Modern Econometric Analysis (eBook)

Preface 5
Contents 7
1 Developments and New Dimensions in Econometrics 9
1.1 Introduction 9
1.2 Contributions 11
2 On the Specification and Estimation of Large Scale Simultaneous Structural Models 15
2.1 Introduction 15
2.2 SSEMs - the State of the Art 17
2.2.1 Modeling Procedures of SSEMs 17
2.2.2 Statistical Adequacy of SSEMs 17
2.2.3 Statistical Adequacy with Respect to the Criticisms Towards SSEMs 18
2.2.4 Limits of Statistical Adequacy 19
2.3 Statistical Adequacy of SSEMs with 1( 1) Variables 19
2.3.1 A Classification of SSEMs 19
2.3.2 SSEMs with 1( 1) Variables 21
2.3.3 The Role of Economic Theory in SSEMs 26
2.4 Statistical Inference of Large Scale SSEMs 26
2.4.1 Test of Exclusion Restrictions 27
2.4.2 Test of Sufficient Cointegration 28
2.4.3 Test of Overidentification 28
2.4.4 An Integrated Modeling Procedure 28
2.5 Concluding Remarks 29
3 Dynamic Factor Models 33
3.1 Introduction 33
3.2 The Strict Factor Model 34
3.3 Approximate Factor Models 36
3.4 Specifying the Number of Factors 36
3.5 Dynamic Factor Models 38
3.6 Overview of Existing Applications 39
3.6.1 Construction of Economic Indicators 39
3.6.2 Forecasting 39
3.6.3 Monetary Policy Analysis 40
3.6.4 International Business Cycles 41
3.7 Empirical Application 41
3.8 Conclusion 45
4 Unit Root Testing 49
4.1 Introduction 49
4.2 Dickey-Fuller Unit Root Tests 51
4.2.1 Model 51
4.2.2 Distribution 52
4.3 Size and Power Considerations 54
4.3.1 Lag Length Selection 54
4.3.2 Deterministic Components 55
4.3.3 Span vs. Frequency 56
4.4 Structural Breaks 57
4.4.1 Ignoring Breaks 57
4.4.2 Correcting for Breaks 58
4.4.3 Smooth Transitions and Several Breaks 59
5 Autoregressive Distributed Lag Models and Cointegration 65
5.1 Introduction 65
5.2 Assumptions and Representations 66
5.3 Inference on the Cointegrating Vector 69
5.4 Cointegration Testing 71
5.5 Monte Carlo Evidence 75
5.6 Summary 76
6 Structural Vector Autoregressive Analysis for Cointegrated Variables 81
6.1 Introduction 81
6.2 The Model Setup 83
6.2.1 The Identification Problem 83
6.2.2 Computation of Impulse Responses and Forecast Error Variance Decompositions 87
6.3 Estimation 87
6.3.1 Estimating the Reduced Form 87
6.3.2 Estimating the Structural Parameters 89
6.3.3 Estimation of Impulse Responses 90
6.4 Model Specification and Validation 91
6.5 Conclusions 92
7 Econometric Analysis of High Frequency Data 95
7.1 Introduction 95
7.2 Price Discovery 96
7.2.1 Nonsynchronous Trading and Fixed Interval Analysis 97
7.2.2 Motivation and Applications of VECM 97
7.2.3 The Vector Error Correction Model 98
7.2.4 Parameter Estimation with Incomplete Samples 99
7.3 Realized Volatility 100
7.3.1 Measuring Volatility from High Frequency Data 101
7.3.2 Consistency of Realized Variances 101
7.3.3 Conditional Normality of Realized Variances 104
7.3.4 Stylized Features of Realized Volatility 105
8 Using Quantile Regression for Duration Analysis 111
8.1 Introduction 111
8.2 Quantile Regression and Duration Analysis 112
8.2.1 Quantile Regression and Proportional Hazard Rate Model 113
8.2.2 Censoring and Censored Quantile Regression 116
8.2.3 Estimating the Hazard Rate Based on Quantile Regression 118
8.2.4 Unobserved Heterogeneity 120
8.3 Summary 123
9 Multilevel and Nonlinear Panel Data Models 127
9.1 Introduction 127
9.2 Parametric Linear and Multilevel Models 128
9.3 Parametric Nonlinear Models 132
9.4 Non- and Semiparametric Models 135
9.5 Concluding Remarks 139
