Panel Data Analysis User Guide

Panel Data Analysis With Special Application to Monetary Policy Transmission Mechanism

User Guide

Panel Data Analysis With Special Application to Monetary Policy Transmission Mechanism

Prepared By

Dr Esman Nyamongo

Assistant Director Research Department Central Bank of Kenya

Published by COMESA Monetary Institute (CMI)

First Published 2019 by

COMESA Monetary Institute C/O Kenya School of Monetary Studies P.O. Box 65041 – 00618 Noordin Road Nairobi, KENYA Tel: +254 – 20 – 8646207 http://cmi.comesa.int

All rights reserved. Except for fully acknowledged short citations for purposes of research and teaching, no part of this publication may be reproduced or transmitted in any form or by any means without prior permission from COMESA.

Disclaimer

The views expressed herein are those of the author and do not in any way represent the official position of COMESA, its Member States, or the affiliated Institution of the Author.

Typesetting and Design Mercy W. Macharia [email protected]

TABLE OF CONTENTS

List of Figures ...... viii List of Tables ...... viii List of Acronyms ...... ix Preface ...... x Acknowledgements ...... xi

1. INTRODUCTION TO PANEL DATA ANALYSIS ...... 1 1.0 Introduction...... 1 1.1 Types of Panel Data ...... 1 1.1.1 Dated vs. Undated Panels ...... 2 1.1.2 Regular vs. Irregular Dated Panels ...... 2 1.1.3 Balanced vs. Unbalanced Panels ...... 2 1.2 Advantages of Panel Data ...... 4

2. GETTING STARTED IN EVIEWS SOFTWARE ...... 9 2.0 Introduction...... 9 2.1 Getting Started in Eviews ...... 9 2.2 Data preparation in Excel ...... 11 2.3 To Create an Eviews Workfile ...... 11 2.3.1 Importing the data into Eviews ...... 12 2.3.2 Setting up a pool in a workfile ...... 14 2.3.3 Data transformations ...... 19 2.4 Viewing Data ...... 21 2.5 Basic Plots ...... 22 2.6 Descriptive Statistics ...... 24 3. POOLED REGRESSION ANALYSIS ...... 29 3.0 Introduction ...... 29 3.1 The pooled regression model ...... 29 3.1.1 Limitations of Pooled regression ...... 30 3.2 Estimation of the Pooled Regression Model ...... 31 3.2.1 Illustration of pooled regression using general data ...... 31 3.2.2 Organising data in Excel ...... 32 3.2.3 Loading the data into Eviews ...... 34 3.2.4 Pooled regression in Eviews...... 36 3.2.5 Pooled regressions in Eviews Environment ...... 37 3.3 Application of Pooled Regression Approach to Monetary Policy Transmission in Kenya ...... 39 3.3.1 Case Study: Monetary Policy Transmission in Kenya: Evidence from bank level data ...... 39 3.3.2 The Model setup...... 40 References ...... 45

4. ERROR COMPONENT MODEL ANALYSIS: ONE WAY ERROR COMPONENTS MODEL ...... 47 4.0 Introduction ...... 47 4.1 The Error Components Model Specification ...... 47 4.1.1 One-Way Error Component Model ...... 48 4.1.2 The least squares dummy variable estimation method ...... 49 4.2 Case Study: Monetary Policy Transmission in Kenya: Evidence from bank level data ...... 57 4.2.1 Within-Q-estimation method ...... 59 4.3 Pooled Estimation Method Versus the Fixed Effect Method...... 65 4.4 Case Study: Monetary Policy Transmission in Kenya: Evidence from bank level data ...... 68

~ vi ~ 4.5 Random Effects Model ...... 70 4.5.1 Testing the validity of the random effects: Hausman test ...... 71 References ...... 73

5. ERROR COMPONENT MODEL ANALYSIS: TWO WAY ERROR COMPONENTS MODEL ...... 75 5.0 Introduction ...... 75 5.1 Estimation of the Error Components Model ...... 76 5.1.1 Fixed effects model...... 76

6. DYNAMIC PANEL DATA ANALYSIS ...... 83 6.1 Arellano and Bond Estimator ...... 84 6.2 Estimation of Dynamic Panel in Eviews ...... 85 6.3 Step by Step Implementation of the Dynamic GMM Procedure in Eviews ...... 86 References ...... 95

7. NON-STATIONARY PANEL ANALYSIS ...... 97 7.0 Panel Unit-root Tests ...... 97 7.1 Panel Unit-root Test with an Automatic Lag Selection Method ...... 105 References ...... 107

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LIST OF FIGURES Figure 1: Creating a work file ...... 34 Figure 2: Getting the data into Eviews ...... 35 Figure 3: Estimation in a pool object ...... 36 Figure 4: Estimation result ...... 37 Figure 5: BLC based on pooled regressions analysis ...... 44 Figure 6: GMM Model Specification ...... 93

LIST OF TABLES Table 1.1: Panel data set: Normalised bank size for 5 banks ...... 4 Table 3.1: Raw data on bank size and loan ...... 32 Table 3.2: Stacked data on bank size and loan ...... 33 Table 3.3: Data on size and growth rate of loan with cross-section identifiers ...... 38 Table 4.1: Dummy variables ...... 51 Table 4.2: Demeaned data ...... 61 Table 5.1: Data ...... 77 Table 5.2: transformed data: ...... 77 Table 6.1: Stacked data on bank size and loan ...... 86 Table 6.2: The Estimation results ...... 94

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LIST OF ACRONYMS

ADF Augmented Dickey-Fuller AIC Akaike Information Criterion BIC Bayesian Information Criteria BLC Bank Lending Channel CBR Central Bank Rate DPD Dynamic Panel Data GDP Gross Domestic Product GLS Generalised Least Squares GMM Generalised Method of Moments IBR Interbank Rate LSDV Least Squares Dummy Variable MAIC Minimising the modified AIC MIC Modified information criteria OLS Ordinary Least Squares VAR Vector Autoregression

~ ix ~ PREFACE

The preparation of this User’s Guide followed a directive to COMESA Monetary Institute (CMI) by the 22nd Meeting of the COMESA Committee of Governors of Central Banks which was held in Bujumbura, Burundi in March 2017. Governors noted that panel data analysis of monetary policy is an important prerequisite for implementing a sound monetary policy, as it allows a judgement to be formed as to the extent and the timing of monetary policy decisions which are appropriate in order to maintain price stability.

The overall objective of this User’s Guide is to equip Users with skills to undertake analysis of all aspects of panel data analysis. The User’s Guide demonstrates all steps in panel data analysis from data organization to results interpretation, applying bank level data using the EViews software.

Understanding panel data analysis is especially important in order to address dynamics which cannot be addressed using purely cross-section or time series analysis. In the central banking environment, the importance of panel data analysis arises from the need to get answers to policy questions on a wide range of issues on the banking sector such as the effectiveness of monetary policy and the transmission mechanism using the bank lending channel (BLC); factors driving key indicators for the banking sector such as interest rate spreads, profitability, non- performing loans, governance etc. These issues require in-depth analysis of bank level data. In addition, panel data analysis is useful in cross-country studies which may provide an avenue to understand cross country differences which may inform policy on matters related to regional economic integration.

It is hoped that the Guide will be a useful analytical tool on application of advanced panel data analysis to transmission mechanism of monetary policy. It is also hoped that the Guide will be used by COMESA member central banks as a reference material to train their staff.

Ibrahim A. Zeidy Chief Executive Officer

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ACKNOWLEDGEMENTS

Although this User’s Guide is a sole work of the author, its present form is a product of inputs from various training workshops organized by COMESA Monetary Institute (CMI). The Author acknowledges all participants of various CMI training workshops, who provided comments that assisted in making the User’s Guide clearer and more User friendly. The Author also thanks the Director, Mr. Ibrahim Abdullahi Zeidy and the Senior Economist, Dr. Lucas Njoroge for providing technical and expert assistance, and all the staff of the Institute for the facilitation and logistical support towards the completion of the User’s Guide.

The Author especially acknowledges the rich comments from the participants of the Validation Workshop held from 8th to 12th May, 2017 in Nairobi, Kenya that provided the final inputs to the User’s Guide. The workshop was attended by participants from the following COMESA member countries’ Central Banks: Burundi, DR Congo, Ethiopia, Kenya, Madagascar, Rwanda, Sudan, Swaziland, Zambia, and Zimbabwe.

~ xi ~

Chapter 1

Introduction to Panel Data Analysis

1.0 Introduction

Panel data, also known as longitudinal data or cross-sectional time series data, in some special cases, refers to data containing time series observations of a number of cross sections like individuals, households, firms, or governments. This means that observations in panel data involve at least two dimensions: a cross-sectional dimension, indicated by subscript i, and a time series dimension, indicated by subscript t. In a more complicated setup, panel data could have a more complicated clustering or hierarchical structure. For example, variable y may be the measurement of the share of government spending on budget item j (e.g. defense, education, health etc.) in country i at time t.

There are two distinct sets of information that can be derived from cross- sectional time series data. The cross-sectional component of the data set reflects the differences observed between the individual subjects or entities whereas the time series component which reflects the differences observed for one subject over time. For instance, researchers could focus on the differences in data between each person in a panel study and/or the changes in observed phenomena for one person over the course of the study (e.g., the changes in income over time of person 1 in Panel Data Set).

1.1 Types of Panel Data

Panel data may be characterized in a variety of ways. For purposes of creating panel work files in EViews, there are several concepts that are of particular interest. Guidelines on Panel Data Analysis

1.1.1 Dated vs. Undated Panels A panel data set is said to be dated or undated depending on its cell ID. When the observations of individual cross sections can be observed over specific periods of time, we have a dated panel of the given frequency. If, for example, our cell IDs are defined by a variable like QUARTER, we say we have a quarterly frequency panel. Similarly, if the cell IDs are week or year identifiers, we say we have a weekly or annual panel.

On the other hand, an undated panel uses group specific default integers as cell IDs; by default, the cell IDs in each group are usually given by the default integers (1, 2, ...N).

1.1.2 Regular vs. Irregular Dated Panels Dated panels follow a regular or an irregular frequency. A panel is said to be a regular frequency panel if the cell IDs for every group follow a regular frequency. If one or more groups have cell ID values which do not follow a regular frequency, the panel is said to be an irregular frequency panel. However, it is possible to convert an irregular frequency panel into a regular frequency panel by adding observations to remove gaps in the calendar for all cross-sections.

1.1.3 Balanced vs. Unbalanced Panels If every group in a panel has an identical set of cell ID values, we say that the panel is fully balanced. All other panel datasets are said to be unbalanced.

In the simplest form of balanced panel data, every cross-section follows the same regular frequency, with the same start and end dates—for example, data with 20 cross-sections, each with annual data from 1961 to 1970. In this case, we say that the panel is balanced.

