Semi‐linear mode regression

In this paper, I estimate the slope coefficient parameter β of the regression model , where the error term e satisfies almost surely and ? is an unknown function. It is possible to achieve ‐consistency for estimating β when ? is known up to a finite‐dimensional parameter. I present a consistent and asymptotically normal estimator for β, which does not require prescribing a functional form for ?, let alone a parametrization. Furthermore, the rate of convergence in probability is equal to at least , and approaches if a certain density is sufficiently differentiable around the origin. This method allows both heteroscedasticity and skewness of the distribution of . Moreover, under suitable conditions, the proposed estimator exhibits an oracle property, namely the rate of convergence is identical to that when ? is known. A Monte Carlo study is conducted, and reveals the benefits of this estimator with fat‐tailed and/or skewed data. Moreover, I apply the proposed estimator to measure the effect of primogeniture on economic achievement.     

Model‐selection tests for conditional moment restriction models

We propose a Vuong‐type model‐selection test for models defined by conditional moment restrictions. The moment restrictions that define the models can be standard equality restrictions that point‐identify the model parameters, or moment equality or inequality restrictions that partially identify the model parameters. The test uses a new average generalized empirical likelihood criterion function designed to incorporate full restriction of the conditional model. We also introduce a new adjustment to the test statistic that makes it asymptotically pivotal whether the candidate models are nested or non‐nested. The test uses simple standard normal critical values and is shown to be asymptotically similar, to be consistent against all fixed alternatives, and to have non‐trivial power against ‐local alternatives. Monte Carlo simulations demonstrate that the finite sample performance of the test is in accordance with the theoretical prediction.     

Nonparametric tests of conditional treatment effects with an application to single‐sex schooling on academic achievements

We develop a general class of nonparametric tests for treatment effects conditional on covariates. We consider a wide spectrum of null hypotheses regarding conditional treatment effects, including the following: (a) the null hypothesis of the conditional stochastic dominance between treatment and control groups; (b) the null hypothesis that the conditional average treatment effect is nonpositive for each value of covariates; (c) the null hypothesis of no distributional (or average) treatment effect conditional on covariates. The test statistics are based on L₁‐type functionals of uniformly consistent nonparametric kernel estimators of conditional expectations that characterize the null hypotheses. We show that our tests using the standard normal critical values have asymptotically correct size. We also show that the proposed nonparametric tests are consistent against general fixed alternatives and have non‐negligible powers against some local alternatives to the null hypothesis with inequality constraints and local alternatives to the null hypothesis with equality constraints, where h is a bandwidth, n is the sample size and d is the dimension of continuous covariates. We illustrate the usefulness of our tests by applying them to the effect of single‐sex schooling on academic achievements using Korean data.     

Identification and estimation of partially linear censored regression models with unknown heteroscedasticity

In this paper, we introduce a new identification and estimation strategy for partially linear regression models with a general form of unknown heteroscedasticity, that is, and , where ε is independent of and the functional forms of both and are left unspecified. We show that in such a model, β₀ and can be exactly identified while can be identified up to scale as long as permits sufficient nonlinearity in X. A two‐stage estimation procedure motivated by the identification strategy is described and its large sample properties are formally established. Moreover, our strategy is flexible enough to allow for both fixed and random censoring in the dependent variable. Simulation results show that the proposed estimator performs reasonably well in finite samples.     

Least‐squares estimation of GARCH(1,1) models with heavy‐tailed errors

GARCH(1,1) models are widely used for modelling processes with time‐varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log‐transform‐based least‐squares approach to the estimation of GARCH(1,1) models. Within this approach, the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data, we show that knowledge of the tuning constant is not crucial for Value at Risk prediction. However, this does not apply to many other applications where correct identification of the volatility scale is required. In order to overcome this difficulty, we propose two alternative two‐stage least‐squares estimators and we derive their asymptotic properties under very mild moment conditions for the errors. In particular, we establish the consistency and asymptotic normality at the standard convergence rate of for our estimators. Their finite sample properties are assessed by means of an extensive simulation study.     

