Hitchhiker’s Guide to
EViews and Econometrics
January 2000
Byung-Joo Lee
Department of Economics
University of Notre Dame
Notre Dame, IN 46556
ByungJoo.Lee.81@nd.edu
574-631-6837
EViews’ User’s Guide
This is a short guide to use EViews, the econometric software that we will use in this
course. EViews program is available on the campus cluster computers with windows
operating system installed. We do not have Macintosh version of this program installed
on the campus computers (Macintosh version is available for individual purchase directly
from the publisher).
Summary of the Program
EViews is a windows graphical interfaced statistical software. This program simplifies
many complicated statistical problems with a few simple mouse clicks. However, this
program is also powerful enough to handle many state of the art econometrics problems.
This program is a successor of MicroTSP from the same company. This program handles
time-series analysis better than cross section data analysis. More flexible maximum
likelihood estimation procedure is one major lacking point of EViews.
There are two ways to execute this program. First you can perform many statistical
functions with just using menu bar. You can also do the same task using EViews
commands. We will use both ways to handle statistical problems.
Getting Started
When you start EViews program, EViews window appears. The first line in the window
is the title bar, labeled Econometrics Views. The second line is called the menu bar
beginning with File. Each one of the entries has its own submenu as you double click
your mouse. They are very similar to standard windows menu bar items. Each of those
items will be explained later whenever necessary. There is a blank line right below the
menu bar, and it is called the command window. This is the area that you type in the
EViews command to perform statistical functions (As I mentioned in the previous
section, you can just use menu bar to do the same task). The main area is the work area
that will display the results of statistical tasks. Each result will have its own window and
as you perform multiple statistical tasks, you will see several windows cascaded. You
can drag each window to different position for your own viewing convenience. The very
bottom line is the status line. This line is divided into three sections. The first one is a
message section (from EViews to users), the second section shows the default directory
that EViews will use to look for data and program. You can change the default directory
by clicking the Update Default Directory in the directory setting window. The last
section displays the current work file name. When you open EViews, this section shows
that work file is untitled (because you did not name the work file yet).
1
Introductory Session
This is an introductory session of EViews. This session only covers the most basic and
necessary tools that we need to perform minimal regression analysis. The next section,
Econometric Review, covers brief but fairly comprehensive topics of the most
commonly used econometric models.
We will practice an actual statistical analysis using small data set. In this practice, I will
explain both using menu bar and EViews command. EViews command will be
boldfaced. Our practice will appear as italics.
1. Begin EViews session and prepare for the workfile.
You need to create workfile for any EViews session. Click on the
File|New|Workfile. (Type CREATE in a command mode) A dialog box appears to
ask the frequency of data: annual, semi-annual, quarterly, monthly, weekly, daily or
undated. Select appropriate frequency and enter the starting and end period of data.
For example, in the start period area, type 1960 for annual or 1960:1 for quarterly,
monthly or weekly (you can use period instead of colon, e.g., 1960.1). The end
period can be entered as 1969 (annual), 1969:4 (quarterly) or 1969:12(monthly), etc
(see step 11 to enter data). For cross section data, choose none for data frequency and
enter 1 in the start period and n (number of sample size) in the end period. Then,
click OK. Now the workfile appears (currently showing as workfile:UNTITLED)
and there are two variables already in the workfile: C(constant) and resid(Residuals).
2. Type in data for three series CONS, INCOME and CPI.
To enter data manually, click on Quick|Empty Group(Edit Series). (Type DATA).
Blank spreadsheet appears with the pre-specified frequency you entered in step 1.
Click in the gray cell to enter the series (variable) name. This window is called the
Group within your own work file. For each operation you do in your work file, you
