tutorial8 estimation

8/11/2019 Tutorial8 Estimation

http://slidepdf.com/reader/full/tutorial8-estimation 1/62

EViews TrainingBasic Estimation



Basic Regression Analysis• EViews has a very powerful and easy-to-use estimation toolkit that

allows you to estimate from the simplest to the most complexregression analysis.

• This tutorial explains basic regression techniques in EViews for singleequation regressions using cross-section data.

• The main topics include: Specifying and estimating an equation Equation Objects (saving, labeling, freezing, printing) Equation Output: Analyzing and Interpreting results Multiple Regression Analysis Estimation with Data Expressions and Functions

Post Estimation: Working with Equations Hypothesis testing Estimation Options (robust standard errors, weighted least squares)

2



Estimation: the Basics

Note: Information for examples in this portion of tutorial:Data: Tutorial12_data.xlsResults: Tutorial12_results.wf1 Practice Workfile: Tutorial12.wf1



Description of Data File• Data_wf1 has the following data on 9,275 individuals*

Wealth – net total financial wealth (in thousands of dollars)Income – annual income (in thousands of dollars)Male – dummy variable, equal to 1 if male, 0 otherwiseMarried – dummy variable, equal to 1 if married, 0 otherwise

Age – age in years (minimum age in the dataset is 25 years).Fsize – family size; number of individuals living in the family.

4

* This data is from Wooldridge, Introductory Econometrics (4 th Edition).



Equation Object: Specification andEstimation



The Equation Object• Single equation regression estimation in EViews is performed using the

Equat ion Object .

There are a number of ways to create a simple OLS Equation Object:

6

1. From the Main menu,select Object → NewObject → Equation.

2. From the Main menu, select Quick → Estimate Equation.

3. On the command windowtype: ls



The Equation Box• In all cases, the Equat ion Es t imat ion box appears.

You need to specify three things in this dialogue box:1. The equation specification.2. The estimation method.3. The sample.

7

Specify your equation either by:a) Listb) Formula (explained in future

tutorials)

Specify your estimation method

Specify your sample



Specifying an Equation by List• The easiest way to specify a linear equation is to provide a list of variables

that you wish to use in the equation.

8

• Suppose that you would like toknow how well income explainsf inanc ial wealth .

• To accomplish this, type in the

Equation Estimation box1. The dependent variable ( wealth ).2. “c” for constant. 3. The independent variable

(i n c o m e ).

Notice that all the entries are all

separated by spaces.



Specifying Equation by List (cont’d)

• Alternatively, you can also create an Equation simply by selecting theseries and opening them as Equation.

9

To create an equation:1. Select weal th and i n c o m e by

clicking on these series in theworkfile (press CTRL to select

multiple series). Notice that youneed to select the independentvariable ( wealth ) first.

2. Right click and select Open → as Equation.



Specifying Equation by List (cont’d)

3. The Equation Estimation dialog box opens, listing your independent, dependent variables, andthe constant.

4. Click OK to estimate regression.

10



Estimation Method• After you specify the variable list, you

need to select an estimation method.• Click on the Method option, and you

see a drop-down menu listing thevarious estimation method you canperform in EViews.

• Standard, single equation regression, is

performed using “Least Squares” (LS).• In this tutorial we will use Least Squares

and defer discussion of more advancedestimation techniques in subsequenttutorials.

11



Estimation Sample• The third item you need to specify in the equation box is the Sample .• You can specify the sample period in the sample space of the equation box.

For example, to estimate the following regression over the entire sample:1. You need to include all observations (1 to 9275).2. Click OK to estimate the regression. As seen in Equation Output, EViews has included

all observations when estimating this regression.

12



Estimation Sample (cont’d)

• What if you want to estimate the effect of income on wealth, but only for a subset ofindividuals, e.g., married men?

To target a specific sample you need to:1. Specify the sample: in this case male and single so type: if married=1 and

male=1 .2. Click OK to estimate the regression. As seen in Equation Output, EViews has included

only a subset of total observations (534 obs.)

13



Equation Object:Saving, Labeling, Freezing, Printing



Equation Objects:Saving, Labeling, Freezing, Printing

• After you estimate an equation, you can save the output.