10 Nonparametric Models and Their Estimation 144
10.1 Introduction 144
10.2 Scatterplot Smoothing 145
10.2.1 Sketch of Local Smoothing 145
10.2.3 Sketch of Penalized Spline (P- Spline) Smoothing 148
10.2.4 Software for Smoothing 149
10.2.5 Example (Scatterplot Smoothing) 149
10.3 Non and Semiparametric Models 150
10.3.1 Generalized Additive and Varying Coefficient Models 150
10.3.2 Example (Generalized Additive Models) 151
10.3.3 Further Models 153
10.3.4 Multivariate and Spatial Smoothing 154
10.3.5 Example (Bivariate Smoothing) 154
10.3.6 Model Diagnostics 155
10.4 Discussion 156
11 Microeconometric Models and Anonymized Micro Data 160
11.1 Introduction 160
11.2 Principles of Microeconometric Modelling 161
11.2.1 Binary Probit (and Logit) Model 162
11.2.2 Ordinal Probit Model 162
11.2.3 Discrete Choice Model 162
11.2.4 Count Data Models 163
11.2.5 Duration Models 163
11.2.6 Tobit Models 165
11.2.7 Estimation and Testing 165
11.3 Anonymization of Micro Data 166
11.3.1 General Remarks 166
11.3.2 Microaggregation 166
11.3.3 Addition of Noise 167
11.3.4 Randomized Response and Post Randomization 168
11.4 The Probit Model under PRAM 168
11.4.1 Estimation of the Model 168
11.4.2 Marginal Effect in Case of the 'Naive' Probit Estimator 170
11.4.3 Estimation of Unknown Randomization Probabilities 170
12 Ordered Response Models 174
12.1 Introduction 174
12.2 Standard Ordered Response Models 176
12.3 Generalized Ordered Response Models 177
12.3.1 Generalized Threshold Model 178
12.3.2 Random Coefficients Model 178
12.3.3 Finite Mixture Model 180
12.3.4 Sequential Model 181
12.4 Empirical Illustration 183
12.5 Concluding Remarks 185
13 Some Recent Advances in Measurement Error Models and Methods 189
13.1 Introduction 189
13.2 Measurement Error Models 190
13.3 Identifiability 191
13.4 Naive Estimation and Bias Correction 191
13.5 Functional Estimation Methods 192
13.5.1 Corrected Score (CS) Estimator 192
13.5.2 Simulation- Extrapolation (SIMEX) Estimator 193
13.6 Structural Estimation Methods 194
13.6.1 Maximum likelihood (ML) Estimator 194
13.6.2 The Quasi Score (QS) Estimator 194
13.6.3 The Regression Calibration (RC) Estimator 195
13.7 Efficiency Comparison 196
13.8 Survival Analysis 197
13.8.1 Measurement Error in Cox-type Models 197
13.8.2 Accelerated Failure Time Models 198
13.9 Misclassification 199
13.10 Concluding Remarks 199
14 The Microeconometric Estimation of Treatment Effects - An Overview 205
14.1 Introduction 205
14.2 The Evaluation Framework 206
14.2.1 Potential Outcome Approach and the Fundamental Evaluation Problem 206
14.2.2 Treatment Effects and Selection Bias 207
14.2.3 Potential Outcome Framework and Heterogeneous Treatment Effects 208
14.3 Non- Experimental Evaluation Methods 209
14.3.1 Matching Estimator 210
14.3.2 Linear Regression Approach 211
14.3.3 Instrumental Variables Estimator 212
14.3.4 Selection Model 213
14.3.5 Difference-in-Differences Estimator 213
14.3.6 Regression Discontinuity Model 214
14.3.7 Dynamic Evaluation Concepts 215
14.4 Summary - Which Estimator to Choose? 217
15 Survey Item Nonresponse and its Treatment 221
15.1 Introduction 221
15.2 Item Nonresponse in the German Socioeconomic Panel 223
15.2.1 Prevalence of Item Nonresponse in the GSOEP 223
15.2.2 Determinants and Effects of Item Nonresponse 223
15.3 Dealing with Item Nonresponse 225
15.3.3 Imputation Techniques 227
15.3.4 Model- based Procedures 229
15.3.5 Evidence from a Comparison Study 230
15.4 Conclusions and Recommendations 232

