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Economic and Econometric Models
 The model of the economic behaviour that has been derived fro a
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theory is the economic model
After the unknown parameters have been estimated by using
economic data foe the variables and by using an appropriate
econometric estimation method, one has obtained an econometric
model.
It is common to use greek characters to denote the parameters.
C=f(Y) economic model
C=β1 + β2 Y , C=15.4+0.81Y econometric model
Economic data
 Time series data, historical data
 Cross sectional data
 Panel data
Variables of an economic model
Dependent variable
Independet variable, explanatory variable, control
variable
The nature of economic variables can be endogeneous , exogeneous
or lagged dependent
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 A variable is an endogenous variable if the variable is dtermined in
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the model. Therefore dependant variable is always an endogenous
variable
The exogenous variables are determined outside of the model.
Lagged dependent or lagged endogenous variables are
predetermined in the model hikmet
The model is not necessary a model of only one equation if more
equations have been specified to determine other endogenous
variables of the system then the system is called a simultaneous
equation model (SEM)
If the number of equation is identical to the number of
endogenous variables, then that system of equation is called
complete. A complete model can be solved for the endogenous
variables.
 Static model
 A change of an explanatory variable in period t is fully reflected in
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the dependent variable in the same period t.
Dynamic model
The equation is called a dynamic model when lagged variables have
been specified.
Structural equations
The equations of the economic model as specified in the economic
theory, are called the structural equations.
Reduced form model
A complete SEM can be solved for the endogenous variables. The
solution is called the reduced form model. The reduced form wil
be used to stimulate a policy or to compute forecasts for the
endogenous variables.
 Parameters and elasticities,
 The parameters are estimated by an estimator and the result is
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called an estimate
The log transformation is a popular transformation in
econometric research, because it removes non-linearities to some
extent.1
Stochastic term
A disturbance term will be included at the right hand side of the
equation and is not observed
At the right hand side of the equation, two parts of the
specification ; the systematic part which concerns the
specification of ariables based on the economic theory; and the
non-systematic part which is remaining random non-systematic
variation.2
Applied quantitative economic research
 The deterministic assumptions;
 It concerns the specification of the economic model, which is
formulation of the null hypothesis about the relationship between
the economic variables of interest. The basic specification of the
model originates from the economic theory. An important decision
is made about the size of the model, whether one or more equation
have to be specified.
 the choice of which variables have to be included in the model stems
from the economic theory
 The availability and frequency of the data can influence the
assumptions that have to be made
 The mathematical form of the model has to be dtermined. Linear or
nonlinear. Linear is more convenient to analyse.
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 Evaluation of the estimation results,
 The evaluation concerns the verification of the validity and
reliability of all the assumptions that have been made
 A first evaluation is obtained by using common sense and economic
knowledge. This is followed by testing the stochastic assumptions by
using a normality test, autocorrelation test, heteroscedasticity tests,
etc. looking at a plot of the residuals can be very informative about
cycles or outliers
 If the stochastic assumptions have not been rejectd , the
deterministic assuptions can be tested by using statistical tests to
test restrictions on parameters. The t-test and F-test can be
performed. The coeffcient of determination R2 can be interpreted.
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REDUCED FORM MODEL
 In the reduced form equations the endogeneous variables are
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expressed in terms of the exogeneous and lagged variables. A special
reduced form model is the model with only exogenous explanatory
variables . Such model is called classical regression model.
Three specifications of the linear model.1
1- the classical regression model
2-the reduced form model
3-the structural model
TESTING THE DETERMINISTIC ASSUMPTIONS
 The coefficient of determination, R2
 Is a measure of goodness of fit of the estimated model to the data this
coefficient can be considered as an indicator concerning the quality of
the estimated linear model.when it is close to one, it can be an
indication that the estimated linear model gives a good description of
the economy.1
 Test principles
 1- Likelihood ratio test (LR) . It can be applied after both the
unrestricted and restricted models have been estimated the restricted
model has to be nested in unrestricted model. This test can only be
used to test the hypothesis that variables can be excluded from the
model. 2
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 2- Wald test: test for testing restrictions on parameters, only the
unrestricted model has to be estimated
 3- Lagrange Multiplier tests (LM): only the restricted model
has to be estimated to test restrictions on parameters.
