Marlene Müller

Semiparametric analysis of German East-West migration intentions: Facts and theory

East-West migration in Germany peaked at the beginning of the 90s although the average wage gap between Eastern and Western Germany continues to average about 25%. We analyze the propensity to migrate using microdata from the German Socioeconomic Panel. Fitting a parametric Generalized Linear Model (GLM) yields nonlinear residual behavior. This finding is not compatible with classical Marshallian theory of migration and motivates the semiparametric analysis. We estimate a Generalized Partial Linear Model (GPLM) where some components of the index of explanatory variables enter nonparametrically. We find the estimate of the nonparametric inuence in concordance with a number of alternative migration theories, including the recently proposed option-value-of-waiting theory.

Xplore: learning guide

I: First Steps.- 1 Getting Started.- 1.1 Using XploRe.- 1.1.1 Input and Output Windows.- 1.1.2 Simple Computations.- 1.1.3 First Data Analysis.- 1.1.4 Exploring Data.- 1.1.5 Printing Graphics.- 1.2 Quantlet Examples.- 12.1 Summary Statistics.- 1.2.2 Histograms.- 1.2.3 2D Density Estimation.- 1.2.4 Interactive Kernel Regression.- 1.3 Getting Help.- 1.4 Basic XploRe Syntax.- 1.4.1 Operators.- 1.4.2 Variables.- 1.4.3 Variable Names.- 1.4.4 Functions.- 1.4.5 Quantlet files.- 2. Descriptive Statistics.- 2.1 Data Matrices.- 2.1.1 Creating Data Matrices.- 2.1.2 Loading Data Files.- 2.1.3 Matrix Operations.- 2.2 Computing Statistical Characteristics.- 2.1.1 Minimum and Maximum.- 2.2.2 Mean, Variance and Other Moments.- 2.2.3 Median and Quantiles.- 2.2.4 Covariance and Correlation.- 2.2.5 Categorical Data.- 2.2.6 Missing Values and Infinite Values.- 2.3 Summarizing Statistical Information.- 2.3.1 Summarizing Metric Data.- 2.3.2 Summarizing Categorical Data.- 3 Graphics.- 3.1 Basic Plotting.- 3.1.1 Plotting a Data Set.- 3.1.2 Plotting a Function.- 3.1.3 Plotting Several Functions.- 3.1.4 Coloring Data Sets.- 3.1.5 Plotting Lines from Data Sets.- 3.1.6 Several Plots.- 3.2 Univariate Graphics.- 3.2.1 Boxplots.- 3.2.2 Dotplots.- 3.2.3 Bar Charts.- 3.2.4 Quantile-Quantile Plots.- 3.2.5 Histograms.- 3.3 Multivariate Graphics.- 3.3.1 Three-Dimensional Plots.- 3.3.2 Surface Plots.- 3.3.3 Contour Plots.- 3.3.4 Sunflower Plots.- 3.3.5 Linear Regression.- 3.3.6 Bivariate Plots.- 3.3.7 Star Diagrams.- 3.3.8 Scatter-Plot Matrices.- 3.3.9 Andrews Curves.- 3.3.10 Parallel Coordinate Plots.- 3.4 Advanced Graphics.- 3.4.1 Moving and Rotating.- 3.4.2 Simple Predefined Graphic Primitives.- 3.4.3 Color Models.- 3.5 Graphic Commands.- 3.5.1 Controlling Data Points.- 3.5.2 Color of Data Points.- 3.5.3 Symbol of Data Points.- 3.5.4 Size of Data Points.- 3.5.5 Connection of Data Points.- 3.5.6 Label of Data Points.- 3.5.7 Title and Axes Labels.- 3.5.8 Axes Layout.- 4 Regression Methods.- 4.1 Simple Linear Regression.- 4.2 Multiple Linear Regression.- 4.3 Nonlinear Regression.- 5 Teachware Quantlets.- 5.1 Visualizing Data.