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Articles 1 - 30 of 59
Full-Text Articles in Economics
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
Kernel-based estimators are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the Normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the loss in coverage for conventional confidence intervals. For a …
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
>Kernel-based estimators are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the loss in coverage for conventional confidence intervals. For a …
Dynamic Panel Gmm With Near Unity, Peter C.B. Phillips
Dynamic Panel Gmm With Near Unity, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Limit theory is developed for the dynamic panel GMM estimator in the presence of an autoregressive root near unity. In the unit root case, Anderson-Hsiao lagged variable instruments satisfy orthogonality conditions but are well-known to be irrelevant. For a fixed time series sample size (T) GMM is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross section sample size n → ∞. But when T → ∞, either for fixed n or as n → ∞, GMM is √ T consistent and its limit distribution is a ratio of random variables that converges to twice a standard Cauchy …
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
Kernel-based estimators are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the Normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the loss in coverage for conventional confidence intervals. For a …
Identifying Latent Structures In Panel Data, Liangjun Su, Zhentao Shi, Peter C.B. Phillips
Identifying Latent Structures In Panel Data, Liangjun Su, Zhentao Shi, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized regression techniques. We focus on linear models where the slope parameters are heterogeneous across groups but homogenous within a group and the group membership is unknown. Two approaches are considered — penalized least squares (PLS) for models without endogenous regressors, and penalized GMM (PGMM) for models with endogeneity. In both cases we develop a new variant of Lasso called classifier-Lasso (C-Lasso) that serves to shrink individual coefficients to the unknown group-specific coefficients. C-Lasso achieves simultaneous classification and consistent estimation in a single …
True Limit Distributions Of The Anderson-Hsiao Iv Estimators In Panel Autoregression, Peter C.B. Phillips, Chirok Han
True Limit Distributions Of The Anderson-Hsiao Iv Estimators In Panel Autoregression, Peter C.B. Phillips, Chirok Han
Cowles Foundation Discussion Papers
This note derives the correct limit distributions of the Anderson Hsiao (1981) levels and differences instrumental variable estimators, provides comparisons showing that the levels IV estimator has uniformly smaller variance asymptotically as the cross section ( n ) and time series ( T ) sample sizes tend to infinity, and compares these results with those of the first difference least squares (FDLS) estimator.
Restricted Likelihood Ratio Tests In Predictive Regression, Peter C.B. Phillips, Ye Chen
Restricted Likelihood Ratio Tests In Predictive Regression, Peter C.B. Phillips, Ye Chen
Cowles Foundation Discussion Papers
Chen and Deo (2009a) proposed procedures based on restricted maximum likelihood (REML) for estimation and inference in the context of predictive regression. Their method achieves bias reduction in both estimation and inference which assists in overcoming size distortion in predictive hypothesis testing. This paper provides extensions of the REML approach to more general cases which allow for drift in the predictive regressor and multiple regressors. It is shown that without modification the REML approach is seriously oversized and can have unit rejection probability in the limit under the null when the drift in the regressor is dominant. A limit theory …
A New Hedonic Regression For Real Estate Prices Applied To The Singapore Residential Market, Liang Jiang, Peter C.B. Phillips, Jun Yu
A New Hedonic Regression For Real Estate Prices Applied To The Singapore Residential Market, Liang Jiang, Peter C.B. Phillips, Jun Yu
Cowles Foundation Discussion Papers
This paper develops a new hedonic method for constructing a real estate price index that utilizes all transaction price information that encompasses both single-sale and repeat-sale properties. The new method is less prone to specification errors than standard hedonic methods and uses all available data. Like the Case-Shiller repeat-sales method, the new method has the advantage of being computationally efficient. In an empirical analysis of the methodology, we fit the model to all transaction prices for private residential property holdings in Singapore between Q1 1995 and Q2 2014, covering several periods of major price fluctuation and changes in government macroprudential …
The Double Role Of Ethnic Heterogeneity In Explaining Welfare-State Generosity, Markus Jäntti, Gerald David Jaynes, John E. Roemer
The Double Role Of Ethnic Heterogeneity In Explaining Welfare-State Generosity, Markus Jäntti, Gerald David Jaynes, John E. Roemer
Cowles Foundation Discussion Papers
Based on theoretical models of budget-balanced social insurance and individual choice, we argue that in addition to the well-known empathy mechanism whereby ethnic heterogeneity undermines sentiments of solidarity among a citizenry to reduce welfare generosity, population heterogeneity affects the generosity of a polity’s social insurance programs through another distinct mechanism, political conflict . Ethnic heterogeneity likely intensifies political conflict and reduces welfare generosity because heterogeneity of unemployment risk makes it more difficult to achieve social consensus concerning tax-benefit programs. Utilizing two separate regression analyses covering highly diverse polities, the 50 U.S. states and District of Columbia (CPS data), and 13 …