7 Econometric Analysis of High Frequency Data (p. 86-87)

Helmut Herwartz
Institut fiir Statistik und Okonometrie,

Christian Albrechts-Universitat zu Kiel
herwartzstat-econ.uni-kiel.de

Summary: Owing to enormous advances in data acquisition and processing technology the study of high (or ultra) frequency data has become an important area of econometrics. At least three avenues of econometric methods have been followed to analyze high frequency financial data: Models in tick time ignoring the time dimension of sampling, duration models specifying the time span between transactions and, finally, fixed time interval techniques. Starting from the strong assumption that quotes are irregularly generated from an underlying exogeneous arrival process, fixed interval models promise feasibility of familiar time series techniques. Moreover, fixed interval analysis is a natural means to investigate multivariate dynamics. In particular, models of price discovery are implemented in this venue of high frequency econometrics. Recently, a sound statistical theory of 'realized volatility' has been developed. In this framework high frequency log price changes are seen as a means to observe volatility at some lower frequency.

7.1 Introduction

With the enormous advances in computer technology, data acquisition, storage and processing has become feasible at higher and higher frequencies. In the extreme case of ultra high frequency financial data the analyst has access to numerous characteristics, called marks, of each transaction (price and quantity traded, corresponding bid and ask quotes etc.) and to the time of its occurrence, measured in seconds. As a consequence, numerous financial market microstructure hypotheses undergo empirical tests based on ultra frequency data. Typical issues in this vein of microstructure analysis are, for instance, the informational content of traded volumes for (future) prices (KarpofF, 1987), the relation between prices and clustering of transactions (Easley and O'Hara, 1992), or the significance of bid ask spreads as a means to identify the presence of informed traders in the market (Admati and Pfleiderer, 1988). Prom an econometric perspective such hypotheses naturally require an analysis of the marks in tick time, and, eventually motivate a duration model. The methodology for the analysis of marked point processes as well as durations has experienced substantial progress since the introduction of Autoregressive Conditional Duration (ACD) models by Engle and Russell (1998). For a recent overview the reader may consult Engle and Russell (2005).

Another area of market microstructure modeling is information diffusion across markets trading the same asset or close substitutes. Then, it is of interest if independent price discovery (Schreiber and Schwartz, 1986) takes place in some major market or, alternatively, if the efficient price is determined over a cross section of interacting exchanges. Following Harris et al. (1995) or Hasbrouck (1995) price discovery is investigated by means of vector error correction models (VECM) mostly after converting transaction time to fixed time intervals of 1, 10 or 30 minutes, say. Although the latter conversion goes at the cost of loosing information on the trading intensity, it appears inevitable since the price quotations of interest are collected as a vector valued variable. Owing to irregular time spacing of quotes the statistical analysis of fixed interval data has to cope with methodological issues arising from the incidence of missing values. A condensed review over econometric approaches to model price discovery will be given in Section 7.2.

Apart from market microstructure modeling high frequency data have recently attracted large interest in econometrics as a means to estimate conditional volatility of asset prices at lower frequencies (Anderson et al., henceforth, ABDL, 2001, 2003). Owing to its consistency for the process of conditional variances this estimator has particular appeal since it makes the latent volatility observable in the limit. A sound statistical theory on 'realized volatility' is now available making it a strong competitor to parametric approaches to modeling time varying second order moments. Section 7.3 will provide theoretical and empirical features of 'realized volatility'.

7.2 Price Discovery

A particular issue in empirical finance is the analysis of dynamic relationships between markets trading simultaneously a given security. Since cross sectional price differentials cannot persist, it is of interest, if the involved market places contribute jointly to the fundamental value of the asset or if particular markets lead the other. The process of incorporating new information into the efficient price has become popular as price discovery (Schreiber and Schwartz, 1986).