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i Applied Financial Econometrics Slides Rolf Tschernig | Florian Brezina University of Regensburg Version: 18 July 20121 1 c Rolf Tschernig. I very much thank Joachim Schnurbus for his important corrections and suggestions
In this course, we strive to familiarize you with key building blocks of applied econometrics: where data comes from and how it can be analyzed. We will do so in an applied fashion, using actual data and software tools
Applied
Econometrics 3rd Edition
Dimitrios Asteriou Professor in Econometrics, Hellenic Open Universily, Creece
Stephen G. Hall Professor of Economics and Pro-Vice Chancellor, Universily of Leicester, UK
palgrave
Contents
List ofFigures
xxi
ListofTables
xxiii
Preface
xxvii
Acknowledgements
xxx
Part I
Statistical Background and Basic Data Handling
1
1
Fundamental Concepts Introduction A simple example A Statistical framework Properties of the sampling distribution of the mean Hypothesis testing and the central limit theorem Central limit theorem Conclusion
3 4 4 6 7 8 10 13
2
The Structure of Economic Data and Basic Data Handling Learning objectives The structure of economic data Cross-sectional data Time series data Panel data Basic data handling Looking at raw data Graphical analysis Summary statistics
14 14 15 15 15 16 17 17 17 19
Part II 3
The Classical Linear Regression Model
Simple Regression Learning objectives Introduction to regression: the classical linear regression model (CLRM) Why do we do regressions? The classical linear regression model ix
27 29 29 30 30 30
X Contents
4
The Ordinary Least Squares (OLS) method of estimation Alternative expressions for ß The assumptions of the CLRM General The assumptions Violations of the assumptions Properties of the OLS estimators Linearity Unbiasedness Efficiency and BLUEness Consistency The overall goodness of fit Problems associated with R2 Hypothesis testing and confidence intervals Testing the significance of the OLS coefficients Conßdence intervals How to estimate a simple regression in EViews and Stata Simple regression in EViews Simple regression in Stata Reading the Stata simple regression results output Reading the EViews simple regression results output Presentation of regression results Economic theory applications Application 1: the demand function Application 2: the production function Application 3: Okun's law Application 4: the Keynesian consumption function Computer example: the Keynesian consumption function Solution Questions and exercises
Multiple Regression Learning objectives Introduction Derivation of multiple regression coefficients The three-variable model The /(-variables case Derivation of the coefficients with matrix algebra The structure of the X'X and X'Y matrices The assumptions of the multiple regression model The variance-covariance matrix of the errors Properties of multiple regression model OLS estimators Linearity Unbiasedness Consistency BLUEness R2 and adjusted R2 General criteria for model selection
Contents xi Multiple regression estimation in EViews and Stata Multiple regression in EViews Multiple regression in Stata Reading the EViews multiple regression results Output Hypothesis testing Testing individual coefficients Testing linear restrictions The F-form of the Likelihood Ratio test Testing the joint significance of the Xs F-test for overall significance in EViews Adding or deleting explanatory variables Omitted and redundant variables test in EViews How to perform the Wald test in EViews The t test (a special case of the Wald procedure) The Lagrange Multiplier (LM) test The LM test in EViews Computer example: Wald, omitted and redundant variables tests A Wald test of coefficient restrictions A redundant variable test An omitted variable test Computer example: commands for Stata Financial econometrics application: the Capital Asset Pricing Model in action A few theoretical remarks regarding the CAPM The empirical application of the CAPM EViews programming and the CAPM application Advanced EViews programming and the CAPM application Questions and exercises Part III 5
Violating the Assumptions of the CLRM
Multicollinearity Learning objectives Introduction Perfect multicollinearity Consequences of perfect multicollinearity Imperfect multicollinearity Consequences of imperfect multicollinearity Detecting problematic multicollinearity Simple correlation coefficient R2 from auxiliary regressions Computer examples Example 1: induced multicollinearity Example 2: with the use of real economic data Questions and exercises
Heteroskedasticity Learning objectives Introduction: what is heteroskedasticity? Consequences of heteroskedasticity for OLS estimators A general approach A mathematical approach Detecting heteroskedasticity The informal way The Breusch-Pagan LM test The Glesjer LM test The Harvey-Godfrey LM test The Park LM test Criticism of the LM tests The Goldfeld-Quandt test White's test Computer example: heteroskedasticity tests The Breusch-Pagan test The Glesjer test The Harvey-Godfrey test The Park test The Goldfeld-Quandt test White's test Commands for the Computer example in Stata Engle's ARCH test Computer example of the ARCH-LM test Resolving heteroskedasticity Generalized (or weighted) least squares Computer example: resolving heteroskedasticity Questions and exercises Autocorrelation Learning objectives Introduction: what is autocorrelation? What causes autocorrelation? First- and higher-order autocorrelation Consequences of autocorrelation for the OLS estimators A general approach A more mathematical approach Detecting autocorrelation The graphical method Example: detecting autocorrelation using the graphical method The Durbin-Watson test Computer example of the DW test The Breusch-Godfrey LM test for serial correlation Computer example of the Breusch-Godfrey test Durbin's h test in the presence of lagged dependent variables Computer example of Durbin's h test
