Transcript ECONOMETRICS I

http://yilmaz.mersin.edu.tr/
Textbook
• Damodar N. Gujarati (2004)
Basic Econometrics,
4th edition,
The McGraw-Hill Companies
ECONOMETRICS I
INTRODUCTION
What is econometrics?
• Literally econometrics mean economic
measurement.
• 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. (Goldberger, 1964)
Why A Separate Discipline?
• Econometrics is an amalgam of economic
theory, mathematical economics, economic
statistics, and mathematical statistics. So why
do we need to study econometrics as a
seperate discipline?
Why A Separate Discipline?
• Economic theory makes statements or
hypotheses that are mostly qualitative in
nature. The theory itself does not provide any
numerical measure. We need econometrics,
because econometrics gives emperical content
to most economic theory.
For example, think about the law of demand...
Why A Separate Discipline?
• The main concern of mathematical economics
is to express economic theory in mathematical
form (equations) without regard to
measurability or emperical verification of the
theory.
• Verification of the theory is the job of
econometricians.
Why A Separate Discipline?
• Economic statistics is mainly concerned with
collecting, processing, and presenting
economic data in the form of charts and
tables.
• Econometrician uses the collected data to test
economic theories.
Why A Separate Discipline?
• The data econometrician uses are
nonexperimental data. The econometrician
uses these data as given.
• Such data are likely to contain errors of
measurement, and the econometrician may
use special methods of analysis to deal with
such errors of measurement.
Methodology of Econometrics
1. Statement of theory or hypothesis
2. Specification of the mathematical model of the theory
3. Specification of 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 show these steps we will consider the well-known Keynesian
theory of consumption.
1. Statement of theory or hypothesis
• Keynes said:
The fundamental psychological law ... is that men 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. (Keynes, 1936)
• Keynes postulated that the marginal
propensity to consume (MPC) is between 0
and 1.
2. Specification of the mathematical
model of consumption
• Keynes did not specify the precise form of the functional
relationship between the two. For simplicity, a mathematical
economist might suggest the following form of the Keynesian
consumption function:
• This equation is the consumption function, where Y =
consumption expenditure, X = income...
β1 and β2 are the parameters of the model, β1 is the intercept
and β2 is the slope coeffient.
2. Specification of the mathematical
model of consumption
Terminology
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Parameters
Slope coefficient
Intercept
Model: a set of mathematical equations
Single equation model
Multiple equation model
Dependent variable
Independent (explanatory) variable
3. Specification of the econometric
model of consumption
• The relationship between economic variables are
generally inexact. To allow for the inexact
relationship between economic variables, the
econometrician would modify the deterministic
consumption function as follows:
where u is the disturbance (error) term. The error
term represents all those factors that affect
consumption but are not taken into account
explicitly.
3. Specification of the econometric
model of consumption
Terminology
• Disturbance (error) term
• Econometric model
• Linear regression model
4. Obtaining data
• To estimate the econometric model, that is, to
obtain the numerical values of β1 and β2, we
need data.
• In the following slide, Y is personal
consumption expenditure and X is gross
national product of the US. Both are in 1992
billions of dollars.
4. Obtaining data
4. Obtaining data
5. Estimation of the econometric
model
• The actual mechanics of estimating the parameters will be
discussed in Chapter 3. For now, note that the statistical
technique of regression analysis is the main tool used to
obtain the estimates. Using this technique and the data given
in Table I.1, we obtain the following estimates of β1 and β2,
namely, −184.08 and 0.7064.
Thus, the estimated consumption function is:
6. Hypothesis Testing
• The estimated value of β2 is about 0.71. This number is
between 0 and 1, as expected, but is it statistically significant?
Is this estimate sufficiently below 1 to convince us that this is
not a chance occurrence or peculiarity of the particular data
we used? Is 0.71 statistically less than 1?
• In order to answer these questions we need to do hypothesis
testing.
• The branch of statistical theory which deals with confirmation
or refutation of economic theories on the basis of sample
evidence is called statistical inference (hypothesis testing).
7. Forecasting or Prediction
• If the chosen model does not refute the
hypothesis or theory under consideration, we
may use it to predict the future value(s) of the
dependent, or forecast, variable Y on the
basis of known or expected future value(s) of
the explanatory, or predictor, variable X.
7. Forecasting or Prediction
• The actual value of the consumption expenditure reported
in 1997 was 4913.5 billion dollars. The estimated model
thus overpredicted the actual consumption expenditure by
about 37.82 billion dollars. We could say the forecast error
is about 37.82 billion dollars, which is about 0.76 percent of
the actual GDP value for 1997.
7. Forecasting or Prediction
• We can use the estimated MPC to guess the
value of income multiplier (M):
• M = 1/(1-0.71) = 3.4
8. Use of the model for control or
policy purposes
• Suppose the government believes that consumer expenditure of
about 4900 (billions of 1992 dollars) will keep the unemployment
rate at the level of about 4.2 percent. What level of income will
guarantee the target amount of consumption expenditure?
• So X must be equal to 7197, approximately. That is, an income level
of about 7197 (billion) dollars, given an MPC of about 0.71, will
produce an expenditure of about 4900 billion dollars.
8. Use of the model for control or
policy purposes
• As these calculations suggest, an estimated
model may be used for control, or policy,
purposes. By appropriate fiscal and monetary
policy mix, the government can manipulate
the control variable X to produce the desired
level of the target variable Y.
Anatomy of econometric modelling
Types of econometrics
• Theoretical econometrics is concerned with the development of
appropriate methods for measuring economic relationships
specified by econometric models. In this aspect, econometrics
leans heavily on mathematical statistics. For example, one of the
methods used extensively in this book is least squares.
• In applied econometrics we use the tools of theoretical
econometrics to study some special fields of economics and
business, such as the production function, investment function,
demand and supply functions, portfolio theory, etc.