388 Index Differencing test ,232 Distributed lags , 147 arithmetic lag.

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1 INDEX Aggregation Almon lag ,149 AR(1) process ,240,246, ,366,370,374 ARCH ARlMA Asymptotically unbiased... 13,50 Autocorrelation , , , Autoregressive Distributed Lag Bartlett's test Bernoulli distribution , 13-14, 26, 27 Best linear unbiased (BLUE) ,65,71, 157,238,252,315 Best linear unbiased predictor (BLUP)... 54,242, ,317 Best Quadratic Unbiased (BQU) Beta distribution Between estimator Binary Response Model Regression Binomial distribution... 18,27,29,33,34,205,336 Box-Cox model Box-Jenkins method Breusch-Godfrey test , 123, 128, 144, 150 Breusch-Pagan test , 113,322 Censored Normal Distribution ,360 Censored Regression Model ,.362 Central limit theorem ,71,101,382 Change of variable Characteristic roots , 246, 3 12, 316 Characteristic vectors Chebyshev's Inequality Chow test , 191, 194, 210, 311, 3 18 Classical assumptions ,71,89,97-98, 102, 134, 156 Cointegration , Concentrated log-likelihood Confidence intervals , 54, Consistency... 14,47, 115,271,274,277 Constant returns to scale... 80,89, 166,282 Cook's statistic Cramer-Rao lower bound ,29-31, 50, , 316 CUSUM , 232 CUSUMSQ Deterministic time trend model Diagnostics , 228, 230 Dickey-Fuller ,375,380 augmented ,380

2 388 Index Differencing test ,232 Distributed lags , 147 arithmetic lag ,137,138 po1ynorniallags (see Almon lag) Distribution function method Double length regression (DLR) Dummy variables , 94, 160, 172, 176, 191, , 331 Durbin-Watsontest ,128,131,150 Durbin'sh-test ,150 Durbin's method Dynarnicmodels ,142 Econometrics critiques , 5 definition history Efficiency... II, 65,121,124,247, ,263 Elasticity , 65 Endogeneity Equicorrelated case Error components models Error-correction model (ECM) Errors in measurement Exponential Distribution I, 33 Forecasting ,367 standard errors , 176 Frisch-Waugh-Lovell Theorem ,192,327 Ganunadistribution... 31,33,36,140 Gauss-Markov theorem... 48, 156 Gauss-Newton regression ,339 Generalized inverse ,211,295 Generalized least squares (GLS) , 184,237,249 Geometric distribution... 30, 32, 140 Goodness of fit measures ,342 Granger causality Granger representation theorum Grouped data Group heteroskedasticity Hausman test , ,323,328 Hessian , 346, 348 Heterogeneity Heteroskedasticity , , ,183,216, , 249, ,332, ,339, Heteroskedasticity test Breusch-Pagantest ,113,127 Glejser's test , Ill, 112, 127

3 Index 389 Goldfeld-Quandt test , 112 Harvey's test , 113, 127 Speannan's Rank Correlation test , 112, 127 White's test ,113,127 Homoskedasticity (see heteroskedasticity) Idempotentmatrix ,177,183,309 Identification problem , order condition ,303,375 rank condition , 303 Indirect least squares , ,304 Infinite distributed lag , 146 Influential observations , 60, Information matrix , , Instrumental variable estimator ,297,303 Inverse matrix partitioned Inverse Mills ratio JA test ,219 Jacobian... 50, 161, 241 J arque-bera test , 216 Just-identified , , 300 Koyck lag , 146 Lagged dependent variable model Lagrange-multiplier test , , ,247,257,260,266,322 standardized Law of iterated expectations Least squares numerical properties... 43, 52, 63 Likelihoodfunction... 8,19-20,29-32,50,106,118, 161,180,241,316,337,346, Likelihood ratio test ,30-33, , , 258, 260, 266, 288, 381 Limited dependent variables... 86, Linear probability model ,343 Linear restrictions... 78, 150, 170 Ljung-Box statistic Logit models ,337, Matrix algebra , 182 Matrix properties... " 155, 182 Maximum likelihood estimation... 8, 50, 118, 161, 167, 180, 241, 316, 337, 346, Mean square error Measurement error... 99,304 Method of moments ,30-32, 156,278,305 Moment generating function , Moving average, MA(1) , 141, 144, 146, 150,365,371 Multicollinearity , 82, 134,257,273,309 Multinomial choice models