Informational Robustness And Solution Concepts, Dirk Bergemann, Stephen Morris
Informational Robustness And Solution Concepts, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
Consider the following “informational robustness” question: what can we say about the set of outcomes that may arise in equilibrium of a Bayesian game if players may observe some additional information? This set of outcomes will correspond to a solution concept that is weaker than equilibrium, with the solution concept depending on what restrictions are imposed on the additional information. We describe a unified approach encompassing prior informational robustness results, as well as identifying the solution concept that corresponds to no restrictions on the additional information; this version of rationalizability depends only on the support of players’ beliefs and implies …
Informational Robustness And Solution Concepts, Dirk Bergemann, Stephen Morris
Informational Robustness And Solution Concepts, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We discuss four solution concepts for games with incomplete information. We show how each solution concept can be viewed as encoding informational robustness. For a given type space, we consider expansions of the type space that provide players with additional signals. We distinguish between expansions along two dimensions. First, the signals can either convey payoff relevant information or only payoff irrelevant information. Second, the signals can be generated from a common (prior) distribution or not. We establish the equivalence between Bayes Nash equilibrium behavior under the resulting expansion of the type space and a corresponding more permissive solution concept under …
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
A Simple Adjustment For Bandwidth Snooping, Timothy B. Armstrong, Michal Kolesár
Cowles Foundation Discussion Papers
Kernel-based estimators such as local polynomial estimators in regression discontinuity designs are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals may not have correct coverage, even if the estimator is unbiased. This paper proposes a simple adjustment that gives correct coverage in such situations: replace the normal quantile with a critical value that depends only on the kernel and ratio of the maximum and minimum bandwidths the researcher has entertained. We tabulate these critical values and quantify the …
Wealth Effects On World Private Financial Saving, Ray C. Fair
Wealth Effects On World Private Financial Saving, Ray C. Fair
Cowles Foundation Discussion Papers
This paper shows that about 70 percent of the variance of the yearly change in the world private financial saving rate can be explained by lagged changes in world stock and housing prices for the sample period 1982-2013. The results suggest that increased fluctuations in asset prices since 1995 have led to increased fluctuations in the world private financial saving rate. Wealth effects on private demand appear to be large.
Financial Bubble Implosion, Peter C.B. Phillips, Shu-Ping Shi
Financial Bubble Implosion, Peter C.B. Phillips, Shu-Ping Shi
Cowles Foundation Discussion Papers
Expansion and collapse are two key features of a financial asset bubble. Bubble expansion may be modeled using a mildly explosive process. Bubble implosion may take several different forms depending on the nature of the collapse and therefore requires some flexibility in modeling. This paper develops analytics and studies the performance characteristics of the real time bubble monitoring strategy proposed in Phillips, Shi and Yu (2014b,c, PSY) under alternative forms of bubble implosion that can be represented in terms of mildly integrated processes which capture various return paths to market normalcy. We propose a new reverse sample use of the …
Testing Equality Of Covariance Matrices Via Pythagorean Means, Jin Seo Cho, Peter C.B. Phillips
Testing Equality Of Covariance Matrices Via Pythagorean Means, Jin Seo Cho, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We provide a new test for equality of covariance matrices that leads to a convenient mechanism for testing specification using the information matrix equality. The test relies on a new characterization of equality between two k dimensional positive-definite matrices A and B : the traces of AB –1 and BA –1 are equal to k if and only if A = B . Using this criterion, we introduce a class of omnibus test statistics for equality of covariance matrices and examine their null, local, and global approximations under some mild regularity conditions. Monte Carlo experiments are conducted to explore the …
Optimal Uniform Convergence Rates And Asymptotic Normality For Series Estimators Under Weak Dependence And Weak Conditions, Xiaohong Chen, Timothy M. Christensen
Optimal Uniform Convergence Rates And Asymptotic Normality For Series Estimators Under Weak Dependence And Weak Conditions, Xiaohong Chen, Timothy M. Christensen
Cowles Foundation Discussion Papers
We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e., sup-norm) convergence rate ( n /log n ) - p /(2p+ d ) of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate is achieved even for heavy-tailed martingale difference errors with finite (2 + ( d/p ))th absolute moment for d/p < 2. We also establish the asymptotic normality of t statistics for possibly nonlinear, irregular functionals of the conditional mean function under weak conditions. The results are proved by deriving a new exponential inequality for sums of weakly dependent random matrices, which is of independent interest.
