Econometrics lecture 1

1. ECONOMETRICS
lecture1

2. WHAT IS ECONOMETRICS….?
 Literally econometrics means ‘economic
measurement’.
 Econometrics, the result of a certain outlook on the
role of economics, 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 is concerned with the empirical
determination of economic laws.
 Econometrics is an amalgam of economic theory,
mathematical economics ,economic statistics and
mathematical statistics

3. WHY A SEPARATE DISCIPLINE….?
 Economic theory - makes statements or hypotheses
that are mostly in qualitative in nature like demand and
price thus economic theory postulates a inverse
relationship but the theory itself does not provide any
numerical measure of the relationship. it is the job
econometrician to provide numerical estimates.
 Mathematical economics-is to express economic
theory in mathematical form without regard of
measurability or empirical verification of the theory .
Econometrician uses mathematical equations
proposed by mathematical economist .this conversion
requires a great deal of ingenuity and practical skill

4.  Economic statistics- this is mainly concerned with
collecting ,processing and presenting economic
data in the form of charts and tables. this is the job
of an economic statistician .he is not concerned
about testing the economic theories
 Mathematical statistics- provides many tools used
in trade, the econometrician often needs special
methods in view of the unique nature of most
economic data the data are not generated as the
result of a controlled experiment.

5. METHODOLOGY OF ECONOMETRICS
Statement of Economic theory
Specification of the Mathematical model
Specification of the Econometric model
Obtaining Data
Estimation of econometric model
Hypothesis testing
Forecasting or prediction
Use of the model for policy purposes

6.  Statement of Economic theory- Keynes
postulated that the Marginal propensity to consume
,the rate of change of consumption for a unit
,change in income is greater than zero but less than
1.
 Specification of the Mathematical model-keynes
postulated a positive relationship between
consumption and income ,he did not specify the
precise form of the functional relationship between
the two
Y=ß1+ß2X 0<ß2<1
 Where Y=consumption expenditure and X=income,
ß1 and ß2 known as parameters as well as intercept
and slope respectively .

7. The ß2 measures the MPC. Consumption is linearly
related to income .the relationship between
consumption and income is consumption
function.the variable appearing on left side i.e
consumption is dependent variable and on right
side i.e income is called explanatory variable. A
model having one equation is single equation
model and more than one is multiple equation
model.
CONSUMPTION
EXPENDITURE
INCOME
ß2=MPC
ß1

8.  Specification of the econometric model of
consumption- it assumes that there is an exact or
deterministic relationship between consumption and
income. But relationships between economic
variables are generally inexact .for example 500
families, we would not expect all 500 observations to
lie exactly on the straight line because in addition to
income, others variables affect consumption
expenditure like size of family, age of members
,religion etc.the econometrician would modify the
deterministic consumption function .
Y=ß1+ß2X+u
where u is known as the disturbance or error terms a
random (stochastic)variable that has well defined
probabilistic properties

9.  Obtaining of data-to estimate the econometric
model ,to obtain the numerical values of ß1 and ß2 we
need data .
 Estimation of econometric model -now that we
data ,our next task is to estimate the parameters of
the consumption function .the numerical estimates of
the parameters give empirical content to the
consumption function. the statistical techniques of
regression analysis is the main tool used to obtain
the estimates.
 Hypothesis testing-assuming that the fitted model
is reasonably good approximation of reality, we have
to develop suitable criteria to find out whether the
estimates obtained are in accord with the
expectations of the theory that is being tested

10.  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 of the dependent or forecast variable y on the
basis of the known or expected future value of the
explanatory or predictor, variable X.
 Use of models for control or policy purpose-
as the estimated model is used to make policies by
appropriate mix of fiscal and monetary the
government can manipulate the control variable X
to produce a desired level of the target variable Y.

11. RELATIONSHIPS
 Statistical versus deterministic- In statistical
relationships among variables we essentially deal
with random variables ,in deterministic relationships
it also deals with variables
 Regression versus causation- there is no
statistical reason to assume that rainfall doesn’t
depend on crop yield. commonsense says that
inverse relationship in itself cannot logically imply
causation.

