Testing the validity of the random effects: Hausman test

4.5 Random Effects Model

4.5.1 Testing the validity of the random effects: Hausman test

Testing the validity of the Random effects uses the Hausman test. The test tests whether the random effects are correlated with the other regressors.

Select random effects option from the drop-down menu here

Step 1: Estimate the random effects model:

Step 2: The Hausman test:

The Decision rule is as shown in the table.

Random Effects Fixed Effects Hypothesis

0 ] / [ui Xi 

E E[ui/Xi]0

Basis of test _FE_RE

Decision If p-value > 0.05, fail to reject the null that the model is correctly specified as a RE

Error Component Model Analysis

References

Ashcraft, Adam B., 2006. New evidence on the lending channel. Journal of Money, Credit and Banking, 38, 751-775.

Altunbas, Y., Fazylov, O., and Molyneux, P., (2002). Evidence on the Bank Lending Channel in Europe. Journal of Banking and Finance. 26:11. 2093-2110.

Bernanke, B.S. and Gertler, M., (1995). Inside the black box: The credit channel of monetary policy. Journal of Economic Perspectives. 9:4. 27-48.

De Bondt, Gabe, J., 1999. Credit channels in Europe: Cross-country investigation.

Research Memorandum WO&E no. 569. De Nederlandsche Bank, February.

Ehrmann, M., Gambacorta, L., Martinez-Pages, J., Sevestre, P., and Worms, A., (2001). Financial systems and the role of banks in monetary policy transmission in the euro area. European Central Bank Working Paper No.

105.

Favero, Carlo A., Giavazzi, Francesco, Flabbi, Luca, 1999. The Transmission mechanism of monetary policy in Europe: Evidence form banks’ balance sheets. National Bureau of Economic Research, Working Paper no. 7231.

Gambacorta, Leonardo, 2005. Inside the bank lending channel. European Economic Review, 49, 1737-1759.

Kashyap, A.K., and Stein, J.C, (2000). What Do a Million Observations on Banks Say about the Transmission of Monetary Policy? American Economic Review. 90:3. 407-428.

Kashyap, Anil K., Stein, Jeremy C., 1995. The impact of monetary policy on bank balance sheets. Carnegie-Rochester Conference Series on Public Policy 42, 151-195.

Kashyap, Anil K., Stein, Jeremy C., 1997. The role of banks in monetary policy: A survey with implications for the European Monetary Union. Economic Perspectives, Federal Reserve Bank of Chicago 21, pp. 2–19.

Kishan, Ruby P., Opiela, Timothy P., 2000. Bank size, bank capital, and the bank lending channel. Journal of Money, Credit and Banking, 32, 121-141.

Sichei, M. (2005). Bank Lending Channel in South Africa: Bank-Level Dynamic Panel Data Analysis. Working Paper: 2005-2010, Department of Economics, University of Pretoria.

Sichei, M.M., and Njenga, G., (2012), Does Bank-Lending Channel Exist in Kenya? Bank-Level Panel Data. AERC Research Paper No. 249.

Chapter 5

Error Component Model Analysis:

Two Way Error Components Model

5.0 Introduction

In Chapter 4 we demonstrated how to estimate the one-way-error components model using both the long- and short- cut methods implemented in Eviews. In this part we now turn to the estimation of the two-way-error components model. Recall the general panel model specification

y 



 X



u ₁

Where the error term u is represented as follows:

u_it v_i 



_t 



_it 2

Where: v… the cross –section effect (time invariant), t, time effect (cross-section invariant) and e the error term with the usual properties (details to be provided). In the case where both vi and ti are non-zero, i.e.:

u_it v_i 



_t 



_it 3c

This is referred to as a 2-way-error components model.

5.1 Estimation of the Error Components Model

Estimation of the two-way-error components model follows the same approach as the one-way error components model. However, the mechanics are more involving as we now demonstrate in this section. We now demonstrate the fixed effect and random effect estimation methods in the context of 2-way error components model.

5.1.1 Fixed effects model

The fixed effects model assumes that vi are separate parameters. To estimate these separate parameters we use one of the following two equivalent methods: the least squares dummy variable method and the within-q- estimation method.

5.1.1.1 Two –way – error components model: The least squares dummy variable estimation method

The specific steps involved in estimating this equation are as follows:

Step 1: preparation of data: We present the data as shown in Table 5.1 and also compute time- and cross-section means as shown in the green columns for each variables Size and Loan. In addition, we compute the mean of means shown on the year cell in the table.