15

To accomplish this task:1. On the Equation box, click the

button on the top menu. The Objec tName dialog box opens.

2. Type the name of the equation (in thiscase new_equation ) and click OK .

3. The equation will appear in the workfilewindow marked with the icon.



To accomplish this task:

1. Click the button onthe top menu of theEquation Box.

Equation Objects:Saving, Labeling, Freezing, Printing (cont’d)

• If you want to save the equation output so that it won’t ever change (even ifyou re-estimate the regression), you can Freeze the results.

• Freezing the equation makes a copy of the current view in the form of a tablewhich is detached from the Equation Object.

16



17

2. A table view of the equationresults opens up (shown tothe right).

3. You can save this table, byclicking the button inthe Table Object and namethe table in the Object Namebox (shown below; in thiscase we name it table_eq1 ).

Equation Objects:Saving, Labeling, Freezing, Printing (cont’d)



Equation Output:Analyzing and Interpreting Results



Equation Output• Let’s analyze the results from our simple estimation, which includes only one

explanatory variable ( i n c o m e ) and an intercept.

• The Equation box has three main parts, which we will discuss in turn:1. The top panel summarizes the input for the regression.2. The middle panel summarizes information about regression coefficients.3. The bottom panel provides summary statistics about the entire regression.

19

Top Panel

Middle Panel

Bottom Panel



Equation Output (cont’d)

• The top panel provides information about regression inputs.

20

Element Description

Dependent Variable Denotes the dependent variables.

Method Denotes the method of estimation (least squares in this example).

Date/Time Shows the date and time when the regression was carried out.

Sample Shows the sample period over which the regression is carried out.

IncludedObservation

Shows the number of observations included in estimation.




• The middle panel provides information about the estimated coefficients.

21

Element DescriptionCoefficient Values • Income coefficient measures the marginal contribution of income to

wealth.• C is the estimated constant (or intercept) of the regression.

Standard Errors • Reports the standard errors of the coefficient estimates.• The larger the standard errors, the more noisy the estimates.

t-Statistic • Reports the t-statistics, computed by dividing coefficient estimatesby their standard errors.• Is used to test whether the coefficient in that row equals zero.

Prob. (p-value) • Reports probability of drawing a t-statistic as extreme as the oneactually estimated.

• Is used to test whether the coefficient is equal to zero (against atwo-sided alternative).




• The bottom panelprovides informationregarding the summarystatistics for the entireregression.

22

Statistic Description

R-squared Measures the success of the regression in predicting the values ofdepended variable.

Adjusted R-squared Adjusts for the number of independent regressors by penalizing R-squared for additional regressors.

S.E. of regression Is a summary measure based on estimated variance of the residuals.

Sum squared resid Reports the sum of squared residuals. The same as (S.E. ofregression) 2 * (T-k-1) , where T is the number of observations (9,275here), k is the number of independent variables (k=1 here).

Log-likelihood Reports the log likelihood function evaluated at coefficient estimatesassuming normally distributed errors.

F-statistic Tests whether all slope coefficients (excluding the constant) are zero.

Prob(F-Static) Reports the probability of drawing an F-statistics as the one estimated.




23

Statistic DescriptionMean dependent var Shows the mean of the dependent variable (in this case, wealth ).

S.D. dependent var Shows the standard deviation of the dependent variable (i.e, wealth ).

Akaike info criterion Used in model selection; smaller values are preferred.

Schwarz criterion An alternative to Akaike information (AIC) used also for model selection.Imposes a larger penalty for including additional explanatory variables

Hannan-Quinn criter. An alternative to AIC and Schwarz criteria used for model selection. Itemploys a slightly different penalty function than the other two.

Durbin-Watson stat Measures serial correlation in the residuals. As a rule of thumb, a DWstatistic less than 2 is an indication of positive serial correlation.



Multiple Regression Analysis



Multiple Regression Analysis: Estimation

For this, augment the previous modelwith the new independent variables bytyping in the equation box:

1. Wealth – dependent variable2. c – for constant3. Income – the 1st independent variable4. Age – 2nd independent variable5. Fsize – 3rd independent variable

25

• It stands to reason that a better model to explain wealth would be one that includesthe age of the individuals as well as the family size, in addition to their income.