Heteroscedasticity‐robust Cp model averaging

This paper proposes a new model‐averaging method, called the hetero‐scedasticity–robust (HR) method, for linear regression models with heteroscedastic errors. We provide a feasible form of the Mallows’ ‐like criterion for choosing the weight vector for averaging. Under some regularity conditions, we show that the HR method has asymptotic optimality. The simulation results show that our method works well and performs better than alternative methods in finite samples when the number of candidate models is large and/or the population coefficient of determination is not small.     

Novel panel cointegration tests emending for cross‐section dependence with N fixed

In this paper, we propose new cointegration tests for single equations and panels. In both cases, the asymptotic distributions of the tests, which are derived with N fixed and , are shown to be standard normals. The effects of serial correlation and cross‐sectional dependence are mopped out via long‐run variances. An effective bias correction is derived, which is shown to work well in finite samples, particularly when N is smaller than T. Our panel tests are robust to possible cointegration across units.     

Double/debiased machine learning for treatment and structural parameters

We revisit the classic semi‐parametric problem of inference on a low‐dimensional parameter θ₀ in the presence of high‐dimensional nuisance parameters η₀. We depart from the classical setting by allowing for η₀ to be so high‐dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate η₀, we consider the use of statistical or machine learning (ML) methods, which are particularly well suited to estimation in modern, very high‐dimensional cases. ML methods perform well by employing regularization to reduce variance and trading off regularization bias with overfitting in practice. However, both regularization bias and overfitting in estimating η₀ cause a heavy bias in estimators of θ₀ that are obtained by naively plugging ML estimators of η₀ into estimating equations for θ₀. This bias results in the naive estimator failing to be consistent, where N is the sample size. We show that the impact of regularization bias and overfitting on estimation of the parameter of interest θ₀ can be removed by using two simple, yet critical, ingredients: (1) using Neyman‐orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters to estimate θ₀; (2) making use of cross‐fitting, which provides an efficient form of data‐splitting. We call the resulting set of methods double or debiased ML (DML). We verify that DML delivers point estimators that concentrate in an ‐neighbourhood of the true parameter values and are approximately unbiased and normally distributed, which allows construction of valid confidence statements. The generic statistical theory of DML is elementary and simultaneously relies on only weak theoretical requirements, which will admit the use of a broad array of modern ML methods for estimating the nuisance parameters, such as random forests, lasso, ridge, deep neural nets, boosted trees, and various hybrids and ensembles of these methods. We illustrate the general theory by applying it to provide theoretical properties of the following: DML applied to learn the main regression parameter in a partially linear regression model; DML applied to learn the coefficient on an endogenous variable in a partially linear instrumental variables model; DML applied to learn the average treatment effect and the average treatment effect on the treated under unconfoundedness; DML applied to learn the local average treatment effect in an instrumental variables setting. In addition to these theoretical applications, we also illustrate the use of DML in three empirical examples.     

Identification and estimation of heteroscedastic binary choice models with endogenous dummy regressors

In this paper, we consider the semiparametric identification and estimation of a heteroscedastic binary choice model with endogenous dummy regressors and no parametric restriction on the distribution of the error term. Our approach addresses various drawbacks associated with previous estimators proposed for this model. It allows for: general multiplicative heteroscedasticity in both selection and outcome equations; a nonparametric selection mechanism; and multiple discrete endogenous regressors. The resulting three‐stage estimator is shown to be asymptotically normal, with a convergence rate that can be arbitrarily close to if certain smoothness assumptions are satisfied. Simulation results show that our estimator performs reasonably well in finite samples. Our approach is then used to study the intergenerational transmission of smoking habits in British households.     

Estimating and testing multiple structural changes in linear models using band spectral regressions

We provide methods for estimating and testing multiple structural changes occurring at unknown dates in linear models using band spectral regressions. We consider changes over time within some frequency bands, permitting the coefficients to be different across frequency bands. Using standard assumptions, we show that the limit distributions obtained are similar to those in the time domain counterpart. We show that when the coefficients change only within some frequency band, we have increased efficiency of the estimates and power of the tests. We also discuss a very useful application related to contexts in which the data are contaminated by some low‐frequency process (e.g. level shifts or trends) and that the researcher is interested in whether the original non‐contaminated model is stable. All that is needed to obtain estimates of the break dates and tests for structural changes that are not affected by such low‐frequency contaminations is to truncate a low‐frequency band that shrinks to zero at rate . Simulations show that the tests have good sizes for a wide range of truncations so that the method is quite robust. We analyse the stability of the relation between hours worked and productivity. When applying structural change tests in the time domain, we document strong evidence of instabilities. When excluding a few low frequencies, none of the structural change tests are significant. Hence, the results provide evidence to the effect that the relation between hours worked and productivity is stable over any spectral band that excludes the lowest frequencies, in particular it is stable over the business‐cycle band.     

