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- Identification (13)
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Articles 61 - 89 of 89
Full-Text Articles in Social and Behavioral Sciences
The Politic 2011 Spring, The Politic, Inc.
Local Identification Of Nonparametric And Semiparametric Models, Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney Newey
Local Identification Of Nonparametric And Semiparametric Models, Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney Newey
Cowles Foundation Discussion Papers
In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true value that are sufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models, single-index IV models, and semiparametric consumption-based asset pricing models.
Robustness Of Bootstrap In Instrumental Variable Regression, Lorenzo Camponovo, Taisuke Otsu
Robustness Of Bootstrap In Instrumental Variable Regression, Lorenzo Camponovo, Taisuke Otsu
Cowles Foundation Discussion Papers
This paper studies robustness of bootstrap inference methods for instrumental variable regression models. In particular, we compare the uniform weight and implied probability bootstrap approximations for parameter hypothesis test statistics by applying the breakdown point theory, which focuses on behaviors of the bootstrap quantiles when outliers take arbitrarily large values. The implied probabilities are derived from an information theoretic projection from the empirical distribution to a set of distributions satisfying orthogonality conditions for instruments. Our breakdown point analysis considers separately the effects of outliers in dependent variables, endogenous regressors, and instruments, and clarifies the situations where the implied probability bootstrap …
Second-Order Refinement Of Empirical Likelihood For Testing Overidentifying Restrictions, Yukitoshi Matsushita, Taisuke Otsu
Second-Order Refinement Of Empirical Likelihood For Testing Overidentifying Restrictions, Yukitoshi Matsushita, Taisuke Otsu
Cowles Foundation Discussion Papers
This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order refinement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007) who considered parameter hypothesis testing for overidentified models. In simulation studies we find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.
Continuous Workout Mortgages, Robert J. Shiller, Rafal M. Wojakowski, M. Shahid Ebrahim, Mark B. Shackleton
Continuous Workout Mortgages, Robert J. Shiller, Rafal M. Wojakowski, M. Shahid Ebrahim, Mark B. Shackleton
Cowles Foundation Discussion Papers
This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments by employing a market-observable variable such as the house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae for mortgage payment and mortgage balance of a repayment CWM; (c) a closed form formula for the actuarially fair mortgage rate of an interest-only CWM. For repayment CWMs we extend our analysis to include two negotiable parameters: adjustable “workout proportion” and adjustable “workout threshold.” These results are of importance as they not only help …
Empirical Likelihood For Nonparametric Additive Models, Taisuke Otsu
Empirical Likelihood For Nonparametric Additive Models, Taisuke Otsu
Cowles Foundation Discussion Papers
Nonparametric additive modeling is a fundamental tool for statistical data analysis which allows flexible functional forms for conditional mean or quantile functions but avoids the curse of dimensionality for fully nonparametric methods induced by high-dimensional covariates. This paper proposes empirical likelihood-based inference methods for unknown functions in three types of nonparametric additive models: (i) additive mean regression with the identity link function, (ii) generalized additive mean regression with a known non-identity link function, and (iii) additive quantile regression. The proposed empirical likelihood ratio statistics for the unknown functions are asymptotically pivotal and converge to chi-square distributions, and their associated confidence …
Breakdown Point Theory For Implied Probability Bootstrap, Lorenzo Camponovo, Taisuke Otsu
Breakdown Point Theory For Implied Probability Bootstrap, Lorenzo Camponovo, Taisuke Otsu
Cowles Foundation Discussion Papers
This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analyzing behaviors of the bootstrap quantiles when outliers take arbitrarily large values, and derive the breakdown points for those bootstrap quantiles. The breakdown point properties characterize the situation where the implied probability bootstrap is more robust than the uniform weight bootstrap against outliers. Simulation studies illustrate our theoretical findings.
