ECS3706 – ECONOMETRICS EXAM PREP

ECS3706 - ECONOMETRICES LEARNING UNIT 1: An overview of regression analysis 1.1 What is econometrics? 1.2 Uses of econometrics 1.3 What is regression analysis? 1.4 A simple example of regression analysis 1.5 Using regression analysis to explain housing prices LEARNING UNIT 2: Ordinary least squares (OLS) 2.1 Estimating single-independent-variable models with OLS 2.2 Estimating multivariate regression models with OLS 2.3 Evaluating the quality of a regression equation 2.4 Describing the overall fit of the estimated model 2.5 An example of the misuse of R 2 2.6.1 Using a PC to perform OLS LEARNING UNIT 3: Learning to use regression analysis 3.1 Steps in applied regression analysis 3.2 Using regression analysis to pick restaurant locations 3.3 Data PART II: Statistics LEARNING UNIT 12: STATISTICAL PRINCIPLES 12.1 Probability distributions 12.2 Sampling 12.3 Estimation LEARNING UNIT 4: The classical model 4.1 The classical assumptions 4.2 The sampling distribution of
4.3 Gauss-Markov theorem and properties of OLS estimators 4.4 Standard econometric notation LEARNING UNIT 5: Basic statistics and hypothesis testing 5.1 What is hypothesis testing? 5.2 The t-test 5.3 Examples of t-tests 5.4 Limitations of the t-test 5.5 The f-test PART III: Specification LEARNING UNIT 6: Choosing the independent variables 6.1 Omitted variables 6.2 Irrelevant variables 6.3 Specification searches LEARNING UNIT 7: Choosing a functional form 7.1 The use and interpretation of the constant term 7.2 Alternative functional forms 7.2.1 Linear form 7.2.2 Double-log form 7.2.3 Semilog form 7.2.4 Polynomial forms 7.2.5 Inverse form 7.3 Lagged independent variables 7.4 Using dummy variables 7.5 Slope dummy variables 7.6 Problems with functional forms PART IV: Dealing with econometric problems LEARNING UNIT 8: Multicollinearity 8.1 Perfect versus imperfect multicollinearity (the nature of the problem) 8.2 Consequences of multicollinearity 8.4 Remedies for multicollinearity LEARNING UNIT 9: Serial correlation 9.1 Pure versus impure serial correlation (the nature of the problem) 9.2 Consequences of serial correlation 9.3 The Durbin-Watson d test (detecting serial correlation) 9.4 Remedies for serial co rrelation LEARNING UNIT 10: Heteroskedasticity 10.1 Pure versus impure heteroskedasticity 10.2 Consequences of heteroskedasticity 10.3 Testing for heteroskedasticity 10.4 Remedies for heteroskedasticity LEARNING UNIT 11: Running your own regression project H.Crassas – 2016 – ECS3706 – ECONOMETRICS Page 2 STUDY UNIT 1 – AN OVERVIEW OF REGRESSION ANALYSIS 1.1 WHAT IS ECONOMETRICS The goal of econometrics is the estimation of economic relationships. Its method is mainly regression analysis using actual data. Econometric models are used mainly for describing economic reality, hypothesis testing, simulation and forecasting. Econometrics makes use of the following inputs/disciplines: • Economic theory • Economic data • Statistics Economic Theory In previous economics modules you encountered the following two economic relationships: • The demand curve: P=a+bQd from microeconomics. (P: price, Qd: quantity demanded) • The consumption function: C= C+cY from macroeconomics. C: private consumption, Y: income, c: marginal propensity to consume) The coefficients of these equations (a and b in the demand curve) were assumed to have some predetermined values. To be of real use one requires accurate estimates thereof. Econometrics provides methods to estimate these coefficients, using actual data. The theory of economics is important as it helps us to choose the variables and the functional form to be used (eg = a+bX or log(Y) = a + bX). The process of converting economic theory into a mathematical form is called the specification of a model. This involves the selection of the dependent variable (the Y-variable), the variables that cause the effect (the X-variables), and the functional form. In the field of monetary theory, the relationship between income (Y) and the money stock (M) where Y is the real level of economic activity and M reflects the money stock. Of course, changes in M arise mainly because of the amount of net new loans created by banks. The main issue was: does M → Y, or does Y → M? This affects the way in which the model is specified. The two schools of thought were the monetarists and the post-Keynesians. 1. The monetarists believed that Y=f (M) where the direction of causality runs from M → Y and where M is controlled by the central bank. The monetarist transmission mechanism is both direct (for example ΔM affects the prices of assets which affects real spending) and indirect (ΔM affects the interest rate which induces changes in real investment). 