Consistent tests for conditional treatment effects

We construct tests for the null hypothesis that the conditional average treatment effect is non‐negative, conditional on every possible value of a subset of covariates. Testing such a null hypothesis can provide more information than the sign of the average treatment effects parameter. The null hypothesis can be characterized as infinitely many of unconditional moment inequalities. A Kolmogorov–Smirnov test is constructed based on these unconditional moment inequalities, and a simulated critical value is proposed. It is shown that our test can control the size uniformly over a broad set of data‐generating processes asymptotically, that it is consistent against fixed alternatives and that it is unbiased against some local alternatives. Several extensions of our test are also considered and we apply our tests to examine the effect of a job‐training programme on real earnings.     

Estimation of graphical models using the norm

Gaussian graphical models are recently used in economics to obtain networks of dependence among agents. A widely used estimator is the graphical least absolute shrinkage and selection operator (GLASSO), which amounts to a maximum likelihood estimation regularized using the matrix norm on the precision matrix Ω. The norm is a LASSO penalty that controls for sparsity, or the number of zeros in Ω. We propose a new estimator called structured GLASSO (SGLASSO) that uses the mixed norm. The use of the penalty controls for the structure of the sparsity in Ω. We show that when the network size is fixed, SGLASSO is asymptotically equivalent to an infeasible GLASSO problem which prioritizes the sparsity‐recovery of high‐degree nodes. Monte Carlo simulation shows that SGLASSO outperforms GLASSO in terms of estimating the overall precision matrix and in terms of estimating the structure of the graphical model. In an empirical illustration using a classic firms' investment data set, we obtain a network of firms' dependence that exhibits the core–periphery structure, with General Motors, General Electric and US Steel forming the core group of firms.     

Estimating a nonparametric triangular model with binary endogenous regressors

We consider identification and estimation in a nonparametric triangular system with a binary endogenous regressor and nonseparable errors. For identification, we take a control function approach utilizing the Dynkin system idea. We articulate various trade‐offs, including continuity, monotonicity and differentiability. For estimation, we use the idea of local instruments under smoothness assumptions, but we do not assume additive separability in latent variables. Our estimator uses nonparametric kernel regression techniques and its statistical properties are derived using the functional delta method. We establish that it is ‐consistent and has a limiting normal distribution. We apply the method to estimate the returns on a college education. Unlike existing work, we find that returns on a college education are consistently positive. Moreover, the returns curves we estimate are inconsistent with the shape restrictions imposed in those papers.     

Estimation of discrete games with correlated types

In this paper, I focus on the identification and estimation of static games of incomplete information with correlated types. Instead of making the independence assumption on players' types in order to simplify the equilibrium set, I propose an approach that allows me to identify subsets of the space of covariates (i.e. publicly observed state variables in payoff functions), for which there exists a unique pure strategy Bayesian Nash equilibrium (BNE) and the equilibrium strategies are monotonic functions. Moreover, I characterize the monotonic pure strategy BNE in a simple manner and propose an estimation procedure that uses observations only from the subset of the covariate space where the game admits a unique monotonic pure strategy BNE. Furthermore, I show that the proposed estimator is ‐consistent and has a limiting normal distribution.     

Two‐stage estimation of limited dependent variable models with errors‐in‐variables

Summary This paper deals with censored or truncated regression models where the explanatory variables are measured with additive errors. We propose a two‐stage estimation procedure that combines the instrumental variable method and the minimum distance estimation. This approach produces consistent and asymptotically normally distributed estimators for model parameters. When the predictor and instrumental variables are normally distributed, we also propose a maximum likelihood based estimator and a two‐stage moment estimator. Simulation studies show that all proposed estimators perform satisfactorily for relatively small samples and relatively high degree of censoring. In addition, the maximum likelihood based estimators are fairly robust against non‐normal and /or heteroskedastic random errors in our simulations. The method can be generalized to panel data models.     