Error Component Model Analysis

Table 5.1: Data

Step 2: data transformation: In this case the new data (transformed data) is obtained by subtracting the mean of cross-sections, mean of time periods and adding back the mean of means to obtain the following data:

Table 5.2: transformed data:

BANK SIZE

Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5 Spread_Bank1 Spread_Bank2 Spread_Bank3 Spread_Bank4 Spread_Bank5

2000 6.3 4.6 6.7 4.1 3.5 5.0 4.4 5.7 5.3 15.9 4.6 7.2

SizeT2_Bank1 SizeT2_Bank2 SizeT2_Bank3 SizeT2_Bank4 SizeT2_Bank5 SpreadT2_Bank1 SpreadT2_Bank2 SpreadT2_Bank3 SpreadT2_Bank4 SpreadT2_Bank5

2000 1.7 0.8 -4.2 2.8 -1.0 -2.8 -1.4 -1.9 8.8 -2.6

INTEREST RATE SPREAD BY BANK BANK SIZE

Step 3: Copy and paste the data presented on Table 5.2 and paste it in Eviews in a manner similar to the one discussed in Chapter 3 and 4. You follow the steps by first going to the main tool bar and choose

‘Object’….. New object….pool’. Once you choose ‘pool’ you will be prompted to list the ‘cross-section identifiers’ and you if you had settled on some specific identifiers you then will be able to see an output similar to the one below.

Step 4: Estimation: once the cross section identifiers have been listed then process to the tool bar on that dialog box and click on ‘Estimate’ to obtain the dialog box ‘pool estimation’ shown above. Then populate it with the dependent variable ‘spreadt2’and regressors ‘SizeT2’ and a constant ‘C’ as shown in Step 3. To obtain the estimation result click on ‘OK’ to obtain the following output:

Error Component Model Analysis

The output presented is based on a long method but is a step by step way of demonstrating how the 2-way –error components model is estimated using fixed effects. We now turn to a short cut when is implemented by copying and pasting the raw data from Excel to Eviews (i.e. without transformation

‘Loan’(spread and ‘Size’). Once this is done, follow the process of creating a pool object as discussed above to obtain the following screen:

Step 5: populating the ‘pool estimation’ dialog box. For one to implement the 2 way fixed effects model we first need to input the dependent variable in the space ‘Dependent variable’ in our case the dependent variable is ‘Spread’ and also the space for regressors’ in our case the regressors are ‘Size’ and C.

To indicate that this is a two-way- error component’ we go to ‘Estimation Method’. Click on the arrow down in the area marked ‘cross-section’ and select ‘Fixed’ and go the area indicated as Period and select ‘Fixed as well’.

Do not change any of the spaces provided as shown in Panel A. This will result in the output in Panel B:

Panel A Panel B

Now you may notice that the result obtained above is similar to the one obtained earlier. For comparison see the following set of output. Notice that the coefficient for bank size is the same in both cases as shown below:

is this correct?

Error Component Model Analysis

Chapter 6

Dynamic Panel Data Analysis

So far we have estimated static panels. However, in the case were the lagged dependent variable is included as an explanatory variable this results is econometric problems. It does not sound right A simple dynamic model may be presented as follows:

y_it y_i_,_t_1X_it _i _t _it variable then strict exogeneity of the regressors no longer holds. The lagged variable introduces endogeneity problem in which case the LSDV is no longer consistent when N tends to infinity and T is fixed.

The LSDV estimator is consistent for the static model whether the effects are fixed or random. Therefore need to show that the LSDV is inconsistent for a dynamic panel data with individual effects, whether the effects are fixed or random. The bias of the LSDV estimator in a dynamic model is generally known as dynamic bias or Nickell’s bias (1981).

To deal with this we use a number of estimators:

6.1 Arellano and Bond Estimator

To get consistent estimates in GMM for a dynamic panel model, Arellano and Bond appeals to orthogonality condition that exists between Y

it-1 and v

to choose the instruments. Consider the following simple AR(1) model:

 

To get a consistent estimate of  as N-> infinity with fixed T, we need to difference this equation to eliminate individual effects.

y_it  y_it_₁ 

 

y_i₂  y_i₁

 

 u_i₃ u_i₂



Consider t=3 [first year with data]

y

 y

   y

 y

   u

 u



In this case y

i1 is a valid instrument of (Y

i2-y

i1), since it is highly correlated with (y

i2-y

i1) and not correlated with (v

i3-v

i2) Consider t=4

yi4  yi3 

 

yi3  yi2

 

 ui4 ui3



For period T, set of instrument (w) will be:

W   y

_i₁

, y

_i₂

... y

_iT_₂



The combination of the instruments could be defined as

Dynamic Panel Data Analysis

Because the instruments are not correlated with the remaining error term, then our moment condition is stated as:



wi^ui



^⁰

Pre-multiplying our difference equation by WI yields:

^W^^^y^^W^



^^y₁



^^W^^^v

Estimating this equation by GLS yields the preliminary Arellano and Bond one-step consistent estimator. In case there are other regressors then:

