Statistical Foundations of Econometric Modelling Book

	Foreword	xi
	Preface	xv
	Acknowledgements	xx
	List of symbols and abbreviations	xxi
Part I	Introduction
1	Econometric modelling, a preliminary view	3
1.1	Econometrics--a brief historical overview	3
1.2	Econometric modelling--a sketch of a methodology	15
1.3	Looking ahead	22
2	Descriptive study of data	23
2.1	Histograms and their numerical characteristics	23
2.2	Frequency curves	27
2.3	Looking ahead	29
Part II	Probability theory
3	Probability	33
3.1	The notion of probability	34
3.2	The axiomatic approach	37
3.3	Conditional probability	43
4	Random variables and probability distributions	47
4.1	The concept of a random variable	48
4.2	The distribution and density functions	55
4.3	The notion of a probability model	60
4.4	Some univariate distributions	62
4.5	Numerical characteristics of random variables	68
5	Random vectors and their distributions	78
5.1	Joint distribution and density functions	78
5.2	Some bivariate distributions	83
5.3	Marginal distributions	85
5.4	Conditional distributions	89
6	Functions of random variables	96
6.1	Functions of one random variable	96
6.2	Functions of several random variables	99
6.3	Functions of normally distributed random variables, a summary	108
6.4	Looking ahead	109
Appendix 6.1	The normal and related distributions	110
7	The general notion of expectation	116
7.1	Expectation of a function of random variables	116
7.2	Conditional expectation	121
7.3	Looking ahead	127
Appendix 7.1	Inequalities	129
8	Stochastic processes	130
8.1	The concept of a stochastic process	131
8.2	Restricting the time-heterogeneity of a stochastic process	137
8.3	Restricting the memory of a stochastic process	140
8.4	Some special stochastic processes	144
8.5	Summary	162
9	Limit theorems	165
9.1	The early limit theorems	165
9.2	The law of large numbers	168
9.3	The central limit theorem	173
9.4	Limit theorems for stochastic processes	178
9.5	Summary	180
10	Introduction to asymptotic theory	183
10.1	Introduction	183
10.2	Modes of convergence	185
10.3	Convergence of moments	192
10.4	The 'big O' and 'little o' notation	194
10.5	Extending the limit theorems	198
10.6	Error bounds and asymptotic expansions	202
Part III	Statistical inference
11	The nature of statistical inference	213
11.1	Introduction	213
11.2	The sampling model	215
11.3	The frequency approach	219
11.4	An overview of statistical inference	221
11.5	Statistics and their distributions	223
Appendix 11.1	The empirical distribution function	228
12	Estimation I--properties of estimators	231
12.1	Finite sample properties	232
12.2	Asymptotic properties	244
12.3	Predictors and their properties	247
13	Estimation II--methods	252
13.1	The method of least-squares	253
13.2	The method of moments	256
13.3	The maximum likelihood method	257
14	Hypothesis testing and confidence regions	285
14.1	Testing, definitions and concepts	285
14.2	Optimal tests	290
14.3	Constructing optimal tests	296
14.4	The likelihood ratio test procedure	299
14.5	Confidence estimation	303
14.6	Prediction	306
15	The multivariate normal distribution	312
15.1	Multivariate distributions	312
15.2	The multivariate normal distribution	315
15.3	Quadratic forms related to the normal distribution	319
15.4	Estimation	320
15.5	Hypothesis testing and confidence regions	323
16	Asymptotic test procedures	326
16.1	Asymptotic properties	326
16.2	The likelihood ratio and related test procedures	328
Part IV	The linear regression and related statistical models
17	Statistical models in econometrics	339
17.1	Simple statistical models	339
17.2	Economic data and the sampling model	342
17.3	Economic data and the probability model	346
17.4	The statistical generating mechanism	349
17.5	Looking ahead	352
Appendix 17.1	Data	355
18	The Gauss linear model	357
18.1	Specification	357
18.2	Estimation	359
18.3	Hypothesis testing and confidence intervals	363
18.4	Experimental design	366
18.5	Looking ahead	367
19	The linear regression model I--specification, estimation and testing	369
19.1	Introduction	369
19.2	Specification	370
19.3	Discussion of the assumptions	375
19.4	Estimation	378
19.5	Specification testing	392
19.6	Prediction	402
19.7	The residuals	405
19.8	Summary and conclusion	408
Appendix 19.1	A note on measurement systems	409
20	The linear regression model II--departures from the assumptions underlying the statistical GM	412
20.1	The stochastic linear regression model	413
20.2	The statistical parameters of interest	418
20.3	Weak exogeneity	421
20.4	Restrictions on the statistical parameters of interest	422
20.5	Collinearity	432
20.6	'Near' collinearity	434
21	The linear regression model III--departures from the assumptions underlying the probability model	443
21.1	Misspecification testing and auxiliary regressions	443
21.2	Normality	447
21.3	Linearity	457
21.4	Homoskedasticity	463
21.5	Parameter time invariance	472
21.6	Parameter structural change	481
Appendix 21.1	Variance stabilising transformations	487
22	The linear regression model IV--departures from the sampling model assumption	493
22.1	Implications of a non-random sample	494
22.2	Tackling temporal dependence	503
22.3	Testing the independent sample assumption	511
22.4	Looking back	521
Appendix 22.1	Deriving the conditional expectation	523
23	The dynamic linear regression model	526
23.1	Specification	527
23.2	Estimation	533
23.3	Misspecification testing	539
23.4	Specification testing	548
23.5	Prediction	562
23.6	Looking back	567
24	The multivariate linear regression model	571
24.1	Introduction	571
24.2	Specification and estimation	574
24.3	A priori information	579
24.4	The Zellner and Malinvaud formulations	585
24.5	Specification testing	589
24.6	Misspecification testing	596
24.7	Prediction	599
24.8	The multivariate dynamic linear regression (MDLR) model	599
Appendix 24.1	The Wishart distribution	602
Appendix 24.2	Kronecker products and matrix differentiation	603
25	The simultaneous equations model	608
25.1	Introduction	608
25.2	The multivariate linear regression and simultaneous equations models	610
25.3	Identification using linear homogeneous restrictions	614
25.4	Specification	619
25.5	Maximum likelihood estimation	621
25.6	Least-squares estimation	626
25.7	Instrumental variables	637
25.8	Misspecification testing	644
25.9	Specification testing	649
25.10	Prediction	654
26	Epilogue: towards a methodology of econometric modelling	659
26.1	A methodologist's critical eye	659
26.2	Econometric modelling, formalising a methodology	661
26.3	Conclusion	671
	References	673
	Index	689