Asymptotic Size Of Kleibergen's Lm And Conditional Lr Tests For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Asymptotic Size Of Kleibergen's Lm And Conditional Lr Tests For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
An influential paper by Kleibergen (2005) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures has not been determined in the literature. This paper does so. This paper shows that the LM test has correct asymptotic size and is asymptotically similar for a suitably chosen parameter space of null distributions. It shows that the CLR tests also have these properties when the dimension p …
A Multivariate Stochastic Unit Root Model With An Application To Derivative Pricing, Offer Lieberman, Peter C.B. Phillips
A Multivariate Stochastic Unit Root Model With An Application To Derivative Pricing, Offer Lieberman, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (SUR) models to a multivariate case including a comprehensive asymptotic theory for estimation of the model’s parameters. The extensions are useful because they lead to a generalization of the Black-Scholes formula for derivative pricing. In place of the standard assumption that the price process follows a geometric Brownian motion, we derive a new form of the Black-Scholes equation that allows for a multivariate time varying coefficient element in the price equation. The corresponding formula for the value of a European-type call option is obtained and shown …
Threshold Regression With Endogeneity, Ping Yu, Peter C.B. Phillips
Threshold Regression With Endogeneity, Ping Yu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies estimation and specification testing in threshold regression with endogeneity. Three key results differ from those in regular models. First, both the threshold point and the threshold effect parameters are shown to be identified without the need for instrumentation. Second, in partially linear threshold models, both parametric and nonparametric components rely on the same data, which prima facie suggests identification failure. But, as shown here, the discontinuity structure of the threshold itself supplies identifying information for the parametric coefficients without the need for extra randomness in the regressors. Third, instrumentation plays different roles in the estimation of the …
Weak Convergence To Stochastic Integrals For Econometric Applications, Hanying Liang, Peter C.B. Phillips, Hanchao Wang, Qiying Wang
Weak Convergence To Stochastic Integrals For Econometric Applications, Hanying Liang, Peter C.B. Phillips, Hanchao Wang, Qiying Wang
Cowles Foundation Discussion Papers
Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on function space weak convergence. In establishing weak convergence of sample covariances to stochastic integrals, the literature commonly uses martingale and semimartingale structures. While these structures have wide relevance, many applications in econometrics involve a cointegration framework where endogeneity and nonlinearity play a major role and lead to complications in the limit theory. This paper explores weak convergence limit theory to stochastic integral functionals in such settings. We use a novel decomposition of sample covariances of functions of I(1) and I(0) …
A Note On Minimax Testing And Confidence Intervals In Moment Inequality Models, Timothy B. Armstrong
A Note On Minimax Testing And Confidence Intervals In Moment Inequality Models, Timothy B. Armstrong
Cowles Foundation Discussion Papers
This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low dimensional parameter, which leads naturally to a definition of “distance” that, in full generality, would be arbitrary in minimax testing problems. This definition of distance is justified by the fact that it leads to a duality between minimaxity of confidence intervals and tests, which does not hold for other definitions of distance. Thus, the use of moment inequalities for inference in a low …
The Early Impact Of The Affordable Care Act State-By-State, Amanda E. Kowalski
The Early Impact Of The Affordable Care Act State-By-State, Amanda E. Kowalski
Cowles Foundation Discussion Papers
I examine the impact of state policy decisions on the early impact of the ACA using data through the first half of 2014. I focus on the individual health insurance market, which includes plans purchased through exchanges as well as plans purchased directly from insurers. In this market, at least 13.2 million people were covered in the second quarter of 2014, representing an increase of at least 4.2 million beyond pre-ACA state-level trends. I use data on coverage, premiums, and costs and a model developed by Hackmann, Kolstad, and Kowalski (2013) to calculate changes in selection and markups, which allow …
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
Cowles Foundation Discussion Papers
This paper derives asymptotic power functions for Cramer-von Mises (CvM) style tests for conditional moment inequality models in the set identified case. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for tests based on kernel estimates, kernel bandwidth. The results show that KS tests are preferred to CvM tests, and that a truncated variance weighting is preferred to bounded weightings under a minimax criterion, and for a class of alternatives that arises naturally in these models. The results also provide insight into how moment selection and …
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
Cowles Foundation Discussion Papers
This paper derives asymptotic approximations to the power of Cramer-von Mises (CvM) style tests for inference on a finite dimensional parameter defined by conditional moment inequalities in the case where the parameter is set identified. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for tests based on kernel estimates, kernel bandwidth. The results show that, in the setting considered here, KS tests are preferred to CvM tests, and that a truncated variance weighting is preferred to bounded weightings.