We may balance a panel by adding observations to the unbalanced data. The procedure is quite simple—for each cross-section or group, we add observations corresponding to cell IDs that are not in the current group, but appear elsewhere in the data. By adding observations with these

~ 2 ~ Introduction to Panel Data Analysis

“missing” cell IDs, we ensure that all of the cross-sections have the same set of cell IDs.

To complicate matters, we may partially balance a panel. There are three possible methods—we may choose to balance between the starts and ends, to balance the starts, or to balance the ends. In each of these methods, we perform the procedure for balancing data described above, but with the set of relevant cell IDs obtained from a subset of the data. Performing all three forms of partial balancing is the same as fully balancing the panel.

Balancing data between the starts and ends involves adding observations with cell IDs that are not in the given group, but are both observed elsewhere in the data and lie between the start and end cell ID of the given group. If, for example, the earliest cell ID for a given group is “2000” and the latest ID is “2010”, the set of cell IDs to consider adding is taken from the list of observed cell IDs that lie between these two dates. The effect of balancing data between starts and ends is to create a panel that is internally balanced, that is, balanced for observations with cell IDs ranging from the latest start cell ID to the earliest end cell ID.

Assuming one is interested in analysing data for 5 banks over the period 2000 to 2016. A typical balanced panel dataset may appear as shown on Table 1:

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Table 1.1: Panel data set: Normalised1 bank size for 5 banks Bank1 Bank2 Bank3 Bank4 Bank5 2000 6.3 4.6 6.7 4.1 3.5 2001 5.8 5.1 6.7 2.9 3.2 2002 4.5 3.4 6.7 1.8 3.3 2003 2.1 2.2 9.3 -1.4 3.3 2004 2.0 2.0 9.8 -2.1 3.6 2005 1.9 1.7 9.8 -1.5 3.6 2006 2.0 1.5 9.8 -1.4 3.6 2007 1.5 -2.2 9.8 -2.4 3.6 2008 0.5 1.6 9.8 -2.2 3.6 2009 0.6 0.1 9.8 -1.4 1.1 2010 1.0 1.2 10.5 -1.3 0.8 2011 6.4 1.8 9.8 -1.8 0.8 2012 1.5 2.0 8.5 -1.1 2.8 2013 2.4 2.4 9.8 -0.7 2.8 2014 2.5 2.5 9.8 0.1 2.7 2015 3.7 1.5 9.8 0.5 2.7 2016 3.3 3.4 9.8 0.4 2.7

1.2 Advantages of Panel Data

Panel data, by blending the inter-individual differences and intra-individual dynamics have several advantages over cross-sectional or time-series data:

More accurate inference of model parameters. Panel data usually contain more degrees of freedom and more sample variability than cross-sectional data which may be viewed as a panel with T = 1, or time series data which is a panel with N = 1, hence improving the efficiency of econometric estimates (e.g. Hsiao et al., 1995).

Greater capacity for capturing the complexity of human behaviour than a single cross-section or time series data. These include:

1 Bank Size is measured by total assets. 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. The result is a normalized bank size with banks whose size is larger than the sample average having a positive value and banks with a size smaller than the sample average having a negative value.

~ 4 ~ Introduction to Panel Data Analysis i. Constructing and testing more complicated behavioural hypotheses. For instance, consider the example of Ben-Porath (1973) that a cross-sectional sample of married women was found to have an average yearly labor-force participation rate of 50 percent. These could be the outcome of random draws from a homogeneous population or could be draws from heterogeneous populations in which 50 percent were from the population who always work and 50 percent never work. If the sample was from the former, each woman would be expected to spend half of her married life in the labor force and half out of the labor force. The job turnover rate would be expected to be frequent and the average job duration would be about two years. If the sample was from the latter, there is no turnover. The current information about a woman’s work status is a perfect predictor of her future work status. A cross-sectional data is not able to distinguish between these two possibilities, but panel data can because the sequential observations for a number of women contain information about their labor participation in different subintervals of their life cycle. Another example is the evaluation of the effectiveness of social programs (e.g. Heckman et al., 1998; Hsiao et al., 2006; Rosenbaum and Rubin, 1985). Evaluating the effectiveness of certain programs using cross-sectional sample typically suffers from the fact that those receiving treatment are different from those without. In other words, one does not simultaneously observe what happens to an individual when she receives the treatment or when she does not. An individual is observed as either receiving treatment or not receiving treatment. Using the difference between the treatment group and control group could suffer from two sources of biases, selection bias due to differences in observable factors between the treatment and control groups and selection bias due to endogeneity of participation in treatment. For instance, Northern Territory (NT) in Australia decriminalized possession of small amount of marijuana in 1996. Evaluating the effects of decriminalization on marijuana smoking behavior by comparing the differences between NT and other states that were still non-decriminalized could suffer from either or both

~ 5 ~ Guidelines on Panel Data Analysis

sorts of bias. If panel data over this time period are available, it would allow the possibility of observing the before- and effects on individuals of decriminalization as well as providing the possibility of isolating the effects of treatment from other factors affecting the outcome. ii. Controlling the impact of omitted variables. It is frequently argued that the real reason one finds (or does not find) certain effects is due to ignoring the effects of certain variables in one’s model specification which are correlated with the included explanatory variables. Panel data contain information on both the intertemporal dynamics and the individuality of the entities may allow one to control the effects of missing or unobserved variables. For instance, MaCurdy’s (1981) life-cycle labor supply model under certainty implies that because the logarithm of a worker’s hours worked is a linear function of the logarithm of her wage rate and the logarithm of worker’s marginal utility of initial wealth, leaving out the logarithm of the worker’s marginal utility of initial wealth from the regression of hours worked on wage rate because it is unobserved can lead to seriously biased inference on the wage elasticity on hours worked since initial wealth is likely to be correlated with wage rate. However, since a worker’s marginal utility of initial wealth stays constant over time, if time series observations of an individual are available, one can take the difference of a worker’s labor supply equation over time to eliminate the effect of marginal utility of initial wealth on hours worked. The rate of change of an individual’s hours worked now depends only on the rate of change of her wage rate. It no longer depends on her marginal utility of initial wealth. iii. Uncovering dynamic relationships. “Economic behavior is inherently dynamic so that most econometrically interesting relationship are explicitly or implicitly dynamic” (Nerlove, 2002). However, the estimation of time adjustment pattern using time series data often has to rely on arbitrary prior restrictions such as Koyck or Almon distributed lag models because time series observations of

~ 6 ~ Introduction to Panel Data Analysis

current and lagged variables are likely to be highly collinear (e.g. Griliches, 1967). With panel data, we can rely on the inter-individual differences to reduce the collinearity between current and lag variables to estimate unrestricted time-adjustment patterns (e.g. Pakes and Griliches, 1984). iv. Accurate predictions. Generating more accurate predictions for individual outcomes by pooling the data rather than generating predictions of individual outcomes using the data on the individual in question. If individual behaviours are similar conditional on certain variables, panel data provide the possibility of learning an individual’s behaviour by observing the behaviour of others. Thus, it is possible to obtain a more accurate description of an individual’s behaviour by supplementing observations of the individual in question with data on other individuals (e.g. Hsiao et al., 1993, 1989). v. Providing micro foundations for aggregate data analysis. Aggregate data analysis often invokes the “representative agent” assumption. However, if micro units are heterogeneous, not only can the time series properties of aggregate data be very different from those of disaggregate data (e.g. Granger, 1990; Lewbel, 1994; Pesaran, 2003), but policy evaluation based on aggregate data may be grossly misleading. Furthermore, the prediction of aggregate outcomes using aggregate data can be less accurate than the prediction based on micro-equations (e.g. Hsiao et al., 2005). Panel data containing time series observations for a number of individuals is ideal for investigating the “homogeneity” versus “heterogeneity” issue. vi. Simplifying computation and statistical inference. Panel data involve at least two dimensions, a cross-sectional dimension and a time series dimension. Under normal circumstances one would expect that the computation of panel data estimator or inference would be more complicated than cross-sectional or time series data. However, in certain cases, the availability of panel data actually simplifies computation and inference. For instance:

~ 7 ~ Guidelines on Panel Data Analysis

 Analysis of nonstationary time series. When time series data are not stationary, the large sample approximation of the distributions of the least-squares or maximum likelihood estimators are no longer normally distributed, (e.g. Anderson, 1959; Dickey and Fuller, 1979, 1981; Phillips and Durlauf, 1986). But if panel data are available, and observations among cross-sectional units are independent, then one can invoke the central limit theorem across cross-sectional units to show that the limiting distributions of many estimators remain asymptotically normal (e.g. Binder et al., 2005; Im et al., 2003; Levin et al., 2002; Phillips and Moon, 1999).  Measurement errors. Measurement errors can lead to under- identification of an econometric model (e.g. Aigner et al., 1984). The availability of multiple observations for a given individual or at a given time may allow a researcher to make different transformations to induce different and deducible changes in the estimators, hence to identify an otherwise unidentified model (e.g. Biørn, 1992; Griliches and Hausman, 1986; Wansbeek and Koning, 1989).  Dynamic Tobit models. When a variable is truncated or censored, the actual realized value is unobserved. If an outcome variable depends on previous realized value and the previous realized value are unobserved, one has to take integration over the truncated range to obtain the likelihood of observables. In a dynamic framework with multiple missing values, the multiple integration is computationally unfeasible. With panel data, the problem can be simplified by only focusing on the subsample in which previous realized values are observed (e.g. Arellano et al., 1999).

~ 8 ~ Chapter 2

Getting Started in Eviews Software

2.0 Introduction

Data analysis within the context of panel may be conducted using a variety of software currently available in the market. For the purpose of this User’s Guide we demonstrate how to use EVIEWS to analyse panel data sets. In addition, while acknowledging that we need to use bank data we, however, use fictitious data to demonstrate how to get started in EVIEWS. Therefore, in this chapter we will data generated purposely for demonstration.

Panel data analysis is normally handled after learners have become conversant with time series and cross section data analysis. Therefore, in this User’s Guide we will largely abstract from detailed demonstration of how to handle these two types of data sets. For purposes of this User’s Guide we work with Eviews version 6. Most of the functionalities of the different versions of Eviews have not changes over time. Therefore, any version may be used for teaching purposes.

2.1 Getting Started in Eviews

The starting point towards understanding the use of Eviews is to know how to access or open Eviews software in a computer. In most cases, if Eviews is installed on a computer you will notice an icon on the desktop which appears like the one here, Guidelines on Panel Data Analysis depending on the version of the software. For you to open and operate Eviews, take the cursor to this icon and double click the mouse.

Once you click on the icon you will see the window similar to the one here below. Across the top are Drop down Menus that make implementing EViews procedures quite simple. Below the menu items is the Command window. It can be used as an alternative to the menus, once you become familiar with basic commands and syntax.

Across the bottom is the Current Path for reading data and saving files. The EViews Help Menu is going to become a close friend. Use it when you need guidance on how to navigate the software.

Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5 2000 6.3 4.6 6.7 4.1 3.5 2001 5.8 5.1 6.7 2.9 3.2 2002 4.5 3.4 6.7 1.8 3.3 2003 2.1 2.2 9.3 -1.4 3.3 2004 2.0 2.0 9.8 -2.1 3.6 2005 1.9 1.7 9.8 -1.5 3.6 2006 2.0 1.5 9.8 -1.4 3.6 2007 1.5 -2.2 9.8 -2.4 3.6 2008 0.5 1.6 9.8 -2.2 3.6 2009 0.6 0.1 9.8 -1.4 1.1 2010 1.0 1.2 10.5 -1.3 0.8 2011 6.4 1.8 9.8 -1.8 0.8 2012 1.5 2.0 8.5 -1.1 2.8 2013 2.4 2.4 9.8 -0.7 2.8 2014 2.5 2.5 9.8 0.1 2.7 2015 3.7 1.5 9.8 0.5 2.7 2016 3.3 3.4 9.8 0.4 2.7

~ 10 ~ Getting Started in Eviews Software

2.2 Data preparation in Excel

Before we get data into Eviews for analysis there is data preparation which needs to be done in excel. The first step in data preparation in excel is to get data for all variables and prepare it using the following procedure. We demonstrate data preparation using data using normalised Bank level data on Bank size. After this has been demonstrated then any data set may be prepared in the same version. The first step in data preparation in excel is to get data for each individual cross sections, putting similar data together, that is, if one is organising a range of data sets on banks, we require that, for example, data on ‘Bank size’, be put together while noting the name of the bank where the bank relates to. In our present case we have 5 cross sections (five banks) as shown in the table. The second step is to provide cross section identifiers. In the table you may notice that the variable name is ‘Size’. In order to identify the data with the bank we include an extension. Here we add an underscore (_) followed by the unique name for each cross section. In our present case the variable for the five cross sections are as follows ‘Size_Bank1; Size_Bank2; Size_Bank3; Size_Bank4; Size_Bank5’. In case one has more than one variable the same procedure is followed. We will explain this further under the naming conventions in the pool object.

2.3 To Create an Eviews Workfile

Having known how to get started in Eviews as shown in Section 2.1, we now proceed to explain how to create a work file in Eviews. To create a workfile in Eviews, click File, New, Workfile and you will see the window similar to the one here.

In this window you need to specify whether your data is dated or undated by selecting the appropriate option under the workfile structure type. Our data is dated so we select Dated – regular frequency. For now, let us leave out the Balanced panel frequency.

~ 11 ~ Guidelines on Panel Data Analysis

Additionally, we need to specify the frequency using the drop down menu under the Date specification tab. In this case, our data is annual so we select accordingly. Under the same tab we need to specify the start and end date of our data. We can provide a name to our workfile say BANK_PANEL. You can provide a page name of your choice, in our case we have named it SIZE.

Once you have populated the window as indicated above, click on ‘OK’ to obtain the following screen. Now save your workfile in your preferred location by clicking file, save.

2.3.1 Importing the data into Eviews To import data, click Quick, Empty group (Edit series)

~ 12 ~ Getting Started in Eviews Software

Copy the series including their names and paste here from the series names.

Copy your data in excel excluding the year and paste as shown below;

Here we have imported data on Bank size as a group. For us to recognise the group we give it a name. The name given is usually the variable name, in our case ‘SIZE’.

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Click ok and close the group. Your workfile now looks as follows;

2.3.2 Setting up a pool in a workfile We shall be working with pooled data; therefore, the first thing we have to do in order to work with pooled data is to create a Pool workfile. This is nothing more than the Pool object in EViews found in Object, New Object, Pool. Note that the Pool object operates within the EViews workfile, where all your data must be stored; that is, the Pool object does not, in itself hold any of the data. Note that the data range/sample is determined by the workfile, not the

~ 14 ~ Getting Started in Eviews Software

Pool object. When working with pooled data, note that the series that are being pooled need not be of the same dimension, so for example we can have time series for various variables comprising different samples. The data in our workfiles are balanced, that is, they have a common sample period.

The Pool object serves two roles in EViews:

i. First, it allows you to perform certain aspects of data management; that is, we can transform variables (e.g., take first differences) or even create variables (e.g., define inflation from the price level, or create dummy variables). In some cases, this is very useful, as it can save you a lot of time when you need to create the same transformation for a number of variables. Note, however, that the data transformations are rather limited, for instance, you cannot apply the HP-filter or seasonal adjustment to series. ii. The second role of the Pool object is to provide procedures for the estimation of econometric models (these will be discussed below).

To create a pool workfile we carry out the following simple steps;

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Step 1: Click object, new object, and the following window emerges;

~ 16 ~ Getting Started in Eviews Software

Step 2: Select pool and give it a name as shown below;

Type the name of your pool object here e.g. Pool1

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Step 3: Click ok and the window below asking you to supply cross-sectional identifiers emerges;

Type cross section identifiers here starting with underscore e.g. _Bank1 then enter to type the next identifier e.g. _Bank2 and so on as shown below in section 2.3.3

Step 4: Naming conventions

In a Pool object, we can have two types of definitions: cross-section identifiers and definitions of groups (the latter is optional). In the workfile for, we have defined our variable size_xx, where xx are the cross-section identifiers. In this case, they are the different banks’ names. Bank1; Bank2; Bank3; Bank1; and Bank5 as shown below.

~ 18 ~ Getting Started in Eviews Software

2.3.3 Data transformations The Pool object provides a fast, efficient and useful way to manipulate and manage data. Within the Pool object window, we have a tab PoolGenr which allows us to transform the data within the Pool object. Our data is normalized bank size. For example, we could compute the growth rates of a variable of interest as follows;

Click PoolGenr, and a new window opens as shown below;

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Click on the PoolGenr for options on data transformation

We would then proceed by typing the relevant equation to compute new series (in this case, growth rate) as follows;

~ 20 ~ Getting Started in Eviews Software

Note the use of the ‘?’ character. The ? tells EViews to apply the transformation to the cross-sectional series in the Pool. The lags of the series (-1) must be placed after the ?. One can also define and/or adjust the sample size under the sample window.

Note that this is just for demonstration on how to conduct data transformations. So we are not going to perform this procedure. There are many other transformations which can be done within the pool object, this is just one of them.

2.4 Viewing Data

At this stage, we can manipulate data as we would normally do. We can even conduct unit root tests on the series and the cross-section without having to consider the Pool object in EViews. The latter is EViews’ main object for managing time-series/cross-section data. We shall do that first and compare results with the Pool object later.

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PANEL A PANEL B

In terms of viewing the data, we can either plot the series individually or open them as a Group (note that a group is not the same as a Pool object for EViews. A Group object is mainly used for working with collections of series.) If you select all (or some of the) series and right click, you can open them as a Group. Non-continuous time series are chosen by pressing the Ctrl key and keeping it pressed while selecting individual time series.

In our case we have already created a group, SIZE. To open this group double click on it. You will see the window below;

2.5 Basic Plots

Once that data has been successful imported into Eviews, the next step is to know how to conduct basic analysis. Plot the series by selecting view, graph. Select the Multiple graphs option in the Multiple series window and click ok.

~ 22 ~ Getting Started in Eviews Software

Copy the figure by right clicking on it and selecting copy to clipboard. The series are displayed in the figure below.

Whenever we begin working with a new data set, it is always a good idea to take some time to simply examine the data. This will help ensure that there were no mistakes in the data itself or in the process of reading in the data. It also provides us with a chance to observe the general (time-series)

~ 23 ~ Guidelines on Panel Data Analysis behaviour of the series we will be working with. Points to look out for include the possible existence of time trends or structural breaks in the underlying data. The first thing one should always do is to plot the data to make sure that it looks fine.

2.6 Descriptive Statistics

Once data has been entered into Eviews as indicated above and basic graphical representations have been done. The next step is to conduct descriptive statistics. In this case there are two avenues available: (i) computing descriptive statistics for the group (ii) conducting descriptive statistics for all the groups in the panel at one.

1. Descriptive statistics for the group

Step 1: Selecting the group: In our case, as shown in Panel A, we are interested in the descriptive statistics for Bank Size. If you double click on the group named ‘Size’ you will obtain the sheet shown on Panel B. This sheet contains observations for the individual cross-sections for Size for the period 2000-2016.

Step 2: Obtaining the descriptive statistics: Once the data has been presented on the screen as shown on panel B, you then click ‘view’ on

~ 24 ~ Getting Started in Eviews Software

the tool bar that contains the series. Then you will get a drop down window which contains a number of options. In our case choose ‘Descriptive stat’. Once this is highlighted you will need to choose whether you need statistics for individual series in the group or common statistics. If you click on ‘individual series, you will obtain the following:

2. Descriptive statistics within a panel environment: In case you are interested in the descriptive statistics for all cross sections in the panel. You may follow the following steps:

Step 1: create a pool object: Steps on creating a pool object are explained in section 2.3.2. Follow these steps to create the pool object. Once a pool object has been created, click View, Descriptive statistics…

A blank screen shown below pops-up. The next step is to list all the variables of interest in the space provided. Remember to include ‘?’ after listing the variable as shown below.

~ 25 ~ Guidelines on Panel Data Analysis

To obtain ‘descriptive statistics’ click on ‘OK’ to obtain the output shown in below.

~ 26 ~ Getting Started in Eviews Software

The descriptive statistics provided relate to the totality of the cross-sections for each variable. For example, you may notice that for Variable X, the Jarque-Bera test (p-value<0.05, therefore we reject the null hypothesis that residuals are normal) shows that the variable is not normally distributed. This finding contrasts with the one obtained for the individual cross sections… but we are interested in panel data behaviour and not the individual series!

~ 27 ~

Chapter 3

Pooled Regression Analysis

3.0 Introduction

There are a number of methods of analysis of panel data. However, the pooled regression analysis is the most basic. In this chapter we present the theoretical workings of the pooled regression analysis, the data presentation in the pooled regression framework and the estimation.

3.1 The pooled regression model

A pooled regression involves obtaining the data for all the cross sections of interest over time and stacking them and run a simple ordinary least squares (OLS) to obtain the estimates which are BEST. In this case we visualise the pooled regression model as follows:

y1t  1 xit  e1t

y2t  2 x2t  e2t ......

yit  i xit  eit

Yi,t  Xi,t i,t 1

Where is Y, the dependent variable, is observed for all cross sections (i= 1,

2…. N), over time t, (t=1, 2 …T). X is the independent variable while  it is the error term. For a better representation of Equation 1, each of the variables shown may be presented as for each cross section as follows: Guidelines on Panel Data Analysis

 y  x1 x2 ... xk       i1  i1 i1 i1  1   i1   1 2 k   yi2  xi2 xi2 ... xi2  2  i2  .    .  .    .     yi  x i      i  .  .  .  .        .   . .   .       y   1 2 k       iT  xiT xiT ... xiT   k   ik 

where yit is the value of the dependent variable for cross-section unit i at time t (i = 1, … , n; t = 1, … , T),  it refers to the disturbance term for the j i-th unit at time t and xit is the value of the j-th explanatory variable for cross-section unit i at time t. There are k explanatory variables indexed by j = 1, …, k. Equation 1 is a giant model for all cross sections over time which may then be estimated using OLS.