can name these as separate group or you can just discard to close the group windows.
You can use any ASCII characters up to 8 characters. Start type in numeric data
immediately below the series name. Type CONS (consumption) and press down
arrow (DATA CONS) and start to type in 325, 335,… Data is at the end of this
exercise. After finishing cons, go to the next column and in the gray area, type
INCOME and type in 350, 364, 385,… Repeat this for another series CPI. (You can
do all these three series at once by DATA CONS INCOME CPI).
If you want to read a data from other file(ASCII file, Lotus *.WK3, or Excel *.XLS),
click on Proc/Import Data in the workfile menu. Choose proper file format to read
in and select data file from your directory. You will have a data dialog window that
is asking the order of data (by observation or by series: most data is arranged by
2
observation) and series names (if they don’t have names). If data already have series
names, simply type in how many series in the data set. EViews will read in all
necessary data into the workfile. You can export selected series into any data file
format by click on Proc/Export Data in the workfile menu.
3. Save and retrieve your current working file.
When you are done entering all your data, you need to save your work file so that you
can use it later. To save your working file, click on File|SaveAs and give appropriate
file name (work file has an automatic extension of *.wf1) and path for your own
(SAVE filename). In a later session when you need this work file back, you can
retrieve by File|Open and find your appropriate work file (LOAD filename).
4. Generate real variables using nominal variables and price index.
Note that CONS and INCOME are nominal terms. In order to use these variables in
real terms, we need to modify these variables into real terms. In your current work
file menu bar, there is a button for GENR. Click GENR (GENR), you will have a
window asking equation and sample period. Enter appropriate equations to change
nominal variables into real terms. Type RCONS(Real consumption)=CONS/CPI and
adjust for sample period. Sample period is already entered as the entire period. Do
the same for RINCOME (Real income).
5. Print CONS, INCOME, CPI, RCONS, RINCOME.
If you want to look at your data, you can use SHOW command in the work file menu
bar and type appropriate series name(s) (SHOW CONS INCOME). For a single
series, you can just double click on its series name in the workfile directory. For a
multiple series, highlight the entire series name in the workfile directory and click
SHOW. You can type more than one series name in the series name window. You
can print using PRINT menu in the work group menu bar (PRINT CONS
INCOME).
6. Plot each series separately and simultaneously.
You can a graph for a single or multiple series. You can also do this by
View|Graphics under the Group menu (This is only available under the View in the
Group menu, where you see the actual list of series, for example) (PLOT series name
or PLOT series1, series2). Each series is plotted using different color. You can
make multiple graphs by choosing View|Multiple Graphs in the Group menu.
3
7. Draw and print the scatter diagram of RCONS and RINCOME.
To see the relationship between two variables, you can draw a scatter diagram
between two variables (SCAT CONS, INCOME, first variable in the vertical axis
and the second one in the horizontal axis). You can print this scatter diagram using
PRINT command in the scatter diagram menu bar.
8. Calculate the correlation, covariance and test the Granger causality
between RCONS and RINCOME.
You can obtain descriptive statistics of each variables using Quick|Series Statistics
for single series or Quick|Group Statistics for multiple series. You can obtain the
same statistics under the View|Descriptive Stats under the Group menu. There are
eight statistics that you can obtain under the View menu such that descriptive
statistics, crosstab, correlations, covariances, correlogram, cross correlation,
cointegration test, Granger causality.
9. Estimate the least squares regression of RCONS on RINCOME with
intercept. Also estimate the same regression using nominal variables.
If you want to run regression of RCONS on RINCOME with intercept, click on
Object|New Object|Equation (or Quick|Estimate Equation). Before you click OK
button, you can (optionally) give the name for your Object. It is not necessary, but
this will make it easier for you to refer to your estimated equation later. In the
Equation Specification window, you can type regression equation that you want to
