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Baltagi, B. H., et al. (2018). "Robustlinear static panel data models using ε-contamination." Journal ofEconometrics 202(1):108-123.
Thepaper develops a general Bayesian framework for robust linear static panel datamodels usingε-contamination. A two-step approach is employed to derive theconditional type-II maximum likelihood (ML-II) posterior distribution of thecoefficients and individual effects. The ML-II posterior means are weightedaverages of the Bayes estimator under a base prior and the data-dependentempirical Bayes estimator. Two-stage and three stage hierarchy estimators aredeveloped and their finite sample performance is investigated through a seriesof Monte Carlo experiments. These include standard random effects as well asMundlak-type, Chamberlain-type and Hausman–Taylor-type models. The simulationresults underscore the relatively good performance of the three-stage hierarchyestimator. Within a single theoretical framework, our Bayesian approachencompasses a variety of specifications while conventional methods requireseparate estimators for each case.
Belotti, F. and G. Ilardi (2018)."Consistent inference in fixed-effects stochastic frontier models." Journalof Econometrics 202(2):161-177.
Theclassical stochastic frontier panel data models provide no mechanism todisentangle individual time invariant unobserved heterogeneity frominefficiency. Greene (2005a, b) proposed the so-called 「true」 fixed-effectsspecification that distinguishes these two latent components. However, due tothe incidental parameters problem, his maximum likelihood estimator may lead tobiased variance estimates. We propose two alternative estimators that achieveconsistency for n→∞ with fixed T. Furthermore, we extend the Chen et al.(2014) results providing a feasible estimator when the inefficiency isheteroskedastic and follows a first-order autoregressive process. Weinvestigate the behavior of the proposed estimators through Monte Carlosimulations showing good finite sample properties, especially in small samples.An application to hospitals』 technical efficiency illustrates the usefulness ofthe new approach.
Breunig, C., et al. (2018)."Nonparametric estimation in case of endogenous selection." Journalof Econometrics 202(2):268-285.
Thispaper addresses the problem of estimation of a nonparametric regressionfunction from selectively observed data when selection is endogenous. Ourapproach relies on independence between covariates and selection conditionallyon potential outcomes. Endogeneity of regressors is also allowed for. In theexogenous and endogenous case, consistent two-step estimation procedures areproposed and their rates of convergence are derived. Pointwise asymptotic distributionof the estimators is established. In addition, bootstrap uniform confidencebands are obtained. Finite sample properties are illustrated in a Monte Carlosimulation study and an empirical illustration.
Caner, M. and A. B. Kock (2018)."Asymptotically honest confidence regions for high dimensional parametersby the desparsified conservative Lasso." Journal of Econometrics 203(1): 143-168.
Inthis paper we consider the conservative Lasso which we argue penalizes morecorrectly than the Lasso and show how it may be desparsified in the sense ofvan de Geer et al. (2014) in order to construct asymptotically honest(uniform) confidence bands. In particular, we develop an oracle inequality forthe conservative Lasso only assuming the existence of a certain number ofmoments. This is done by means of the Marcinkiewicz–Zygmund inequality. Weallow for heteroskedastic non-subgaussian error terms and covariates. Next, wedesparsify the conservative Lasso estimator and derive the asymptoticdistribution of tests involving an increasing number of parameters. Oursimulations reveal that the desparsified conservative Lasso estimates theparameters more precisely than the desparsified Lasso, has better sizeproperties and produces confidence bands with superior coverage rates.
Chen, B. and L. Huang (2018)."Nonparametric testing for smooth structural changes in panel datamodels." Journal of Econometrics 202(2): 245-267.
Detectingand modeling structural changes in time series models have attracted greatattention. However, relatively little effort has been paid to the testing ofstructural changes in panel data models despite their increasing importance ineconomics and finance. In this paper, we propose a new approach to testingstructural changes in panel data models. Unlike the bulk of the literature onstructural changes, which focuses on detection of abrupt structural changes, weconsider smooth structural changes for which model parameters are unknowndeterministic smooth functions of time except for a finite number of timepoints. We use nonparametric local smoothing method to consistently estimatethe smooth changing parameters and develop two consistent tests for smoothstructural changes in panel data models. The first test is to check whether allmodel parameters are stable over time. The second test is to check potentialtime-varying interaction while allowing for a common trend. Both tests have anasymptotic N(0,1) distribution under the null hypothesis of parameter constancyand are consistent against a vast class of smooth structural changes as well asabrupt structural breaks with possibly unknown break points alternatives.Simulation studies show that the tests provide reliable inference in finitesamples and two empirical examples with respect to a cross-country growth modeland a capital structure model are discussed.
