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Chapter 11: Panel Data

• Panel data, also known as longitudinal data, have both time series and cross-sectional dimensions.
• Panel data arise when measuring the same group of people or objects over time.
• Econometrically, the setup is: y_it = a + βx_it + u_it, where y_it is the dependent variable, a is the intercept term, β is a vector of parameters, x_it are explanatory variables, t = 1, ..., T, i = 1, ..., N.
• The simplest way to deal with panel data is pooled regression on all observations.
• However, pooling assumes no heterogeneity (same relationship for all data).

Advantages of using Panel Data

• Panel data allows for more complex analysis than time series or cross-sectional data.
• Allows the examination of dynamic changes in variables or relationships between variables over time.
• Certain omitted variables bias in regression results can be removed with proper model structure.

Seemingly Unrelated Regression (SUR)

• This approach makes full use of the data structure, initially proposed by Zellner (1962).
• Commonly used in finance to model related variables over time.
• SUR is called seemingly unrelated because dependent variables may appear unrelated at first glance, although related upon careful analysis.
• The contemporaneous relationships among error terms in equations are accounted for by using a generalized least squares (GLS) technique.
• SUR transforms the model to make error terms uncorrelated.
• If error correlations are zero to start with, SUR is equivalent to separate OLS regressions.

Fixed and Random Effects Panel Estimators

• The applicability of SUR is limited by the need for at least as many time series observations per cross-sectional unit as there are units.
• SUR also entails numerous parameters that must be estimated.
• A random effects approach provides more flexibility and is the preferred method for panel data.
• Two primary panel techniques are fixed effects and random effects estimators.

Fixed Effects Models

• The fixed effects model is represented as y_it= a + βx_it + μ_i + u_it, where μ_i encapsulates cross-sectional effects (e.g., industry, individual characteristics, etc.).
• μ_i is captured by using dummy variables.
• Least squares dummy variable (LSDV) approach estimates using dummy variables, allowing for different intercepts for each unit.

Fixed Effects Models (Continued)

• The LSDV model, which can be represented as y_it = a + βx_it + μ₁D₁_i + μ₂D₂_i + … + μ_ND_Ni + u_it , has N+ k parameters.
• Simplification is achieved using the within transformation.

The Within Transformation

• The within transformation involves subtracting the time-mean of each entity from the variable values.
• Demeaned variables are used in the regression, removing the intercept term.
• This regression can be estimated by Ordinary Least Squares (OLS), but requires a degree of freedom correction.

The Between Estimator

• An alternative to demeaning is the between estimator.
• This involves running estimates on time-averaged values which potentially reduces the impact of measurement error.

Time Fixed Effects Models

• Allows for time-varying intercepts (but constant across entities) such as changes in regulatory environment.
• The equation for a time fixed effects model is Vit = a + βxit + λt + Vit.

Time Fixed Effects Models (Continued)

• Time variation in intercepts can be modeled using dummy variables.
• A within transformation may be used to remove cross-sectional averages.
• A two-way error components model is possible.

Investigating Banking Competition with a Fixed Effects Model

• The UK banking sector is, generally, highly profitable, with competitive forces potentially not sufficiently strong, and barriers to entry.
• A Matthews, Murinde, and Zhao (2007) study investigated UK banking competitive conditions between 1980 and 2004 using the Panzar-Rosse approach.
• The model assesses contestability.

Methodology

• The empirical investigation involves deriving the Panzar-Rosse H-statistic, a sum of revenue elasticities with respect to factor costs (input prices).
• H values between 0 and 1 suggest monopolistic competition; H < 0 implies monopoly; H = 1 suggests perfect competition.
• The model used by Matthews et al. captures revenue and cost factors including risk assets, size, branch ratio, and GDP growth.

Methodology (Continued)

• Variables included in the model capture time-variation in bank-specific effects on revenue and costs.
• These include RISKASS, ASSET, BR, and GROWTH.
• A test for equilibrium checks the validity of assuming equilibrium, and uses lnROA as a dependent variable.
• A fixed effect panel data model is used for analysis.

Analysis of Equilibrium Test Results

• The study examined whether the Banking Market is in equilibrium – rejecting the null hypotheses at a 1% significance level in the results for the full sample, but not necessarily the sub-samples.
• The equilibrium test showed limited disequilibrium in the results of the full sample.
• The investigation concludes that the banking market appears to be in equilibrium.

Results from Test of Banking Market Equilibrium

• Results from the equilibrium test are presented in tables for the period 1980-2004, 1980-1991 and 1992-2004 (various dependent variables are examined ).

Analysis of Competition Test Results

• The contestability parameter decreased over the period, suggesting that competition in UK retail banking weakened.
• Results showed that a 1% significance level exists such that the null hypothesis for the market is characterized by monopolistic competition.
• The results and the additional bank control variables consistently demonstrate their intuitive signs and significance in impacting the analysis of the financial market and the profitability of banks.

The Random Effects Model

• An alternative to the fixed effects model, the random effects model, also known as the error components model, assumes different intercepts for each entity that are constant over time.
• Random effects assume the same relationships exist in explained variables, across entities, and over time.

How the Random Effects Model Works

• Unlike the fixed effects model, no dummy variables are used to capture heterogeneity.
• The assumptions require zero mean and constant variance for new cross-sectional error terms and independence of individual observation error terms from explanatory variables.
• Generalized least squares (GLS) is used to estimate parameters.

