Elements of Econometrics

Random variables and sampling theory:

• Probability distribution of a random variable
• Expected value of a random variable
• Expected value of a function of a random variable
• Population variance of a discrete random variable and alternative expression for it
• Expected value rules Independence of two random variables
• Population covariance, covariance and variance rules, and correlation
• Sampling and estimators
• Unbiasedness Efficiency
• Loss functions and mean square error
• Estimators of variance, covariance and correlation
• The normal distribution
• Hypothesis testing
• Type II error and the power of a test
• T tests
• Confidence intervals
• One-sided tests
• Convergence in probability and plim rules
• Consistency
• Convergence in distribution (asymptotic limiting distributions) and the role of central limit theorems.

Simple regression analysis

• Simple regression model
• Derivation of linear regression coefficients Interpretation of a regression equation
• Goodness of fit.

Dummy variables

• Dummy variables
• Dummy classification with more than two categories
• The effects of changing the reference category
• Multiple sets of dummy variables
• Slope dummy variables
• Chow test Relationship between
• Chow test and dummy group test.

Specification of regression variables

• Omitted variable bias
• Consequences of the inclusion of an irrelevant variable
• Proxy variables
• F test of a linear restriction
• Reparameterization of a regression model (see the Further Material hand-out)
• T test of a restriction
• Tests of multiple restrictions
• Tests of zero restrictions.

Heteroscedasticity:

• Meaning of heteroscedasticity
• Consequences of heteroscedasticity
• Goldfeld–Quandt and White tests for heteroscedasticity
• Elimination of heteroscedasticity using weighted or logarithmic regressions
• Use of heteroscedasticity-consistent standard errors.

Models using time series data:

• Static demand functions fitted using aggregate time series data
• Lagged variables and naive attempts to model dynamics
• Autoregressive distributed lag (ADL) models with applications in the form of the partial adjustment and adaptive expectations models
• Error correction models
• Asymptotic properties of OLS estimators of ADL models, including asymptotic limiting distributions
• Use of simulation to investigate the finite sample properties of parameter estimators for the ADL(1,0) model
• Use of predetermined variables as instruments in simultaneous equations models using time series data.

Autocorrelation:

• Assumptions for regressions with time series data
• Assumption of the independence of the disturbance term and the regressors
• Definition of autocorrelation
• Consequences of autocorrelation
• Breusch–Godfrey lagrange multiplier, Durbin–Watson d, and Durbin h tests for autocorrelation
• AR(1) nonlinear regression
• Potential advantages and disadvantages of such estimation, in comparison with OLS. Cochrane–Orcutt iterative process
• Autocorrelation with a lagged dependent variable
• Common factor test and implications for model selection
• Apparent autocorrelation caused by variable or functional misspecification
• General-to-specific versus specific-to-general model specification

Properties of the regression coefficients

• Types of data and regression model.
• Assumptions for Model A.
• Regression coefficients as random variables.
• Unbiasedness of the regression coefficients.
• Precision of the regression coefficients.
• Gauss–Markov theorem.
• T test of a hypothesis relating to a regression coefficient
• Type I error and Type II error
• Confidence intervals
• One-sided tests
• F test of goodness of fit.

Multiple regression analysis

• Multiple regression with two explanatory variables
• Graphical representation of a relationship in a multiple regression model
• Properties of the multiple regression coefficients
• Population variance of the regression coefficients
• Decomposition of their standard errors
• Multicollinearity
• F tests in a multiple regression model
• Hedonic pricing models
• Prediction.

Transformation of variables

• Linearity and nonlinearity
• Elasticities and double-logarithmic models
• Semilogarithmic models
• The disturbance term in nonlinear models.
• Box–Cox transformation
• Models with quadratic and interactive variables
• Nonlinear regression.

Stochastic regressors and measurement errors:

• Stochastic regressors
• Assumptions for models with stochastic regressors
• Finite sample and asymptotic properties of the regression coefficients in models with stochastic regressors
• Measurement error and its consequences
• Friedman’s Permanent Income Hypothesis
• Instrumental variables (IV)
• Asymptotic properties of IV estimators, including the asymptotic limiting distribution of where is the IV estimator of 2 in a simple regression model
• Use of simulation to investigate the finite-sample properties of estimators when only asymptotic properties can be determined analytically.

Simultaneous equations estimation:

• Definitions of endogenous variables, exogenous variables, structural equations and reduced form
• Inconsistency of OLS
• Use of instrumental variables
• Exact identification, underidentification, and overidentification
• Two-stage least squares (TSLS)
• Order condition for identification
• Application of the Durbin–Wu–Hausman test.

Binary choice models and maximum likelihood estimation:

• Linear probability model
• Logit model
• Probit model
• Maximum likelihood estimation of the population mean and variance of a random variable
• Maximum likelihood estimation of regression coefficients
• Likelihood ratio tests

Introduction to nonstationary processes:

• Stationary and nonstationary processes
• Granger– Newbold experiments with random walks
• Unit root tests
• Akaike Information Criterion and Schwarz’s Bayes Information Criterion
• Cointegration
• Error correction models.