Hübler / Frohn Modern Econometric Analysis

Surveys on Recent Developments
1. Auflage 2007
ISBN: 978-3-540-32693-9
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 236 Seiten

In this book leading German econometricians in different fields present survey articles of the most important new methods in econometrics. The book gives an overview of the field and it shows progress made in recent years and remaining problems.

Autoren/Hrsg.

Frohn, Joachim

Hübler, Olaf

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;1 Developments and New Dimensions in Econometrics;9
3.1;1.1 Introduction;9
3.2;1.2 Contributions;11
4;2 On the Specification and Estimation of Large Scale Simultaneous Structural Models;15
4.1;2.1 Introduction;15
4.2;2.2 SSEMs - the State of the Art;17
4.2.1;2.2.1 Modeling Procedures of SSEMs;17
4.2.2;2.2.2 Statistical Adequacy of SSEMs;17
4.2.3;2.2.3 Statistical Adequacy with Respect to the Criticisms Towards SSEMs;18
4.2.4;2.2.4 Limits of Statistical Adequacy;19
4.3;2.3 Statistical Adequacy of SSEMs with 1( 1) Variables;19
4.3.1;2.3.1 A Classification of SSEMs;19
4.3.2;2.3.2 SSEMs with 1( 1) Variables;21
4.3.3;2.3.3 The Role of Economic Theory in SSEMs;26
4.4;2.4 Statistical Inference of Large Scale SSEMs;26
4.4.1;2.4.1 Test of Exclusion Restrictions;27
4.4.2;2.4.2 Test of Sufficient Cointegration;28
4.4.3;2.4.3 Test of Overidentification;28
4.4.4;2.4.4 An Integrated Modeling Procedure;28
4.5;2.5 Concluding Remarks;29
5;3 Dynamic Factor Models;33
5.1;3.1 Introduction;33
5.2;3.2 The Strict Factor Model;34
5.3;3.3 Approximate Factor Models;36
5.4;3.4 Specifying the Number of Factors;36
5.5;3.5 Dynamic Factor Models;38
5.6;3.6 Overview of Existing Applications;39
5.6.1;3.6.1 Construction of Economic Indicators;39
5.6.2;3.6.2 Forecasting;39
5.6.3;3.6.3 Monetary Policy Analysis;40
5.6.4;3.6.4 International Business Cycles;41
5.7;3.7 Empirical Application;41
5.8;3.8 Conclusion;45
6;4 Unit Root Testing;49
6.1;4.1 Introduction;49
6.2;4.2 Dickey-Fuller Unit Root Tests;51
6.2.1;4.2.1 Model;51
6.2.2;4.2.2 Distribution;52
6.3;4.3 Size and Power Considerations;54
6.3.1;4.3.1 Lag Length Selection;54
6.3.2;4.3.2 Deterministic Components;55
6.3.3;4.3.3 Span vs. Frequency;56
6.4;4.4 Structural Breaks;57
6.4.1;4.4.1 Ignoring Breaks;57
6.4.2;4.4.2 Correcting for Breaks;58
6.4.3;4.4.3 Smooth Transitions and Several Breaks;59
7;5 Autoregressive Distributed Lag Models and Cointegration;65
7.1;5.1 Introduction;65
7.2;5.2 Assumptions and Representations;66
7.3;5.3 Inference on the Cointegrating Vector;69
7.4;5.4 Cointegration Testing;71
7.5;5.5 Monte Carlo Evidence;75
7.6;5.6 Summary;76
8;6 Structural Vector Autoregressive Analysis for Cointegrated Variables;81
8.1;6.1 Introduction;81
8.2;6.2 The Model Setup;83
8.2.1;6.2.1 The Identification Problem;83
8.2.2;6.2.2 Computation of Impulse Responses and Forecast Error Variance Decompositions;87
8.3;6.3 Estimation;87
8.3.1;6.3.1 Estimating the Reduced Form;87
8.3.2;6.3.2 Estimating the Structural Parameters;89
8.3.3;6.3.3 Estimation of Impulse Responses;90
8.4;6.4 Model Specification and Validation;91
8.5;6.5 Conclusions;92
9;7 Econometric Analysis of High Frequency Data;95
9.1;7.1 Introduction;95
9.2;7.2 Price Discovery;96
9.2.1;7.2.1 Nonsynchronous Trading and Fixed Interval Analysis;97
9.2.2;7.2.2 Motivation and Applications of VECM;97
9.2.3;7.2.3 The Vector Error Correction Model;98
9.2.4;7.2.4 Parameter Estimation with Incomplete Samples;99
9.3;7.3 Realized Volatility;100
9.3.1;7.3.1 Measuring Volatility from High Frequency Data;101
9.3.2;7.3.2 Consistency of Realized Variances;101
9.3.3;7.3.3 Conditional Normality of Realized Variances;104
9.3.4;7.3.4 Stylized Features of Realized Volatility;105
10;8 Using Quantile Regression for Duration Analysis;111
10.1;8.1 Introduction;111
10.2;8.2 Quantile Regression and Duration Analysis;112
10.2.1;8.2.1 Quantile Regression and Proportional Hazard Rate Model;113
10.2.2;8.2.2 Censoring and Censored Quantile Regression;116
10.2.3;8.2.3 Estimating the Hazard Rate Based on Quantile Regression;118
10.2.4;8.2.4 Unobserved Heterogeneity;120
10.3;8.3 Summary;123
11;9 Multilevel and Nonlinear Panel Data Models ;127
11.1;9.1 Introduction;127
11.2;9.2 Parametric Linear and Multilevel Models;128