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Testing the Stochastic Assumptions and
Model Stability
 A normality test
 Jargua-bera (JB) test. The null hypothesis Ho: the residuals are
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normally distributed. The normality assumption is rejected at the
5% significance level if JB>5.99
Tests for residuals autocorrelation
The Breusch-Godfrey LM test. The X2 distribution.
X0.052 (3)=7.815
The Box-Pierce and Ljung-Box tests
The Durbin Watson test. DW=2 no residual autocorrelation
DW<2 positive residual autocorrelation
DW>2 negative residual autocorrelation
 Test for heteroscedasticity
 The White test; more convenient for the analysis of cross section
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data than time series data.1
Ho: the variance of the disturbance term is constant
H1:the variance of the disturbance term is heteroscedastic of
unknown form.
The white test is actually an LM test, so the nR2 is used againg as a
test statistic.
The Breusch-pagan test;
The Goldfeld-Quandt test; for cross section data.2
 Checking the parameter stability
 CUSUM test
 CUSUM of square test
 FORECASTING
 The chow forecast test;
 OUTLIERS
 If thevariable Yt has an outlier which is not explained by one of the
explanatory variables this outlier is located back in the residuals. A
dummy variable can be specified to eliminate that outliers, if you
know the reason for this outliers.
 SEASONALITY
 If the dependent variable exhibits a seasonal pattern and the
explanatory variables do not exhibit a seasonal pattern, then the
14 seasonal behaviour cannot be explained by these variables.1
SUR MODEL
 SUR model is a multiple equation model with seemingly
unrelated regression equations. It consists of equations explaining
identical variables, but for different samples.for example a
number of coffee consumption equations can be estimated for
various countries, or a number of production functions
concerning the same product can be estimated for different
companies.
 The idea behind this model is that these equations are
independent, but that correlation between the disturbance terms
of the equations exists, representing identical unsystematic
influences like world market developments or similar influences
of economic cycles.the different aquations are seemingly
unrelated.1
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 Heteroscedastic disturbances
 It is mainly a prblem in modelling with cros sectional data. But
the problem can also exist in causal models for time series data.
 The heteroscedasticty can be tackled in two ways. The first
method is the application of the GLS procedure. The method is
called weighted least squares. correction of white.1
 ARCH AND GARCH models. 2
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 MODELS WITH ENDOGENOUS EXPLANATORY
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VARIABLES
The Instrumental variable (IV) estimator;
If endogeneous explanatory variables are included in the model, the
disturbance term and these endogeneous variables are dependantly
distributed.
For the IV estimator, instrumental variables are necesary,. The
instruments are chosen in such a way that the instrumental variables
and the disturbance term are independent.1
2SLS estimator and application. 2
 Simultaneous Equation Models
 It is a multiple equation model, where explanatory variables from
one equation can be dependent variables in other equations.
 In a SEM we have to deal with endogenous explanatory variables
that are explicitly specified in a structural equation. We know that
endogenous explanatory variables are correlated with the
disturbance terms in all the structural terms in all all the
structural equations of SEM, which results in incosistent OLS
estimates.1
 Use the estimation method such as IV, 2SLS, and LIML.2
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 Qualitative Dependent Variables,
 Binary dummies take zero or one as values and such dependent
variable is called a dichotomous or binary variable
 Linear Probability Model;
Pi  1   2 X i 2
 Can be estimated by OLS. The disturbances of this model cannot
be normally distributed. They must have a binomial distribution.
 Efficient estimates can be computed by usnig a weighted least
squares estimator (GLS)
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 Probit and logit models
 Latent variable Yi*,
Pi
ln(
)  1   2 X i 2  ui
1  Pi Yi* is an unobservable variable. For example it represents
 Where
the amount of money that person I has spent on buying a PC.
What we observe is a dummy variable Yi defined by:
1, ifYi *  0
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Yi  
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0, otherwise.
 The logit model is a nonlinear model, its parameters have to be
estimated by a nonlinear estimation method.
ln(
Pi
)  1   2 X i 2  ui
1  Pi
 The results of the logit and probit models will not differ very
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much.
 Estimation of the binary
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