2. The post-Keynesians believe that M=f(Y), which is the current generally accepted view. The direction of causality is Y → M, which is opposite to the monetarist case. The post-Keynesians believe that M cannot be controlled. If Y increases, this causes an increase in the demand for M in order to finance the increased level of Y. Econometrics depends on economic theory to provide the variables involved, the direction of causality and the nature of the functional form. Econometrics cannot resolve theoretical differences between different schools of thought. Causality depends only on theory. Econometrics can only determine correlation, which is the strength and nature of a relationship. H.Crassas – 2016 – ECS3706 – ECONOMETRICS Page 3 Economic data In econometrics, we use either time-series data (subscript “t”), where the same variable is measured over time (e.g. the real GDP for the period ). Cross-sectional data (subscript “i”), which provide a measure of several variables at a point in time (e.g. population census data as of 1 March 2003). Data are often adjusted in order to enhance their use. Examples of adjusted data are the following: • A price index time series is adjusted relative to the price of a base year, e.g. the CPI is expressed as 2005=100. • It is often more revealing to view the annual percentage change of a variable, rather than its level. A common example is the inflation rate calculated from the consumer price index. • Time-series data are often adjusted to remove the seasonal effect. These are called seasonally adjusted data. • To remove the effect of changes in prices, values are often deflated (calculated at constant prices), e.g. real GDP The data observed is of the non-experimental type, which reflects the combined impact of many variables simultaneously. It is left to the econometrician to suggest causality, that is, cause and effect relationships between variables. Statistics Econometrics makes extensive use of statistical techniques such as regression analysis and hypothesis testing. Econometricians must be familiar with statistical concepts such as a sampling distribution, the normal distribution, t-tests, the expected value of a sample estimate, standard errors and more. Because of the unique nature of economic data and/or models, special statistical techniques have been developed to cope with these difficulties, that is, multicollinearity, serial correlation and heteroskedasticity. 1.2 USES OF ECONOMETRICS The main uses of econometrics are for structural analysis, forecasting and policy evaluation. 1. Structural Analysis - Structural analysis entails the quantification of economic relationships. It means that we gain quantitative knowledge about relationships between economic variables. 2. Policy evaluation - Models can be used by government to compare the effects of policy measures. Alternative policy instruments are quantified and fed into an econometric model. The model is solved to provide a quantitative outcome for each policy option. 3. Forecasting - Entails a forward simulation of an econometric model. Assumptions are made regarding the exogenous variables (the level of government expenditure, the gold price, the growth of overseas economies, etc.) and these are fed into the model, which then provides forecasts of the endogenous variables (income, private consumption, etc.). Using this model has the advantage that the results are internally consistent, meaning that no important factors are ignored and that proper account has been taken of the interrelationships between variables. The econometric approach to forecasting is particularly useful in the medium to longer term, when structural relationships are more dominant than short-term or random effects. Econometric models are used at different levels and degrees of complexity. 1. Klein's "Link" project, referred to in the introduction, aims to coordinate econometric models of various countries to help forecast international trade and capital movements. 2. Most central banks have large, complex models of their national economies. These are mostly simultaneous-equation type of models which are used to direct monetary and fiscal policy. The South African Reserve Bank uses an econometric model to forecast inflation. The current inflation targeting monetary policy framework is inherently forward looking and relies heavily on the forecasts provided by this model. 3. The department of finance uses an econometric model to forecast tax income and to simulate the effects of alternative policy options. 4. Commercial banks use econometric models to better understand how different economic sectors and industries may react to shocks on the economy. 5. Simple type of models may be used by business and industry for forecasting and planning. A firm might use, for example