3.1.1 Limitations of Pooled regression In the pooled regression analysis, the cross sections are assumed to be homogenous. For that reason, it is assumed that the estimated coefficients (intercept and slope) are common since there is no heterogeneity. However, in the real life heterogeneity exists, meaning that if we assume a pooled regression then we may have a bias, usually referred to as heterogeneous bias. The heterogeneous bias is presented in the figure below. In this case the pooled regression coefficients are B0 and B1. However, it is noted that each individual cross-sections has its own and probably unique coefficients. In our example, these individual and unique coefficients reflect the heterogeneous (unique) nature of every individual bank.

~ 30 ~ Pooled Regression Analysis

3.2 Estimation of the Pooled Regression Model

3.2.1 Illustration of pooled regression using general data This User’s Guide seeks to demonstrate how to estimate a model in a panel context based on the transmission of monetary policy transmission. Prior to this, we realise that it is important to first demonstrate how the data is organised and estimated using fictitious example. Once this is appreciated then we can proceed to implement the example based on bank level data to demonstrate the effectiveness of monetary policy transmission. In our case we will seek to demonstrate whether the bank lending channel works in Kenya.

In addition, the pooled model being the most basic of the known methods of panel data analysis, we will devote time to explain how this approach works. After that is done then it will be very clear on how data is organised and model estimated in any panel specification. For convenience we seek to illustrate the panel data estimation using the model shown in Equation 1, reproduced here as:

Yi,t  Xi,t i,t

~ 31 ~ Guidelines on Panel Data Analysis

To estimate this model, we require data on Y (growth rate of loan) and X (bank size) for all the cross sections. For illustration purposes we assume that we have 5 cross sections (banks) namely Bank1-Bank5. For each cross section we assume we are observing data for the period 2000- 2016.

3.2.2 Organising data in Excel To estimate this model, we follow the following steps:

Step 1: Organising data in Excel: Consider a banking system consisting of five (5) banks. Table 1 below shows two variables namely Bank Size (measured by the normalized size of each banks’ assets) and Loan by bank. The dataset therefore consists of two variables with three 5 cross-sections observed over the period 2000-2016. In its primitive form, the data for these two variables may be presented as shown in the table below:

Table 3.1: Raw data on bank size and loan

BANK SIZE LOAN BY BANK Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5 Loan_Bank1 Loan_Bank2 Loan_Bank3 Loan_Bank4 Loan_Bank5 2000 6.3 4.6 6.7 4.1 3.5 4.4 5.7 5.3 15.9 4.6 2001 5.8 5.1 6.7 2.9 3.2 2.8 4.6 5.2 4.8 4.0 2002 4.5 3.4 6.7 1.8 3.3 12.9 6.1 6.6 5.3 6.2 2003 2.1 2.2 9.3 -1.4 3.3 9.2 6.9 1.3 3.5 6.9 2004 2.0 2.0 9.8 -2.1 3.6 3.5 4.4 6.1 4.9 8.3 2005 1.9 1.7 9.8 -1.5 3.6 3.4 8.0 7.5 1.6 5.5 2006 2.0 1.5 9.8 -1.4 3.6 2.4 7.1 17.1 3.0 5.5 2007 1.5 -2.2 9.8 -2.4 3.6 1.3 4.3 13.6 7.7 5.4 2008 0.5 1.6 9.8 -2.2 3.6 1.2 4.5 6.0 5.5 4.3 2009 0.6 0.1 9.8 -1.4 1.1 10.3 6.0 1.5 4.4 4.9 2010 1.0 1.2 10.5 -1.3 0.8 4.2 5.3 1.7 15.8 7.3 2011 6.4 1.8 9.8 -1.8 0.8 11.9 6.1 8.1 8.7 4.8 2012 1.5 2.0 8.5 -1.1 2.8 14.5 6.4 1.6 3.8 4.8 2013 2.4 2.4 9.8 -0.7 2.8 8.5 8.8 4.0 4.8 7.3 2014 2.5 2.5 9.8 0.1 2.7 7.8 5.2 5.0 1.6 7.7 2015 3.7 1.5 9.8 0.5 2.7 0.9 4.5 5.7 3.8 5.1 2016 3.3 3.4 9.8 0.4 2.7 1.0 6.1 3.8 4.9 7.5

As shown in Table 1, we observe that data for bank size and loan are observed for each cross section for the period 2000-2016. For example, in the case of Bank1, the observed size and loan are 4.4 and 6.3, respectively in 2000. To estimate a panel model using this data we stack this data as shown in Table 2. Stacking involves getting the data for size and loan for each cross section and arranging them with size and its corresponding loan arranged as follows:

~ 32 ~ Pooled Regression Analysis

Table 3.2: Stacked data on bank size and loan

Loan Size 1 6.3 4.4 2 5.8 2.8 3 4.5 12.9 4 2.1 9.2 5 2.0 3.5 6 1.9 3.4 7 2.0 2.4 8 1.5 1.3 9 0.5 1.2 Bank1 10 0.6 10.3 11 1.0 4.2 12 6.4 11.9 13 1.5 14.5 14 2.4 8.5 15 2.5 7.8 16 3.7 0.9 17 3.3 1.0 18 4.6 5.7 19 5.1 4.6 20 3.4 6.1 21 2.2 6.9 22 2.0 4.4 23 1.7 8.0 24 1.5 7.1 25 -2.2 4.3 Bank2 26 1.6 4.5 27 0.1 6.0 28 1.2 5.3 29 1.8 6.1 30 2.0 6.4 31 2.4 8.8 32 2.5 5.2 33 1.5 4.5 34 3.4 6.1 35 6.7 5.3 36 6.7 5.2 37 6.7 6.6 38 9.3 1.3 39 9.8 6.1 40 9.8 7.5 41 9.8 17.1 42 9.8 13.6 43 9.8 6.0 Bank3 44 9.8 1.5 45 10.5 1.7 46 9.8 8.1 47 8.5 1.6 48 9.8 4.0 49 9.8 5.0 50 9.8 5.7 51 9.8 3.8 52 4.1 15.9 53 2.9 4.8 54 1.8 5.3 55 -1.4 3.5 56 -2.1 4.9 57 -1.5 1.6 58 -1.4 3.0 59 -2.4 7.7 60 -2.2 5.5 Bank4 61 -1.4 4.4 62 -1.3 15.8 63 -1.8 8.7 64 -1.1 3.8 65 -0.7 4.8 66 0.1 1.6 67 0.5 3.8 68 0.4 4.9 69 3.5 4.6 70 3.2 4.0 71 3.3 6.2 72 3.3 6.9 73 3.6 8.3 74 3.6 5.5 75 3.6 5.5 76 3.6 5.4 77 3.6 4.3 Bank5 78 1.1 4.9 79 0.8 7.3 80 0.8 4.8 81 2.8 4.8 82 2.8 7.3 83 2.7 7.7 84 2.7 5.1 85 2.7 7.5

~ 33 ~ Guidelines on Panel Data Analysis

It is important to note that it does not matter which cross section is arranged first. As shown in Table 2, we simply started with Bank1, but we could have as well started with Bank2. You may now notice that in stacking the data the time dimension is lost meaning that the data is now undated with 85 observations (17x5). From Table 2, it is clear that we have two variables: loan, the dependent variable and size, the independent variable. This data is consistent with the model set up shown in Equation 1.

3.2.3 Loading the data into Eviews Step 2: Getting started in Eviews: Considering that the data shown in step 1 does not show any panel data features we will get it into Eviews using the following procedure. Once Eviews work space is opened as discussed in Chapter 1, we will follow the following steps.

File--New-- Workfile, to obtain Panel A, in Figure 1. Figure 1: Creating a work file Panel A Panel B

~ 34 ~ Pooled Regression Analysis

You may notice that in Panel A, a dialog box will emerge requiring you to create workfile. If you click on the ‘Workfile Structure Type’ you will obtain 3 options (Dated-regular frequency, Unstructured/Undated, Balanced panel). However, as noted earlier, this dataset is undated, therefore you need to choose ‘Unstructured/Undated’ in the drop down menu named ‘Dated-regular frequency’. In addition, you are required to choose the ‘Data Range’. In our case we have 85 observations. If you click on ‘OK’ then you will obtain Panel B in Figure 2.

Step 3: Getting the Data into Eviews: Panel B in Figure 1 has been configured to accept data with a range of 1-85… 85 obs for each bank). The data we are interested in getting into Eviews as shown in Table 2 is in Excel, therefore it needs to be copied from Excel and pasted into Eviews as follows: In the Eviews workfile, on the main tool bar, click on ‘Quick’. Here you will find several options, but choose ‘empty Group’. In the empty group, paste the data to obtain the following

Figure 2: Getting the data into Eviews

Variables Size and Observations loan appear here for loan

~ 35 ~ Guidelines on Panel Data Analysis

You will notice that the workfile has 2 variables size and loan. This shows that the data has been loaded into Eviews successfully and is ready for further analysis.

3.2.4 Pooled regression in Eviews Step 4: Estimation: You may recall in our model set up such that loan is the dependent variable while size is the independent variable. To estimate this model, you need to proceed to the main tool bar and click on ‘Object’, followed by … New Object’ to obtain the output on Panel A. You may notice that the New Object option gives you a range of options to pick from. In our case, we are interested in an ‘Equation Object’. Once you highlight the Equation Object and click ‘OK’ button you will obtain the Box shown in Panel B of Figure 3. This provides you with instructions on how to estimate the Equation. You will then populate the blank space with the variable of interest, starting with the dependent variable loan, followed by the rest including the constant, C as shown in Panel B:

Figure 3: Estimation in a pool object Panel A Panel B

You will notice that the estimation method is required. At the bottom of the Box you will see a provision for ‘Estimation Setting’ – Method. The Default method is the LS- Least Squares (NLS and ARMA). In the pooled regression

~ 36 ~ Pooled Regression Analysis approach, the estimation method is the LS, therefore if you click on ‘OK’, you will obtain the following output:

Figure 4: Estimation result

3.2.5 Pooled regressions in Eviews Environment Though informative, the step by step estimation of a pooled regression, may be time consuming as it requires one to stack the data and depending on the number of cross-sections and time dimension, errors may emerge. For example, we had to limit our cross- sections to 5 and the number of observations per cross section to 17 to be able to illustrate how the pooled regression is done is Eviews.