Chen, S., et al. (2018)."Nonparametric identification and estimation of sample selection modelsunder symmetry." Journal of Econometrics 202(2): 148-160.
Undera conditional mean restriction Das et al. (2003) considered nonparametricestimation of sample selection models. However, their method can only identifythe outcome regression function up to a constant. In this paper we strengthenthe conditional mean restriction to a symmetry restriction under whichselection biases due to selection on unobservables can be eliminated throughproper matching of propensity scores; consequently we are able to identify andobtain consistent estimators for the average treatment effects and thestructural regression functions. The results from a simulation study suggestthat our estimators perform satisfactorily.
Cho, J. S. and P. C. B. Phillips (2018)."Pythagorean generalization of testing the equality of two symmetric positivedefinite matrices." Journal of Econometrics 202(1): 45-56.
Weprovide a new test for equality of two symmetric positive-definite matricesthat leads to a convenient mechanism for testing specification using theinformation matrix equality or the sandwich asymptotic covariance matrix of theGMM estimator. The test relies on a new characterization of equality betweentwo k dimensional symmetric positive-definite matrices A and B: the traces ofAB−1 and BA−1 are equal to k if and only if A=B. Using this simple criterion,we introduce a class of omnibus test statistics for equality and examine theirnull and local alternative approximations under some mild regularityconditions. A preferred test in the class with good omni-directional power isrecommended for practical work. Monte Carlo experiments are conducted toexplore performance characteristics under the null and local as well as fixedalternatives. The test is applicable in many settings, including GMMestimation, SVAR models and high dimensional variance matrix settings.
Čížek, P. and J. Lei (2018)."Identification and estimation of nonseparable single-index models inpanel data with correlated random effects." Journal of Econometrics203(1): 113-128.
Theidentification in a nonseparable single-index models with correlated randomeffects is considered in panel data with a fixed number of time periods. Theidentification assumption is based on the correlated random effects structure.Under this assumption, the parameters of interest are identified up to amultiplicative constant and could be estimated by an average difference ofderivatives estimator based on the local polynomial smoothing. We suggest tolinearly combine the estimators obtained for different orders of differencesand derive the variance-minimizing weighting scheme. The asymptoticdistribution of the proposed estimators is derived both for stationary andnon-stationary explanatory variables along with a test of the stationarity.Finally, Monte Carlo experiments reveal finite sample properties of theproposed estimator.
D』Haultfœuille, X., et al. (2018)."Extremal quantile regressions for selection models and the black–whitewage gap." Journal of Econometrics 203(1): 129-142.
Weconsider the estimation of a semiparametric sample selection model withoutinstrument or large support regressor. Identification relies on theindependence between the covariates and selection, for arbitrarily large valuesof the outcome. We propose a simple estimator based on extremal quantileregression and establish its asymptotic normality by extending previous resultson extremal quantile regressions to allow for selection. Finally, we apply ourmethod to estimate the black–white wage gap among males from the NLSY79 andNLSY97. We find that premarket factors such as AFQT and family background playa key role in explaining the black–white wage gap.
Dias, G. F. and G. Kapetanios (2018)."Estimation and forecasting in vector autoregressive moving average modelsfor rich datasets." Journal of Econometrics 202(1): 75-91.
Weaddress the issue of modelling and forecasting macroeconomic variables usingrich datasets by adopting the class of Vector Autoregressive Moving Average(VARMA) models. We overcome the estimation issue that arises with this class ofmodels by implementing an iterative ordinary least squares (IOLS) estimator. Weestablish the consistency and asymptotic distribution of the estimator for weakand strong VARMA(p,q) models. Monte Carlo results show that IOLS is consistentand feasible for large systems, outperforming the MLE and other linearregression based efficient estimators under alternative scenarios. Ourempirical application shows that VARMA models are feasible alternatives whenforecasting with many predictors. We show that VARMA models outperform theAR(1), ARMA(1,1), Bayesian VAR, and factor models, considering different modeldimensions.