Quasi-Demeaning the Data

• Defines quasi-demeaned data as y_i,t – y_i.,, where y_i., is the time average of values for entity i.
• This transformation is required to ensure there are no cross-correlations among error terms in a generalized least squares (GLS) context.

Fixed or Random Effects?

• Random effects models are often preferred when entities in samples are randomly selected from a larger population.
• The fixed effects approach is more suitable when the entities in the sample comprise the entire population.

Fixed or Random Effects ( Continued )

• The random approach has its limitation because it is valid only when the total errors are uncorrelated with the explanatory variables.

Credit Stability of Banks in Central and Eastern Europe

• Foreign banking participation may improve competition and efficiency.
• Foreign banks may stabilize credit provision during economic downturns and diversification helps these banks.

The Data

• Policies for credit provision may vary depending on how the subsidiary abroad is formed
• A de Haas and van Lelyveld (2006) study examined 250 banks in Central and Eastern European countries between 1993 and 2000 to examine foreign vs. domestic bank responses to economic factors and banking crises.

The Model

• The model involves a random effects regression.
• Variables included are those impacting bank credit growth (takeovers, Greenfield investments, crises in the host country, macroeconomic conditions in host and home countries).

The Model (Continued)

• Contr, a vector of bank specific control variables (bank-specific weakness, solvency, liquidity, asset size, profitability and efficiency, are also included in determining bank specific credit growth.

Estimation Options

• OLS is not appropriate due to differences in average credit.
• The random effects model, and not a fixed effects model, is more appropriate because it is less complex.
• A Hausman test is used to select the model.

Results

• Domestic banks significantly reduce credit growth, whereas foreign banks see little change during banking crises.
• Foreign bank growth is positively related to host GDP growth, while domestic banks see a negative relationship.
• Lending rates have little impact on credit market share growth.

Analysis of Results (Continued)

• Results indicate that foreign banks and their investment strategies may not strongly correspond with the degree of home country performance versus host country performance.

Panel Unit Root and Cointegration Tests

• Dickey-Fuller and Phillips-Perron have low power in many situations due to the sample size limitations.
• Increased sample allows for time series and cross-sectional information.
• Panel frameworks for unit root and cointegration tests are more complex.

The MADF Test

• This test is a multivariate version of the Dickey-Fuller (ADF) approach that uses a SUR approach.
• It can be applied when T (time) is much larger than N (number of entities) and the test requires careful consideration of the testing framework.

The LLC Test

• Levin, Lin, and Chu (2002)'s test (LLC) has been generalized for different conditions.
• The test's complexity stems from a need to incorporate nuisance elements, allowing for heterogeneity both over time and across entities.

The LLC Test (Continued)

• The test focuses on evidence against non-stationarity for when the test is performed on different sets.
• The test statistics are normally distributed under the LLC assumption.

Panel Unit Root Tests with Heterogeneous Processes

• The IPS approach (Im, Pesaran, and Shin, 2003), offers an alternative framework that tests for a proportion of stationary series without requiring identical autoregressive dynamics within all series.

The Maddala and Wu (1999) and Choi (2001) Tests

• Maddala and Wu (1999) and Choi (2001) have variants of the IPS approach that work on the p-values, allowing for combined series.
• Cross-sectional independence and Monte Carlo simulations are crucial parameters for a robust analysis.

Allowing for Cross-Sectional Heterogeneity

• Models based on the assumption of independent error terms may produce biased or inaccurate results in situations where that assumption is violated.
• Adjusting critical values and using Panel Corrected Standard Errors (PCSEs) can help account for cross-sectional dependencies.

Allowing for Cross-Sectional Heterogeneity 2

• To accommodate cross-sectional correlation, separating highly correlated data into common factors and idiosyncratic parts is a more robust approach.
• Using panel corrected standard errors (PCSEs) is also useful in addressing the issue of cross-sectional heterogeneity.

Panel Cointegration Tests

• Testing for cointegration in panel data is complex due to factors such as:
  • Cross-sectional cointegration across groups of variables.
  • Methods of the Engle-Granger type.

The Pedroni Approach to Panel Cointegration

• The Pedroni approach has two main alternative hypotheses, which can handle both homogenous (similar dynamics across series) and heterogeneous (differences in series dynamics) cases.

Panel Unit Root Example: The Link between Financial Development and GDP Growth

• The study examines the connection between financial market development and economic growth in a set of countries
• The study includes real output, financial depth, investment share, and inflation.

Panel Unit Root Example: Results

• Results of tests conducted on multiple datasets show that four variables are non-stationary in levels but stationary in their respective difference models.

Panel Cointegration Test: Example

• The LLC approach, when used with the Harris-Tzavalis technique, yields robust tests of potential cointegration, as tested in each given dataset.
• These tests help determine whether a relationship between variables persists despite heterogeneity in the panel data.

Panel Cointegration Test: Findings

• When financial depth is used instead of output as the dependent variable, cointegration relationship tests show that the null hypothesis is not rejected.
• The results strongly suggest one cointegrating relationship exists between the four variables.

Panel Cointegration Test: Table of Results

• Results of panel cointegration tests (LLC and Harris-Tzavalis) on different datasets are presented in tables, showing significant results for different dependent variables.

Test your knowledge on the key concepts and methodologies used in banking studies. This quiz covers various aspects such as GROWTHt parameters, regression equations, and the fixed effects model. Get ready to assess your understanding of the analytical techniques applied in banking research.