4 390 Index Multiple regression model Multiplicative heteroskedasticity , 124 Neyman-Pearson lemma Newton-raphson iterative procedure Nonlinear restrictions Nonstochastic regresors... 45,98 Normal equations... 43,71-72,102, ,223,273,275,301,337 Order condition ,303,374 Over-identification restrictions ,289 Panel data National Logitudinal Survey (NLS) Panel Study ofincome Dynamics (PSID)... 87, 307 Partial autocorrelation Partial correlations Partitioned regression , 178 Perfect multicollinearity , 82, 273, 309 Poisson distribution... 30,33, Prais-Winsten ,240, Prediction ,53,64, 164, 176,242,246,249, 317,331 Probability limit Probit models , , 341 Projection matrix , 183,276, 309 Quadratic form Random number generator... 28, 38 Random effects model , 316, 327 Randomsample ,14, 16, 18,21,23,26,27,29,31-34,43,47, 112 Random walk ,370, , 384, 385 Rank condition , 303 Rational expectations Recursive residuals , 231 Recursive systems Reducedform ,269,270,282,285, ,294 Regression stability Repeated observations , 108 Residual analysis... 55, 189 Residual interpretation... 72,88 Restricted least squares ,173, ,265 Restricted maximum likelihood , , Sample autocorrelation function ,379 Sample correlogram Sample selectivity Score test... 24, 170 Seasonal adjustment... 84,385 Seemingly unrelated regressions , Unequal observations

5 Index 391 Simultaneous bias Simultaneous equations model Single equation estimation Spearman's rank correlation test Specification analysis overspecification underspecification Specification error tests Differencing test , 232, Spectral decomposition , 312 Spurious regression ,376 Stationarity... : covariance stationary difference stationary ,372 trend stationary , 372 Stationary process Stochastic explanatory variables Studentized residuals Sufficient statistic , 31 Superconsistent ,382,384 SUR System estimation Three-stage least squares ,295 Tobit model ,355, 360 Truncated regression model Truncated uniform density Two-stage least squares , , Uniform distribution Unit root Unordered response models Vector autoregression (V AR) , 381 Wald test , , ,247,323,339,358 Weighted least squares , 123,332 White noise , , 382 White test ,113,127, Within estimator , , 323, 327 Zellner's SUR Zero mean assumption

6 392 Index TABLE A: Area Under the Standard Normal Distribution z c'f>(1.65) = Pr[z f.1.65} = z Source: The SAS function PROBNORM was used to generate this table.

7 Index 393 TABLE B: Right-Tail Critical Values for the t-distribution 0 ta. Pr[t,,>ta=2.306j = DF ex =.10 ex =.05 ex =.025 ex =.010 ex = Source: The SAS function TINV generated this table.

8 v,!v, \0 11 U m 21 n H V D m 31 D n H \ \ TABLE C: Right-Tail Critical Values for the F-Distribution: Upper 5% Points \ \ \ \ Source: The SAS function FINV was used to generate this table. vi = numerator degrees of freedom; v2 = denominator degrees of freedom. c.j \Q 5" a.

9 vivl TABLE D: Righl- Tail Critical Values for the F-Distribution: Upper 1 % Points _ _ _ _ _ _ _ _ _919 2_ _ _ _ Source: The SAS function FINV was used to generate this table. VI = numerator degrees of freedom; v2 = denominator degrees of freedom. 5" Q. IN \0 Ut

10 396 Index TABLE E: Right-Tail Critical Values for the Chi-Square Distribution Pr [X; > ] = 0.05 \) Source: The SAS function CINV was used to generate this table. v denotes the degrees of freedom.

11 Figures 2.1 Efficiency Comparisons Bias vs. Variance Type I and II Error Critical Region for Testing Ilo = 2 Against III = 4 for n = Critical Values Wald Test LM Test Poisson Probability Distribution, Mean = Poisson Probability Distribution, Mean = l 'True' Consumption Function An Estimated Consumption Function Consumption Function with cov(x,u) > Random Disturbances Around the Regression Line % Confidence Bands Positively Correlated Residuals Residual Variation Growing with X Residual Plot Cigarette Consumption of 46 States in Plot of Residuals v.s. LNP Cigarette Consumption of 46 States in Plot of 95% Confidence Band for Predicted Values oflnc Plots of Residuals v.s. Log Y Durbin-Watson Critical Values Linear Distributed Lag... l A Polynomial Lag with End Point Constraints The Orthogonal Decomposition of y CUSUM Critical Values' CUSUM Plot of Consumption-Income Data The Rainbow Test Linear Probability Model Truncated Normal Distribution l3.3 Truncated Regression Model U.S. Consumption and Income, Corre1ogram of Consumption Correlogram of AC

12 Tables 3.1 Simple Regression Computations EXAMPLE #1: Cigarette Consumption Cigarette Consumption Regression Earnings Regression for U.S. Gasoline Data: U. S. Consumption Data, Regression With Arithmetic Lag Restriction Almon Polynomial, r = 2, s = 5 and Near End-Point Constraint Almon Polynomial, r = 2 s = 5 and Far End-Point Constraint Cigarette Regression Diagnostic Statistics for Cigarettes Example Regression of Real Per-Capita Consumption of Cigarettes Consumption-Income Example Non-Nested Hypothesis Testing Utts (1982) Rainbow Test Non-Nested J and JA Test Gasoline Demand Data: One-Way Error Components Results Comparison of the Linear Probability, Logit and Probit Models: Union Participation Actual Versus Predicted: Union Participation