Dungey, M., et al. (2018). "Testingfor mutually exciting jumps and financial flights in high frequency data."Journal of Econometrics 202(1):18-44.
Wepropose a new nonparametric test to identify mutually exciting jumps in highfrequency data. We derive the asymptotic properties of the test statistics andshow that the tests have good size and reasonable power in finite sample cases.Using our mutual excitation tests, we empirically characterize the dynamics offinancial flights in forms of flight-to-safety and flight-to-quality. Theresults indicate that mutually exciting jumps and risk-off trades mostly occurin periods of high market stress. Flight-to-safety episodes (from stocks togold) arrive more frequently than do flight-to-quality spells (from stocks tobonds). We further find evidence that reverse cross-excitations orseeking-return-strategies exhibit significant asymmetry over the business cycle,reflecting the fact that investors appear to be selling gold – rather thanbonds – to invest in stocks during good market conditions.
Gallant, A. R., et al. (2018). "ABayesian approach to estimation of dynamic models with small and large numberof heterogeneous players and latent serially correlated states." Journalof Econometrics 203(1):19-32.
Wepropose a Bayesian approach to estimating dynamic models that can have statevariables that are latent, serially correlated, and heterogeneous. Our approachemploys sequential importance sampling and is based on deriving an unbiasedestimate of the likelihood within a Metropolis chain. Under fairly weakregularity conditions unbiasedness guarantees that the stationary density ofthe chain is the exact posterior, not an approximation. Results are verified byMonte Carlo simulation using two examples. The first is a dynamic game of entryinvolving a small number of firms whose heterogeneity is based on their currentcosts due to feedback through capacity constraints arising from past entry. Thesecond is an Ericson and Pakes (1995) style game with a large number of firmswhose heterogeneity is based on the quality of their products with firmscompeting through investment in product quality that affects their market shareand profitability. Our approach facilitates estimation of dynamic games witheither small or large number of players whose heterogeneity is determined bylatent state variables, discrete or continuous, that are subject to endogenousfeedback from past actions.
Gupta, A. (2018). "Autoregressivespatial spectral estimates." Journal of Econometrics 203(1): 80-95.
Nonparametricspectral density estimates find many uses in econometrics. For stationaryrandom fields on a regular spatial lattice, we propose an autoregressivenonparametric spectral density estimate that is guaranteed positive even whensuitable edge-effect correction is employed and is simple to compute usingleast squares. Our estimate is based on truncating a true half-plane infiniteautoregressive representation, while also allowing the truncation length todiverge in all dimensions to avoid the potential bias due to truncation at afixed lag-length. Uniform consistency of the proposed estimate is established,and new criteria for order selection are also suggested and studied inpractical settings. The asymptotic distribution of the estimate is shown to bezero-mean normal and independent at fixed distinct frequencies, mirroring thebehaviour for time series. A small Monte Carlo experiment examines finitesample performance. Technically the key to the results is the covariancestructure of stationary random fields defined on regularly spaced lattices. Weshow the covariance matrix to satisfy a generalization of the Toeplitz propertyfamiliar from time series analysis.
Gupta, A. (2018). "Nonparametricspecification testing via the trinity of tests." Journal ofEconometrics 203(1):169-185.
Testsare developed for inference on a parameter vector whose dimension grows slowlywith sample size. The statistics are based on the Lagrange Multiplier, Wald and(pseudo) Likelihood Ratio principles, admit standard normal asymptoticdistributions under the null and are straightforward to compute. They are shownto be consistent and possessing non-trivial power against local alternatives.The settings considered include multiple linear regression, panel data modelswith fixed effects and spatial autoregressions. When a nonparametric regressionfunction is estimated by series we use our statistics to propose specificationtests, and in semiparametric adaptive estimation we provide a test for correcterror distribution specification. These tests are nonparametric but handled inpractice with parametric techniques. A Monte Carlo study suggests that ourtests perform well in finite samples. Two empirical examples use them to testfor correct shape of an electricity distribution cost function and linearityand equality of Engel curves.
Gupta, A. and P. M. Robinson (2018)."Pseudo maximum likelihood estimation of spatial autoregressive modelswith increasing dimension." Journal of Econometrics 202(1): 92-107.