In view of this, Eviews is configured to estimate a model within the panel framework by following a certain procedure. In this part we discuss and illustrate the procedure used in estimating a pooled regression in Eviews based on the following steps:

Step 1: Data Preparation in Excel: The first step in the preparation of data shown in Table 1 above, is to introduce cross-section identifiers. Steps on how to introduce cross section identifiers in Eviews were demonstrated in section 2.3.2. Cross-section identifiers are extensions added to the variable names in order for Eviews to recognise in the stack

~ 37 ~ Guidelines on Panel Data Analysis

procedure that data for a particular cross section started at a particular point and ends at another point. In our case our variables of interest are bank size and loan. We therefore add identifiers as explained in Chapter 1, in which case, the five cross sections: Bank1-Bank5 will be recorded as follows:

Table 3.3: Data on size and growth rate of loan with cross-section identifiers

LOAN BY BANK BANK SIZE 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 2001 2.8 4.6 5.2 4.8 4.0 5.8 5.1 6.7 2.9 3.2 2002 12.9 6.1 6.6 5.3 6.2 4.5 3.4 6.7 1.8 3.3 2003 9.2 6.9 1.3 3.5 6.9 2.1 2.2 9.3 -1.4 3.3 2004 3.5 4.4 6.1 4.9 8.3 2.0 2.0 9.8 -2.1 3.6 2005 3.4 8.0 7.5 1.6 5.5 1.9 1.7 9.8 -1.5 3.6 2006 2.4 7.1 17.1 3.0 5.5 2.0 1.5 9.8 -1.4 3.6 2007 1.3 4.3 13.6 7.7 5.4 1.5 -2.2 9.8 -2.4 3.6 2008 1.2 4.5 6.0 5.5 4.3 0.5 1.6 9.8 -2.2 3.6 2009 10.3 6.0 1.5 4.4 4.9 0.6 0.1 9.8 -1.4 1.1 2010 4.2 5.3 1.7 15.8 7.3 1.0 1.2 10.5 -1.3 0.8 2011 11.9 6.1 8.1 8.7 4.8 6.4 1.8 9.8 -1.8 0.8 2012 14.5 6.4 1.6 3.8 4.8 1.5 2.0 8.5 -1.1 2.8 2013 8.5 8.8 4.0 4.8 7.3 2.4 2.4 9.8 -0.7 2.8 2014 7.8 5.2 5.0 1.6 7.7 2.5 2.5 9.8 0.1 2.7 2015 0.9 4.5 5.7 3.8 5.1 3.7 1.5 9.8 0.5 2.7 2016 1.0 6.1 3.8 4.9 7.5 3.3 3.4 9.8 0.4 2.7

Step 2: 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 - 2016 as follows:

~ 38 ~ Pooled Regression Analysis

Recall the steps in creating a pool workfile and cross section identifiers from section 2.3.2

Step 3: Estimate model: You should use the Method dropdown menu to choose between LS - Least Squares (LS and AR), TSLS - Two-Stage Least Squares (TSLS and AR), and GMM / DPD – Generalized Method of Moments / Dynamic Panel Data (DPD) techniques. In this case we are interested in the LS - Least Squares (LS and AR). Click on ‘OK’ to obtain the following:

Panel A Panel B

3.3 Application of Pooled Regression Approach to Monetary Policy Transmission in Kenya

So far we have used variables bank size and growth rate of loans by bank to illustrate how one navigates the Eviews software to generate output. However, for illustration based on ‘monetary transmission mechanism’ it is not possible to parade bank specific data. To meet this objective, however, we present and interpret the results based on a study on Kenya:

3.3.1 Case Study: Monetary Policy Transmission in Kenya: Evidence from bank level data In study we investigate the existence, if any, and strength of the Bank Lending Channel of monetary policy transmission in Kenya. We use micro-

~ 39 ~ Guidelines on Panel Data Analysis bank level data on 39 commercial banks using monthly data for 2001-2015. To accomplish this task, we adopt a framework similar to that of Kashyap and Stein (2000) and Walker (2013) which exploits the heterogeneous nature of commercial banks to establish whether or not the BLC exists in Kenya.

3.3.2 The Model setup In this study, we estimate the following basic model:

n  ln(L )    ln(L )   IR   log(Size )  i,t 1 i,t1 2  tn 3 i,t 1 n0

 4 Liqi,t  5 KAPi,t  6 X t  7 Dit  vi   i,t

Where;  ln( Li,t ) is the change in total lending by bank i at time t; IR is the monetary policy variable, usually interest rate at t; log(Sizei,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,t is the total liquid assets to total assets of bank i at time t; Xt is a vector of macroeconomic variables which may affect the operating environments for banks; Di,t is a various qualitative characteristics of commercial banks such as private or public; domestic or foreign; vi is the time invariant error component;  i,t is 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: 2  Lit / Bitmt  0 where Lit is a measure of lending by bank i at time t, Bit is a measure of strength of balance sheet of Bank i at time t while mt is a measure of the monetary policy stance at time t. The implication of this hypothesis is as follows: firstly, that the degree to which lending is 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.

~ 40 ~ 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 uninsured sources of finance. The role of size has been emphasized, for example, in Kashyap and Stein (1995): small banks are assumed to suffer from informational asymmetry problems more than large banks do, and find it therefore more difficult to raise uninsured funds in times of monetary tightening. Again, this should force them to reduce their bank lending relatively more when compared to large banks. The sensitivity of 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:

~ 41 ~ Guidelines on Panel Data Analysis

N logS   it S  logS  i1 it N t ;

 Where S the adjusted bank size and N is the number of banks in the sample.

Following Kashyap and Stein (2000), it is shown that given the same characteristics of banks, except the level of liquidity, the banks will react 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.

N logL   it L  logL  i1 it N t As shown in the literature (see Peek and Rosengren, 1995) poorly 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.

N  E  log     E  i1  A  K  log  it  A N  it t

~ 42 ~ 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.

~ 43 ~ Guidelines on Panel Data Analysis

Figure 5: BLC based on pooled regressions analysis

Panel A: Simple BLC Panel B: BLC based on Pooled regressions with control variables

IBR is negative and highly significant

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.

~ 44 ~ 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.

~ 45 ~ Guidelines on Panel Data Analysis

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.

~ 46 ~ 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  0  1xit  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, into three distinct parts or components as follows:

uit  vi  t  it 2 Guidelines on Panel Data Analysis

In 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 assuming t  0, in which case Equation 2 collapses to:

uit  vi  it 3a

In this formulation we allow for only cross section differences to be investigated while assuming away the time variations. On the other hand, if we assume vi  0 , the Equation 2 becomes:

uit  t  it 3b

In 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:

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yit  0  1xit  t  it 4a Or

yit  0  1xit  vi  it 4b

Equations 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 ( ) and ( ) are separate parameters. For illustration purposes we use the case where we estimate the ( ). In estimating the separate parameters ( ) 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:

yi  X i 1T vi  i

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In this case the parameters for X are estimated. In addition, dummies for each of the cross sections are estimated. In its non-compact form, it is represented as follows:

 y   X  1 . . 0   v     1   1   T   1   1   .   .   0  0   .   .       .   .   0  0   .   .                       yi   X n   0 0 0 1T  vn   i 

y  X  In 1T v    X  Dv  

This model is appealing but the number of parameters to be estimated is 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).

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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

Dummy for Bank1 Dummy for Bank2 Dummy for Bank3 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 2001 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2002 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2003 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2004 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2005 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2006 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2007 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2008 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2009 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2010 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2011 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2012 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2013 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2014 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2015 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 2016 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 Dummy for Bank4 Dummy for Bank5 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 2001 0 0 0 1 0 0 0 0 0 1 2002 0 0 0 1 0 0 0 0 0 1 2003 0 0 0 1 0 0 0 0 0 1 2004 0 0 0 1 0 0 0 0 0 1 2005 0 0 0 1 0 0 0 0 0 1 2006 0 0 0 1 0 0 0 0 0 1 2007 0 0 0 1 0 0 0 0 0 1 2008 0 0 0 1 0 0 0 0 0 1 2009 0 0 0 1 0 0 0 0 0 1 2010 0 0 0 1 0 0 0 0 0 1 2011 0 0 0 1 0 0 0 0 0 1 2012 0 0 0 1 0 0 0 0 0 1 2013 0 0 0 1 0 0 0 0 0 1 2014 0 0 0 1 0 0 0 0 0 1 2015 0 0 0 1 0 0 0 0 0 1 2016 0 0 0 1 0 0 0 0 0 1

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:

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Cross-section Data range is stated identifiers are listed

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:

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Give variable name here

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,

To estimate this model, click on ‘estimate’

The 7 variables are entered and each is identified as a group

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.

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Enter Dependent variable here followed by ? Enter independent variables here each followed by ?

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.

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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:

Enter ‘C’ here

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:

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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

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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:

n  ln(Li,t )  1 ln(Li,t 1)  2  IRt n  3 log(Sizei,t )  4 Liqi,t  n0 1

5KAPi,t  6 X t  7 Dit  vi   i,t

Where;  ln( Li,t ) is the change in total lending by bank i at time t; IR is the 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;

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:

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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 policy stance will result in a 0.15 percent change in the total credit to the private sector, in the opposite direction. The fact that the estimated coefficient is negative and significant suggests that monetary policy is effective in Kenya.

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 The estimated coefficient of bank size is found to be positive and significant at 1 percent as well, suggesting that larger banks lend to change lending to the private sector more than the small banks.  The other coefficients, mainly those with an extension of ‘_C’ are the cross section specific coefficients relate to whether the estimated intercept for each individual bank is significant or not.

4.2.1 Within-Q-estimation method In light of the limitations of the LSDV, regarding the number of parameters to be estimated, the within estimation method overcomes this challenge by computing the individual effects. Recall the fixed effects is applicable in the case where there is potential endogeneity between the fixed effects ( vi ) and

Xit as stated here:

yit  X it  vi   it

E X it vi   0 5

E X it  it   0

In this case the problem of endogeneity arises because of the correlation between Xit and vi. To overcome this problem, we appeal to the Annihilator matrix transformations. The transformation procedure involves eliminating the Vi from Equation 5 in order to obtain reliable estimates of the slope coefficient3.Once the estimates are obtained then the fixed effects are computed. In terms of implementation of the transformations on the data, we follow the following steps:

Step 1: Computation of the mean: Compute the mean of each variable for all cross-sections as follows:

yi  X i  vi   i 1 T 1 T 1 T y   yit ; X   X it ;v  vi T t1 T t1 T t1

3 The procedure involves transformations based on the Annihilator matrix transformations. For detailed discussion see Liebler’s Basic Matrix Algebra with Algorithms and Applications

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Step 2: Demeaning the data: For each variable subtract the mean obtained from step 1 to obtain the following:

yit  yi  Xit  Xi vi vi it i

In its compact form it may be presented as:

~ ~ ~ y it   X it  it

Then stack by observation as follows: ~  ~y   X  ~   1   1   1   .   .   .           .  . .   ~     ~y    ~   n   X n   n 

~ ~ ~y   X  

The within-group fixed-effects estimator is pooled OLS on the transformed regression that has been stacked by observations:

n 1 n ~ ~ 1 ~  ~ ~  ~ ˆ   ~ ~ FE  X X  X y   X i X i   X i yi  i1  i1

This procedure may be implemented in Excel and Eviews by making the following steps:

Step 1: Data preparation: Organise the data for the variables loan, and bank size and also compute the mean value for each of the cross- sections.

