# Elements of Econometrics

Econometrics is the application of statistical methods to the quantification and critical assessment of hypothetical economic relationships using data.

This course gives students an opportunity to develop an understanding of econometrics to a standard that will equip them to understand and evaluate most applied analysis of cross-sectional data and to be able to undertake such analysis themselves.

**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.

If you complete the course successfully, you should be able to:

- Describe and apply the classical regression model and its application to cross-section data.
- Describe and apply the:
- Gauss-Markov conditions and other assumptions required in the application of the classical regression model;
- Reasons for expecting violations of these assumptions in certain circumstances;
- Tests for violations;
- Potential remedial measures, including, where appropriate, the use of instrumental variables.
- Recognise and apply the advantages of logit, probit and similar models over regression analysis when fitting binary choice models. Competently use regression, logit and probit analysis to quantify economic relationships using standard regression programmes (Stata and EViews) in simple applications.
- Describe and explain the principles underlying the use of maximum likelihood estimation.
- Apply regression analysis to fit time-series models using stationary time series, with awareness of some of the econometric problems specific to time series applications (for example, autocorrelation) and remedial measures.
- Recognise the difficulties that arise in the application of regression analysis to nonstationary time series, know how to test for unit roots, and know what is meant by cointegration.

- Dougherty, C. Introduction to Econometrics. Oxford: Oxford University Press.