estimate, and choose appropriate estimation method (LS: Least Squares, TSLS: Two
Stage Least Squares for Simultaneous Equation Estimation, ARCH, LOGIT and
PROBIT etc). For simple least squares, type RCONS C RINCOME (LS RCONS C
RINCOME) for regression of RCONS(Dependent Variable) on C(intercept) and
RINCOME(explanatory variable).
10. Estimate the least squares regression of RCONS on last year’s RCONS,
RINCOME with intercept.
If you want to estimate the regression using different specification or different
estimation technique or different sample period, repeat step 9 and modify appropriate
estimation option. You can also include lagged values in the regression by using
RCONS(-1) as one period lagged value of RCONS or RINCOME(-2) as two period
lagged value of RINCOME.
4
11. The following is the dada set we used for this introductory session.
Year
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
Cons
325
335
355
375
401
433
466
492
537
576
Income Cpi
350
0.887
364
0.896
385
0.906
405
0.917
438
0.929
473
0.945
512
0.972
547
1.000
590
1.042
630
1.098
5
Data Handling
1. Data Transformation
You can transform most of data using GENR button in the workfile menu bar.
Following are the most commonly used functions and operations.
+, -, *, /
>, <, =, <>
<=, =>
AND, OR
add, subtract, multiply and divide
GT, LT, equal and not equal
LTE, GTE
Logical Operator. (X AND Y) is 1 if both are true
X2=X^2
LY=LOG(X)
EX=EXP(X)
AX=ABS(X)
SQX=SQR(X)
RND, NRND
RX=@INV(X)
Raise to the Power
Natural Log Transformation
Exponential Function
Absolute Value
Square Root
Random Number Generator, Uniform and Normal
Inverse or Reciprocal of X
DX=D(X)
DnX=D(X,n)
LX=X(-1)
First Difference of X, X(t)-X(t-1)
nth Order Differencing, (1-L)nX, where L is a Lag Operator
One Lagged Value of X
2. Descriptive Statistics
@SUM(X)
@MEAN(X)
@VAR(X)
@COV(X,Y)
@COR(X,Y)
@DNORM(X)
@CNORM(X)
Sum of X
Mean of X
Variance of X
Covariance between X and Y
Correlation between X and Y
Standard Normal Density Function of X
CDF of Standard Normal Random Variable
3. Regression Statistics
If you assign the name of your Object for your regression, you can use the regression
name to retrieve various regression statistics. For example, assume our regression
name is TEST. Then, TEST@R2 is an R2 value of the TEST regression. If you did
not assign regression name, @R2 refers to R2 value of the most recently estimated
equation.
@R2, @RBAR
@SE, @SSR
@DW, @F, @LOGL
R2 and adjusted R2
Standard error of regression, sum of squared residual
Durbin-Watson, F-statistic, value of log-likelihood function
6
4. Pooled time-series and cross section data
You need to assign names of the cross section members. For example, assume that
you are analyzing cross country study of income Y, consumption CONS, interest rate
R and price level P for three countries, US, JAPAN and CANADA. I assume that
you already have data read into the Workfile and their names are: YUS, YJP, YCA,
CONSUS, CONSJP, CONSCA, RUS, RJP, RCA, PUS, PJP and PCA.
To obtain the Pooled regression window, click Objects|New Object|Pool, and you
will get Pooled Estimation window. In the regression window, you have Cross
Section Identifiers: (Enter identifiers below this line). Type US, JP and CA in
each line. For each series you defined before, you will have three series. For
example, Y? is YUS, YJP and YCA. Same is true for all other variables CONS, R and
P.
7
Econometric Review
This section provides a quick review of econometric technique commonly used for many
empirical economic research projects. However, this section does not intend to teach
econometric theory. Those who are interested in learning more econometric theory can
read Gujarati (1996)’s Basic Econometrics, 3rd ed., or more advanced book, Econometric
Analysis, 4th ed., by W. Greene (2000).
In this section, I assume that data is already loaded and ready to use and all the variables
are defined. If you are not familiar with this, go back to the steps 2 and 3 in previous
section. For EViews command, I will provide both menu bar and EViews command for
each operation whenever possible. Throughout this section, I will assume the following
regression model and variable notations. I also assume that you know how to interpret
regression output.
Yt  β 0  β 1X t1  β 2 X t2  u t
Yt (or Yt1, Yt2) is a dependent variable and Xt1 and Xt2 are independent variables and  s
are parameters to estimate.
1. Ordinary Least Squares (OLS) Estimation.
This is the most commonly and widely used estimation method when classical
assumptions of regression are all met. The classical assumptions are:
1) Eut X t   0
2) X t and u t are uncorrelated, EX t  u t   0


