Файловый архив студентов. Файловый архив студентов.
1261 вуз, 4607 предмет.
/ Регистрация
FAQ Обратная связь Вопросы и предложения
Добавил:
Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Челябинский Государственный Университет
Предмет:
[НЕСОРТИРОВАННОЕ]
Файл:
Eviews5 / EViews5 / Docs / EViews 5 Users Guide.pdf
Скачиваний:
152
Добавлен:
23.03.2015
Размер:
11.51 Mб
Скачать
☆
►Содержание►

650—Chapter 21. Discrete and Limited Dependent Variable Models

Procedures for Censored Equations

EViews provides several procedures which provide access to information derived from your censored equation estimates.

Make Residual Series

Select Proc/Make Residual Series, and select from among the three types of residuals. The three types of residuals for censored models are defined as:

Ordinary

 

 

eoi

=

yi −

E( yi

 

ˆ

ˆ

 

 

 

xi, β,

σ)

 

 

 

 

 

 

 

 

 

 

 

 

Standardized

 

 

 

 

 

yi −

E( yi

 

ˆ

ˆ

 

 

 

esi

=

xi, β,

σ)

 

 

 

--------------------------------------------var( yi

 

 

ˆ

ˆ

 

 

 

 

 

 

 

 

 

 

 

 

 

 

xi, β, σ)

 

 

 

 

 

 

 

 

 

 

 

 

Generalized

 

 

 

 

( ( ci

− xi

ˆ

 

ˆ

 

 

 

egi = −

f

′β) ⁄

σ)

1

( yi ≤ ci)

 

---------------------------------------------

 

 

ˆ

 

ˆ

 

 

 

 

σF( ( ci − xi′β)

⁄ σ)

 

 

 

 

 

 

 

 

ˆ

ˆ

 

 

 

 

 

−

f′( ( ci − xi′β) ⁄ σ)

1( ci < yi ≤ ci)

 

σF---------------------------------------------

 

 

 

ˆ

ˆ

 

 

( (ci − xi′β) ⁄ σ)

 

 

 

 

 

 

f( ( ci −

ˆ

ˆ

 

 

 

 

 

+

xi′β) ⁄ σ)

1

( yi ≤ ci)

 

 

− F

( ( ci

− xi

ˆ

 

ˆ

 

σ( 1

′β) ⁄

σ) )

 

 

where f , F are the density and distribution functions, and where 1 is an indicator function which takes the value 1 if the condition in parentheses is true, and 0 if it is false. All of the above terms will be evaluated at the estimated β and σ . See the discussion of forecasting for details on the computation of E( yi xi, β, σ) .

The generalized residuals may be used as the basis of a number of LM tests, including LM tests of normality (see Lancaster, Chesher and Irish (1985), Chesher and Irish (1987), and Gourioux, Monfort, Renault and Trognon (1987); Greene (1997), provides a brief discussion and additional references).

Forecasting

EViews provides you with the option of forecasting the expected dependent variable,

E( y

i

 

x , β, σ) , or the expected latent variable, E( y

 

 

x , β, σ) . Select Forecast from the

 

 

 

 

 

i

i

 

 

i

equation toolbar to open the forecast dialog.

To forecast the expected latent variable, click on Index - Expected latent variable, and enter a name for the series to hold the output. The forecasts of the expected latent variable E( yi xi, β, σ) may be derived from the latent model using the relationship:

Procedures for Censored Equations—651

ˆ

 

 

ˆ ˆ

ˆ

(21.29)

 

yi

= E( yi

 

xi, β, σ) =

xi′β .

To forecast the expected observed dependent variable, you should select Expected dependent variable, and enter a series name. These forecasts are computed using the relationship:

ˆ

 

 

 

ˆ

 

ˆ

ci Pr( yi = ci

 

ˆ

ˆ

 

 

(21.30)

 

 

 

 

 

 

yi = E( yi

 

xi, β,

σ) =

 

xi, β, σ)

 

 

 

 

ci

 

< ci;

ˆ ˆ

 

 

 

< ci

 

ˆ

ˆ

 

 

 

 

+ E( yi

 

< yi

xi, β, σ)

Pr( ci < yi

 

xi, β, σ)

+ ci Pr( yi = ci

 

ˆ

ˆ

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

xi, β, σ)

 

 

 

 

 

 

 

Note that these forecasts always satisfy i ≤ ˆ i ≤ i . The probabilities associated with c y c

being in the various classifications are computed by evaluating the cumulative distribution function of the specified distribution. For example, the probability of being at the lower limit is given by:

Pr( yi = ci

 

ˆ ˆ

Pr( yi

 

≤ ci

 

ˆ ˆ

ˆ

ˆ

(21.31)

 

 

 

 

xi, β, σ) =

 

 

xi, β, σ) =

F( ( ci − xi′β) ⁄ σ) .

Censored Model Illustration

As an example, we replicate Fair’s (1978) tobit model that estimates the incidence of extramarital affairs. The dependent variable, number of extramarital affairs (Y_PT), is left censored at zero and the errors are assumed to be normally distributed. The bottom portion of the output is presented below:

 

Coefficient

Std. Error

z-Statistic

Prob.

