Mr. Moody

Text

Pindyck and Rubinfeld, Econometric Models and Economic Forecasts (PR) .

Kennedy, Peter, A Guide to Econometrics, Second Edition (K)

References on reserve:

Maddala, G.S. Introduction to Econometrics (M)

Kelejian and Oates, Introduction to Econometrics (KO) HB139.K44

Rao and Miller, Applied Econometrics (RM) HB74.M3R32

Describing the relationship between two variables

Scatter diagrams

Correlation

Simple regression

Estimation and the Theory of Least Squares

Gauss-Markov assumptions

linear function of Y

betahat is random variable with a mean and a variance

betahat is an unbiased estimator of beta

deriving the variance of beta

Gauss-Markov theorem (ols is BLUE)

ols is a maximum likelihood estimator

Properties of estimators

small sample properties: bias, efficiency, mean square error, relative
efficiency, robustness

large sample (asymptotic) properties: consistency, mse, consistency, asymptotic
distributions

consistency "carries over" transformations while unbiasedness
does not

References: M ch 2.6, PR pp. 27-30, RM ch 3, K ch 2,3

Inference and Hypothesis Testing

Assume the error term is distributed normally, then the sampling distribution
of betahat is also normal with

mean = beta (truth)

variance = var(u)/Sum of x2

however, we must estimate var(u)

testing hypotheses concerning beta

confidence intervals

testing the goodness of fit: F test

t, F, and chi-square distributions

Reference: K ch 4

Multiple Regression

Why? Because life is complicated: omitted variable bias

three variable regression model

interpretation of formulas

omitted variables and irrelevant variables

goodness of fit: R2

M ch 4, PR ch 4-5, KO ch 4

dummy variables

References: PR pp. 104-108, 121-123, M pp. 251-266, KO ch 5.2, RM
pp. 88-104, 138-159, K ch 13

Useful Tests

F-test

Chow test

J-test for non-nested hypotheses

Pe test for log-linear vs linear models

Granger causality test

References: PR 110-112, 115-117, 216-219; M 329-331, 443-446

Maximum likelihood and the likelihood ratio test

References: M pp. 83-86, K ch 4.4

Digression: torturing the data until it tells you what you
want to hear:

Leamer, "Let's Take the Con out of Econometrics" American
Economic Review, March, 1983, 31-43.

Econometrics: What if the Gauss-Markov Assumptions
are Violated?

Heteroskedasticity

Definition: nonconstant error variance, a common problem in cross sections

Tests: plot residuals, White

Effects: (1) ols estimates remain unbiased, but (2) inefficient, (3) standard
errors and t-scores are incorrect

Cure: weighted least squares

1.known variances: weighted least squares

2.unknown variances: assume that the error variance is a function of an
observable variable (the usual case)

White's heteroskedastic robust standard errors

References: M ch 5, PR ch 6.1, KO ch 6.3, K ch 7

Specification Bias

Rule: if one or more of the explanatory variables in a regression are correlated with the error term, the resulting ols estimates are biased and inconsistent

Causes of correlation between X and u

incorrect functional form

omitted variables

errors of measurement in the independent variables

simultaneous equations

Errors in variables

Definition

Effects: ols is biased and inconsistent

Cure: instrumental variables (two stage least squares)

Problem: choice between a biased but efficient estimator (ols) and
an unbiased but inefficient estimator (IV) References:
M ch 11.1-11.3, 11.5-11.7, PR ch 7

Simultaneous equations

When an equation is part of a simultaneous equation system, such that causation runs from Y to X as well as X to Y, then X is correlated with the error term and ols is biased and inconsistent.

Example: the consumption function

Endogenous and exogenous variables, structural versus reduced form

Cure: instrumental variables (2sls)

The identification problem

the order condition for identification

Types of equation systems: general, recursive, block recursive

Strategies: ols, ols with lags, reduced form, 2sls, VAR

Basmann test for over-identification restrictions

Hausman test for mis-specification

System estimation methods: ZELS, 3SLS

References: M ch 9, M ch 12.10, PR ch 11; KO ch 7, K ch 9.

Linear Dynamic Models

Autocorrelation

Definition: ut correlated with ut-1 (and/or ut-2, etc.)

Effects

ols remains unbiased

variance of betahat will not be minimum (loss of efficiency)

standard errors will be underestimated and t-scores overestimated

predictions will be inefficient

if regressors include a lagged dependent variable, then ols estimators
will be biased and inconsistent as well as inefficient.

Tests: Durbin-Watson statistic

Breush-Godfrey (Lagrange Multiplier) test

There are two reasons for autocorrelation (1) serial correlation in the error term and (2) omitted variables with time components.

If the autocorrelation is due to omitted lagged variables, then we can't
fix it with Cochrane-Orcutt. We need to test to see if we have serial correlation
or mis-specified dynamics.

Testing for mis-specified dynamics: likelihood ratio test.

Cure: add lags or Cochrane-Orcutt

References: M ch 6,PR ch 6.2, RM ch 3.3, KO ch 6.2, K ch 7.4

Granger and Newbold, "Spurious Regressions in Econometrics" Journal
of Econometrics 2, (1974) 111-120.

Random walks and unit root tests

Cointegration and long run equilibrium

Testing for cointegration

Estimating the cointegrating regression

Spurious regressions

Nonsense and unbalanced regressions

References: Granger "Introduction," P&R ch 15.3, 15.4

motivation: cure for one kind of omitted variable bias,
efficient use of data, increases degrees of freedom

digression: estimating production functions

least squares dummy variables (LSDV) or fixed effects

variance-components or random effects

autocorrelation and heteroskedasticity

Reference: PR ch 9.4

Omitted variable bias

review: multiple regression formula

determining the direction of bias

There is only one way to be right and many ways to be wrong.

It is wrong to include an irrelevant variable (inefficiency)

and it is wrong to leave out a relevant variable (bias).

However, omitting a relevant variable whose value is less than its
standard error will decrease mse's.

proxy variables, M ch 11.6

Wallace noncentral F test for mse

References: PR ch 7.3, 7.5.1; KO ch 6.4, RM pp. 29-67. Goodnight
and Wallace "Operational Techniques and Tables for Making Weak MSE
Tests for Restrictions in Regression." Econometrica (7/72) 699-709

Regression Diagonistics

Influential Observations

Multicollinearity

References: M ch 7, KO ch 6.1