2. G ETTING S TARTED IN E VIEWS S OFTWARE
3.3 Application of Pooled Regression Approach to Monetary
3.3.2 The Model setup
In this study, we estimate the following basic model:
t monetary policy variable, usually interest rate at t; log(Sizei,t) is a measure of size of bank i at time t; Liqi,t is a measure of liquidity of bank i at time t;
t
KAPi, is the total liquid assets to total assets of bank i at time t; Xtis a vector of macroeconomic variables which may affect the operating environments for banks; Di,tis a various qualitative characteristics of commercial banks such as private or public; domestic or foreign; viis the time invariant error component; i,tis the error term with the usual properties.
Following the Kashyap and Stein (2000), tradition, the testable hypothesis for the existence and strength of the BLC is stated as follows: liquidity-constrained intensifies when monetary policy is tighter; secondly, that the sensitivity of lending to monetary policy is greater for banks with weaker balance sheets. This therefore suggest that it is important to understand the balance sheet items which may impact on banks’ ability to lend and therefore impacting on the BLC.
Pooled Regression Analysis
The validity of the bank lending channels requires that commercial banks which experience a change in their deposits or reserves on account of monetary policy action should adjust their lending. Suggesting that a negative relationship is expected between a monetary policy indicator and commercial banks’ lending. However, as shown in the literature the choice of a monetary policy variable is controversial. As shown by Kashyap and Stein (2000), there is no general agreement on the appropriate choice of an indicator of monetary policy. In the literature a set of possible indicators have been suggested: change in short term interest rate under the control of the central bank, the residuals from a vector autoregression (VAR) representing the reaction function of the central bank (Bernanke and Mihov, 1998), the narrative approach (Boschen and Mills, 1995). Etc. In this study we proxy monetary policy by the Central Bank Rate (CBR) and/or the interbank rate.
In the BLC literature the bank size is identified as a critical determinant of the transmission of monetary policy signals to the real economy. As shown in the literature, different bank sizes face varying degrees of access to lending volume to monetary policy for a particular bank is greater for banks with weaker balance sheets. Small banks tend to experience more friction to raise uninsured finance. However, large banks have an easier time raising uninsured finance, which would make their lending less dependent on monetary policy shocks, irrespective of their internal liquidity positions. In this study bank size (S) is defined as the natural logarithm of the total asset.
In order to control for the trend in size, total assets for each bank is normalized by subtracting the log of total assets for each bank from the sample average as:
t differently to a monetary policy shock. That is assuming two banks which both face difficulties in raising external finance, and are alike in all respects except that one has a more liquid balance sheet (as measured by the ratio of securities to assets) than the other. In the event of a monetary shock, it is easier for the more liquid bank to protect its loan portfolio, as it can draw down on its buffer stock of securities. In contrast, the less liquid bank will have to cut its new loans to a greater extent to prevent its securities holdings from falling too low. Whereas relatively liquid banks can draw down their liquid assets to shield their loan portfolio, this is not feasible for less liquid banks. This therefore suggests that more liquid banks tend to be less sensitive to monetary policy shock compared with those with low liquidity.
Therefore, maintaining high liquidity levels is not conducive for monetary policy transmission. How then do we measure liquidity? There are various ways, in this study, however, we measure as a ratio of liquid assets to total assets. capitalized banks have a more limited access to non-deposit financing and as such should be forced to reduce their loan supply by more than well capitalized banks do. Capitalization is defined as the ratio of equity to total assets.
Pooled Regression Analysis
Where K the adjusted capitalization of commercial banks, E is the total equity and A is the total assets.
The distributional effects of monetary policy on banks are captured by the interaction between the monetary policy indicators (interest rate and money supply) and the individual bank characteristics. We now proceed to explain our a priori expectations with respect to the signs of the interaction terms.
We expect the interaction between the size of the bank and the interest rate/money supply to be positive because lending by large banks are less sensitive to a change in monetary policy relative to small banks. Secondly, we expect the interaction between monetary policy indicators and liquidity to be positive because more liquid banks are less sensitive to changes in the interest rate/money supply relative to small banks. This is because more liquid banks are able to provide more lending by drawing down on their stock of liquid assets. Finally, we also expect the interaction between bank capitalization and the interest rates/money supply to be positive because more capitalized banks are less sensitive to changes in monetary policy.
Ownership: The role of governments in the banking markets similarly reduces the risk of depositors: An active role of the state in the banking sector is obviously able to reduce the amount of informational asymmetries significantly. Publicly owned or guaranteed banks are therefore unlikely to suffer a disproportionate drain of funds after a monetary tightening, and distributional effects in their loan reactions are hence unlikely to occur. On the other hand, ownership on the basis of whether a bank is locally or foreign versus local: The network arrangement between banks can also have important consequences for the reaction of bank loan supply to monetary policy. In networks with strong links between the head institutions and the lower tier, the large banks in the upper tier can serve as liquidity providers in times of a monetary tightening, such that the system would experience a net flow of funds from the head institutions to the small member banks.