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INTEREST RATE Loan BY BANK BANK SIZE Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5 Loan_Bank1 Loan_Bank2 Loan_Bank3 Loan_Bank4 Loan_Bank5 2000 6.3 4.6 6.7 4.1 3.5 4.4 5.7 5.3 15.9 4.6 2001 5.8 5.1 6.7 2.9 3.2 2.8 4.6 5.2 4.8 4.0 2002 4.5 3.4 6.7 1.8 3.3 12.9 6.1 6.6 5.3 6.2 2003 2.1 2.2 9.3 -1.4 3.3 9.2 6.9 1.3 3.5 6.9 2004 2.0 2.0 9.8 -2.1 3.6 3.5 4.4 6.1 4.9 8.3 2005 1.9 1.7 9.8 -1.5 3.6 3.4 8.0 7.5 1.6 5.5 2006 2.0 1.5 9.8 -1.4 3.6 2.4 7.1 17.1 3.0 5.5 2007 1.5 -2.2 9.8 -2.4 3.6 1.3 4.3 13.6 7.7 5.4 2008 0.5 1.6 9.8 -2.2 3.6 1.2 4.5 6.0 5.5 4.3 2009 0.6 0.1 9.8 -1.4 1.1 10.3 6.0 1.5 4.4 4.9 2010 1.0 1.2 10.5 -1.3 0.8 4.2 5.3 1.7 15.8 7.3 2011 6.4 1.8 9.8 -1.8 0.8 11.9 6.1 8.1 8.7 4.8 2012 1.5 2.0 8.5 -1.1 2.8 14.5 6.4 1.6 3.8 4.8 2013 2.4 2.4 9.8 -0.7 2.8 8.5 8.8 4.0 4.8 7.3 2014 2.5 2.5 9.8 0.1 2.7 7.8 5.2 5.0 1.6 7.7 2015 3.7 1.5 9.8 0.5 2.7 0.9 4.5 5.7 3.8 5.1 2016 3.3 3.4 9.8 0.4 2.7 1.0 6.1 3.8 4.9 7.5 Average 2.8 2.1 9.1 -0.4 2.8 5.9 5.9 5.9 5.9 5.9

Step 2: Demeaning the data: This transformation requires that you subtract the mean for each cross-section from each observation to yield the following:

Table 4.2: Demeaned data

LOAN BY BANK BANK SIZE SizeT_Bank1 SizeT_Bank2 SizeT_Bank3 SizeT_Bank4 SizeT_Bank5 LoanT_Bank1 LoanT_Bank2 LoanT_Bank3 LoanT_Bank4 LoanT_Bank5 2000 3.4 2.5 -2.5 4.6 0.7 -1.5 -0.1 -0.6 10.1 -1.3 2001 3.0 3.1 -2.5 3.3 0.3 -3.1 -1.2 -0.7 -1.1 -1.9 2002 1.7 1.4 -2.5 2.3 0.5 7.0 0.3 0.7 -0.6 0.3 2003 -0.7 0.2 0.1 -1.0 0.5 3.3 1.0 -4.5 -2.3 1.0 2004 -0.8 0.0 0.6 -1.6 0.8 -2.4 -1.5 0.2 -0.9 2.4 2005 -0.9 -0.4 0.6 -1.1 0.8 -2.5 2.1 1.6 -4.2 -0.4 2006 -0.8 -0.5 0.6 -0.9 0.8 -3.5 1.2 11.2 -2.9 -0.4 2007 -1.3 -4.3 0.6 -1.9 0.8 -4.5 -1.6 7.7 1.8 -0.5 2008 -2.3 -0.5 0.6 -1.7 0.8 -4.7 -1.3 0.1 -0.4 -1.6 2009 -2.2 -2.0 0.6 -0.9 -1.7 4.4 0.1 -4.4 -1.5 -1.0 2010 -1.8 -0.8 1.3 -0.9 -2.0 -1.6 -0.6 -4.2 9.9 1.4 2011 3.6 -0.3 0.6 -1.4 -2.0 6.0 0.2 2.2 2.8 -1.0 2012 -1.3 0.0 -0.7 -0.6 0.0 8.6 0.5 -4.2 -2.1 -1.1 2013 -0.4 0.3 0.6 -0.3 0.0 2.6 2.9 -1.9 -1.0 1.4 2014 -0.3 0.5 0.6 0.5 -0.1 1.9 -0.7 -0.9 -4.3 1.8 2015 0.9 -0.6 0.6 0.9 -0.1 -5.0 -1.4 -0.2 -2.1 -0.8 2016 0.5 1.4 0.6 0.9 -0.1 -4.9 0.2 -2.0 -1.0 1.6

Step 3: copy the transformed data and paste it in Eviews. But first open a new file with the same dimensions as before. While following the steps for creating a panel object, we estimate the equation with transformed data (SizeT and DloanT) as shown below:

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Step 4: Estimation: Then click on the OK button to obtain the following result.

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LSDV method, this is a long method, but it is useful in terms of appreciating the inner workings of the method. Eviews has a shortcut to this procedure in which you adjust the panel estimation screen to the following:

Click on drop down and select ‘Fixed’

Step 5: choice of estimation method: Next, click on the Panel Options tab to specify additional panel specific estimation settings. First, you should account for individual and period effects using the Effects specification dropdown menus. By default, Eviews assumes that there are no effects so that both dropdown menus are set to None. You may change the default settings to allow for either Fixed or Random effects in either the cross- section or period dimension, or both.

Since we are estimating a fixed effect within the context of cross-sections, you click on the drop down arrow and select ‘Fixed’ while the regressors are Size? You should be aware that when you select a fixed or random effects specification, Eviews will automatically add a constant to the common coefficients portion of the specification if necessary, to ensure that the effects sum to zero.and C. Choosing ‘Fixed’ here tells Eviews that you are estimating the model using the Within Q estimation method. If you click “OK’ you will obtain the following result:

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The fixed effects have no std. error etc. because they are computed.

The LSDV and within-q- methods are equivalent: you may now see that the LSDV and the Within-q- method are equivalent as shown in panels A and B where the results for bank size (SIZE?) are exactly the same.

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Panel A Panel B

4.3 Pooled Estimation Method Versus the Fixed Effect Method

As indicated above the pooled regression allows for estimation of common coefficients while the fixed effects model allows estimation individual intercepts. It is therefore not possible to make a good guess as to which model is appropriate. In this case we conduct the F-test to establish which model is appropriate. To illustrate this, recall the following:

yit  0  1xit  vi it

The test being implemented here calls seeks to establish whether ( vi ) exists or not by testing the following hypothesis:

H 0 : v1  v2  ......  vN1  0

We test the null hypothesis of no individual effects within applied Chow or F-test, combining the residual sum of squares for the regression both with constraints (under the null) and without (under alternative). The F-statistics is stated as:

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RSS URSS/N 1 F   F URSS /NT  N  K  N 1NTN K 

To implement the F-test we follow the following steps:

Step 1: Estimate the fixed effects model: In our example above we obtained the following result based on cross-section effects:

Step 2: Once the result above is obtained, go to the tools bar and click on ‘view’ then choose ‘Fixed/Random Effects testing’ followed by ‘Redundant Fixed Effects—likelihood ratio’ and obtain the following:

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Step 3: The Decision rule: the part of the result which is critical to our decision is indicated here below. The decision rule is as follows: if the P- value < 0.05 we reject the null hypothesis, implying that the fixed effects are not redundant. However, if P-value > 0.05, we fail to reject the null hypothesis, implying that the fixed effects are redundant and therefore pooled estimation is valid.

Redundant Fixed Effects Tests Pool: POOL01 Test cross-section fixed effects

Effects Test Statistic d.f. Prob.

Cross-section F 88.223735 (4,79) 0.0000 Cross-section Chi-square 144.392433 4 0.0000

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In this case it is observed that the Cross-Section F statistics is 88.2 with (4, 79) degrees of freedom whose associated p-value is 0.000, which is less than 0.05, therefore we reject the null hypothesis. In the present case fixed effects are critical and need to be considered.

4.4 Case Study: Monetary Policy Transmission in Kenya: Evidence from bank level data

As indicated in Chapter 2, 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:

n ln(Li,t )  1ln(Li,t 1)  2  IRt n  3 log(Sizei,t )  1 n0

4Liqi,t  5KAPi,t  6 X t  7 Dit  vi  i,t

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Step 1: Setting up- the Within Estimation. In the within model set up, the important aspect is the computation of the individual specific coefficients. Eviews is configured to implement this approach. To implement the fixed effects, you check the Estimation Method - the Fixed and Random effects are automated. The default shows cross-section: ‘None” and Period: ‘None’. First, you should account for individual and period effects using the Effects specification dropdown menus. By default, Eviews assumes that there are no effects so that both dropdown menus are set to None. You may change the default settings to allow for either Fixed or Random effects in either the cross- section or period dimension, or both. The dependent variable as before is “tcad?”. To allow for fixed effects, you click on Cross-section and choose ‘Fixed’.

Step 2: Estimation: After choosing the estimation method as ‘Fixed’ 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:

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private sector, in the opposite direction. The fact that the estimated coefficient is negative and significant suggests that monetary policy is effective in Kenya.  The estimated coefficient of bank size is found to be positive and significant at 1 percent as well, suggesting that larger banks lend to change lending to the private sector more than the small banks.  The other coefficients, mainly those with an extension of ‘_C’ are the fixed effects. You may notice the fixed effects do not have –statistics nor standard errors, meaning they are not estimated but computed.

Step 3: Testing the validity of the fixed effects: As indicated earlier we run an F-test to obtain the result shown. The result of the test shows that the estimated F-statistic is 3.56, with the p- value of 0.000. Based on the p- value, we reject the null hypothesis, suggesting that the fixed effects are not redundant. The implication of this test is that the model shown in Chapter 2, is invalid and therefore it cannot be used to make inferences regarding the effectiveness of the bank lending channel in Kenya. With the F-test allowing us to estimate the fixed effects model, it therefore means that the estimated model in Step 2 above is valid and can be used to make inferences about the existence the bank lending channel in Kenya.

4.5 Random Effects Model

Recall the model in Equation 4a, stated as yit  0  1xit  vi it , in the random effects approach the vi are said exist but are randomly distributed and are not correlated with other regressors. In this case, the are not a set of fixed parameters to be estimated but random variables,

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To estimate the random effects model we follow the same procedure like the one for the fixed effects model. In this case we follow the following steps:

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

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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

E[ui / X i ]  0 E[ui / X i ]  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

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References

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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 shortcut 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:

uit  vi  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.:

uit  vi  t  it 3c This is referred to as a 2-way-error components model.

