ECS3706 - ECONOMETRICES
LEARNING UNIT 1: An overview of regression analysis LEARNING UNIT 7: Choosing a functional form
1.1 What is econometrics? 7.1 The use and interpretation of the constant term
1.2 Uses of econometrics 7.2 Alternative functional forms
1.3 What is regression analysis? 7.2.1 Linear form
1.4 A simple example of regression analysis 7.2.2 Double-log form
1.5 Using regression analysis to explain housing prices 7.2.3 Semilog form
7.2.4 Polynomial forms
LEARNING UNIT 2: Ordinary least squares (OLS) 7.2.5 Inverse form
2.1 Estimating single-independent-variable models with OLS 7.3 Lagged independent variables
2.2 Estimating multivariate regression models with OLS 7.4 Using dummy variables
2.3 Evaluating the quality of a regression equation 7.5 Slope dummy variables
2.4 Describing the overall fit of the estimated model 7.6 Problems with functional forms
2.5 An example of the misuse of R 2
2.6.1 Using a PC to perform OLS PART IV: Dealing with econometric problems
LEARNING UNIT 8: Multicollinearity
LEARNING UNIT 3: Learning to use regression analysis 8.1 Perfect versus imperfect multicollinearity (the nature of the
3.1 Steps in applied regression analysis problem)
3.2 Using regression analysis to pick restaurant locations 8.2 Consequences of multicollinearity
3.3 Data 8.4 Remedies for multicollinearity
PART II: Statistics LEARNING UNIT 9: Serial correlation
LEARNING UNIT 12: STATISTICAL PRINCIPLES 9.1 Pure versus impure serial correlation (the nature of the problem)
12.1 Probability distributions 9.2 Consequences of serial correlation
12.2 Sampling 9.3 The Durbin-Watson d test (detecting serial correlation)
12.3 Estimation 9.4 Remedies for serial co rrelation
LEARNING UNIT 4: The classical model LEARNING UNIT 10: Heteroskedasticity
4.1 The classical assumptions 10.1 Pure versus impure heteroskedasticity
4.2 The sampling distribution of 10.2 Consequences of heteroskedasticity
4.3 Gauss-Markov theorem and properties of OLS estimators 10.3 Testing for heteroskedasticity
4.4 Standard econometric notation 10.4 Remedies for heteroskedasticity
LEARNING UNIT 5: Basic statistics and hypothesis testing LEARNING UNIT 11: Running your own regression project
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
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,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.
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,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 1960-1996). 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,
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, 1.3 WHAT IS REGRESSION ANALYSIS
Regression analysis is used to make quantitative estimates of economic relationships that previously have been completely
theoretical. Anybody can claim that the quantity of compact discs demanded will increase if the price of those discs decreases
(holding everything else constant), but not many people can put specific numbers into an equation and estimate by how many
compact discs the quantity demanded will increase for each dollar that price decreases.
• To predict the direction of the change, you need a knowledge of economic theory and the general characteristics of the
product in question.
• To predict the amount of the change, you need a sample of data, and you need a way to estimate the relationship.
The most frequently used method to estimate such a relationship in econometrics is regression analysis.
Dependent Variables, Independent Variables, and Causality
Regression analysis is a statistical technique that attempts to "explain" movements in one variable, the dependent variable, as
a function of movements in a set of other variables, called the independent (or explanatory) variables, through the
quantification of a single equation.
• Dependent Variable: Is what you measure in the experiment and what is affected during the experiment. It responds to
the independent variable. It "depends" on the independent variable
• An independent variable: is the variable you have control over, what you can choose and manipulate and what you
think will affect the dependent variable.
For example;
• Q is the dependent variable Q = f(P, , Yd)
• P, Ps, and Yd are the independent variables.
Regression analysis is a natural tool for economists because most (though not all) economic propositions in that the quantity
demanded (dependent variable) is a function of price, the prices of substitutes, and income (independent variables).
Much of economics and business is concerned with cause-and-effect propositions. If the price of a good increases by one unit,
then the quantity demanded decreases on average by a certain amount, depending on the price elasticity of demand (defined
as the percentage change in the quantity demanded that is caused by a one percent increase in price). Similarly, if the quantity
of capital employed increases by one unit, then output increases by a certain amount, called the marginal productivity of
capital. Propositions such as these pose an if-then, or causal, relationship that logically postulates that a dependent variable's
movements are determined by movements in a number of specific independent variables.
Single-Equation Linear Models
The simplest single-equation linear regression model is:
= + Fig. 1: Graphical representation of the coefficients of the
• The equation states that Y (dependent variable) is a single-equation regression line.
linear function of X, (independent variable)
• The model is a single equation model as it's the only equation specified.
• The model is linear as it is a straight line rather than a curve.
• The β’s are the coefficients that determine the coordinates of the
straight line at any point.
• is the constant or intercept term; indicates the value of Y when X
equals zero
• is the slope coefficient, indicates the amount that Y will change when
X increases by one unit.
• The solid line illustrates the relationship between the coefficients and
the graphical meaning of the regression equation.
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