3) Error terms are homoskedastic, Var u t X t   E u t X t  σ 2
2
4) There is no autocorrelation, Covut ,us X  Eut  us X  0
Yt  β 0  β 1X t1  β 2 X t2  u t ,

u t ~ N 0, σ 2

Quick|Estimate Equation (You have the equivalent menu Objects|New
Objects|Equation, and this is the same as throughout all regression procedure). Give
appropriate regression name in the Name of Object window. Click OK to get
regression window and type Y C X1 X2 in the Equation Specification window.
Choose Least Squares in the Estimation Settings window. Specify appropriate
sample period.
LS Y C X1 X2
8
2. Generalized Least Squares (GLS) Estimation.
When the classical assumptions of regression are violated, we still can have
consistent estimates by OLS, but we no longer have efficient estimators. To obtain
efficient estimators, we need to use various modifications of OLS, collectively called
GLS.
Yt  β 0  β 1X t1  β 2 X t2  u t ,

ut ~ N 0, σX
2

2.1. Weighted Least Squares for Heteroskedasticity.
If you have a prior knowledge of the pattern of heteroskedasticity, e.g.,
2
2
σX   σ 2  X 1 , then you can transform the heteroskedasticity into
homoskedasticity by dividing all variables by X 1 . This is called the weighted
least squares estimation.
Quick|Estimate Equation and type Y C X1 X2 in the Equation Specification
window. Click Options button, and select Weighted LS/TSLS and type in
appropriate series name (e.g., X1) for weights in the Weight box.
2.2. Heteroskedasticity Consistent Covariance Matrix.
When the heteroskedasticity structure is unknown, we can still estimate the
covariance matrix consistently by either White’s or Newey-West
heteroskedasticity consistent estimation method. It is recommended that when
you suspect heteroskedasticity problem, but you are not sure about the structure of
heteroskedasticity.
Quick|Estimate Equation and type Y C X1 X2 in the Equation Specification
window. Click Options button, and select Heteroskedasticity Consistent
Covariance and choose either White or Newey-West.
2.3. Autocorrelation (Serial Correlation) problem.
Autocorrelation problem arises when the error term follows autocorrelation
structure such that u t  ρu t 1  ε t . In the OLS regression output, if DurbinWatson statistic is close to 0 or 4, we may suspect that there is the first order
autocorrelation problem. This model is estimated by Cochrane-Orcutt iterative
procedure and lose one lagged observation.
Quick|Estimate Equation and type Y C X1 X2 AR(1) in the Equation
Specification window. Choose Least Squares in the Estimation Settings
window. For higher order autocorrelation (hth), simply add AR(h), and we loose
lagged h observations.
9
LS Y C X1 X2 AR(1)
LS Y C X1 X2 AR(1) AR(2)
Regression output reports parameter estimates of the model and the
autocorrelation parameters.
2.4. ARIMA Model.
When error term follows the general ARIMA(p,0,q) structure such that
u t  ρ 1u t 1      ρ pu t p  θ 1ε t 1      θ q ε t q , we have the ARIMA model.
Quick|Estimate Equation and type Y C X1 X2 AR(1) MA(1) in the Equation
Specification window. Choose Least Squares in the Estimation Settings
window.
LS Y C X1 X2 AR(1) MA(1)
3. Autoregressive Conditional Heteroskedasticity ((G)ARCH).
ARCH model is similar to the ARIMA model, but ARCH model assumes the ARIMA
relationship in the second moment, i.e., the conditional variance of u t follows
autoregressive (ARCH) and/or moving average (GARCH) components in
heteroskedasticity structure. These models are frequently used to analyze the
financial data where some periods of large price volatility (measured by the variance)
follows by the periods of relative tranquility.