12.  Regression versus correlation- the strength of
association between two variables is correlation ,it
is measured by correlation coefficient .to estimate
or predict the average value of one variable on the
basis of the fixed variable .in regression analysis
there is an symmetry in the way the dependent and
explanatory variables are treated. in correlation
,variables are symmetrically.

13.  Explained variable
 Predictand
 Regressand
 Response
 Endogenous
 Outcome
 Controlled variable
 Independent variable
 Predictor
 Regressor
 Stimulus
 Exogenous
 Covariate
 Control variable
Dependent variable Explanatory variable

14. TYPES OF DATA
 Time series data- it is a set of observations on the
values that a variable takes at different times.such
data may be collected at regular intervals like daily
,weekly, quarterly,annually etc.time series data is
stationary it means that mean and variance not vary
systematically over the time
 Cross section data- data collected at the same
point of time

15.  Pooled data –it is combined ,data are elements of
both time series and cross section data
 Panel ,longitudinal or Micropanel data- it is a
special type of pooled data in which the same
cross sectional unit is surveyed over time

16. THE MEANING OF LINEAR
 Linearity in variables – the regression curve of
above equation is linear or straight line .if E(Y/Xi)=
ß1+ß2Xi2 is the equation, as the power of the
variable Xi is 2 ,this cannot be a linear equation.
 Linearity in parameters- the regression equation is
E(Y/Xi)= ß1+ß2 2Xi ,this is an example of non linear
regression model

17. THE CONCEPT OF POPULATION REGRESSION
 The conditional mean E(Y/Xi) is a function of Xi
,where Xi is a given value of x
E(Y/Xi)=f(Xi)
Where f(Xi) denotes some function of the explanatory
variable Xi. E(Y/Xi) is a linear function of Xi this is
conditional expectation function (CEF) or population
regression function.
E(Y/Xi)=ß1+ß2Xi
This is a linear population regression function

18. SAMPLE REGRESSION FUNCTION
Yˆi= ߈1+߈2Xi+uˆi
Yˆi = estimator of E(Y/Xi)
߈1 = estimator of ß1
߈2 = estimator of ß2
uˆi= estimator of PRF

19. STOCHASTIC SPECIFICATION OF PRF
E(Y/Xi)=ß1+ß2Xi
Yi= ß1+ß2Xi+ui
Yi= E(Y/Xi) +ui
ui=Yi- E(Y/Xi)
 Ui is a non systematic ,random ,stochastic term.it is
an unobseverable random variable taking positive
or negative values
Yi= E(Y/Xi) +ui
now if we take the expected value on both the sides
E(Y/Xi)= E(E(Y/Xi) )+E(ui/Xi)

20.  E(Y/Xi)= E(Y/Xi) )+E(ui/Xi)
 Expected value of a constant is that of constant
itself.this implies E(ui/Xi)= 0
 Thus the assumption that the regression line
passes through the conditional means of Y implies
that the conditional means of ui are zero.

21. SIGNIFICANCE OF STOCHASTIC TERM
 Vagueness of theory- in the given theory ,we
might be ignorant about or unsure about the other
variables affecting the dependent variables
(Y).therefore ‘ui’ may be used as a substitute for all
excluded or omitted variables of model.
 Unavailability of data-even if we know some
excluded variables ,we may not have the
quantitative information about those variables
example family wealth

22.  Core variables versus peripheral variables-
considering the variables it is quite possible that the
joint influence of all may be more or less. one
hopes that their combined effect can be treated as
random variable
 Intrinsic randomness of behavior- this random
variables may very well reflect this intrinsic
randomness
 Poor proxy variables-there may be errors of
measurement for example Milton’s friedman,
regards permanent consumption as function of
permanent income .since data on these variables
are not directly observable, we use proxy variable
current consumption and current income. since they
are not equal

23.  Principle of parsimony –if the theory is not strong
enough to suggest what other variables might be
included so why to introduce more
variabled,instead add a random variable (ui) just to
keep the model simple
 Wrong functional form- there may be wrong
formation of the relationship between X and Y
variables. For two variable models it is easy by
scatter diagram but in mutiple regression model it is
not possible to visualise,