Local Identification Of Nonparametric And Semiparametric Models, Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney Newey
Local Identification Of Nonparametric And Semiparametric Models, Xiaohong Chen, Victor Chernozhukov, Sokbae Lee, Whitney Newey
Cowles Foundation Discussion Papers
In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that there are corresponding sufficient conditions for nonparametric models. A nonparametric rank condition and differentiability of the moment conditions with respect to a certain norm imply local identification. It turns out these conditions are slightly stronger than needed and are hard to check, so we provide weaker and more primitive conditions. We extend the results to semiparametric models. We illustrate the sufficient conditions with endogenous quantile and single index examples. We …
Quantile Regression With Censoring And Endogeneity, Victor Chernozhukov, Iván Fernández-Val, Amanda E. Kowalski
Quantile Regression With Censoring And Endogeneity, Victor Chernozhukov, Iván Fernández-Val, Amanda E. Kowalski
Cowles Foundation Discussion Papers
In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control …
Cost Innovation: Schumpeter And Equilibrium. Part 1. Robinson Crusoe, Martin Shubik, William D. Sudderth
Cost Innovation: Schumpeter And Equilibrium. Part 1. Robinson Crusoe, Martin Shubik, William D. Sudderth
Cowles Foundation Discussion Papers
Modifying a parallel dynamic programming approach to a simple deterministic economy, we consider the effect of an innovation in the means of production. The success of the innovation is assumed to depend on the availability of financing, locus of financial control, the amount of resources invested, and on a random event. The relationship between money and physical assets is critical. In this first part stress is laid on the innovation behavior of Robinson Crusoe in a premonetary economy, then on his actions in a monetary economy in partial equilibrium. Part 2 considers the closed monetary economy with several differentiated agents.
Identification In A Class Of Nonparametric Simultaneous Equations Models, Steven T. Berry, Philip A. Haile
Identification In A Class Of Nonparametric Simultaneous Equations Models, Steven T. Berry, Philip A. Haile
Cowles Foundation Discussion Papers
We consider identification in a class of nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine standard exclusion restrictions with a requirement that each structural error enter through a “residual index” function. We provide constructive proofs of identification under several sets of conditions, demonstrating tradeoffs between restrictions on the support of the instruments, shape restrictions on the joint distribution of the structural errors, and restrictions on the form of the residual index function.
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces two new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) tests and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For two of the three tests, all that is required is that the moment functions and their derivatives have 2 + γ bounded moments for some γ > 0 in i.i.d. scenarios. In stationary strong mixing time series cases, the same condition suffices, but the magnitude of …
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces a new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) test and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2+γ bounded moments for some γ>0. No conditions are placed on the expected Jacobian of the moment functions, on the …
A Simple Test For Identification In Gmm Under Conditional Moment Restrictions, Francesco Bravo, Juan Carlos Escanciano, Taisuke Otsu
A Simple Test For Identification In Gmm Under Conditional Moment Restrictions, Francesco Bravo, Juan Carlos Escanciano, Taisuke Otsu
Cowles Foundation Discussion Papers
This paper proposes a simple, fairly general, test for global identification of unconditional moment restrictions implied from point-identified conditional moment restrictions. The test is based on the Hausdorff distance between an estimator that is consistent even under global identification failure of the unconditional moment restrictions, and an estimator of the identified set of the unconditional moment restrictions. The proposed test has a chi-squared limiting distribution and is also able to detect weak identification alternatives. Some Monte Carlo experiments show that the proposed test has competitive finite sample properties already for moderate sample sizes.
Identification In A Class Of Nonparametric Simultaneous Equations Models, Steven T. Berry, Philip A. Haile
Identification In A Class Of Nonparametric Simultaneous Equations Models, Steven T. Berry, Philip A. Haile
Cowles Foundation Discussion Papers
We consider identification in a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine standard exclusion restrictions with a requirement that each structural error enter through a “residual index” function. We provide constructive proofs of identification under several sets of conditions, demonstrating tradeoffs between restrictions on the support of the instruments, restrictions on the joint distribution of the structural errors, and restrictions on the form of the residual index function.