Pseudomaximum likelihood estimates are developed for higher-order spatial autoregressivemodels with increasingly many parameters, including models with spatial lags inthe dependent variables both with and without a linear or nonlinear regressioncomponent, and regression models with spatial autoregressive disturbances.Consistency and asymptotic normality of the estimates are established. MonteCarlo experiments examine finite-sample behaviour.
Han, X. (2018). "Estimation andinference of dynamic structural factor models with over-identifyingrestrictions." Journal of Econometrics 202(2): 125-147.
Thispaper develops a new estimator for the impulse response functions in structuralfactor models with a fixed number of over-identifying restrictions. Theproposed identification scheme nests the conventional just-identified recursivescheme as a special case. We establish the asymptotic distributions of the newestimator and develop test statistics for the over-identifying restrictions.Simulation results show that adding a few more over-identifying restrictionscan lead to a substantial improvement in estimation accuracy for impulseresponse functions at both zero and nonzero horizons. We estimate the effectsof a monetary policy shock using a U.S. data set. The results show that ourover-identified scheme can help to detect incorrect specifications that lead tospurious impulse responses.
Hwang, E. and D. W. Shin (2018)."Two-stage stationary bootstrapping for bivariate average realizedvolatility matrix under market microstructure noise and asynchronicity." Journalof Econometrics 202(2):178-195.
Underthe two important modern financial market features of noise andnon-synchronicity for multiple assets, for consistent estimators of theintegrated covariations, we adopt the two-time scale average realizedvolatility matrix (ARVM) which is a matrix extension of the two-time scalerealized volatilities of Zhang et al. (2005). An asymptotic normal theoryis provided for the two-time scale ARVM and resulting realized covariations.The asymptotic normality is not directly applicable in practice to constructstatistical methods owning to nuisance parameters. To bypass the nuisanceparameter problem, two-stage stationary bootstrapping is proposed. We establishconsistencies of the bootstrap distributions, and construct confidence intervalsand hypothesis tests for the integrated covariance, regression coefficient andcorrelation coefficient. The validity of the stationary bootstrap for the highfrequency heterogeneous returns is proved by showing that there existparameters of the stationary bootstrap blocks so that the bootstrapconsistencies hold. The proposed bootstrap methods extend thei.i.d. bootstrapping methods for realized covariations by Dovononet al. (2013), that are confined to synchronous noise-free sampling. Forhigh frequency noisy asynchronous samples, a Monte-Carlo experiment showsbetter finite sample performances of the proposed stationary bootstrap methodsbased on the two-time scale ARVM estimator than the wild blocks of blocksbootstrap methods of Hounyo (2017), based on pre-averaged truncated estimator.
Ichimura, H. and S. Lee (2018)."Corrigendum to 「Characterization of the asymptotic distribution ofsemiparametric M-estimators」 [J. Econometrics 159 (2) (2010) 252–266]." Journalof Econometrics 202(2):306-307.
Thisnote provides correction to Ichimura and Lee (2010).
Johansen, S. and M. Ø. Nielsen (2018)."The cointegrated vector autoregressive model with general deterministicterms." Journal of Econometrics 202(2): 214-229.
Inthe cointegrated vector autoregression (CVAR) literature, deterministic termshave until now been analyzed on a case-by-case, or as-needed basis. We give acomprehensive unified treatment of deterministic terms in the additive modelXt=γZt+Yt, where Zt belongs to a large class of deterministic regressors and Ytis a zero-mean CVAR. We suggest an extended model that can be estimated byreduced rank regression, and give a condition for when the additive andextended models are asymptotically equivalent, as well as an algorithm forderiving the additive model parameters from the extended model parameters. Wederive asymptotic properties of the maximum likelihood estimators and discusstests for rank and tests on the deterministic terms. In particular, we giveconditions under which the estimators are asymptotically (mixed) Gaussian, suchthat associated tests are χ2-distributed.
Kim, D., et al. (2018). "Adaptivethresholding for large volatility matrix estimation based on high-frequencyfinancial data." Journal of Econometrics 203(1): 69-79.