Guidelines on Panel Data Analysis

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

To estimate the two way-error components model we estimate the following transformed model:

yit  yi  yt  y   xit  xi  xt  x   Is this complete??? vit  vi  vt  v 

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.

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Table 5.1: Data

INTEREST RATE SPREAD BY BANK BANK SIZE Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5 Average Spread_Bank1 Spread_Bank2 Spread_Bank3 Spread_Bank4 Spread_Bank5 Average 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 2001 5.8 5.1 6.7 2.9 3.2 4.7 2.8 4.6 5.2 4.8 4.0 4.3 2002 4.5 3.4 6.7 1.8 3.3 4.0 12.9 6.1 6.6 5.3 6.2 7.4 2003 2.1 2.2 9.3 -1.4 3.3 3.1 9.2 6.9 1.3 3.5 6.9 5.6 2004 2.0 2.0 9.8 -2.1 3.6 3.1 3.5 4.4 6.1 4.9 8.3 5.4 2005 1.9 1.7 9.8 -1.5 3.6 3.1 3.4 8.0 7.5 1.6 5.5 5.2 2006 2.0 1.5 9.8 -1.4 3.6 3.1 2.4 7.1 17.1 3.0 5.5 7.0 2007 1.5 -2.2 9.8 -2.4 3.6 2.1 1.3 4.3 13.6 7.7 5.4 6.5 2008 0.5 1.6 9.8 -2.2 3.6 2.7 1.2 4.5 6.0 5.5 4.3 4.3 2009 0.6 0.1 9.8 -1.4 1.1 2.0 10.3 6.0 1.5 4.4 4.9 5.4 2010 1.0 1.2 10.5 -1.3 0.8 2.4 4.2 5.3 1.7 15.8 7.3 6.9 2011 6.4 1.8 9.8 -1.8 0.8 3.4 11.9 6.1 8.1 8.7 4.8 7.9 2012 1.5 2.0 8.5 -1.1 2.8 2.7 14.5 6.4 1.6 3.8 4.8 6.2 2013 2.4 2.4 9.8 -0.7 2.8 3.3 8.5 8.8 4.0 4.8 7.3 6.7 2014 2.5 2.5 9.8 0.1 2.7 3.5 7.8 5.2 5.0 1.6 7.7 5.5 2015 3.7 1.5 9.8 0.5 2.7 3.6 0.9 4.5 5.7 3.8 5.1 4.0 2016 3.3 3.4 9.8 0.4 2.7 3.9 1.0 6.1 3.8 4.9 7.5 4.7 Average 2.8 2.1 9.1 -0.4 2.8 3.3 5.9 5.9 5.9 5.9 5.9 5.9

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:

INTEREST RATE SPREAD BY BANK BANK SIZE 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 2001 1.5 1.6 -3.9 1.9 -1.1 -1.5 0.3 0.9 0.5 -0.3 2002 1.0 0.7 -3.2 1.6 -0.2 5.5 -1.3 -0.8 -2.1 -1.3 2003 -0.6 0.4 0.3 -0.8 0.7 3.6 1.3 -4.2 -2.0 1.3 2004 -0.6 0.2 0.8 -1.4 1.0 -2.0 -1.1 0.6 -0.5 2.9 2005 -0.7 -0.2 0.8 -0.9 1.0 -1.8 2.8 2.3 -3.6 0.3 2006 -0.7 -0.3 0.8 -0.7 1.0 -4.7 0.1 10.0 -4.0 -1.5 2007 -0.1 -3.0 1.8 -0.7 2.0 -5.1 -2.1 7.1 1.2 -1.0 2008 -1.7 0.2 1.2 -1.1 1.4 -3.1 0.2 1.7 1.2 0.0 2009 -1.0 -0.7 1.9 0.3 -0.5 4.9 0.6 -3.9 -1.0 -0.5 2010 -1.0 0.0 2.2 -0.1 -1.2 -2.6 -1.6 -5.2 8.9 0.4 2011 3.5 -0.4 0.5 -1.5 -2.1 4.0 -1.9 0.2 0.8 -3.1 2012 -0.8 0.5 -0.1 -0.1 0.5 8.2 0.2 -4.6 -2.4 -1.4 2013 -0.5 0.3 0.6 -0.3 -0.1 1.8 2.1 -2.7 -1.8 0.6 2014 -0.5 0.2 0.4 0.3 -0.3 2.4 -0.3 -0.4 -3.9 2.3 2015 0.5 -0.9 0.3 0.5 -0.4 -3.1 0.5 1.7 -0.2 1.1 2016 -0.2 0.7 0.0 0.2 -0.7 -3.7 1.4 -0.8 0.2 2.8

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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:

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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:

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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?

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~ 81 ~

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:

yit  yi,t1  X it i  t it

E  it   0 2 E  it  js    

E  it  js   0

Here the choice between FE and RE formulation has implications for estimations that are of a different nature than those associated with the static panels. If the lagged dependent variable also appears as explanatory 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:

Guidelines on Panel Data Analysis

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 and v it-1 it to choose the instruments. Consider the following simple AR(1) model:

yit  yit1  vi  uit 2 vi  iid0, v  2 uit  iid0, u 

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

yit  yit1  yi2  yi1  ui3  ui2 

Consider t=3 [first year with data]

yi3  yi2  yi2  yi1  ui3  ui2 

In this case y is a valid instrument of (Y -y ), since it is highly correlated i1 i2 i1 with (y -y ) and not correlated with (v -v ) i2 i1 i3 i2

Consider t=4

yi4  yi3  yi3  yi2  ui4  ui3 

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

W  yi1, yi2...yiT 2 

The combination of the instruments could be defined as

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yi1 0 . . 0   0 y , y . . .    i1 i2  

Wi   . . . . .     . . . . 0     0 . . 0 yi1, yi2 ...... yiT2 

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

E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:

n ln(Li,t )  1ln(Li,t 1)  2  IRt n  3 log(Sizei,t )  4Liqi,t  n0

5KAPi,t  6 X t  7 Dit  vi  i,t

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time invariant error component;  i,t is the error term with the usual 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

Spread Size 1 6.3 4.4 2 5.8 2.8 3 4.5 12.9 4 2.1 9.2 5 2.0 3.5 6 1.9 3.4 7 2.0 2.4 8 1.5 1.3 9 0.5 1.2 Bank1 10 0.6 10.3 11 1.0 4.2 12 6.4 11.9 13 1.5 14.5 14 2.4 8.5 15 2.5 7.8 16 3.7 0.9 17 3.3 1.0 18 4.6 5.7 19 5.1 4.6 20 3.4 6.1 21 2.2 6.9 22 2.0 4.4 23 1.7 8.0 24 1.5 7.1 25 -2.2 4.3 26 1.6 4.5 Bank2 27 0.1 6.0 28 1.2 5.3 29 1.8 6.1 30 2.0 6.4 31 2.4 8.8 32 2.5 5.2 33 1.5 4.5 34 3.4 6.1 35 6.7 5.3 36 6.7 5.2 37 6.7 6.6 38 9.3 1.3 39 9.8 6.1 40 9.8 7.5 41 9.8 17.1 42 9.8 13.6 43 9.8 6.0 Bank3 44 9.8 1.5 45 10.5 1.7 46 9.8 8.1 47 8.5 1.6 48 9.8 4.0 49 9.8 5.0 50 9.8 5.7 51 9.8 3.8 52 4.1 15.9 53 2.9 4.8 54 1.8 5.3 55 -1.4 3.5 56 -2.1 4.9 ~ 86 ~ 57 -1.5 1.6 58 -1.4 3.0 59 -2.4 7.7 60 -2.2 5.5 61 -1.4 4.4 62 -1.3 15.8 63 -1.8 8.7 64 -1.1 3.8 65 -0.7 4.8 66 0.1 1.6 67 0.5 3.8 68 0.4 4.9 69 3.5 4.6 70 3.2 4.0 71 3.3 6.2 72 3.3 6.9 73 3.6 8.3 74 3.6 5.5 75 3.6 5.5 76 3.6 5.4 77 3.6 4.3 78 1.1 4.9 79 0.8 7.3 80 0.8 4.8 81 2.8 4.8 82 2.8 7.3 83 2.7 7.7 84 2.7 5.1 85 2.7 7.5 Spread Size 1 6.3 4.4 2 5.8 2.8 3 4.5 12.9 4 2.1 9.2 5 2.0 3.5 6 1.9 3.4 7 2.0 2.4 8 1.5 1.3 9 0.5 1.2 10 0.6 10.3 11 1.0 4.2 12 6.4 11.9 13 1.5 14.5 14 2.4 8.5 15 2.5 7.8 16 3.7 0.9 17 3.3 1.0 18 4.6 5.7 19 5.1 4.6 20 3.4 6.1 21 2.2 6.9 22 2.0 4.4 23 1.7 8.0 24 1.5 7.1 25 -2.2 4.3 26 1.6 4.5 27 0.1 6.0 28 1.2 5.3 29 1.8 6.1 30 2.0 6.4 31 2.4 8.8 32 2.5 5.2 33 1.5 4.5 34 3.4 6.1 35 6.7 5.3 36 6.7 5.2 37 6.7 6.6 38 9.3 1.3 39 9.8 6.1 40 9.8 7.5 41 9.8 17.1 42 9.8 13.6 43 9.8 6.0 44 9.8 1.5 45 10.5 1.7 46 9.8 8.1 47 8.5 1.6 48 9.8 4.0 49 9.8 5.0 Dynamic Panel Data Analysis 50 9.8 5.7 51 9.8 3.8 52 4.1 15.9 53 2.9 4.8 54 1.8 5.3 55 -1.4 3.5 56 -2.1 4.9 57 -1.5 1.6 58 -1.4 3.0 59 -2.4 7.7 60 -2.2 5.5 Bank4 61 -1.4 4.4 62 -1.3 15.8 63 -1.8 8.7 64 -1.1 3.8 65 -0.7 4.8 66 0.1 1.6 67 0.5 3.8 68 0.4 4.9 69 3.5 4.6 70 3.2 4.0 71 3.3 6.2 72 3.3 6.9 73 3.6 8.3 74 3.6 5.5 75 3.6 5.5 76 3.6 5.4 77 3.6 4.3 Bank5 78 1.1 4.9 79 0.8 7.3 80 0.8 4.8 81 2.8 4.8 82 2.8 7.3 83 2.7 7.7 84 2.7 5.1 85 2.7 7.5

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.

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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 84th 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.

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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):

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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:

Click here to start estimating the dynamic GMM

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

~ 90 ~ Dynamic Panel Data Analysis

are cautioned not to use the wizard to specify a static panel data model. After this information set, you can then click on ‘Next’ button.  Step 1: Specify the dependent variable: The wizard then shows you that there are 6 steps in 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)’.

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 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

~ 92 ~ 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:

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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.

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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.

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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 each bank and examine whether they are I(0) or I(1).