Yt  β 0  β 1X t1  β 2 X t2  u t , h t  E u t Ω t 1 : Conditional variance of u t , Ω t 1
is the all available information set up to time (t-1).
2
3.1. ARCH(p)
h t  α 0  α1  u t 1  α 2  u t 2  ...  αp  u t p
2
2
2
3.2. GARCH(p,q)
h t  α 0  α1  u t 1  α 2  u t 2  ...  αp  u t p  β1  h t 1  β 2  h t 2  ...  β q  h t q
2
2
2
3.3. ARCH-M model
Allow the mean of a sequence is a function of conditional variance. Useful model
to study asset market.
Yt  β 0  β1X t1  β 2 X t2  δ  h t  u t , where u t follows ARCH(p) model.
10
3.4. TARCH, EGARCH
These are variations of ARCH to allow asymmetric nature of price volatility.
Quick|Estimate Equation and choose ARCH in the Estimation Settings window.
Type your regression function as before in the Mean Equation Specification
window. Choose appropriate settings for GARCH(p,q) (GARCH(1,1) is default) and
indicate whether you have ARCH-M model or not. ARCH is already selected in the
Estimation Settings window.
ARCH(p,q) Y C X1 X2
3.5. Test for ARCH Model
To test the existence of ARCH, Lagrange Multiplier (LM) test is often used. To
carry out this test, choose View|Residual Test|ARCH LM Test from the main
windows menu bar.
4. Panel Data Analysis (Pooled Time Series and Cross Section
Regression).
4.1. Pooled Time Series and Cross Section
Pooled time series and cross section regression equation is as following:
Yit  X it β  uit .
'
Depending on the error structure of uit , we can allow cross-sectional
heteroskedasticity or cross-sectional correlation. To estimate this model, you
need to understand the way EViews handle the pooled data structure. (See the
previous section for pooled data handling).
To estimate this model, click Objects|New Object|Pool, and you will get Pooled
Estimation window. Specify appropriate entries (dependent variable, sample
period and regressors). In the Regressors window, you need to specify which
variables have the common coefficients and which have different coefficients
(cross section specific coefficients). In above model, we assume that all variables
have the same coefficients (no cross section specific coefficients). To allow
cross-sectional heteroskedasticity, select Cross section weights, and to allow
cross-sectional correlation, select SUR estimation. For intercept choose either
none or common.
4.2. Panel Data Analysis
11
Panel data analysis is a special case of pooled time series and cross section data
analysis. This is often found in the longitudinal data structure where same
individual is followed over periods of time. Therefore, there may exist individual
specific effect (heterogeneity) constant over time. There are two ways to handle
this problem, fixed effect or random effect.
Fixed Effect Model:
Yit  αi  X it β  uit
Random Effect Model:
Yit  α  X it β  ui  ε it
'
'
Fixed effect assume the individual heterogeneity is explained by the different
intercept terms, while random effect handles this using random disturbance term
ui which is constant through time. In this model, we can specify that some
variable have a cross section specific coefficients.
To estimate the panel data regression, follow above instruction to obtain the
Pooled Estimation window and choose the Fixed effects or Random effects on
intercept term selection.
5. Limited Dependent Variable Analysis (Logit or Probit).
Limited dependent variable analysis is appropriate when dependent variable takes
binary values ( Yt  1 or 0 ). This analysis comes from the following model.
Yt  β 0  β1  X t  ut
*
*
The latent variable ( Yt ) is unobservable, but the binary variable Yt is observed one
if β 0  β1  X t  u t  0 and zero otherwise. Depending on the assumptions about the
error term, we define either Logit model ( u t has a Weibull distribution) or Probit
model ( u t has a normal distribution). These models are estimated by maximum
likelihood estimation with numerical iteration (typically by Newton-Raphson or
BHHH method).
Quick|Estimate Equation and type Y C X1 X2 in the Equation Specification
window. Choose Logit or Probit in the Estimation Settings window. Specify
appropriate sample period.
LOGIT Y C X1 X2
PROBIT Y C X1 X2
6. Non-Linear Least Squares.
12
EViews automatically applies nonlinear least squares to any equation that is nonlinear
in its coefficients. You can just specify nonlinear equation in the Equation
Specification window. For example, if you want to estimate the CES production
function with the following specification:

