ECONOMETRICS I (EKN309)

Required textbook:

Gujarati, D. N. (2003), Basic Econometrics, McGraw-Hill, Inc., 4th

Edition.

Optional textbook:

Kennedy, P. (2003), A Guide to Econometrics, Blackwell Publishing, 5th

Edition.

Wooldridge, J. M. (2006), Introductory Econometrics: A Modern

Approach, Thomson South-Western, 3rd Edition.

INTRODUCTION

I.1 WHAT IS ECONOMETRICS?

Literally, “economic measurement”.

Econometrics, (…) consists of the application of mathematical statistics to

economic data to lend empirical support to the models constructed by

mathematical economics and to obtain numerical results.

Econometrics may be defined as the social science in which the tools of

economic theory, mathematics, and statistical inference are applied to the

analysis of economic phenomena.

I.2 WHY A SEPARATE DISCIPLINE?

econometrics is a combination of economic theory, mathematical economics, economic statistics, and mathematical statistics.

Economic theory:

• makes statements or hypotheses that are mostly qualitative in nature.

• i.e. Demand theory from microeconomics: (other things remaining the same) a reduction in the price of a commodity is expected to increase the quantity demanded of that commodity - 𝑃↓, 𝑄𝑑↑

• Not providing any numerical measure of the relationship between the two, however econometrics does.

Mathematical economics:

• expresses economic theory in mathematical form (equations), but without

regard to measurability or empirical verification of the theory.

• Econometrics’ main interest: the empirical verification of economic theory.

Economic statistics:

• Its main concern: collecting, processing, and presenting economic data in

the form of charts and tables (i.e. data on GNP, employment, etc.);

• But does not concern with using the collected data to test economic

theories.

Mathematical statistics:

• Provide many of the tools used in trade, and do not normally deal with the

special problems of the data;

• However, econometricians develop special methods of analysis to deal

with the problems of the data – i.e. errors of measurement.

(that cannot be controlled directly; thus called nonexperimental data)

I.3 METHODOLOGY OF ECONOMETRICS

(how do econometricians proceed in their analysis of an economic problem?)

The traditional or classical methodology proceeds along the following lines:

1. Statement of theory of hypothesis

2. Specification of the mathematical model of the theory

3. Specification of the econometric model of the theory

4. Obtaining the data

5. Estimation of the parameters of the econometric model

6. Hypothesis testing

7. Forecasting or prediction

8. Using the model for control or policy purposes

To illustrate those steps, lets consider the Keynesian theory of consumption:

1. Statement of theory or hypothesis:

Keynes (1936: 96) stated:

The fundamental psyschological law … is that men [women] are disposed, as

a rule and on average, to increase their consumption as their income

increases, but not as much as the increase in their income.

Marginal propensity to consume (MPC): the rate of change of consumption for a unit (say a dollar) change in income is greater than

zero but less than 1.

2. Specification of the mathematical model of consumption:

• A positive relation between consumption and income;

• BUT not the precise form of functional relationship between the two.

Y = β1 + β2X, 0 < β2 < 1 (I. 3.1)

Y: consumption expenditure, X: income,

𝜷𝟏: intercept AND 𝜷𝟐: slope coefficients

The slope coefficient - 𝜷𝟐 - measures the MPC.

FIGURE I.1: KEYNESIAN CONSUMPTION FUNCTION

Y = β1 + β2X, 0 < β2 < 1 I. 3.1

The variable on the left-hand side is called the dependent variable;

The variable(s) on the right-hand side are called the independent (explanatory) variables.

Here:

The dependent variable: consumption (expenditure)

The independent/explanatory variable: income

AND a single equation model (where the model has only one equation)

- Multiple equation model if the model has more than one equation -

3. Specification of the econometric model of consumption:

Y = β1 + β2X, 0 < β2 < 1 I. 3.1

It assumes that there is an exact or deterministic relationship between X (income) and Y (consumption).

However, relationships between economic variables are generally inexact.

To allow for the inexact relationship between economic variables, the econometrician would modify the function in (I.3.1) as follows:

Y = β1 + β2X + u (I. 3.2)

𝑢: disturbance or error term

(I.3.2): an example of a linear regression model

The econometric model of the consumption function can be depicted as shown in Figure I.2:

4. Obtaining data:

To estimate the econometric model given in (I.3.2) OR to obtain the

numerical values of β1 and β2; we need DATA.

Lets look at the data given in Table I.1 for US economy where

Y: the aggregate personal consumption expenditure,

X: Gross Domestic Product (a measure of income)

Both given in real terms – being measured in constant (1992) prices -

Table I.1: Data on Y (personal consumption expenditure) and X (Gross Domestic Product), 1982-1996, all in 1992 billions of dollars

5. Estimation of the Econometric Model:

The actual mechanics of estimating the parameters will be captured in Chapter 3.