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
On The Choice Of Test Statistic For Conditional Moment Inequalities, Timothy B. Armstrong
Cowles Foundation Discussion Papers
This paper derives asymptotic power functions for Cramer-von Mises (CvM) style tests for inference on a finite dimensional parameter defined by conditional moment inequalities in the case where the parameter is set identified. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for tests based on kernel estimates, kernel bandwidth. The results show that KS tests are preferred to CvM tests, and that a truncated variance weighting is preferred to bounded weightings under a minimax criterion, and for a class of alternatives that arises naturally in these …
Economics: Between Prediction And Criticism, Itzhak Gilboa, Andrew Postlewaite, Larry Samuelson, David Schmeidler
Economics: Between Prediction And Criticism, Itzhak Gilboa, Andrew Postlewaite, Larry Samuelson, David Schmeidler
Cowles Foundation Discussion Papers
We suggest that one way in which economic analysis is useful is by offering a critique of reasoning. According to this view, economic theory may be useful not only by providing predictions, but also by pointing out weaknesses of arguments. It is argued that, when a theory requires a non-trivial act of interpretation, its roles in producing predictions and offering critiques vary in a substantial way. We offer a formal model in which these different roles can be captured.
Approximate Solutions Of The Walrasian Equilibrium Inequalities With Bounded Marginal Utilities Of Income, Donald J. Brown
Approximate Solutions Of The Walrasian Equilibrium Inequalities With Bounded Marginal Utilities Of Income, Donald J. Brown
Cowles Foundation Discussion Papers
Recently Cherchye et al. (2011) reformulated the Walrasian equilibrium inequalities, introduced by Brown and Matzkin (1996), as an integer programming problem and proved that solving the Walrasian equilibrium inequalities is NP-hard. Brown and Shannon (2002) derived an equivalent system of equilibrium inequalities, i.e., the dual Walrasian equilibrium inequalities. That is, the Walrasian equilibrium inequalities are solvable iff the dual Walrasian equilibrium inequalities are solvable. We show that solving the dual Walrasian equilibrium inequalities is equivalent to solving a NP-hard minimization problem. Approximation theorems are polynomial time algorithms for computing approximate solutions of NP-hard minimization problems. The primary contribution of this …
Adaptive Testing On A Regression Function At A Point, Timothy B. Armstrong
Adaptive Testing On A Regression Function At A Point, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Hölder classes, up to a log log n term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the boundary, and the proportion of true null hypotheses in a multiple testing problem.
Strongly Symmetric Equilibria In Bandit Games, Johannes Hörner, Nicolas Klein, Sven Rady
Strongly Symmetric Equilibria In Bandit Games, Johannes Hörner, Nicolas Klein, Sven Rady
Cowles Foundation Discussion Papers
This paper studies strongly symmetric equilibria (SSE) in continuous-time games of strategic experimentation with Poisson bandits. SSE payoffs can be studied via two functional equations similar to the HJB equation used for Markov equilibria. This is valuable for three reasons. First, these equations retain the tractability of Markov equilibrium, while allowing for punishments and rewards: the best and worst equilibrium payoff are explicitly solved for. Second, they capture behavior of the discrete-time game: as the period length goes to zero in the discretized game, the SSE payoff set converges to their solution. Third, they encompass a large payoff set: there …
Approximate Solutions Of Walrasian Equilibrium Inequalities With Bounded Marginal Utilities Of Income, Donald J. Brown
Approximate Solutions Of Walrasian Equilibrium Inequalities With Bounded Marginal Utilities Of Income, Donald J. Brown
Cowles Foundation Discussion Papers
Recently Cherchye et al. (2011) reformulated the Walrasian equilibrium inequalities, introduced by Brown and Matzkin (1996), as an integer programming problem and proved that solving the Walrasian equilibrium inequalities is NP-hard. Brown and Shannon (2002) derived an equivalent system of equilibrium inequalities, i.e., the dual Walrasian equilibrium inequalities. That is, the Walrasian equilibrium inequalities are solvable iff the dual Walrasian equilibrium inequalities are solvable. We show that solving the dual Walrsian equilibrium inequalities is equivalent to solving a NP-hard minimization problem. Approximation theorems are polynomial time algorithms for computing approximate solutions of NP-hard minimization problems. The primary contribution of this …