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