Identification In A Class Of Nonparametric Simultaneous Equations Models, Steven T. Berry, Philip A. Haile
Identification In A Class Of Nonparametric Simultaneous Equations Models, Steven T. Berry, Philip A. Haile
Cowles Foundation Discussion Papers
We consider identification in a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine standard exclusion restrictions with a requirement that each structural error enter through a “residual index” function. We provide constructive proofs of identification under several sets of conditions, demonstrating some of the available tradeoffs between conditions on the support of the instruments, restrictions on the joint distribution of the structural errors, and restrictions on the form of the residual index function.
Economists As Worldly Philosophers, Robert J. Shiller, Virginia M. Shiller
Economists As Worldly Philosophers, Robert J. Shiller, Virginia M. Shiller
Cowles Foundation Discussion Papers
While leading figures in the early history of economics conceived of it as inseparable from philosophy and other humanities, there has been movement, especially in recent decades, towards its becoming an essentially technical field with narrowly specialized areas of inquiry. Certainly, specialization has allowed for great progress in economic science. However, recent events surrounding the financial crisis support the arguments of some that economics needs to develop forums for interdisciplinary interaction and to aspire to broader vision.
Hodges-Lehmann Optimality For Testing Moment Conditions, Ivan Canay, Taisuke Otsu
Hodges-Lehmann Optimality For Testing Moment Conditions, Ivan Canay, Taisuke Otsu
Cowles Foundation Discussion Papers
This paper studies the Hodges and Lehmann (1956) optimality of tests in a general setup. The tests are compared by the exponential rates of growth to one of the power functions evaluated at a fixed alternative while keeping the asymptotic sizes bounded by some constant. We present two sets of sufficient conditions for a test to be Hodges-Lehmann optimal. These new conditions extend the scope of the Hodges-Lehmann optimality analysis to setups that cannot be covered by other conditions in the literature. The general result is illustrated by our applications of interest: testing for moment conditions and overidentifying restrictions. In …
Wealth Effects Revisited, 1978-2009, Karl E. Case, John M. Quigley, Robert J. Shiller
Wealth Effects Revisited, 1978-2009, Karl E. Case, John M. Quigley, Robert J. Shiller
Cowles Foundation Discussion Papers
We re-examine the link between changes in housing wealth, financial wealth, and consumer spending. We extend a panel of U.S. states observed quarterly during the seventeen-year period, 1982 through 1999, to the thirty-one year period, 1978 through 2009. Using techniques reported previously, we impute the aggregate value of owner-occupied housing, the value of financial assets, and measures of aggregate consumption for each of the geographic units over time. We estimate regression models in levels, first differences and in error-correction form, relating per capita consumption to per capita income and wealth. We find a statistically significant and rather large effect of …
Moderate Deviations Of Generalized Method Of Moments And Empirical Likelihood Estimators, Taisuke Otsu
Moderate Deviations Of Generalized Method Of Moments And Empirical Likelihood Estimators, Taisuke Otsu
Cowles Foundation Discussion Papers
This paper studies moderate deviation behaviors of the generalized method of moments and generalized empirical likelihood estimators for generalized estimating equations, where the number of equations can be larger than the number of unknown parameters. We consider two cases for the data generating probability measure: the model assumption and local contaminations or deviations from the model assumption. For both cases, we characterize the first-order terms of the moderate deviation error probabilities of these estimators. Our moderate deviation analysis complements the existing literature of the local asymptotic analysis and misspecification analysis for estimating equations, and is useful to evaluate power and …
Large Deviations Of Generalized Method Of Moments And Empirical Likelihood Estimators, Taisuke Otsu
Large Deviations Of Generalized Method Of Moments And Empirical Likelihood Estimators, Taisuke Otsu
Cowles Foundation Discussion Papers
This paper studies large deviation properties of the generalized method of moments and generalized empirical likelihood estimators for moment restriction models. We consider two cases for the data generating probability measure: the model assumption and local deviations from the model assumption. For both cases, we derive conditions where these estimators have exponentially small error probabilities for point estimation.