Universalthresholding methods have been developed to estimate the large sparseintegrated volatility matrix of underlying assets based on high-frequencyfinancial data. Since the integrated volatility matrix often has entries with awide range of variability, universal thresholding estimators do not take thevarying entries into consideration and may have unsatisfactory performances.This paper investigates adaptive thresholding estimation of the largeintegrated volatility matrix. We first construct an estimator for theasymptotic variance of the pre-averaging realized volatility estimator and thenuse the two estimators to develop an adaptive thresholding estimator of thelarge volatility matrix. It is shown that the adaptive thresholding estimatorcan achieve the optimal rate of convergence over the class of the sparseintegrated volatility matrix when both the number of assets and sample size areallowed to go to infinity, while the universal thresholding estimator canachieve only the sub-optimal convergence rate. Also we discuss how to harnessthe adaptive thresholding scheme in the approximate factor model. Thesimulation study is conducted to check the finite sample performance of theadaptive thresholding estimators.
Li, D., et al. (2018). "The ZD-GARCH model:A new way to study heteroscedasticity." Journal of Econometrics 202(1): 1-17.
Thispaper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to studyconditional heteroscedasticity and heteroscedasticity together. Unlike theclassical GARCH model, the ZD-GARCH(1, 1) model is always non-stationaryregardless of the sign of the Lyapunov exponent γ0, but interestingly it isstable with its sample path oscillating randomly between zero and infinity overtime when γ0=0. Furthermore, this paper studies the generalized quasi-maximumlikelihood estimator (GQMLE) of the ZD-GARCH(1, 1) model, and establishes itsstrong consistency and asymptotic normality. Based on the GQMLE, an estimatorfor γ0, a t-test for stability, a unit root test for the absence of the driftterm, and a portmanteau test for model checking are all constructed. Simulationstudies are carried out to assess the finite sample performance of the proposedestimators and tests. Applications demonstrate that a stable ZD-GARCH(1, 1) modelis more appropriate than a non-stationary GARCH(1, 1) model in fitting the KV-Astock returns in Francq and Zakoïan (2012).
Lin, H., et al. (2018). "Efficientestimation and computation for the generalised additive models with unknownlink function." Journal of Econometrics 202(2): 230-244.
Thegeneralised additive models (GAM) are widely used in data analysis. In theapplication of the GAM, the link function involved is usually assumed to be acommonly used one without justification. Motivated by a real data example withbinary response where the commonly used link function does not work, we proposea generalised additive models with unknown link function (GAMUL) for varioustypes of data, including binary, continuous and ordinal. The proposed estimatorsare proved to be consistent and asymptotically normal. Semiparametricefficiency of the estimators is demonstrated in terms of their linearfunctionals. In addition, an iterative algorithm, where all estimators can beexpressed explicitly as a linear function of Y, is proposed to overcome thecomputational hurdle for the GAM type model. Extensive simulation studiesconducted in this paper show the proposed estimation procedure works very well.The proposed GAMUL are finally used to analyze a real dataset about loanrepayment in China, which leads to some interesting findings.
Pei, Y., et al. (2018). "Nonparametricfixed effects model for panel data with locally stationary regressors." Journalof Econometrics 202(2):286-305.
Wedevelop methods for inference in nonparametric time-varying fixed effects paneldata models that allow for locally stationary regressors and for the timeseries length T and cross-section size N both being large. We first develop apooled nonparametric profile least squares dummy variable approach to estimatethe nonparametric function, and establish the optimal convergence rate andasymptotic normality of the resultant estimator. We then propose a teststatistic to check whether the bivariate nonparametric function is time-varyingor the time effect is separable, and derive the asymptotic distribution of theproposed test statistic. We present several simulated examples and two realdata analyses to illustrate the finite sample performance of the proposedmethods.
Sibbertsen, P., et al. (2018). "Amultivariate test against spurious long memory." Journal ofEconometrics 203(1): 33-49.
Thispaper provides a multivariate score-type test against spurious long memory. Weprove the consistency of the test against the alternatives of random levelshifts and smooth trends. The test statistic is based on the weighted sum ofthe partial derivatives of the multivariate local Whittle likelihood function.To apply the test to fractionally cointegrated series, the test statistic iscalculated for the linearly transformed system after estimating thecointegrating matrix. We derive the limiting distribution and show consistencyof this procedure. The test is applied to log-absolute returns and log-realizedvolatilities of the S&P 500, DAX, FTSE, and NIKKEI.
Tang, N., et al. (2018)."Exponentially tilted likelihood inference on growing dimensionalunconditional moment models." Journal of Econometrics 202(1): 57-74.