^W^^^y^^W^



^^y₁



^^W^

 

^^X  ^^W^^^v 6.2 Estimation of Dynamic Panel in Eviews For illustration purposes we use the model stated as:

monetary policy variable, usually interest rate at t; log(Size_i_,t) is a measure of size of bank i at time t; Liq_i_,_t is a measure of liquidity of bank i at time t;

KAPi_, is the total liquid assets to total assets of bank i at time t; X_tis a vector of macroeconomic variables which may affect the operating environments for banks; D_i_,_tis a various qualitative characteristics of commercial banks such as private or public; domestic or foreign; v_iis the

~ 86 ~

time invariant error component;  is the error term with the usual _i,_t properties.

6.3 Step by Step Implementation of the Dynamic GMM Procedure in Eviews

To estimate a model using dynamic GMM we proceed as follows:

Step 1: Organising the data in Excel- Unlike the procedure we have been using in the previous cases, here we stark the data as follows:

Table 6.1: Stacked data on bank size and loan

Dynamic Panel Data Analysis

However, to be able to implement dynamic GMM in Eviews, the number of cross sections should be sufficiently large compared to the time dimension. In the present case we assume we have 84 banks with monthly data spanning 2000M1- 2000M10.

Step 2: Getting started in Eviews: to conduct dynamic GMM in Eviews you proceed as follows: click on: File New workfile this will lead you to the screen in panel A. Then Click on : Workfile Structure type  Balanced panel, to obtain the screen in Panel B, which you then populate with the Start data as 2000M1; End date 2000M10; and Number of cross sections as 84 banks as shown in Panel B.

Spread Size

Panel A Panel B

Step 3: When you click on OK on the screen in Panel B, above you will obtain the screen shown here. You may notice the screen has two new elements namely the dateid and crossid. These elements are essential in ensuring that data on a specific cross section at a particular time can be identified with ease.

 The crossid- this is the element for cross section identification. In our case we have 84 cross sections, so the cross sections have numbers with the first cross section being identified as ‘1’ and the 84^th cross section being identified as 84. In the case of Cross section 1, we know that it has ten observations and assigned to each of these observations is the identifier ‘1’. You may double click on the name

‘crossid’ to view the details as shown in the figure below.

 The dateid- this is the element for date identification. Recall in our case we have 10 time periods (2000M1: 2000M10). You may double click on ‘dateid’ to appreciate the role of this element.

Dynamic Panel Data Analysis

Step 4: Getting the data from Excel to Eviews: The procedure for getting data from Excel to Eviews is as explained in Chapter 1, on working with ‘stacked data’. For illustration, we are working 3 variables: loans disbursed by bank (Loans), bank size (Size) and policy rate (IBR). Following the steps of getting stacked data from excel to Eviews you will obtain the following (adjust for IBR which is cross section wide variable):

Step 5: the regression: in this case you will estimate the equation where the dependent variable is ‘Loan’ and the independent variables are ‘size and IBR’. The procedure for estimating a simple OLS equation applies here. Once this is followed you will then obtain the screen shown below with the dependent variable listed first followed by the independent variables, size and ibr, and then the constant C. To estimate a dynamic GMM model you will need to click on ‘Estimation settings’ and choose the ‘GMM/DPD- Generalised Method of Moments/Dynamic Panel’ method as shown here:

To estimate the dynamic GMM we use the ‘Dynamic Panel Wizard’

shown on the lower left of panel B in the figure above. If you click on the

‘Dynamic Panel Wizard’ button, it will prompt you to the next step of the estimation procedure. You will observe the following screens:

 The first screen welcomes you to the dynamic panel data model wizard. As indicated in the screen, you are informed that the wizard aids you in specifying a

member of the class of dynamic panel data models with fixed effects. You are cautioned that this class of models are designed for panels with a large number of cross-sections and a short time series. In addition, you

Click here to start estimating thedynamic GMM

Dynamic Panel Data Analysis

estimating a dynamic panel. The first step, as shown in in the screen shot is to specify the dependent variable.

As indicated, dynamic panel data models have the feature that lags of the dependent variable appear as regressors. At this step, you are

required to specify the dependent variable. For our case we had specified ‘loan’ as the dependent variable. As indicated earlier, the dynamic panel uses lags of the dependent variable as regressors, therefore you are required to specify the lags you want to use. Eviews has set the lags at 1, however, if you click on the button provided you will select the desired number of lags.

 Step 2: specify any other regressors: Ideally, without specifying any other regressors a dynamic panel will be estimated since the lag of the dependent variable has been included as a regressor. However, at this step you are required to include any other

regressors that you may consider necessary in the regression. In our model we included ‘Size’ and ‘ibr’ as additional regressors as shown in the screen above. In addition, you

are reminded that in case you need period dummy variables (period specific effects), you can click on the box provided on ‘Include period dummy variables (period fixed effects)’.