For now; the main tool used to obtain the estimates=the statistical technique of regression analysis

Using this technique AND the data in Table I.1; we obtain

Y = −184.08 + 0.7064𝑋𝑖 (I. 3.3)

The hat on Y indicates that it is an estimate.

From eq. (I.3.3), we can say that β1 = −184.08 𝑎𝑛𝑑 β2 = 0.7064

Since β2 is the slope coefficient, for the sample period an increase in the real income of one dollar led, on average, to incerases of about 70 cents in the real consumption expenditure.

Figure I.3 shows the regression line obtained in (I.3.3):

6. Hypothesis Testing: (after estimation)

To find out whether the estimates obtained in, say, eq. (I.3.3) are in accord

with the expectations of the theory that is being tested?

HERE: we start with the Keynesion theory of consumption AND 0<MPC<1;

What we have found: MPC=β2=0.7064; but before we accept this finding as

a confirmation of Keynesian consumption theory:

WE NEED ASK: is 0.70 statistically less than 1?

Because this result might be as aresult of chance OR we come across with this

result because of the peculiarity of the data we used.

7. Forecasting or Prediction: (after estimation)

If the chosen model confirms the hypothesis of the theory under

consideration,

we may use it to predict the future value(s) of the dependent variable on

the basis of known or expected future value(s) of the explanatory variable

X.

In that case:

the future value(s) of the dependent variable=forecast variable

known or expected future value(s) of explanatory variables=predictor

variable

Using eq. (I.3.3) to predict the mean consumption expenditure for 1997 where the GDP in 1997 is expected to be (was) 7269.8:

Since GDP=7269.8;

𝑌 1997 = −184.0779 + 0.7064 7269.8 = 4951.3167 (𝐼. 3.4)

The actual value of the consumption expenditure reported in 1997 = 4913.5 billion dollars.

• the estimated model (I.3.3) overpredicted the actual consumption expenditure by about 37.82 billion dollars OR

• the forecast error is about 37.82 billion dollars (0.76 percent of the actual GDP value for 1997)

However, such forecast errors are inevitable given the statistical nature of our analysis.

Another use of the estimated model (I.3.3): Y = −184.08 + 0.7064𝑋𝑖 (I. 3.3)

Suppose the President decides to propose a reduction in the income tax.

The question: What will be the effect of such a policy

• on income and thereby on consumption expenditure

• and on employment?

The answer: income tax ↓, investment expenditure ↑. The effect on the

economy is as folllows:

𝑡ℎ𝑒 𝑖𝑛𝑐𝑜𝑚𝑒 𝑚𝑢𝑝𝑙𝑖𝑒𝑟 = 𝑀 =1

1 −𝑀𝑃𝐶

where MPC=0.70 in (I.3.3), then M=3.33

That is, an increase (decrease) of a dollar in investment will eventually lead to more than

a threefold increase (decrease) in income.

8. Use of the Model for Control or Policy Purposes: (after estimation)

We have estimated Keynesian consumption function given in (I.3.3).

The question: Suppose the government believes that consumer expenditure of about 4900 (billions of 1992 dollars) will keep the unemployment rate at its current level of about 4.2 percent (early 2000). SO, what level of income will guarantee the target amount of consumption expenditure?

4900 = −184.0779 + 0.7064X; then X = 7197 app. (I. 3.6)

That is, an income level of about 7197 (billion) dollars, given an MPC of about 0.70, will produce an expenditure of about 4900 billion dollars.

As these calculations suggest, an estimated model may be used for control,or policy, purposes.

TO SUM UP:

Choosing among Competing Models

Several competing hypotheses trying to explain various economic

phenomena.

We have worked with the Keynesian consumption theory; but there are

others, such as:

• The permanent income hypothesis (by Milton Friedman)

• The life-cycle permanent income hypothesis (by Robert Hall)

has developed a model of consumption, called the

Could one or both of these models also fit the data in Table I.1? So, what to

do? Work with the one that fits the data better.

I.4 TYPES OF ECONOMETRICS

Econometrics may be divided into two broad categories, each of which

has two traditions, namely, classical and Bayesian tradition.

Here: the emphasis is on the classical approach. Not a book of applied

econometrics.

I.5 MATHEMATICAL AND STATISTICAL PREREQUISITIES

Appendix A: nontechnical overview of the basic statistical concepts

Appendix C: the summary of basic regression theory in matrix notation.

Appendix B: a summary of the main results from matrix algebra

I.6 THE ROLE OF THE COMPUTER

Several excellent regression packages to be used in computers:

ET, LIMPED, SHAZAM, MICRO TSP, E-VIEWS, MINITAB, SAS, SPSS, STATA, BMD,

Microfit, PcGive.