臺灣博碩士論文加值系統

In the economic literature, there are many non-nested models and conditional moment restrictions imposed by different economic theories and econometric models. Once these models or restrictions are specified, it is
very important to have specification tests on their validity. This dissertation thus focuses on constructing general model specification tests for non-nested models and conditional moment restrictions. The tests in this dissertation have the following advantages. First, different from the existing literature, the proposed tests are applicable to models with possibly non-smooth moment functions. Second, the tests are consistent and asymptotically pivotal; both characteristics are important issues for specification tests. Therefore, the tests proposed in this dissertation have wide applicability and are easy to implement.


In Chapter 1, we propose a generalized encompassing tests (GET) that extends the existing non-nested tests to models estimated by M-estimation for which the estimating equation may or may not be differentiable. The idea of the GET is to compare the estimating equation with its pseudo-true value, the pseudo-true estimating equation. The limiting distribution of the GET is derived. We present the GET statistics for the models estimated by quantile regression (QR), censored QR, smoothed maximum score, symmetrically trimmed least squares and asymmetrically least squares methods. The asymptotic Cox test (ACT) that extends the Cox tests to M-estimation is also proposed. The ACT and the GET are asymptotically equivalent. The asymptotic variance-covariance matrix of the GET is usually complicated. We also suggest a test based on a centered partial sum process to get an asymptotically pivotal test.


In Chapter 2, we propose a consistent conditional moment test that is applicable regardless of the differentiability of the moment functions. One approach to constructing a consistent conditional moment test is to check infinitely many unconditional moment functions which are necessary and sufficient for the conditional moment restrictions. The test is based on this approach and checks unconditional moment conditions with an indicator weight function indexed by a nuisance parameter. By employing centered sequentially marked empirical processes, the estimation effect of the test is eliminated. The test statistic is thus asymptotically pivotal and converges in distribution to a Kiefer process. The test is applicable to many conditional moment models, such as nonlinear regression models, QR models, likelihood models and conditional parametric models.


It is also known that QR is capable of providing a complete description of the conditional behavior of the dependent variable. The large sample properties of QR estimator have been well studied in the literature. Several efforts have been devoted to the inference of QR for a specific quantile or across quantiles. In addition, the consistent model specification tests for QR for a specific quantile are suggested by some researches. There is no test for the specifications of QR across quantiles. In Chapter 3, a model specification test for QR across quantiles is proposed. By checking infinitely many unconditional moment restrictions that are sufficient and necessary of the the model specifications of QR across quantiles, the proposed test is consistent. The test statistic is asymptotically pivotal and converges in distribution to a Kiefer process. This test does not require estimating the error density function of the model and hence is computationally simpler.

Contents


Abstract. . . . . . . . . . . . . . . . . . . . . . . . .ii


1 The Generalized Encompassing Tests for Non-Nested Models
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . 2
1.2 Non-Nested Tests . . . . . . . . . . . . . . . . . . .5
1.2.1 Non-Nested Models and Tests . . . . . . . . . . . 5
1.2.2 The Encompassing Tests . . . . . . . . . . . . . 6
1.3 The Generalized Encompassing Test . . . . . . . . .. 11
1.3.1 M-estimation . . . . . . . . . . . . . . . . . . 11
1.3.2 The Proposed tests . . . . . . . . . . . . . . . 14
1.3.3 Non-Differentiable Cases . . . . .. . . . . . . .19
1.3.4 Asymptotic Cox test . . . . . . . . . . . . . . .23
1.4 Applications . . . . . . . . . . . . . . . . . . . . 24
1.5 Partial Sum Processes . . . . . . . . . . . . . . . 30
1.6 Monte Carlo Simulations . . . . . . . . . . . . . . .32
1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . 39
Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . 40
Appendix 2 . . . . . . . . . . . . . . . . . . . . . . . 41
References . . . . . . . . . . . . . . . . . . . . . . . 44


2 A Consistent Conditional Moment Test for Possibly Non-Smooth Moment Conditions. . . . . . . . . . . . . . . . .50

2.1 Introduction . . . . . . . . . . . . . . . . . . . . 51
2.2 Conditional Moment Tests . . . . . . . . . . . . . . 54
2.2.1 Conditional Moment Restrictions . . . . . . . . .54
2.2.2 Conditional Moment Tests . . . . . . . . . . . . 57
2.2.3 Bierens’ Tests . . . . . . . . . . . . . . . . .59
2.2.4 Stute’s tests . . . . . . . . . . . . . . . . .61
2.3 Empirical Processes . . . . . . . . . . . . . . . . .62
2.3.1 Brownian Motion and Kiefer Process . . . . . . . 62
2.3.2 Sequentially Marked Empirical Processes . . . . .64
2.3.3 Sequentially Marked Empirical Processes with
Estimators . . . . . . . . . . . . . . . . . . . 67
2.4 A New Consistent Test . . . . . . . . . . . . . . . .69
2.5 Two Examples and Local Alternatives . . . . . . . . .71
2.5.1 Nonlinear Regression Specification . . . . . . . 72
2.5.2 QR specification . . . . . . . . . . . . . . . .73
2.6 Monte Carlo Simulations . . . . . . . . . . . . . . .74
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . 76
Appendix . . . . . . . . . . . . . . . . . . . . . . . . 78
References . . . . . . . . . . . . . . . . . . . . . . . 87


3 A Consistent Test for Joint Quantile Regression Specifications . . . . . . . . . . . . . . . . . . . . . 93

3.1 Introduction . . . . . . . . . . . . . . . . . . . . 94
3.2 Quantile Regression . . . . . . . . . . . . . . . . .96
3.2.1 Estimation . . . . . . . . . . . . . . . . . . . 97
3.2.2 Algorithm . . . . . . . . . . . . . . . . . . . .99
3.2.3 Large Sample Properties . . . . . . . . . . . . 100
3.2.4 Inference and Model Specification Tests for QR .103
3.3 A New Test for QR Processes . . . . . . . . . . . . 107
3.3.1 Model Specifications for QR Process . . . . . . 107
3.3.2 A New Test . . . . . . . . . . . . . . . . . . .109
3.4 Monte Carlo Simulations . . . . . . . . . . . . . . 111
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . .112
Appendix . . . . . . . . . . . . . . . . . . . . . . . .113
References . . . . . . . . . . . . . . . . . . . . . . .118

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CHAPTER 2.

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CHAPTER 3

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