11.3;9.3 Parametric Nonlinear Models;132
11.4;9.4 Non- and Semiparametric Models;135
11.5;9.5 Concluding Remarks;139
12;10 Nonparametric Models and Their Estimation;144
12.1;10.1 Introduction;144
12.2;10.2 Scatterplot Smoothing;145
12.2.1;10.2.1 Sketch of Local Smoothing;145
12.2.2;10.2.3 Sketch of Penalized Spline (P- Spline) Smoothing;148
12.2.3;10.2.4 Software for Smoothing;149
12.2.4;10.2.5 Example (Scatterplot Smoothing);149
12.3;10.3 Non and Semiparametric Models;150
12.3.1;10.3.1 Generalized Additive and Varying Coefficient Models;150
12.3.2;10.3.2 Example (Generalized Additive Models);151
12.3.3;10.3.3 Further Models;153
12.3.4;10.3.4 Multivariate and Spatial Smoothing;154
12.3.5;10.3.5 Example (Bivariate Smoothing);154
12.3.6;10.3.6 Model Diagnostics;155
12.4;10.4 Discussion;156
13;11 Microeconometric Models and Anonymized Micro Data;160
13.1;11.1 Introduction;160
13.2;11.2 Principles of Microeconometric Modelling;161
13.2.1;11.2.1 Binary Probit (and Logit) Model;162
13.2.2;11.2.2 Ordinal Probit Model;162
13.2.3;11.2.3 Discrete Choice Model;162
13.2.4;11.2.4 Count Data Models;163
13.2.5;11.2.5 Duration Models;163
13.2.6;11.2.6 Tobit Models;165
13.2.7;11.2.7 Estimation and Testing;165
13.3;11.3 Anonymization of Micro Data;166
13.3.1;11.3.1 General Remarks;166
13.3.2;11.3.2 Microaggregation;166
13.3.3;11.3.3 Addition of Noise;167
13.3.4;11.3.4 Randomized Response and Post Randomization;168
13.4;11.4 The Probit Model under PRAM;168
13.4.1;11.4.1 Estimation of the Model;168
13.4.2;11.4.2 Marginal Effect in Case of the 'Naive' Probit Estimator;170
13.4.3;11.4.3 Estimation of Unknown Randomization Probabilities;170
14;12 Ordered Response Models;174
14.1;12.1 Introduction;174
14.2;12.2 Standard Ordered Response Models;176
14.3;12.3 Generalized Ordered Response Models;177
14.3.1;12.3.1 Generalized Threshold Model;178
14.3.2;12.3.2 Random Coefficients Model;178
14.3.3;12.3.3 Finite Mixture Model;180
14.3.4;12.3.4 Sequential Model;181
14.4;12.4 Empirical Illustration;183
14.5;12.5 Concluding Remarks;185
15;13 Some Recent Advances in Measurement Error Models and Methods;189
15.1;13.1 Introduction;189
15.2;13.2 Measurement Error Models;190
15.3;13.3 Identifiability;191
15.4;13.4 Naive Estimation and Bias Correction;191
15.5;13.5 Functional Estimation Methods;192
15.5.1;13.5.1 Corrected Score (CS) Estimator;192
15.5.2;13.5.2 Simulation- Extrapolation (SIMEX) Estimator;193
15.6;13.6 Structural Estimation Methods;194
15.6.1;13.6.1 Maximum likelihood (ML) Estimator;194
15.6.2;13.6.2 The Quasi Score (QS) Estimator;194
15.6.3;13.6.3 The Regression Calibration (RC) Estimator;195
15.7;13.7 Efficiency Comparison;196
15.8;13.8 Survival Analysis;197
15.8.1;13.8.1 Measurement Error in Cox-type Models;197
15.8.2;13.8.2 Accelerated Failure Time Models;198
15.9;13.9 Misclassification;199
15.10;13.10 Concluding Remarks;199
16;14 The Microeconometric Estimation of Treatment Effects - An Overview;205
16.1;14.1 Introduction;205
16.2;14.2 The Evaluation Framework;206
16.2.1;14.2.1 Potential Outcome Approach and the Fundamental Evaluation Problem;206
16.2.2;14.2.2 Treatment Effects and Selection Bias;207
16.2.3;14.2.3 Potential Outcome Framework and Heterogeneous Treatment Effects;208
16.3;14.3 Non- Experimental Evaluation Methods;209
16.3.1;14.3.1 Matching Estimator;210
16.3.2;14.3.2 Linear Regression Approach;211
16.3.3;14.3.3 Instrumental Variables Estimator;212
16.3.4;14.3.4 Selection Model;213
16.3.5;14.3.5 Difference-in-Differences Estimator;213
16.3.6;14.3.6 Regression Discontinuity Model;214
16.3.7;14.3.7 Dynamic Evaluation Concepts;215
16.4;14.4 Summary - Which Estimator to Choose?;217
17;15 Survey Item Nonresponse and its Treatment;221
17.1;15.1 Introduction;221
17.2;15.2 Item Nonresponse in the German Socioeconomic Panel;223
17.2.1;15.2.1 Prevalence of Item Nonresponse in the GSOEP;223
17.2.2;15.2.2 Determinants and Effects of Item Nonresponse;223
17.3;15.3 Dealing with Item Nonresponse;225
17.3.1;15.3.3 Imputation Techniques;227
17.3.2;15.3.4 Model- based Procedures;229
17.3.3;15.3.5 Evidence from a Comparison Study;230
17.4;15.4 Conclusions and Recommendations;232

Leseproben

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).