Yul Annual Report; 2010-2011, Yale University Library
Yul Annual Report; 2010-2011, Yale University Library
Yale University Library Annual Reports
No abstract provided.
First Difference Mle And Dynamic Panel Estimation, Chirok Han, Peter C.B. Phillips
First Difference Mle And Dynamic Panel Estimation, Chirok Han, Peter C.B. Phillips
Cowles Foundation Discussion Papers
First difference maximum likelihood (FDML) seems an attractive estimation methodology in dynamic panel data modeling because differencing eliminates fixed effects and, in the case of a unit root, differencing transforms the data to stationarity, thereby addressing both incidental parameter problems and the possible effects of nonstationarity. This paper draws attention to certain pathologies that arise in the use of FDML that have gone unnoticed in the literature and that affect both finite sample peformance and asymptotics. FDML uses the Gaussian likelihood function for first differenced data and parameter estimation is based on the whole domain over which the log-likelihood is …
Specification Testing For Nonlinear Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Specification Testing For Nonlinear Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We provide a limit theory for a general class of kernel smoothed U statistics that may be used for specification testing in time series regression with nonstationary data. The framework allows for linear and nonlinear models of cointegration and regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of functions involving nonstationary time series that converges to the intersection local time process. This result is of independent interest and useful …
A World Macro Saving Fact And An Explanation, Ray C. Fair
A World Macro Saving Fact And An Explanation, Ray C. Fair
Cowles Foundation Discussion Papers
The world macro saving fact concerns the total financial saving of the world’s private sector divided by world GDP. Relative to changes before 1994, there was a huge fall in this ratio between 1995 and 2000, a huge increase between 2000 and 2003, a huge fall between 2003 and 2006, and a huge increase between 2006 and 2009. This fact is documented in this paper. The paper also shows that the fluctuations in this ratio are highly correlated with fluctuations in world stock and housing prices. It thus appears that much of the variation in the world private saving rate …
Inconsistent Var Regression With Common Explosive Roots, Peter C.B. Phillips, Tassos Magdalinos
Inconsistent Var Regression With Common Explosive Roots, Peter C.B. Phillips, Tassos Magdalinos
Cowles Foundation Discussion Papers
Nielsen (2009) shows that vector autoregression is inconsistent when there are common explosive roots with geometric multiplicity greater than unity. This paper discusses that result, provides a co-explosive system extension and an illustrative example that helps to explain the finding, gives a consistent instrumental variable procedure, and reports some simulations. Some exact limit distribution theory is derived and a useful new reverse martingale central limit theorem is proved.
Bias In Estimating Multivariate And Univariate Diffusions, Xiaohu Wang, Peter C.B. Phillips, Jun Yu
Bias In Estimating Multivariate And Univariate Diffusions, Xiaohu Wang, Peter C.B. Phillips, Jun Yu
Cowles Foundation Discussion Papers
Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter. Explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and …
Folklore Theorems, Implicit Maps And New Unit Root Limit Theory, Peter C.B. Phillips
Folklore Theorems, Implicit Maps And New Unit Root Limit Theory, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The delta method and continuous mapping theorem are among the most extensively used tools in asymptotic derivations in econometrics. Extensions of these methods are provided for sequences of functions, which are commonly encountered in applications, and where the usual methods sometimes fail. Important examples of failure arise in the use of simulation based estimation methods such as indirect inference. The paper explores the application of these methods to the indirect inference estimator (IIE) in first order autoregressive estimation. The IIE uses a binding function that is sample size dependent. Its limit theory relies on a sequence-based delta method in the …
Efficient Search By Committee, Dirk Bergemann, Juuso Välimäki
Efficient Search By Committee, Dirk Bergemann, Juuso Välimäki
Cowles Foundation Discussion Papers
This note constructs an efficient mechanism for finding the best candidate for a committee from a sequence of potential candidates. Committee members have independent private values information about the quality of the candidate. The mechanism selects the best candidate according to the standard utilitarian welfare criterion. Furthermore, the mechanism can be modified to have a balanced budget.