) compute residuals (3) regress u against Z,W (4) compute F-statistic testing hypothesis that Z are all zero 5) J-statistic is J = mF

threats to internal validity for experiments

failure to randomize, partial compliance, attrition, experimental effects

threats to external validity for experiments

nonrepresentative sample, nonrepresentative treatment, general equilibrium effects

time series data

data collected on the same observational unit at multiple time periods

use time series data for

(1) forecasting models (2) estimate dynamic causal effects

AR(p) model

uses p lags of Y as regressors; use t or F-tests to determine lag order p

ADL(p,r) model

use when there are other variables that might be useful predictors of Y; p = lags of Y, r = lags of X

HAC standard errors

use HAC because u is serially correlated; robust to both heteroskedasticity and autocorrelation

how to identify number of lags for dynamic causal effects regression

truncation parameter: m = 0.75(T)^1/3

LSA #1 for panel data

E(u | X, a) = 0; no omitted lagged effects; there is not feedback from u to any future X

LSA #2 for panel data

(X,u) are iid draws from their joint distribution; satisfied if entities are randomly sampled from their population by simple random sampling; does not require observations to be iid over time for the same entity

LSA #3 for panel data

(X,u) have finite fourth moments

LSA #4 for panel data

there is no perfect multicollinearity