- 5.2 Random Sampling.- 5.3 The p-Value in Hypothesis Testing.- 5.4 Approximating the Binomial by the Normal Distribution.- 5.5 The Central Limit Theorem.- 5.6 The Pearson Correlation Coefficient.- 5.7 Linear Regression.- II: Statistical Libraries.- 6 Smoothing Methods.- 6.1 Kernel Density Estimation.- 6.1.1 Computational Aspects.- 6.1.2 Computing Kernel Density Estimates.- 6.1.3 Kernel Choice.- 6.1.4 Bandwidth Selection.- 6.1.5 Confidence Intervals and Bands.- 6.2 Kernel Regression.- 6.2.1 Computational Aspects.- 6.2.2 Computing Kernel Regression Estimates.- 6.2.3 Bandwidth Selection.- 6.2.4 Confidence Intervals and Bands.- 6.2.5 Local Polynomial Regression and Derivative Estimation.- 6.3 Multivariate Density and Regression Functions.- 6.3.1 Computational Aspects.- 6.3.2 Multivariate Density Estimation.- 6.3.3 Multivariate Regression.- 7 Generalized Linear Models.- 7.1 Estimating GLMs.- 7.1.1 Models.- 7.1.2 Maximum-Likelihood Estimation.- 7.2 Computing GLM Estimates.- 7.2.1 Data Preparation.- 7.2.2 Interactive Estimation.- 7.2.2 Noninteractive Estimation.- 7.3 Weights & Constraints.- 7.3.1 Prior Weights.- 7.3.2 Replications in Data.- 7.3.3 Constrained Estimation.- 7.4 Options.- 7.4.1 Setting Options.- 7.4.2 Weights and Offsets.- 7.4.3 Control Parameters.- 7.4.4 Output Modification.- 7.5 Statistical Evaluation and Presentation.- 7.5.1 Statistical Characteristics.- 7.5.2 Output Display.- 7.5.3 Significance of Parameters.- 7.5.4 Likelihood Ratio Tests for Comparing Nested Models.- 7.5.5 Subset Selection.- 8 Neural Networks.- 8.1 Feed-Forward Networks.- 8.2 Computing a Neural Network.- 8.2.1 Controlling the Parameters of the Neural Network.- 8.2.2 The Resulting Neural Network.- 8.3 Running a Neural Network.- 8.3.1 Implementing a Simple Discriminant Analysis.- 8.3.2 Implementing a More Complex Discriminant Analysis.- 9 Time Series.- 9.1 Time Domain and Frequency Domain Analysis.- 9.1.1 Autocovariance and Autocorrelation Function.- 9.1.2 The Periodogram and the Spectrum of a Series.- 9.2 Linear Models.- 9.2.1 Autoregressive Models.- 9.2.2 Autoregressive Moving Average Models.- 9.2.3 Estimating ARMA Processes.- 9.3 Nonlinear Models.- 9.3.1 Several Examples of Nonlinear Models.- 9.3.2 Nonlinearity in the Conditional Second Moments.- 9.3.3 Estimating ARCH Models.- 9.3.4 Testing for ARCH.- 10 Kalman Filtering.- 10.1 State-Space Models.- 10.1.1 Examples of State-Space Models.- 10.1.2 Modeling State-Space Models in XploRe.- 10.2 Kalman Filtering and Smoothing.- 10.3 Parameter Estimation in State-Space Models.- 11 Finance.- 11.1 Outline of the Theory.- 11.1.1 Some History.- 11.1.2 The Black-Scholes Formula.- 11.2 Assets.- 11.2.1 Stock Simulation.- 11.2.2 Stock Estimation.- 11.2.3 Stock Estimation and Simulation.- 11.3 Options.- 11.3.1 Calculation of Option Prices and Implied Volatilities.- 11.3.2 Option Price Determining Factors.- 11.3.3 Greeks.- 11.4 Portfolios and Hedging.- 11.4.1 Calculation of Arbitrage.- 11.4.2 Bull-Call Spreads.- 12 Microeconometrics and Panel Data.