Ehrmann and Worms (2001) show that in Germany, indeed, small banks receive a net inflow of funds from their head institutions following a monetary contraction. This indicates that the size of a bank need not be a good proxy to assess distributional effects of monetary policy across banks.
Figure 5: BLC based on pooled regressions analysis
As indicated earlier monetary policy is proxied by the interbank rate (IBR).
As shown in the basic model on panel A, the estimated coefficient of IBR is found to be negative. A look at the standard error and the t-statistic reveals that this coefficient is statistically significant at 1 percent level. This, therefore suggests that there is evidence of the monetary policy in Kenya impacting on the amounts that banks lend to the private sector. Including other variables that is, Liquidity (LIQ); Inflation (CPI), and Capital (KAP), in a manner similar to the existing studies, we obtain the results indicated in panel B. It is also found that the estimated coefficient of the IBR is negative as expected and significant at 1 percent level as indicated by the standard error, t-statistic and p-value associated with IBR.
Panel A: Simple BLC Panel B: BLC based on Pooled regressions with control variables
IBR is negative and highly significant
Pooled Regression 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 4
Error Component Model Analysis:
One Way Error Components Model
4.0 Introduction
In chapter 3, we demonstrated how the pooled regression is estimated. In addition, we discussed the example based on the banking lending channel of monetary policy transmission. Under the pooled regression approach we estimated the regression model which takes the following form:
yit 01xit uit 1 The specification allows for estimation of common coefficients- the intercept and the slope (0,1). As pointed out this is very restrictive and is susceptible to biased predictors. The bias is avoided by allowing for multiple coefficients by appearing to the error components model.
4.1 The Error Components Model Specification
The error component model allows estimation of multiple coefficients for each cross-section by exploiting the information content of the error term,
uit in Equation 1, which is expected to be well behaved. The error components approach allows for decomposition of the error term,uit into three distinct parts or components as follows:
u
it v
i
t
it 2In Equation 2, vi, is the part or component of the error term that varies across cross-sections but does not vary over time, which may be taken to represent those unique characteristics of individual units which cannot be found in the rest of the cross sections. On the other hand, t, is the error component which varies over time but remains unchanged across the various units, these may represent unique events/circumstances which may have taken place in respective time periods which have no resemblance to other events which took place in other periods under investigation.
For analysis, Equation 2 can be analysed as a two-way-error component or a one-way-error components model. In each case the estimation is done using the fixed effects or the random effects model. In order to understand how the error components models are estimated using the fixed- and random effects approaches we discuss in details how the two approaches are implemented and how the output is interpreted.
4.1.1 One-Way Error Component Model
The one-way-error components model framework allows one to analyse the error term,uit by abstracting one channel. For example, Equation 2, can be converted to a one way error component by either assumingt 0, in which case Equation 2 collapses to:
u
it v
i
it 3aIn this formulation we allow for only cross section differences to be investigated while assuming away the time variations. On the other hand, if we assumevi 0, the Equation 2 becomes:
u
it
t
it 3bIn this formulation we analyse the characteristics of the time periods while abstracting from the cross section differences. Including these elements in Equation 1 yields the following:
Error Component Model Analysis
y
it
0
1x
it
t
it 4aOr
y
it
0
1x
it v
i
it 4bEquations 4a and 4b are expressed as one-way-error components models.
In order to analyses the time specific coefficients (t) and the cross-sections specific coefficients (vi) we use either the fixed- or the random- effects models.
Fixed effects assume that individual group/time have different intercept in the regression equation, while random effects hypothesize individual group/time have different disturbance. When the type of effects (group versus time) and property of effects (fixed versus random) combined, there are several specific models: fixed group effect model (one-way), fixed time effect model (one-way), fixed group and time effect model (two-way), random group effect model (one-way), random time effect (one-way), and random group and time effect model (two-way).
4.1.1.1 Fixed Effects Model
The fixed effects model assumes that (vi) and (t) are separate parameters.
For illustration purposes we use the case where we estimate the (vi). In estimating the separate parameters (vi) use the following two equivalent methods: the Least Squares Dummy Variable (LSDV) method and the Within-Q- Estimation method.
4.1.2 The least squares dummy variable estimation method
The least squares dummy variable estimation method calls for estimation of the following model:
y
i X
i 1
Tv
i
iIn this case the parameters for X are estimated. In addition, dummies for large2. In the next section show a step by step estimation of this equation.
To estimate a model using this method the following steps are followed:
Step 1: Organise the data for the key variables size and growth of loan as shown below:
2 The procedure is implemented using the Frisch-Waugh-Lovell (FWL) theorem on partitioned regressions. For details see Davidson, R. and J.G. MacKinnon, 1993, Estimation and Inference in Econometrics (Oxford University Press, New York).
Loan_Bank1 Loan_Bank2 Loan_Bank3 Loan_Bank4 Loan_Bank5 Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5
2000 4.4 5.7 5.3 15.9 4.6 6.3 4.6 6.7 4.1 3.5
Error Component Model Analysis
Step 2: Create cross section dummies. Here the dummies for each cross section as if they are variables. In this case we have 5 cross-section, therefore we need 5 dummies as follows:
Table 4.1: Dummy variables
As shown above we create a dummy for each cross section. For example, in the case for Bank1, we create a dummy with 1 and zeroes elsewhere, for the period 2000 to 20016.