Non‐parametric regression under location shifts

Summary Recent work by Wang and Phillips (2009b, 2011) has shown that ill‐posed inverse problems do not arise in non‐stationary non‐parametric regression and there is no need for non‐parametric instrumental variable estimation. Instead, simple Nadaraya–Watson non‐parametric estimation of a cointegrating regression equation is consistent irrespective of the endogeneity in the regressor. The present paper shows that some closely related results apply in the case of structural non‐parametric regression with independent data when there are continuous location shifts in the regressor. Some interesting cases are discovered where non‐parametric regression is consistent, whereas parametric regression is inconsistent even when the true regression functional form is known and used in regression. This appears to be a paradox, as knowing the true functional form should not in general be detrimental in regression. The paradox arises because additional correct information is not necessarily advantageous when information is incomplete. In this case, endogeneity in the regressor introduces bias when the true functional form is known, but interestingly does not do so in local non‐parametric regression. We propose two new consistent estimators for the parametric regression, which address the endogeneity in the regressor by means of spatial bounding and bias correction using non‐parametric estimation.     

Non‐parametric detection and estimation of structural change

Summary We propose a semi‐non‐parametric approach to the estimation and testing of structural change in time series regression models. Under the null of a given set of the coefficients being constant, we develop estimators of both the time‐varying (non‐parametric) and constant (parametric) components. Given the estimators under null and alternative, generalized F and Wald tests are developed. The asymptotic distributions of the estimators and test statistics are derived. A simulation study examines the finite‐sample performance of the estimators and tests. The techniques are employed in the analysis of structural change in the US productivity and the Eurodollar term structure.     

Poly(ADP‐ribose)polymerase 1 inhibition protects against age‐dependent endothelial dysfunction

Age‐related endothelial dysfunction is closely associated with the local production of reactive oxygen species (ROS) within and in the vicinity of the vascular endothelium. Oxidant‐induced DNA damage can activate the nuclear enzyme poly(ADP‐ribose) polymerase 1 (PARP‐1), leading to endothelial dysfunction in various pathophysiological conditions. The present study aimed to investigate the role of PARP‐1 in age‐dependent changes in endothelial cell function and its underlying mechanism. Wild‐type (WT) and PARP‐1^?/? mice were divided into young (2 months) and old (12 months) groups. Isolated aortic rings were suspended to record isometric tension to assess endothelial function. Nitric oxide (NO) production and content in plasma were detected by spectrophotometry. Superoxide ( production was detected by dihydroethidium. Expression of PARP‐1, endothelial nitric oxide synthase (eNOS), induced nitric oxide synthase (iNOS), and arginase‐2 (Arg2) was assessed by western blot analysis. Endothelium‐dependent relaxation in response to acetylcholine was lost in old WT, but not PARP‐1^?/?, mice. Endothelium‐independent vasodilation was not impaired in aging mice. Production of was greater in aging WT mice than young or aging PARP‐1^?/? mice. eNOS expression was not affected by aging in WT or PARP‐1^?/? mice, but p‐eNOS expression decreased and iNOS and Arg2 levels were upregulated only in aging WT mice. In conclusion, PARP‐1 inhibition may protect against age‐dependent endothelial dysfunction, potentially by regulating NO bioavailability via iNOS. Inhibition of PARP‐1 may help in vascular aging prevention.     

Lag‐augmented two‐ and three‐stage least squares estimators for integrated structural dynamic models

Summary We consider a lag‐augmented two‐ or three‐stage least‐squares estimator for a structural dynamic model of non‐stationary and possibly cointegrated variables without the prior knowledge of unit roots or rank of cointegration. We show that the conventional two‐and three‐stage least‐squares estimators are consistent but contain non‐standard distributions without the strict exogeneity assumption; hence the conventional Wald type test statistics may not be chi‐square distributed. We propose a lag order augmented two‐ or three‐stage least‐squares estimator that is consistent and asymptotically normally distributed. Limited Monte Carlo studies are conducted to shed light on the finite sample properties of various estimators.