# Applied Econometrics 3rd Edition

Applied Econometrics 3rd Edition Dimitrios Asteriou Professor in Econometrics, Hellenic Open Universily, Creece Stephen G. Hall Professor of …...

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

32 34 35 35 36 37 38 38 39 40 42 43 44 45 46 47 48 48 48 49 49 50 50 50 51 52 52 53 53 58

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

62 62 64 64 64 65 66 67 68 69 69 69 70 70 70 72 73

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

74 74 74 75 75 75 75 77 78 78 79 79 80 80 81 82 82 83 83 84 84 87 87 89 90 96 97 101 103 103 104 104 105 106 107 109 109 109 110 110 112 115

xii Contents 6

7

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

117 117 IIB 120 120 121 124 124 125 128 130 131 133 133 135 137 138 140 140 141 142 144 144 146 147 148 148 150 153 156 156 157 157 158 159 159 160 162 162 162 164 166 167 168 170 171

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

172 173 173 175 176 178 178 178 180 180 181 181 181 182 183 183 185 185 185 186 186 187 188 188 189 190 191 191 193 193 195 197 199 202 202 203 204 207 209 209 210

xiv Contents

10

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

231 231 232 232 233 235 236 236 236 237 239 241 241

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

210 210 212 214 215 216 216 217 218 218 220 221 222

243 243 244 245 245 245 246 247 247

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

254 254 255 255 256 256 25 7 257 258 258 259 260 261 263 263 264 265 266 266 267 267 267 270

Part V

273

Time Series Econometrics

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

275 275 276 276 277 277 277 279 281 282 282 282 283 284 285

xvi Contents

14

15

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

336 336 338 338 341 341 344 347 347 348 348 348 351 353 355 355 355 357 357 359 359 361 362 364 366 367 367 368 368 369 370 370 371 371 371 372 372 374 376 376 378 379 380 381

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

424 424 425 426 427 428 428 428 429 429 430 433 438

Contents xix Part VI

Panel Data Econometrics

439

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

441 441 442 443 443 443 444 445 446 447 447 451 452 453 455 456

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

457 457 458 458 458 459 459 459 460 461 461 462 464 464 465

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

467 467 468 468 469 470 471 471 473 473 474 475 476 477 478

xx Contents Part VII 24

Using Econometric Software

483

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

485 486 486 488 488 489 489 490 491 491 492 493 493 494 494 495 495 496 497 497 497 499

Appendix: Statistical Tables

501

Bibliography

507

Index

513