Multiple Regression Analysis:Interpreting Results

26

• Note how the estimation output now

includes the Coefficient, StandardError, t-Statistics and associatedprobability value for each of theregressors in the multiple regression.



Estimation with Data Expressions andFunctions



Estimation with Data Expressions (AutoSeries): Example 1

• For example, a linear regression of wealth on

ag e , assumes that each additional yearincreases wealth by a constant amount ,whether this is the 25 th year of your life or the50 th (remember that the minimum age in thedata is 25).

• A better characterization would be that eachyear (beyond the 25 th) increases wealth by aconstant percentage .

28

• You can use data expressions directly in the equation box to estimate aregression without having to first create these series.*

• Often, log or quadratic functions are used to capture nonlinearities in data.These can be specified directly in the equation box.

*Note: Examples of auto series are alsoprovided in Tutorial on Series & GroupsBasics.



Estimation with Data Expressions (AutoSeries): Example 1 (cont’d)

29

To specify (approximately) a constant percentage effect, type in the equation box:1. log(wealth) – for dependent variable2. c – for constant3. Age – for independent variable




• Notice that our wealth data contains negative values. You cannot take the

logarithm of negative numbers.• By default, EViews will automatically convert any observations which cannot be

evaluated into NAs, and remove them from the regression.• If EViews errors, rather than converting values into NAs, you can change the

default behavior by clicking on Options->General Options->Series and Alphas->Auto-series, and then checking the "Treat evaluation errors as NAs" option.

30




31

• The output of this estimation isshown here. Note how theDependent Variable label as thetop of the output has changed toshow we are now estimating withlog(wealth) as our dependentvariable.

• The Included observations : labelshows that only 6029 observationswere used in the regression. Theremaining 3246 were removed due

to negative wealth values.



Estimation with Data Expressions (AutoSeries): Example 2

• For example, you can estimate aconstant-elasticity model relatingwealth to income.

To specify the constant-elasticitymodel, type in the equation box:

1. log(wealth) – for dependent variable2. c – for constant3. Log(income) – for independent

variable4. This time rather than letting EViews

automatically remove non-valid

observations, we restrict the sampleso that wealth is a positive number.Enter in Sample: if wealth>0.

32

• You can use logs for both dependent and independent variables.



Estimation with Data Expressions (AutoSeries): Example 2 (cont’d).

33

•The results are as shown:



Estimation and Categorical Dummy Variables

• Suppose you want to find out how wealthdepends on the gender of the individualand his/her marital status in addition toincome and age.To determine this, type in the equation box:

1. wealth – for dependent variable2. c – for constant

3. income – 1st independent variable4. Age – 2nd independent variable.5. @expand(male, married) – as additional

independent variables6. Sample: if wealth>0

34

• You can also use @expand function in a regression to estimate the impact of

categorical dummy variables*.• In our dataset:

Male =1 if male, 0 if female Married =1 if married, 0 if single

Note: Examples of categorical dummies are also provided in Tutorial on Dummy Variables.



Estimation and Categorical Dummy Variables(cont’d)

• This happened because the default@expand created a full set of dummyvariables.

• One way to correct this is to exclude theintercept (see Tutorial on DummyVariables for an example).

• An additional method is to keep theintercept, but explicitly exclude one ofthe dummy variables using commands:

@dropf i rs t

@droplas t

@drop

• Let’s use @dropf i rs t in our example.

35

• Notice that something went wrong and you receive the following error message:



Estimation and Categorical Dummy Variables(cont’d )

36

• As seen, one of the dummy variables corresponding to single females ( male=0 and

married=0 ) has dropped out.• The base group therefore is single females; the rest of the dummy coefficients will

be interpreted against this base group.



Post Estimation: Working withEquations



Post Estimation: View Menu

38

• Once the equation object has been estimated you can perform a number of post-estimation tests, diagnostics and other actions from the View and Proc menus.

• Let’s first discuss a few main options in the View menu (others will be discussed insubsequent tutorials):

RepresentationEstimation Output

Actual, Fitted, Residual



Post Estimation: View Menu – Representations

39

• If you click on View → Representation , the equation display changes (asshown below).