 Step 3: Select transformation method: This step allows you to choose a transformation which will be applied to the specification of a dynamic panel to remove cross-section fixed effects. There are two method proposed namely, differences and orthogonal deviations.

 Step 4-5: specify GMM level instruments and regular instruments: In these two steps the wizard requires specification of GMM level instruments in a manner consistent with the Arellano-Bond type dynamic panel instruments with lags that vary by observation as shown in Step 4 of 6 above. In addition, step 5 of 6 allows you to specify other instruments, if any. In case regular instruments are required, then you are required to list those instruments in the appropriate boxes depending on whether or not you require to transform the instruments.

 Step 6: Select the estimation method. In this last step you are reminded that the dynamic panel data models are estimated by GMM. In which case you are expected to 1. Specify the number of iterations. To do this you click on the button libelled

‘GMM Iterations’, then choose

the number of iterations you need, (2) choose the GMM weighting matrix. Here there are two options, namely Period SUR and White

Dynamic Panel Data Analysis

Period. The default set is ‘White Period’. Unless you have reasons to change the setting, you are advised to work with the default settings, and (3) computation of standard errors.

After going through all the steps above click on the ‘Next’ button to obtain screen shown in Panel A below. In this panel you are informed that the wizard will transfer your specification to the GMM equation estimation dialog. The finally, click on the button ‘Finish’ to conclude the procedure.

Otherwise, you have an option to go back by clicking on the ‘Back’ button or abort the process by clicking on the ‘Cancel’ button. If you choose to proceed by clicking on the ‘Finish’ button, you will obtain the screen shown in Panel B below. In this last step you are shown the screen which is similar to the one you started with.

Figure 6: GMM Model Specification

Step 6: viewing the estimation results: To view the estimation results you click on ‘OK’ to obtain the following results:

Table 6.2: The Estimation results

The table above shows the estimation results based on a dynamic GMM procedure. The critical things to check out for in this output are the following:

 The estimated coefficients: in our case we used only two variables: (1) Bank size- which is found to positive and significant at the conventional levels of testing (ii) the policy rate- in which we expected that tight monetary policy will reduce the quantity of loans extended by banks. Here we find that the negative relationship holds, however, the estimated coefficient is not significant at the conventional levels of testing.

 The J-statistic: To test whether the model fits the data well we use the J-statistics. The J-test is a chi square with (M-K) degrees of freedom, with M = number of instruments and K =the number of endogenous variables. With the null hypothesis being that the model is valid, when the computed J is less than the critical values.

Dynamic Panel Data Analysis

References

Ahn, S C and Schmidt, P (1995), ‘Efficient estimation of models for dynamic panel data’, Journal of Econometrics, Vol. 68, No. 1, pages 5-27.

Balestra, P and Nerlove, M (1966), ‘Pooling cross section and time series data in the estimation of a dynamic model: the demand for natural gas’, Econometrica, Vol. 34, No. 3, pages 585-612.

Baltagi, B H and Chihwa Kao, C (2000), ‘Nonstationary panels, cointegration in panels and dynamic panels: a survey’, Chapter 1 in Baltagi, B H (ed), Advances in econometrics, volume 15: nonstationary panels, panel cointegration and dynamic panels, Amsterdam, JAI Press, pages 7-51.

Hausman, J A and Taylor, W E (1981), ‘Panel data and unobservable individual effects’, Econometrica, Vol. 49, No. 6, pages 1377-98.

Nerlove, M and Balestra, P (1992), ‘Formulation and estimation of econometric models for panel data’, Chapter 1 in Mátyás, L and Sevestre, P (eds), The econometrics of panel data: fundamentals and recent developments in theory and practice, Amsterdam, Kluwer Academic Publishers, pages 3-18.

Pesaran, M H, Shin, Y and Smith, R (1999), ‘Pooled mean group estimation of dynamic heterogeneous panels’, Journal of the American Statistical Association, Vol. 94, No. 446, pages 621-34.

Chapter 7

Non-Stationary Panel Analysis

7.0 Panel Unit-root Tests

Panel unit-root tests were originally considered by Levin and Lin (1993) …and published as Levin et al. (2002). We can now look at some of the tests that EViews performs, which include panel unit-root test. As such, it will be interesting to compare the results from the panel unit-root tests with the unit-root tests for the individual series. You may begin with the individual augmented Dickey-Fuller (ADF) unit root tests on (the size for

In document Panel Data Analysis. With Special Application to Monetary Policy Transmission Mechanism. User Guide (Page 83-0)