- 12.1 Limited-Dependent and Qualitative Dependent Variables.- 12.1.1 Probit, Logit and Tobit.- 12.1.2 Single Index Models.- 12.1.3 Average Derivatives.- 12.1.4 Average Derivative Estimation.- 12.1.5 Weighted Average Derivative Estimation.- 12.1.6 Average Derivatives and Discrete Variables.- 12.1.7 Parametric versus Semiparametric Single Index Models.- 12.2 Multiple Index Models.- 12.2.1 Sliced Inverse Regression.- 12.2.2 Testing Parametric Multiple Index Models.- 12.3 Self-Selection Models.- 12.3.1 Parametric Model.- 12.3.2 Semiparametric Model.- 12.4 Panel Data Analysis.- 12.4.1 The Data Set.- 12.4.2 Time Effects.- 12.4.3 Model Specification.- 12.4.4 Estimation.- 12.4.5 An Example.- 12.5 Dynamic Panel Data Models.- 12.6 Unit Root Tests for Panel Data.- 13 Extreme Value Analysis.- 13.1 Extreme Value Models.- 13.2 Generalized Pareto Distributions.- 13.3 Assessing the Adequacy: Mean Excess Functions.- 13.4 Estimation in EV Models.- 13.4.1 Linear Combination of Ratios of Spacings (LRS).- 13.4.2 ML Estimator in the EV Model.- 13.4.3 ML Estimator in the Gumbel Model.- 13.5 Fitting GP Distributions to the Upper Tail.- 13.6 Parametric Estimators for GP Models.- 13.6.1 Moment Estimator.- 13.6.2 ML Estimator in the GP Model.- 13.6.3 Pickands Estimator.- 13.6.4 Drees-Pickands Estimator.- 13.6.5 Hill Estimator.- 13.6.6 ML Estimator for Exponential Distributions.- 13.6.7 Selecting a Threshold by Means of a Diagram.- 13.7 Graphical User Interface.- 13.8 Example.- 14 Wavelets.- 14.1 Quantlib twave.- 14.1.1 Change Basis.- 14.1.2 Change Function.- 14.1.3 Change View.- 14.2 Discrete Wavelet Transform.- 14.3 Function Approximation.- 14.4 Data Compression.- 14.5 Two Sines.- 14.6 Frequency Shift.- 14.7 Thresholding.- 14.7.1 Hard Thresholding.- 14.7.2 Soft Thresholding.- 14.7.3 Adaptive Thresholding.- 14.8 Translation Invariance.- 14.9 Image Denoising.- III: Programming.- 15 Reading and Writing Data.- 15.1 Reading and Writing Data Files.- 15.2 Input Format Strings.- 15.3 Output Format Strings.- 15.4 Customizing the Output Window.- 15.4.1 Headline Style.- 15.4.2 Layer Style.- 15.4.3 Line Number Style.- 15.4.4 Value Formats and Lengths.- 15.4.5 Saving Output to a File.- 16 Matrix Handling.- 16.1 Basic Operations.- 16.1.1 Creating Matrices and Arrays.- 16.1.2 Operators for Numeric Matrices.- 16.2 Comparison Operators.- 16.3 Matrix Manipulation.- 16.3.1 Extraction of Elements.- 16.3.2 Matrix Transformation.- 16.4 Sums and Products.- 16.5 Distance Function.- 16.6 Decompositions.- 16.6.1 Spectral Decomposition.- 16.6.2 Singular Value Decomposition.- 16.6.3 LU Decomposition.- 16.6.4 Cholesky Decomposition.- 16.7 Lists.- 16.7.1 Creating Lists.- 16.7.2 Handling Lists.- 16.7.3 Getting Information on Lists.- 17 Quantlets and Quantlibs.- 17.1 Quantlets.- 17.2 Flow Control.- 17.2.1 Local and Global Variables.- 17.2.2 Conditioning.- 17.2.3 Branching.- 17.2.4 While-Loop.- 17.2.5 Do-Loop.- 17.2.6 Optional Input and Output in Procedures.- 17.2.7 Errors and Warnings.- 17.3 User Interaction.- 17.4 APSS.- 17.5 Quantlibs.