Contents xiii Resolving autocorrelation When p is known Computer example of the generalized differencing approach When p is unknown Computer example of the iterative procedure Resolving autocorrelation in Stata Questions and exercises Appendix 8
Misspecification: Wrong Regressors, Measurement Errors and Wrong Functional Forms Learning objectives Introduction Omitting influential or including non-influential explanatory variables Consequences of omitting influential variables Including a non-influential variable Omission and inclusion of relevant and irrelevant variables at the same time The plug-in Solution in the omitted variable bias Various functional forms Introduction Linear-log functional form Reciprocal functional form Polynomial functional form Functional form including interaction terms Log-linear functional form The double-log functional form The Box-Cox transformation Measurement errors Measurement error in the dependent variable Measurement error in the explanatory variable Tests for misspecification Normali ty of residuals The Ramsey RESET test for general misspecification Tests for non-nested models Computer example: the Box-Cox transformation in EViews Approaches in choosing an appropriate model The traditional view: average economic regression The Hendry 'general to specific approach' Questions and Exercises
Part IV 9
Topics in Econometrics
Dummy Variables Learning objectives Introduction: the nature of qualitative Information
The use of dummy variables Intercept dummy variables Slope dummy variables The combined effect of intercept and slope dummies Computer example of the use of dummy variables Using a constant dummy Using a slope dummy Using both dummies together Special cases of the use of dummy variables Using dummy variables with multiple categories Using more than one dummy variable Using seasonal dummy variables Computer example of dummy variables with multiple categories Financial econometrics application: the January effect in emerging stock markets Tests for structural stability The dummy variable approach The Chow test for structural stability Financial econometrics application: the day-of-the-week effect in action Questions
224 227 227 227 228 230
Dynamic Econometric Models Learning objectives Introduction Distributed lag models The Koyck transformation The Almon transformation Other models of lag structures Autoregressive models The partial adjustment model A Computer example of the partial adjustment model The adaptive expectations model Tests of autocorrelation in autoregressive models Exercises
11 Simultaneous Equation Models Learning objectives Introduction: basic definitions Consequences of ignoring simultaneity The Identification problem Basic definitions Conditions for Identification Example of the Identification procedure A second example: the macroeconomic model of a closed economy
Contents xv Estimation of simultaneous equation models Estimation of an exactly identified equation: the ILS method Estimation of an over-identified equation: the TSLS method Computer example: the IS-LM model Estimation of simultaneous equations in Stata
248 249 249 250 253
12 Limited Dependent Variable Regression Models Learning objectives Introduction The linear probability model Problems with the linear probability model Di is not bounded by the (0,1) ränge Non-normality and heteroskedasticity of the disturbances The coefficient of determination as a measure of overall fit The logit model A general approach Interpretation of the estimates in logit models Goodness of fit A more mathematical approach The probit model A general approach A more mathematical approach Multinomial and ordered logit and probit models Multinomial logit and probit models Ordered logit and probit models The Tobit model Computer example: probit and logit models in EViews and Stata Logit and probit models in EViews Logit and probit models in Stata
13 ARIMA Models and the Box-Jenkins Methodology Learning objectives An introduction to time series econometrics ARIMA models Stationarity Autoregressive time series models The AR(1) model The AR(p) model Properties of the AR models Moving average models The MA(1) model The MA(g) model Invertibility in MA models Properties of the MA models ARMA models
Integrated processes and the ARIMA models An integrated series Example of an ARIMA model Box-Jenkins model selection Identification Estimation Diagnostic checking The Box-Jenkins approach step by step Computer example: the Box-Jenkins approach The Box-Jenkins approach in EViews The Box-Jenkins approach in Stata Questions and exercises
285 285 286 286 287 288 288 289 289 289 293 295
Modelling the Variance: ARCH-GARCH Models Learning objectives Introduction The ARCH model The ARCH(l) model The ARCH(
297 297 298 299 300 300 301 301 302 306 309 309 309 310 311 312 313 316 316 317 318 319 319 320
326 330