Step 3: Getting data into Eviews: As shown in Chapter 1, we need to create a panel file structure with five cross sections for the period 2000- 20016 as follows:
D1_Bank1 D1_Bank2 D1_Bank3 D1_Bank4 D1_Bank5 D2_Bank1 D2_Bank2 D2_Bank3 D2_Bank4 D2_Bank5 D3_Bank1 D3_Bank2 D3_Bank3 D3_Bank4 D3_Bank5
2000 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
D4_Bank1 D4_Bank2 D4_Bank3 D4_Bank4 D4_Bank5 D5_Bank1 D5_Bank2 D5_Bank3 D5_Bank4 D5_Bank5
2000 0 0 0 1 0 0 0 0 0 1
Dummy for Bank1 Dummy for Bank2 Dummy for Bank3
Dummy for Bank4 Dummy for Bank5
Step 4: Getting data into Eviews: To get data into Eviews, click on the
‘Quick button’ followed by ‘Empty Group’. Then the following empty box will appear:
This is the box where data for each individual variable will be entered. In our case we have 2 variables (loan and bank size) and 5 dummy variables.
Therefore, in total we have seven variables to enter separately. For example, we may start with bank size, in which case we cut the data on variable bank size from Excel and paste it in this blank box to give:
Cross-section identifiers are listed Data range is stated
Error Component Model Analysis
The same procedure is followed for the rest of the variables i.e. DLOAN, D1, D2, D3, D4 and D5. Once all the variables have been pasted in Eviews,
Step 5: Estimation of the model: To estimate the model, you click on
‘Estimate’ button as shown above. This will result in the following box.
The 7 variables are entered and each is identified as a group
To estimate this model, click on ‘estimate’
Give variable name here
However, to avoid the Dummy variable trap, we exclude one cross section dummy from the regression. In this particular regression you may notice we have excluded D5. There is no rule regarding the dummy variable to exclude from the regression. The parameter for excluded dummy variable will be accounted for once the estimation procedure is completed. Once all the variables have been entered as shown click on the ‘OK’ button and the following result will show.
Enter Dependent variable here
followed by ? Enter independent variables here each followed by ?
Error Component Model Analysis
As you may notice, this is a long procedure for implementing the DVE approach. However, Eviews has a shortcut which delivers on the same results. In this case, when entering data for the independent variables do not enter dummy variables in the space provided. Instead enter the constant
‘C’ in the space as shown below:
Entering ‘C’ in the space for ‘Cross-section specific coefficients’ allows Eviews to recognise that DVE methods is applicable. Once this has been done click on ‘OK’ button and you will see the following output:
Enter ‘C’ here
You may wish to compare the result from the long- and short- procedure for implementing the DVEM as shown below. For instance, panels A and B show that results for bank size (SIZE?) are exactly the same whether we use dummy variable estimation or the short cut via cross-section identifiers.
Panel A Panel B
Error Component Model Analysis
4.2 Case Study: Monetary Policy Transmission in Kenya:
Evidence from bank level data
As indicated in Chapter 3, where we demonstrated how the pooled regression model is estimated and applied to the monetary policy transmission, in this chapter we demonstrate using the same bank level data to show how to estimate a one-way error components model. As before the model set up is stated as: monetary policy variable, usually interest rate at t; log(Sizei,t) is a measure of size of bank i at time t; Liqi,t is a measure of liquidity of bank i at time t;
t
KAPi, is the total liquid assets to total assets of bank i at time t; Xtis a vector of macroeconomic variables which may affect the operating environments for banks; Di,tis a various qualitative characteristics of commercial banks such as private or public; domestic or foreign; viis the time invariant error component; i,tis the error term with the usual properties. The discussion of the expected results is avoided in order to stay clear of repetitions.
In this illustration we abstract from the basic steps in the data preparations and creating an enabling environment in Eviews for panel data analysis.
Therefore, for us to show how the Least Squares Dummy Variable (LSDV)
estimation method is executed we follow the following steps:
Step 1: Setting up the LSDV. In the LSDV model set up, the important aspect is the estimation of the individual specific coefficients. To implement this, we perform only one modification to the estimation procedure in the pooled regression approach. The dependent variable as before is “tcad?”. To allow for cross section specific coefficients you enter a ‘C’ in the space provided for Cross-section specific coefficients.
Step 2: Estimation of the LSDV: After entering a ‘C’ as indicated above and ensuring that the estimation method is set as ‘LS-Least Squares (and AR), you click on ‘OK’ to obtain the output shown in here. In this particular example the following are observed:
The estimated coefficient of the monetary policy variable (IBR) is negative and significant at 1 percent level of testing. The estimated coefficient is 0.15, implying that a 1 percent change in monetary
The estimated coefficient of the monetary policy variable (IBR) is negative and significant at 1 percent level of testing. The estimated coefficient is 0.15, implying that a 1 percent change in monetary