What about the cross-sectional data? Are they I(0) or I(1)? To obtain an answer, select the 5 bank size series and open them as a Group − note that we have just done that! In the window for the Group, click on View and select Unit Root Test…. A window will open that provides you with a set of options emerge as shown below. Guidelines on Panel Data Analysis

EViews is set up to automatically calculate the following panel unit-root tests: Levin et al. (2002), Breitung (2000), Hadri (1999), Im et al. (2003) and the Fisher-ADF as well as Fisher-PP tests due to Maddala and Wu (1999) and Choi (2001) respectively. Further references and explanations of these tests can be found in, inter alia, Chapter 4 of Maddala and Kim (1998), Chapter 7 of Harris and Sollis (2003) and Breitung and Pesaran (2005).

To begin with, we should note that the first three tests are different from the remaining three. In particular, we can classify panel unit root tests on the basis of whether there are restrictions on the autoregressive process across cross-sections or series. To see this, consider an AR(1) process for panel data: y   y  x   it i i,t1 it i it Where i = 1, 2, …, n are the number of series/countries (in this case the number of base real GDP data series) and t = 1, 2, … , T are the observed periods (in our case 1985 to 2011). Note that the xit represent exogenous variables in the model, including any fixed effects or individual trends, and the uit are iid error terms. We are interested, as in standard unit root tests, in the value of the coefficient, ρi. As with standard univariate series, we say that if |ρi| < 1, y is stationary, whereas if |ρi| = 1, yit contains a unit root.

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Note the subscript i on the autoregressive term, ρi. There are two natural assumptions we can make about the ρi. If we assume that ρi = ρ, then we assume that the persistence parameters are common across cross-sections; this is the test performed by Levin et al. (2002), Breitung (2000) and Hadri (2000). Of those three tests, the null hypothesis for the first two is that the series under investigation is I(1), i.e., non-stationary, whereas the Hadri4 test is performed under the null of stationarity (no unit root).

Alternatively, we can allow ρi to vary freely across the cross-sections, in which case the Im et al.’s (2003), Maddala and Wu’s (1999) Fisher-ADF and Choi’s (2001) Fisher-PP panel unit-root tests are applicable. The null hypothesis for these tests is that the series under investigation is I(1), i.e., non-stationary.

The different panel unit root tests available in EViews are summarised in the Table below;

Test Null Alternative Possible Autocorrelation hypothesis hypothesis deterministic correction components method Levin et al. Unit root No unit root None, F, T Lags Breitung Unit root No unit root None, F, T Lags Im et al. Unit root No unit root F, T Lags Fisher – Unit root No unit root None, F, T Lags ADF Fisher – Unit root No unit root None, F, T Kernel PP Hadri No unit Unit root F, T Kernel root

Notes: None denotes no exogenous variables, F denotes individual fixed effect and T denotes individual fixed effect and individual trend.

What is the best test to perform? That really depends on what the overall aim is, whether you wish to estimate cross-sectional regressions with the same slope coefficients or with different coefficients accounting for the

4 The Hadri panel unit root test is similar to the KPSS unit root test, and has null hypothesis of no unit root in any of the series in the panel.

~ 99 ~ Guidelines on Panel Data Analysis time-series or cross-section dimension (see later on). Note, however, that Pesaran and Smith (1995) have shown that neglecting slope heterogeneity will lead to inconsistent estimates.

For the time being, click on Summary (which is the default option) and select the balanced panel option. Alternatively, you may use the drop-down menu associated with Test type to select an individual panel unit-root test statistic.

Note that, as in the case of the individual series, we can include a constant and/or a time trend i.e. select individual intercept and trend. You may choose to exclude the deterministic time trend – but if the trend is included in one equation, it should be included in all.

You will see the window below;

Unlike the standard EViews single series unit root tests, where t-statistics are reported for the significance of the constant and/or the trend, the panel

~ 100 ~ Non-Stationary Panel Analysis unit tests in EViews report only the actual unit root test. Therefore, we ought to perform all three tests to see whether we get different answers. We now report the results from all these three tests, starting with the most general and ending with the most specific. To start off with, we will assume a fixed, user-specified lag length of one, so you should enter 1 in the User specified box for the lag length as shown above. We note in passing that depending on the specific set-up of the panel unit-root tests, not all six tests are computed all the time.

For the test with a constant and trend, denoted Individual trend and intercept5, we should find the results of the panel unit root tests shown in Table below. As mentioned in the previous paragraph, in this particular case the Hadri test is not computed.

5 Note that selecting Individual intercept is equivalent to including individual fixed effects, while Individual trend and intercept is equivalent to both fixed effects and trends.

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Note that the panel unit-root tests are internally inconsistent, i.e., the five tests that test the same null hypothesis (e.g., Levin et al. and Breitung), are in agreement as to the rejection of the null hypothesis of a unit root in bank size series.

For the test with a constant only (equivalent to individual fixed effects only), we proceed as follows;

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The results of the panel unit root tests are given in the table below.

Similarly, the four available tests (we have lost Breitung’s test) are in agreement as to the rejection of the null hypothesis of a unit root.

Finally, for the test with no constant and no trend, i.e., no deterministic regressors, we proceed as follows;

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We should find the following results of the panel unit-root tests;

All the unit-root tests suggest that the cross-section series are stationary. Note that we have allowed for only one lag in the tests. Good empirical practice calls for some experimentation with alternative lags to determine whether the results change in any way.

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7.1 Panel Unit-root Test with an Automatic Lag Selection Method

Alternative criteria for evaluating the optimal lag length may be selected via the combo box (Akaike, Schwarz, Hannan-Quinn, Modified Akaike, Modified Schwarz, Modified Hannan-Quinn), and you may limit the number of lags to try in automatic selection by entering a number in the Maximum lags box. This procedure sets the lag length to the value of p that minimises the respective information criteria. Ng and Perron (2001) stress that good size and power properties of all unit root tests rely on the proper choice of the lag length p used for specifying the ADF test regression. They argue, however, that traditional model selection criteria such as the AIC and BIC are not well suited for determining p with integrated data. Instead, they suggest modified information criteria (MIC). On the basis of a series of simulation experiments, Ng and Perron recommend selecting the lag length p by minimising the modified AIC (MAIC) in the univariate context. On the basis of this advice, we will also use the MAIC in a panel context. For a test results for a model with constant and trend, denoted Individual trend and intercept, we proceed as follows;

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Make sure you uncheck the Use balanced sample box and we have chosen 8 as the maximum lag length. The results are shown in the table below

Consistent with the previous tests, the results assuming a common unit root procedure indicate the absence of a unit root. Therefore we reject the null hypothesis that the series are I(1). We, therefore, conclude that the series under investigation are stationary.

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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. Arellano, M (1989), ‘A note on the Anderson-Hsiao estimator for panel data’, Economics Letters, Vol. 31, No. 4, pages 337-41. Arellano, M (1993), ‘On the testing of correlated effects with panel data’, Journal of Econometrics, Vol. 59, No. 1-2, pages 87-97. Arellano, M (2003), Panel data econometrics, Oxford, Oxford University Press. Arellano, M and Bond, S R (1991), ‘Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations’, Review of Economic Studies, Vol. 58, No. 2, pages 277-97. Arellano, M and Bover, O (1995), ‘Another look at the instrumental variable estimation of error-components models’, Journal of Econometrics, Vol. 68, No. 1, pages 29-51. 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. Breitung, J and Pesaran, M H (2005), ‘Unit roots and cointegration in panels’, Chapter 9 in Matyas, L and Sevestre, P (eds), The econometrics of panel data: fundamentals and recent developments in theory and practice, Amsterdam, Kluwer Academic Publishers, pages 279-322. http://www.ect.uni- bonn.de/mitarbeiter/joerg- breitung/documents/breitung_pesaran.pdf/view. Engle, R F and Granger, C W J (1987), ‘Co-integration and error correction: representation, estimation and testing’, Econometrica, Vol. 55, No. 2, pages 251-76. Guidelines on Panel Data Analysis

Harris, R and Sollis, R (2003), ‘Panel data models and cointegration’, Chapter 7 in Applied time series modelling and forecasting, Oxford, John Wiley & Sons. Hausman, J A (1978), ‘Specification tests in econometrics’, Econometrica, Vol. 46, No. 6, pages 1251-71. Hausman, J A and Taylor, W E (1981), ‘Panel data and unobservable individual effects’, Econometrica, Vol. 49, No. 6, pages 1377-98. Im, K S, Pesaran, M H and Shin, Y (2003), ‘Testing for unit roots in heterogeneous panels’, Journal of Econometrics, Vol. 115, No. 1, pages 53-74. Johansen, S (1988), ‘Statistical analysis of cointegrating vectors’, Journal of Economic Dynamics and Control, Vol. 12, No. 2/3, pages 231-54. Johansen, S (1991), ‘Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models’, Econometrica, Vol. 59, No. 6, pages 1551-80. Levin, A and Lin, C-F (1993a), ‘Unit root tests in panel data: asymptotic and finite sample properties’, Department of Economics, University of San Diego Discussion Paper 93-23. Levin, A and Lin, C-F (1993b), ‘Unit root tests in panel data: new results’, Department of Economics, University of San Diego Discussion Paper 93-56. Levin, A, Lin, C-F and Chu, C-S J (2002), ‘Unit root test in panel data: asymptotic and finite-sample properties’, Journal of Econometrics, Vol. 108, No. 1, pages 1-24. Maddala, G S and Wu, S (1999), ‘A comparative study of unit root tests with panel data and a new simple test’, Oxford Bulletin of Economics and Statistics, Vol. 61, No. S1, pages 631-52. Mundlak, Y (1978), ‘On the pooling of time series and cross-sectional data’, Econometrica, Vol. 46, No. 1, pages 69-85. 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. Neyman, J and Scott, E L (1948), ‘Consistent estimates based on partially consistent observations’, Econometrica, Vol. 16, No. 1, pages 1-32.

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Pedroni, P (1999), ‘Critical values for cointegration tests in heterogeneous panels with multiple regressors’, Oxford Bulletin of Economics and Statistics, Vol. 61, No. S1, pages 653-78. Pedroni, P (2000), ‘Fully-modified OLS for heterogeneous cointegrated panels’, Chapter 3 in Baltagi, B H (ed), Advances in econometrics, volume 15: nonstationary panels, panel cointegration and dynamic panels, Amsterdam, JAI Press, pages 93-130. Pedroni, P (2001), ‘Purchasing power parity tests in cointegrated panels’, Review of Economics and Statistics, Vol. 83, No. 4, pages 727-31. Pedroni, P (2004), ‘Panel cointegration: asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis’, Econometric Theory, Vol. 20, No. 3, pages 597-625. Pesaran, M H (1999), ‘On the interpretation of panel unit root tests’. http://www.econ.cam.ac.uk/faculty/pesaran/imf-unit.pdf. Pesaran, M H (2007), ‘A simple panel unit root test in the presence of cross- section dependence’, Journal of Applied Econometrics, Vol. 22, No. 2, pages 265-312. 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.

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