Tài liệu Analytical Methods: EViews and Panel Data ppt

Hypothesis Testing In panel data models as in single-equation multiple-regression models we are interested in testing two types of hypotheses: hypotheses about the variances and covarian

Fulbright Economics Teaching Program

First Semester 2002

Analytical Methods

EViews and Panel Data

EViews POOL objects operate on variables that have special two-part names The first part is the name of the variable, and the second part of the name is the cross-section identifier that indicates which cross-sectional unit the variable belongs to It is good practice (though not necessary) to begin cross-section identifiers with an underscore mark to make the full variable names more readable

Example: Suppose we want to work with a panel data set on the USA, Canada, and Mexico The variables that we want to use are GDP, Population, and Trade Flows

Variable Name First Part:

GDP POP TRA Variable Name Second Part (Cross-Section Identifier)

_USA _CAN _MEX Variables

Thus, there are nine variables in our EViews workfile It is easy to see that panel data sets can quickly become very large For example, if we have a panel of 61 Vietnamese provinces for which

we have ten-year time series on 8 variables related to agriculture, then our workfile has (61 x 8) =

488 variables

After you have named all of your variables and have got the data into an EViews workfile, you are ready to create the POOL object You do this by clicking the following sequence:

Objects / New Object / Pool

A window will open with space for you to list your cross-section identifiers:

we type a command using GDP? EViews uses all three GDP series for the USA, Canada, and Mexico

Notice the button PoolGenr PoolGenr is used to create new variables according to rules that are similar to the rules for ordinary Genr For example, if we want to create GDP Per Capita for all three countries in our POOL, we would click PoolGenr and then type the equation:

GDPPC? = GDP? / POP?

For estimation, EViews has one

window in which the user specifies

the equation and the assumptions

regarding the stochastic disturbance

term That window is shown here

We will describe each element of

the specification window

Dependent Variable

The dependent variable will be

typed in according to its name and

question mark For example, you

might use GDPPC?

By default, EViews will use the largest sample possible in each cross-section An observation will

be excluded if any of the explanatory or dependent variables for that cross-section are unavailable

in that period

If the box for Balanced Sample is checked, EViews will eliminate an observation if data are

unavailable for any cross-section in that period.

Common Coefficients

In this field you list all explanatory variables that you assume have the same slope coefficient for every cross-sectional unit Use the format VAR? You may use AR(p) specifications if you want

to model autocorrelation Keep in mind that your panel data set should have a rather long time series dimension in order to get reliable estimators of the autocorrelation coefficients

Cross-Section Specific Coefficients

In this window you type the names of all explanatory variables that you assume have different slope coefficient values for different cross-sectional units Use the format VAR?

Intercept

Here you specify whether your model has

No intercept this case is rare

Common intercept this case is unusual

Fixed Effects the typical specification.1

Random Effects this specification is not often used because it requires strong

assumptions that are difficult to meet in practice

Weighting

Here, weighting refers to "feasible weighted least squares."

No weighting no equation-specific heteroscedasticity

Cross-section weights feasible WLS to correct for equation-specific heteroscedasticity SUR accounts for contemporaneous cross-equation correlation of errors

and equation-specific heteroscedasticity To use this, the time-series dimension must exceed the cross-section dimension (T > N)

1 If you check this option you will see that the EViews output does not report standard errors, t-stats, or p-values for

the estimates of the fixed effects If you are interested in these (especially for conducting Wald test on these

GLS coefficient estimators, then update the feasible GLS coefficient estimators; compute new residuals based on the new GLS

coefficient estimators, then update the feasible GLS coefficient estimators, etc

Options

There is only one option: Whites HCCM can be produced if you do not choose SUR

Hypothesis Testing

In panel data models (as in single-equation multiple-regression models) we are interested in testing two types of hypotheses: hypotheses about the variances and covariances of the stochastic error terms and hypotheses about the regression coefficients The general to simple procedure provides

a good guide

Before testing hypotheses about the regression coefficients, it is important to have a good

specification of the error covariance matrix so that the test statistics for the regression coefficients are reliable

Testing Hypotheses About The Error Covariance Matrix

It is helpful to think about restricted and unrestricted error covariance matrices.