Estimation and testing in generalized partial linear models—A comparative study

A particular semiparametric model of interest is the generalized partial linear model (GPLM) which extends the generalized linear model (GLM) by a nonparametric component.The paper reviews different estimation procedures based on kernel methods as well as test procedures on the correct specification of this model (vs. a parametric generalized linear model). Simulations and an application to a data set on East–West German migration illustrate similarities and dissimilarities of the estimators and test statistics.

Nonparametric Density Estimation

Contrary to the treatment of the histogram in statistics textbooks we have shown that the histogram is more than just a convenient tool for giving a graphical representation of an empirical frequency distribution. It is a serious and widely used method for estimating an unknown pdf. Yet, the histogram has some shortcomings and hopefully this chapter will persuade you that the method of kernel density estimation is in many respects preferable to the histogram.

The multimedia project MM*STAT for teaching statistics

The multimedia project MM*STAT was developed to have an additional tool for teaching statistics. There are some important facts which influenced this development. First, teaching statistics for students in socio-economic sciences must include a broad spectrum of applications of statistical methods in these fields. A pure theoretical presentation is generally considered by the students to be tedious. Second, in practice no statistical analysis is carried out without a computer. Thus, teaching statistics must include the acquisition of computational capabilities. Third, statistics has become more and more complicated over time, because of increasingly complex data structures, statistical methods and models. Thus, an ever-increasing special knowledge of statistics is required and has to be taught. Fourth, notwithstanding these high demands on teaching statistics, the available lecture time, especially for the introductory courses, has remained constant over the years or has even been cut down.

Credit scoring using semiparametric methods

Credit scoring methods aim to assess credit worthiness of potential borrowers to keep the risk of credit loss low and to minimize the costs of failure over risk groups. Typical methods which are used for the statistical classification of credit applicants are linear or quadratic discriminant analysis and logistic discriminant analysis. These methods are based on scores which depend on the explanatory variables in a predefined form (usually linear). Recent methods that allow a more flexible modeling are neural networks and classification trees (see e.g. Arminger, Enache and Bonne, 1997) as well as nonparametric approaches (see e.g. Henley and Hand, 1996).

The efficiency of bias-corrected estimators for nonparametric kernel estimation based on local estimating equations

Stuetzle and Mittal (1979) for ordinary nonparametric kernel regression and Kauermann and Tutz (1996) for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators, without the need for devices such as second derivative estimation and multiple bandwidths of different order. We derive a similar estimator in the context of local (multivariate) estimation based on estimating functions. As expected, this lower order bias is bought at a cost of increased variance. Surprisingly, when compared to ordinary kernel and local linear kernel estimators, the bias-corrected estimators increase variance by a factor independent of the problem, depending only on the kernel used. The variance increase is approximately 40% and more for kernels in standard use. However, the variance increase is still less than that incurred when undersmoothing a local quadratic regression estimator.

Computer-assisted Statistics Teaching in Network Environments

The paper presents the use of interactive tools and interactive graphical displays in introductory and advanced statistics courses. All the examples presented can be used with the statistical computing environment i XploRe, either from a Java applet over WWW or in an generic standalone version on the users local computer.

Single Index Models

A single index model (SIM) summarizes the effects of the explanatory variables X1, ..., Xd within a single variable called the index. As stated at the beginning of Part II, the SIM is one possibility for generalizing the GLM or for restricting the multidimensional regression E(Y|X) to overcome the curse of dimensionality and the lack of interpretability. For more examples of motivating the SIM see Ichimura (1993). Among others, this reference mentions duration, truncated regression (Tobit) and errors-in-variables modeling.

Exploring Credit Data

Credit scoring methods aim to assess the default risk of a potential borrower. This involves typically the calculation of a credit score and the estimation of the probability of default. One of the standard approaches is logistic discriminant analysis, also referred to as logit model. This model maps explanatory variables for the default risk to a credit score using a linear function. Nonlinearity can be included by using polynomial terms or piecewise linear functions. This may give however only a limited reflection of a truly nonlinear relationship. Moreover, an additional modeling step may be necessary to determine the optimal polynomial order or the optimal interval classification. This paper presents semiparametric extensions of the logit model which directly allow for nonlinear relationships to be part of the explanatory variables. The technique is based on the theory generalized partial linear models. We illustrate the advantages of this approach using a consumer retail banking data set.