• This option displays the equation in three forms:EViews command form

Algebraic equation with symbolic coefficientsEquation with estimated coefficients



Post Estimation:View Menu – Actual, Fitted, Residual

40

• The View Menu, Actual, Fitted, Residual option, provides several different ways atlooking at the residuals and the fitted values of an equation.

• If you click on View → Actu al, Fit ted, Resid ual a number of options appear: Actual, Fitted, Residual Table Actual, Fitted, Residual GraphResidual GraphStandardized Residual Graph



Post Estimation:View Menu – Actual, Fitted, Residual (cont’d)

41

• For a first look, perhaps it’s best to select:View → Actu al, Fit ted, Resid ual → Actual, Fit ted, Residual Graph

• This displays three series:The actual series (dependent variable wealth) – (in red) plotted against theright vertical axis.

The fitted values ( ) from the regression – (in green) plotted against theright vertical axis.

Residuals – (in blue) plotted against the left vertical axis.



42


Note: You can get exactly the sameview by clicking the buttonon the top menu of the EquationObject.

• In this case, the fitted values do

not approximate the actualvalues as well as one wouldhope.

• Similarly, the residuals of theequation are relatively large.




43

• If you would like to view specific

numbers from those graphs,select:

View → Actual, Fitted, Residual →Ac tual, Fit ted, Residu al Table



Post Estimation: Proc Menu

44

• The Proc menu, also offers a number of procedures, after estimation is carried out.• Let’s discuss a few main options in the Proc menu (others will be discussed in

subsequent tutorials):Specify/EstimateMake Regressor GroupMake Residual Series



Post Estimation: Proc Menu – Specify/Estimate

45

• If you click on Proc → Specify/Estimate, the Equat ion Specif ica t ion dialog box

opens up.• You can modify your specification using this dialog box (edit equation, change

estimation method, change sample, etc.)

P E i i



Post Estimation:Proc Menu – Make Regressor Group

46

• You can also create a group consisting of all the variables included in the equation(except the constant).To accomplish this,1. Click on Proc → Make Regressor Group .

P E i i



Post Estimation:Proc Menu – Make Residual Series

47

• You may also want to store residuals so you can recall them later.

• Every time you estimate an equation, EViews automatically places theresiduals of the just-estimated equation in the res id series.

• The problem is that this series cannot be used in an estimation command,because the act of estimation itself changes the values stored in res id .New residuals are stored in res id for every new round of estimation.

P E i i



48

If you want to save these residuals for later use, you can do so by following these steps:1. Click on Proc → Make Residual Series.2. The Make Residuals dialog box opens up. Depending on the estimation you may choose

from three types of residuals: ordinary, standardized, and generalized. For ordinary leastsquares, only the ordinary residuals may be saved.

3. Name the residuals (in this case new_resid ).

Post Estimation:Proc Menu – Make Residual Series



Hypothesis Testing



Hypothesis Testing

50

• We have already shown how to test if a single coefficient equals zero.

• EViews allows you to test more complex hypothesis just as easy.To accomplish this, follow these steps:

1. Click View → Coefficient Diagnostics → Wald Test – Coeff ic ient Res t r i c t ions



Hypothesis Testing (cont’d)

51

2. The Wald Test dialog box opens up.

You will notice:EViews names coefficients c(1), c(2),c(3), etc., numbering them in the orderthey appear in the regression (includingthe constant). For example, in theregression below, the coefficient ofage^2 is c(4).

Specify the hypothesis as an equation inthe Wald Test box. For example to test ifthe coefficient of age^2 is zero, typec(4)=0 . For multiple restrictions, enter multiplecoefficient equations, separated bycommas.



Hypothesis Testing: Example

52

• Suppose you would like to test that all dummy coefficients are zero as shown in

the equation below:H0: c (6)=0, c(7)=0, c(8)=0

To test the coefficients:1. Click View → Coefficient

Diagnos t ics → Wald Test – Coeff icient Restr ic t ions .



Hypothesis Testing: Example (cont’d )

53

2. In the Wald Test dialog box, type the specific restrictions: c(6)=0,c(7)=0,c(8)=0

3. Click OK .

• Results of this test are in the tableshown here.