An error covariance matrix is a square matrix with the error variances of the individual cross-sectional equations along the diagonal and with the contemporaneous error covariances on the off-diagonal elements All covariance matrices are symmetric, so if we specify an error covariance matrix for a panel model with five cross-sectional units we have a (5 x 5) matrix with five diagonal units and ten off-diagonal units:

2

2

2

2

2 5

σ

If we click the button for SUR, EViews will estimate all of these parameters On the other hand, if

we believe that the cross-sectional units do not have any contemporaneous cross-equation error covariances, we would click the button for Cross-Section Weighting and EViews would impose zero restrictions on all of the off-diagonal elements of the matrix Only the diagonal elements would be estimated:

1

2 2 2 3 2 4 2 5

0

σ

σ

σ σ σ

The second model involves imposing ten restrictions, compared to the first model

Finally, if we assumed that our stochastic disturbances were free of cross-sectional

heteroscedasticity, we click the No Weighting button and EViews would estimate only one diagonal element instead of five: four restrictions would be imposed, compared to the second model

2

2 2 2 2

0

σ

σ

σ σ σ

Testing these restrictions is easily accomplished by means of a test called a likelihood ratio test EViews output reports a statistic called the Log-Likelihood This is an estimator of the joint

probability of the observed sample, given the point estimates of the parameters As such, it is a number bounded by zero and one

All of our estimation methods aim to maximize this log-likelihood In many applications, maximizing the log-likelihood leads to exactly the same estimator as the Least-Squares method does, but the analytical work required is heavier, so we follow the Least-Squares approach Our interest here is in the extent to which imposing restrictions on the error covariance matrix reduces the log-likelihood statistic

If we form a ratio of the likelihood of a restricted model ˆL divided by the likelihood of an R

unrestricted model ˆL , we expect the ratio to be less than 1 because the maximum likelihood U

subject to a restriction can be no greater than the maximum likelihood of the unrestricted model

Define the likelihood ratio: ˆˆR

U

L L

=

l Then 0 1≤ l ≤

If the restricted model is not significantly different from the unrestricted model we expect the likelihood ratio to be close to 1 The distribution theory of the likelihood ratio is a bit

cumbersome However, it is well known that the distribution of 2 log( )− × l is asymptotically

( ) ( )

2 log( ) 2 log L R log L U approx ~ χ

− × l = − × − where q is the number of

restrictions

Under the null hypothesis we expect 2 log( )− × l to be close to zero; we reject the null

hypothesis if the realized value of the likelihood ratio statistic exceeds an appropriate critical value

or if the p-value of the test is smaller than the pre-selected significance level

Maintained Model

While testing hypotheses about restrictions on the error covariance matrix, some specification of the panel data regression model must be maintained It is recommended that the maintained model

be "general" in the sense that we used that term in describing the "general-to-simple" modeling strategy

Testing Restrictions on the Panel Data Model

After a sound specification for the error covariance structure has been established, tests associated with the general to simple modeling strategy may be undertaken These tests may be the usual Wald tests or t-tests on individual coefficients

Keep in mind that when the cross-section weights or SUR methods or any AR(p) specification is used, the results all asymptotically based so that the t-stats are approximately standard normal and the Wald F-stats are approximately Chi-Squared

Unrestricted Model

The completely unrestricted model is this one:

Y = α + β X + β X + L + β X + ε

In this model, the intercepts and the partial regression coefficients vary across cross-sectional units If either the no-weighting or cross-sectional weights option is chosen for the error

covariance structure, then the results will be exactly the same as applying OLS to the data for each cross sectional unit

If the SUR option is chosen, then efficiency will be enhanced by exploiting the information

contained in the cross-equation error covariances Remember that ( T > N ) is required to use this option

Partially Restricted Model

In many panel data sets the time-series dimension is quite short so it is impractical to estimate the model for which all parameters vary across cross-sectional units In this case the most general

feasible model is the fixed-effects model: only the intercepts vary across cross-sectional units; the partial regression coefficients are the same for all cross-sectional units

Of course, there are models in which some partial regression coefficients are identical across cross-sectional units while others vary

Restricted Model

The most restrictive model is the one in which the intercepts and the partial regression coefficients are identical for all cross-sectional units

Testing model restrictions may be done via the Wald Coefficient test or via the likelihood ratio test The two methods are asymptotically equivalent, though they may give different results for a particular finite sample

As you move through the general-to-simple modeling strategy it is sensible to re-check the error covariance structure as you impose restrictions on the model's partial regression coefficients and intercepts Even though you may fail to reject the hypotheses that represent restrictions that you

impose, the hypotheses may not be perfectly true, and that may affect the estimators and tests of

the error covariances

[Written by Eshragh Motahar based on notes by M D Westbrook, and the EViews manual.]