Yt  A  θ  K t
ρ
 1  θ   L t

1
ρ  ρ
, where A, θ,ρ are parameters to be estimated.
Quick|Estimate Equation , and in the Equation Specification window, type
Y  C(1) * C(2) * K^(-C(3))  1 C(2) * L^(-C(3)^(1/C(3)) , where C’s are
parameters to be estimated nonlinearly. Choose Least Squares in the Estimation
Settings window.
7. Non-Stationary Time Series Analysis
Time series data y t t 1 is nonstationary if its autocorrelation coefficient ( ρ , see
section to above) is one, i.e., this series explodes as time progresses and has no finite
variance. If this is the case, we call that this series has a unit root ( ρ  1 ), or in a
more technical notation, y t ~ I(1) , which means that the series y t has to be
differenced once to be stationary.
T
7.1. Unit Root Test
General unit root test proceeds as follows: Consider the following regression
model: y t  ρ  y t 1  u t . Testing the unit root hypothesis is equivalent to test to
see if ρ  1 . This basic equation is modified to the following three equations.
Δy t  θ  y t 1  u t
Δy t  α  θ  y t 1  u t
Δy t  α  θ  y t 1  β  t  u t
This is the basic Dickey-Fuller unit root test equation, and the testable hypothesis
is θ  0 (i.e., ρ  1 , y t has a unit root). There are three different tables
depending on your testable equation (w/ or w/o intercept and/or trend variable).
More general version of the original DK test is the Augmented DK test (ADF) as
following.
P
Δy t  θ  y t 1   ω p  Δy t -p 1  u t
p 1
P
Δy t  α  θ  y t 1   ω p  Δy t -p 1  u t
p 1
P
Δy t  α  θ  y t 1  β  t   ω p  Δy t -p 1  u t
p 1
13
In the ADF test, we assume the error terms ( u t ) are independent and have
constant variances. Also, the lag length P in the regression equation is rather
arbitrary. To overcome this problem, Phillips-Perron generalized ADF test as
following:
y t  α *  θ  y t 1  u t
~
~
~θ
yt  α
 y t 1  β  t - T 2   u t
Even though these equations look simpler than ADF test, this test allows far more
general data generating process allowable by the ADF test. Both tests use the
same critical values.
Select the series you want to test unit root, and double click (or View|Show) the
series to get the series window. Click View|Unit Root Test and choose
appropriate options (ADF or Phillips-Perron, and appropriate equation for unit
root test).
7.2. Vector Autoregression (VAR)
VAR is a system of stationary time series variables. Each equation has the same
right-hand side variables consisting of exogenous variables and the lagged values
of all endogenous variables in the system. This system is often used to determine
the causality (Granger-causality) between variables. This system is also useful to
investigate the external shock effects on the endogenous variables using impulse
response function.
Yt  α 10  β 11  Yt 1  β 12  Z t 1  β 13  t  u1t
Z t  α 20  β 21  Yt 1  β 22  Z t 1  β 23  t  u2t
Objects|New Object|VAR and select appropriate entries. For VAR specification,
choose Unrestricted VAR and specify Endogenous and Exogenous variables.
Also specify lag length and sample period.
7.3. Cointegration
When time series variables are non-stationary, it is interesting to see if there is a
certain common trend between those non-stationary series. If two non-stationary
series X t ~ I(1), Yt ~ I(1) has a linear relationship such that
Z t  m  α  X t  β  Yt and Z t ~ I(0) , ( Z t is stationary), then we call the two
series X t and Yt are cointegrated. Two broad approaches to test for the
cointegration are Engel and Granger (1987) and Johansen (1988). Broadly
speaking, cointegration test is equivalent to examine if the residuals of regression
between tow non-stationary series are stationary. For Engel-Granger test, regress
Yt on X t (or vice versa), and use the residual to see if it is stationary (unit root
test described above). If it is stationary, two series X t and Yt are cointegrated.
14
Johansen uses more complicated VAR structure to test the cointegration. EViews
use Johansen test for cointegration.
In a multiple non-stationary time series, it is possible that there is more than one
linear relationship to form a cointegration. This is called the cointegration rank.
For cointegration test, select the series (group of variables) to test cointegration to
obtain group window. Choose View|Cointegration Test and specify appropriate
settings for testing. The setting is whether you want to specify intercept and/or
linear deterministic time trend in the cointegration equation.
7.4. Error Correction Model
If two or more non-stationary time series are cointegrated, then there exists an
Error Correction Model (ECM). Cointegration is a necessary condition for ECM.
ECM describes the long run equilibrium relationship between non-stationary
series. Even though individual series are non-stationary, when they are
cointegrated, there is a long run equilibrium relationship, and ECM explains this
relationship.
ΔX t  m1  θ 11  ΔX t 1  θ 12  ΔYt 1   1  Z t 1  u1t
ΔYt  m2  θ 21  ΔX t 1  θ 22  ΔYt 1   2  Z t 1  u2t
ECM is similar to VAR, but the original series are non-stationary and they are
cointegrated. To estimate ECM, follow the same path as VAR estimation.
Objects|New Object|VAR and select appropriate entries. For VAR specification,