• EViews computes an F-statistic which

is used to test multiple restrictionhypothesis.• Based on the Probability value (of F-

statistic), we reject the null (p=0.0429< p=0.05).



Heteroskedasticity and RobustStandard Errors



Testing for Heteroskedasticity• EViews allows you to employ a

number of different heteroskedasticitytests.• We will demonstrate the White

Heteroskedasticity tests*.The White test is a test of the nullhypothesis of no heteroskedasticiy,against heteroskedasticity of unknown,general form.It essentially tests whether theindependent variable (and/or theircross terms, x 1

2, x 22, x 1*x2, etc.) help

explain the squared residuals.

To perform the test, follow these steps:1. On the equation box, select View →

Residual Diagnostics →Heteroskedas t i c i ty Tes t s .

55

*Note: For other heteroskedasticity tests and amore complete description of ResidualDiagnostics, please see Tutorial onSpecification and Diagnostic Tests.



Testing for Heteroskedasticity (cont’d)

56

2. The Heteroskedasticity Tests window opensup. Select White under the drop-down menu.

3. You may chose to include or exclude the crossterms. If you do not wish to include the crossterm, uncheck the box “ Include White crossterms ” (as we do here). The test will simply becarried out with only the squared terms.

4. Click OK .



Testing for Heteroskedasticity (cont’d )

57

• Results from the test are shown here.

• The top panel shows the results of theWhite test, while the bottom panelshows the auxiliary regression used tocompute the test statistics.

• The Obs*R-squared statistic (in thetop panel) is the White statistic with a“x2 “ (Chi-Square) distribution.

• From the Prob. Chi-Square value, wedecidedly reject the null ofhomoskedascity.

• This means that the error term is

heteroskedastic and we should adjuststandard errors accordingly.

Addressing Heteroskedasticity:



Addressing Heteroskedasticity:Robust Standard Errors

• One approach to dealing with heteroskedasticity is to correct the standard errors to

account for heteroskedasticity.• EViews provides built-in tools that allows you to adjust standard errors for

heteroskedasticity of unknown form.

58

To derive the White-heteroskedasticityconsistent standard errors, proceed as

follows*:1. Click on the Equation Box.2. The Equat ion Es t imat ion box opens up.

Click Opt i ons .3. Under the Coefficient Covariance matrix

drop-down menu, choose White .4. Click OK .

Addressing Heteroskedasticity:



Addressing Heteroskedasticity:Robust Standard Errors (cont’d)

• EViews re-estimates the equation, this time adjusting the standard errors for

heteroskedasticity.• In order to compare results, we also show results with unadjusted standard errors.

As expected, the estimated coefficient values do not change.But, the adjusted standard errors (and associated t-statistics) are different from the originalregression, suggesting that heteroskedasticity is present and should be corrected.

59



Weighted Least Squares• Suppose that you know the exact

nature of the heteroskedasticity.• For example, suppose you suspect

that heteroskedastity is present in thefinancial wealth regression becausethe variance of the unobserved factorsaffecting financial wealth increaseswith income.

• To express this as an equation: = 2

• You could transform the model bydividing by as shown here.

60



Weighted Least Squares (cont’d)

• This approach to define the model isn’t ideal – it cumbersome and complicated.

• Fortunately, EViews has a built-in method that allows us to perform weighted leastsquares (WLS) in a much easier and intuitive way.

61

To implement WLS in EViews, followthese steps:

1. Click on the Equation Box.2. The Equat ion Es t imat ion box

opens up. Click Opt i ons .3. Under Weights → Type choose

Inverse s td. dev.

4. Under Weights → Weight s e r ies ,specify the type of weights you will

use to transform your data (in thiscase

1).

5. Click OK .



Weighted Least Squares (cont’d)

• Results are identical to the ones we

showed earlier when the datatransformation was performedmanually.

The top panel displays the estimationsetting showing the weights.

The middle panel shows the estimatedcoefficients, standard errors, and t-stats.

The bottom panel shows two types ofstatistics:a. Weighted Stat i s t i cs – corresponding

to the actual estimated equation.b . Unweighted Sta t i s t i cs – computed

using the unweighted data and the

WLS (weighted least squarecoefficients.

tutorial8 estimation

Documents