Vector Autoregressive (VAR) Models and Causality Tests Learning objectives Vector autoregressive (VAR) models The VAR model Pros and cons of the VAR models
333 333 334 334 335
322
Contents xvii Causality tests The Granger causality test The Sims causality test Financial econometrics application: financial development and economic growth - what is the causal relationship? Estimating VAR models and causality tests in EViews and Stata Estimating VAR models in EViews Estimating VAR models in Stata 16 Non-Stationarity and Unit-Root Tests Learning objectives Introduction Unit roots and spurious regressions What is a unit root? Spurious regressions Explanation of the spurious regression problem Testing for unit roots Testing for the order of Integration The simple Dickey-Fuller (DF) test for unit roots The augmented Dickey-Fuller (ADF) test for unit roots The Phillips-Perron (PP) test Unit-root tests in EViews and Stata Performing unit-root tests in EViews Performing unit-root tests in Stata Application: unit-root tests on various macroeconomic variables Financial econometrics application: unit-root tests for the financial development and economic growth case Questions and exercises 17 Cointegration and Error-Correction Models Learning objectives Introduction: what is cointegration? Cointegration: a general approach Cointegration: a more mathematical approach Cointegration and the error-correction mechanism (ECM): a general approach The problem Cointegration (again) The error-correction model (ECM) Advantages of the ECM Cointegration and the error-correction mechanism: a more mathematical approach A simple model for only one lagged term of X and Y A more general model for large numbers of lagged terms Testing for cointegration Cointegration in Single equations: the Engle-Granger approach Drawbacks of the EG approach The EG approach in EViews and Stata Cointegration in multiple equations and the Johansen approach Advantages of the multiple-equation approach
xviii Contents The Johansen approach (again) The steps of the Johansen approach in practice The Johansen approach in EViews and Stata Financial econometrics application: cointegration tests for the financial development and economic growth case Monetization ratio Turnover ratio Claims and currency ratios A model with more than one financial development proxy variable Questions and exercises
381 382 387 392 393 396 396 398 400
18
Identification in Standard and Cointegrated Systems Learning objectives Introduction Identification in the Standard case The order condition The rank condition Identification in cointegrated systems A worked example Computer example of Identification Conclusion
402 402 403 403 405 406 406 408 410 412
19
Solving Models Learning objectives Introduction Solution procedures Model add factors Simulation and Impulse responses Stochastic model analysis Setting up a model in EViews Conclusion
413 413 414 414 416 417 418 420 423
20
Time-Varying Coefficient Models: A New Way of Estimating Bias-Free Parameters Learning objectives Introduction TVC estimation Theorem 1 Coefficient drivers Assumption 1 (auxiliary Information) Assumption 2 Choosing coefficient drivers First requirement: selecting the complete driver set Second requirement: Splitting the driver set Financial econometrics application: rating agencies' decisions and the sovereign bond spread between Greece and Germany Conclusion
21 Traditional Panel Data Models Learning objectives Introduction: the advantages of panel data The linear panel data model Different methods of estimation The common constant method The fixed effects method The random effects method The Hausman test Computer examples with panel data Inserting panel data in EViews Estimating a panel data regression in EViews The Hausman test in EViews Inserting panel data into Stata Estimating a panel data regression in Stata The Hausman test in Stata
22 Dynamic Heterogeneous Panels Learning objectives Introduction Blas in dynamic panels Bias in the simple OLS estimator Bias in the fixed effects model Bias in the random effects model Solutions to the bias problem (caused by the dynamic nature of the panel) Bias of heterogeneous slope parameters Solutions to heterogeneity bias: alternative methods of estimation The mean group (MG) estimator The pooled mean group (PMG) estimator Application: the effects of uncertainty in economic growth and Investment Evidence from traditional panel data estimation Mean group and pooled mean group estimates
23 Non-Stationary Panels Learning objectives Introduction Panel unit-root tests The Levin and Lin (LL) test The Im, Pesaran and Shin (IPS) test The Maddala and Wu (MW) test Computer examples of panel unit-root tests Panel cointegration tests Introduction The Kao test The McCoskey and Kao test The Pedroni tests The Larsson et al. test Computer examples of panel cointegration tests
Practicalities of Using EViews and Stata About EViews Starting up with EViews Creating a workfile and importing data Copying and pasting data Verifying and saving the data Examining the data Commands, Operators and functions About Stata Starting up with Stata The Stata menu and buttons Creating a file when importing data Copying/pasting data Cross-sectional and time series data in Stata First way - time series data with no time variable Second way - time series data with time variable Time series - daily frequency Time series - monthly frequency All frequencies Saving data Basic commands in Stata Understanding command syntax in Stata