choose Vector Error Correction, and specify appropriate cointegration equation
(i.e., w/ or w/o intercept and/or deterministic time trends).
8. System of Equations
When we have more than one equations to estimate together, we will use additional
information from other equations to improve the efficiency of parameter estimates.
8.1. Seemingly Unrelated Regression
Y1t  β10  β11X1t1  β12 X1t2  u1t
Y2 t  β 20  β 21X2 t1  β 22 X2 t2  u2 t
Y1, Y2  are dependent variables and X1, X2 s are independent variables.
Error terms u1, u2 are contemporaneously correlated, i.e., cov(u1,u2)  0 .
OLS estimators are still consistent, but they are not efficient.
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Objects|New Objects|System and you can give the name of the system in the
Name for Object box for later use. Click OK and then you will have a blank
System window. Type your equations for such that Y1=C(1)+C(2)*
X1+C(3)*X2 for first equation and Y2=C(4)+C(5)* X3+C(6)*X4, etc. Click
Estimate and choose Seemingly Unrelated Regression for SUR model. Since
SUR estimation involves numerical iteration, you can choose appropriate number
of iterations and convergence criteria in the Options button.
8.2. Simultaneous Equation System
Y1t  β10  β11X1t  θ 12 Y2 t  u1t
Y2 t  β 20  β 21X2 t  θ 21Y1t  u2 t
This equation system is different from SUR model in a sense that the dependent
variables appear in the right hand side of each equation. Because of this
endogeneity problem, simple OLS of each equation will yield inconsistent
estimators. To estimate this simultaneous equation system, each equation should
fist satisfy identification condition of order condition and rank condition.
8.2.1. Two Stage Least Squares (TSLS).
This is one of the most often used estimation methods for simultaneous
equation. The first stage of the TSLS estimation involves the estimation of all
endogenous variables on all exogenous variables in the system and some other
instrumental variables. The second stage is the least squares estimation of the
structural equations using the estimated values of the endogenous variables
from the first stage. The structural parameters are estimated in each equation
separately.
8.2.2. Three Stage Least Squares (3SLS)
3SLS is more efficient estimation procedure than TSLS in the sense that 3SLS
estimates entire structural parameters all at once. The first two stages of 3SLS
is equivalent to the TSLS, but 3SLS uses TSLS estimates to estimate covariance structure of entire system. Using the estimated co-variances of the
system, the final stage (the third stage) is the GLS estimation method of the
entire system. This method is more efficient than TSLS.
To use either one of above estimation method, click Objects|New Object|System
as above for SUR estimation. In the System window, type in only the behavioral
equations. Behavioral equations are the ones with structural parameters to
estimate. Ignore any other identities in the system. Type your equations for such
that Y1=C(1)+C(2)* Y2+C(3)*X1 for first equation and Y2=C(4)+C(5)*
Y1+C(6)*X2, etc. Since this is TSLS or 3SLS estimation, you need to specify
instrumental variables for the first stage estimation. After the structural
equations, you need to specify which variables to use as instrumental variables.
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For TSLS and 3SLS, you need all exogenous variables in the system for the
instrumental variables. Type INST X1 X2. Constant is automatically included as
an instrumental variable. Click Estimate in the System menu bar. You will have
a choice of different estimation methods. Choose either Two Stage Least
Squares or Three Stage Least Squares.
8.3. Generalized Method of Moment (GMM) Estimation
GMM estimation is relatively new estimation technique in econometrics and it is
intuitively appealing because of its weak assumptions of estimation process. This
is one example of growing literature of semi-parametric estimation methods.
GMM uses the sample analog of population orthogonality condition to estimate
parameters. For example, if the exogenous variable ( X t ) is independent of
random disturbance term ( u t ), then we have the population orthogonality
condition EX t  u t   0 . Then, we have Eut X t   0 and Eu t  gX t   0 for
any function of g . From this population orthogonality condition, we can form
1 T
sample analogs of population orthogonality conditions such that  u t  0 and
T t 1
T
1
 u t  X t  0 , where ut  Yt  β0  β1  X t . These are called the sample
T t 1
moments, and we estimate the population parameters by minimizing the following
criteria function Sβ  .
 1 T

ut 


'
T
Sβ   m T  WT  m T , where m T   T t 1
 , and WT is a weighting matrix
1 u X 
t
t
 T 

t 1

defined as mT β   mT β 

' 1
.
EViews provides GMM estimation method in the system of equation estimation.
Follow the same step as above for TSLS (3SLS). Type appropriate estimation
equations and instrumental variables list, then choose GMM. Depending on the
data structure, choose appropriate method either for heteroskedasticity or
autocorrelation problem.
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