 

 

 

 

 

C

7.608487

3.905837

1.947979

0.0514

Z1

0.945787

1.062824

0.889881

0.3735

Z2

-0.192698

0.080965

-2.380015

0.0173

Z3

0.533190

0.146602

3.636997

0.0003

Z4

1.019182

1.279524

0.796532

0.4257

Z5

-1.699000

0.405467

-4.190231

0.0000

Z6

0.025361

0.227658

0.111399

0.9113

Z7

0.212983

0.321145

0.663198

0.5072

Z8

-2.273284

0.415389

-5.472657

0.0000

 

 

 

 

 

 

Error

Distribution

 

 

 

 

 

 

 

SCALE:C(10)

8.258432

0.554534

14.89256

0.0000

 

 

 

 

R-squared

0.151569

Mean dependent var

1.455907

Adjusted R-squared

0.138649

S.D. dependent var

3.298758

S.E. of regression

3.061544

Akaike info criterion

2.378473

Sum squared resid

5539.472

Schwarz criterion

2.451661

Log likelihood

-704.7311

Hannan-Quinn criter.

2.406961

Avg. log likelihood

-1.172597

 

 

 

 

 

 

 

Left censored obs

451

Right censored obs

0

Uncensored obs

150

Total obs

 

601

 

 

 

 

 

652—Chapter 21. Discrete and Limited Dependent Variable Models

Tests of Significance

EViews does not, by default, provide you with the usual likelihood ratio test of the overall significance for the tobit and other censored regression models. There are several ways to perform this test (or an asymptotically equivalent test).

First, you can use the built-in coefficient testing procedures to test the exclusion of all of the explanatory variables. Select the redundant variables test and enter the names of all of the explanatory variables you wish to exclude. EViews will compute the appropriate likelihood ratio test statistic and the p-value associated with the statistic.

To take an example, suppose we wish to test whether the variables in the Fair tobit, above, contribute to the fit of the model. Select View/Coefficient Tests/Redundant Variables - Likelihood Ratio… and enter all of the explanatory variables:

z1 z2 z3 z4 z5 z6 z7 z8

EViews will estimate the restricted model for you and compute the LR statistic and p- value. In this case, the value of the test statistic is 80.01, which for eight degrees of freedom, yields a p-value of less than 0.000001.

Alternatively, you could test the restriction using the Wald test by selecting View/Coefficient Tests/Wald - Coefficient Restrictions…, and entering the restriction that:

c(2)=c(3)=c(4)=c(5)=c(6)=c(7)=c(8)=c(9)=0

The reported statistic is 68.14, with a p-value of less than 0.000001.

Lastly, we demonstrate the direct computation of the LR test. Suppose the Fair tobit model estimated above is saved in the named equation EQ_TOBIT. Then you could estimate an equation containing only a constant, say EQ_RESTR, and place the likelihood ratio statistic in a scalar:

scalar lrstat=-2*(eq_restr.@logl-eq_tobit.@logl)

Next, evaluate the chi-square probability associated with this statistic:

scalar lrprob=1-@cchisq(lrstat, 8)

with degrees of freedom given by the number of coefficient restrictions in the constant only model. You can double click on the LRSTAT icon or the LRPROB icon in the workfile window to display the results in the status line.

A Specification Test for the Tobit

As a rough diagnostic check, Pagan and Vella (1989) suggest plotting Powell’s (1986) symmetrically trimmed residuals. If the error terms have a symmetric distribution centered at zero (as assumed by the normal distribution), so should the trimmed residuals. To con-

Procedures for Censored Equations—653

struct the trimmed residuals, first save the forecasts of the index (expected latent variable): click Forecast, choose Index-Expected latent variable, and provide a name for the fitted index, say XB. The trimmed residuals are obtained by dropping observations for which

ˆ

ˆ

ˆ

xi′β < 0

, and replacing yi with 2( xi′β)

for all observations where yi < 2( xi′β) . The

trimmed residuals RES_T can be obtained by using the commands:

series res_t=(y_pt<=2*xb)*(y_pt-xb) +(y_pt>2*xb)*xb

smpl if xb<0

series res_t=na

smpl @all

The histogram of the trimmed residual is depicted below.

This example illustrates the possibility that the number of observations that are lost by trimming can be quite large; out of the 601 observations in the sample, only 47 observations are left after trimming.

The tobit model imposes the restriction that the coefficients that determine the probability of being censored are the same as those that determine the conditional mean of the uncensored observations. To test this restric-

tion, we carry out the LR test by comparing the (restricted) tobit to the unrestricted log likelihood that is the sum of a probit and a truncated regression (we discuss truncated regression in detail in the following section). Save the tobit equation in the workfile by pressing the Name button, and enter a name, say EQ_TOBIT.

To estimate the probit, first create a dummy variable indicating uncensored observations by the command:

series y_c = (y_pt>0)

Then estimate a probit by replacing the dependent variable Y_PT by Y_C. A simple way to do this is to press Object/Copy Object… from the tobit equation toolbar. From the new untitled equation window that appears, press Estimate, replace the dependent variable with Y_C and choose Method: BINARY and click OK. Save the probit equation by pressing the Name button, say as EQ_BIN.

Соседние файлы в папке Docs
Помощь Обратная связь Вопросы и предложения Пользовательское соглашение Политика конфиденциальности