Growing-dimensionaldata with likelihood function unavailable are often encountered in variousfields. This paper presents a penalized exponentially tilted (PET) likelihoodfor variable selection and parameter estimation for growing dimensionalunconditional moment models in the presence of correlation among variables andmodel misspecification. Under some regularity conditions, we investigate theconsistent and oracle properties of the PET estimators of parameters, and showthat the constrained PET likelihood ratio statistic for testing contrasthypothesis asymptotically follows the chi-squared distribution. Theoreticalresults reveal that the PET likelihood approach is robust to modelmisspecification. We study high-order asymptotic properties of the proposed PETestimators. Simulation studies are conducted to investigate the finiteperformance of the proposed methodologies. An example from the Boston HousingStudy is illustrated.
Xu, X. and L.-f. Lee (2018). "Sievemaximum likelihood estimation of the spatial autoregressive Tobit model." Journalof Econometrics 203(1):96-112.
Thispaper extends the ML estimation of a spatial autoregressive Tobit model undernormal disturbances in Xu and Lee (2015b, Journal of Econometrics) todistribution-free estimation. We examine the sieve MLE of the model, where thedisturbances are i.i.d.with an unknown distribution. We show that the spatialautoregressive process with Tobit censoring and related variables are spatialnear-epoch dependent (NED). A related contribution is that we develop someexponential inequalities for spatial NED random fields. With theseinequalities, we establish the consistency of the estimator. Asymptoticdistributions of structural parameters of the model are derived from afunctional central limit theorem and projection. Simulations show that the sieveMLE can improve the finite sample performance upon misspecified normal MLEs. Asan empirical application, we examine the school district income surtax rates inIowa. Our results show that the spatial spillover effects are significant, butthey may be overestimated if disturbances are restricted to be normallydistributed.
Yu, P. and P. C. B. Phillips (2018)."Threshold regression with endogeneity." Journal of Econometrics203(1): 50-68.
Thispaper studies estimation in threshold regression with endogeneity in theregressors and thresholding variable. Three key results differ from those inregular models. First, both the threshold point and the threshold effectparameters are shown to be identified without the need for instrumentation.Second, in partially linear threshold models, both parametric and nonparametriccomponents rely on the same data, which prima facie suggests identificationfailure. But, as shown here, the discontinuity structure of the thresholditself supplies identifying information for the parametric coefficients withoutthe need for extra randomness in the regressors. Third, instrumentation playsdifferent roles in the estimation of the system parameters, deliveringidentification for the structural coefficients in the usual way, but raisingconvergence rates for the threshold effect parameters and improving efficiencyfor the threshold point. Simulation studies corroborate the theory and theasymptotics. An empirical application is conducted to explore the effects of401(k) retirement programs on savings, illustrating the relevance of thresholdmodels in treatment effects evaluation in the presence of endogeneity.
Zhang, X. and J. Yu (2018). "Spatialweights matrix selection and model averaging for spatial autoregressivemodels." Journal of Econometrics 203(1): 1-18.
Spatialeconometrics relies on the spatial weights matrix to specify thecross-sectional dependence; however, the candidate spatial weights matricesmight not be unique. This paper proposes a model selection procedure to choosea weights matrix from several candidates by using a Mallows type criterion. Weprove that when the true weights matrix is not in the candidates, the procedureis asymptotically optimal in the sense of minimizing the squared loss;otherwise, the procedure can select the true weights matrix consistently. Wethen propose a model averaging procedure to reduce the squared loss. We alsoprovide procedures for the spatial model with heteroscedasticity and endogenousregressors and the model with both spatial lag and spatial error. Monte Carloexperiments show that proposed procedures have satisfactory finite sampleperformances. We apply the model selection and model averaging procedures tostudy the market integration in China using historical rice prices.
Zhu, Y. (2018). "Sparse linear modelsand l1-regularized 2SLS with high-dimensional endogenous regressors andinstruments." Journal of Econometrics 202(2): 196-213.
Weexplore the validity of the 2-stage least squares estimator withl1-regularization in both stages, for linear triangular models where thenumbers of endogenous regressors in the main equation and instruments in thefirst-stage equations can exceed the sample size, and the regressioncoefficients are sufficiently sparse. For this l1-regularized 2-stage leastsquares estimator, we first establish finite-sample performance bounds and thenprovide a simple practical method (with asymptotic guarantees) for choosing theregularization parameter. We also sketch an inference strategy built upon thispractical method.
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