generalizing weak instrument robust iv statistics towards multiple parameters unrestricted covariance matrices and identification statistics abstract we generalize the weak instrument robust score or lagrange multiplier and likelihood ratio instrumental variables iv statistics towards multiple parameters and a general covariance matrix so they can be used in the generalized method of moments gmm the gmm extension of moreira s 2003 a conditional likelihood ratio test for structural models econometrica 71 1027 1048 conditional likelihood ratio statistic towards gmm preserves its expression except that it becomes conditional on a statistic that tests the rank of a matrix we analyze the spurious power decline of kleibergen s 2002 pivotal statistics for testing structural parameters in instrumental variables regression econometrica 70 1781 1803 2005 testing parameters in gmm without assuming that they are identified econometrica 73 1103 1124 score statistic and show that an independent misspecification pre test overcomes it we construct identification statistics that reflect if the confidence sets of the parameters are bounded a power study and the possible shapes of confidence sets illustrate the analysis

bootstrap validity for the score test when instruments may be weak it is well known that size adjustments based on bootstrapping the t statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable in this paper we provide a theoretical proof that guarantees the validity of the bootstrap for the score statistic this theory does not follow from standard results since the score statistic is not a smooth function of sample means and some parameters are not consistently estimable when the instruments are uncorrelated with the explanatory variable

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

examining bias in estimators of linear rational expectations models under misspecification most rational expectations models involve equations in which the dependent variable is a function of its lags and its expected future value we investigate the asymptotic bias of generalized method of moment gmm and maximum likelihood ml estimators in such models under misspecification we consider several misspecifications and focus more specifically on the case of omitted dynamics in the dependent variable in a stylized dgp we derive analytically the asymptotic biases of these estimators we establish that in many cases of interest the two estimators of the degree of forward lookingness are asymptotically biased in opposite direction with respect to the true value of the parameter we also propose a quasi hausman test of misspecification based on the difference between the gmm and ml estimators using monte carlo simulations we show that the ordering and direction of the estimators still hold in a more realistic new keynesian macroeconomic model in this set up misspecification is in general found to be more harmful to gmm than to ml estimators

efficient estimation and inference in linear pseudo panel data models we consider pseudo panel data models constructed from repeated cross sections in which the number of individuals per group is large relative to the number of groups and time periods first we show that when time invariant group fixed effects are neglected the ols estimator does not converge in probability to a constant but rather to a random variable second we show that while the fixed effects fe estimator is consistent the usual t statistic is not asymptotically normally distributed and we propose a new robust t statistic whose asymptotic distribution is standard normal third we propose efficient gmm estimators using the orthogonality conditions implied by grouping and we provide t tests that are valid even in the presence of time invariant group effects our monte carlo results show that the proposed gmm estimator is more precise than the fe estimator and that our new t test has good size and is powerful

estimation and inference with weak semi strong and strong identification this paper analyzes the properties of standard estimators tests and confidence sets cs s for parameters that are unidentified or weakly identified in some parts of the parameter space the paper also introduces methods to make the tests and cs s robust to such identification problems the results apply to a class of extremum estimators and corresponding tests and cs s that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification this covers a class of models estimated using maximum likelihood ml least squares ls quantile generalized method of moments generalized empirical likelihood minimum distance and semi parametric estimators the consistency lack of consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions the asymptotic sizes in a uniform sense of standard and identification robust tests and cs s are established the results are applied to the arma 1 1 time series model estimated by ml and to the nonlinear regression model estimated by ls in companion papers the results are applied to a number of other models

testing for weak identification in possibly nonlinear models in this paper we propose a chi square test for identification our proposed test statistic is based on the distance between two shrinkage extremum estimators the two estimators converge in probability to the same limit when identification is strong and their asymptotic distributions are different when identification is weak the proposed test is consistent not only for the alternative hypothesis of no identification but also for the alternative of weak identification which is confirmed by our monte carlo results we apply the proposed technique to test whether the structural parameters of a representative taylor rule monetary policy reaction function are identified

instrumental variable estimation of an error components model on propose des estimateurs efficaces en considerant des hypotheses alternatives sur les sources d endogeneite et les proprietes de variance covariance des perturbations

semiparametric efficient estimation of ar 1 panel data models this study focuses on the semiparametric efficient estimation of random effect panel models containing ar 1 disturbances we also consider such estimators when the effects and regressors are correlated hausman and taylor 1981 we introduce two semiparametric efficient estimators that make minimal assumptions on the distribution of the random errors effects and the regressors and that provide semiparametric efficient estimates of the slope parameters and of the effects our estimators extend the previous work of park and simar j amer statist assoc 89 1994 929 park et al j econometrics 84 1998 273 and adams et al j business econom statist 17 1999 349 theoretical derivations are supplemented by monte carlo simulations we also provide an empirical illustration by estimating relative efficiencies from a stochastic distance function for the u s banking industry over the 1980s and 1990s in markets where regulatory constraints have been lessened or done away with the deregulatory dynamic market shocks may not be adjusted to immediately and may induce a serial correlation pattern in firm s use of best practice banking technologies our semiparametric estimators have an important role in providing robust point estimates and inferences of the productivity and efficiency gains due to such economic reforms

evolutionary periodogram for nonstationary signals presents a novel estimator for the time dependent spectrum of a nonstationary signal by modeling the signal at any given frequency as having a time varying amplitude accurately represented by an orthonormal basis expansion the authors are able to compute a minimum mean squared error estimate of this time varying amplitude repeating the process over all frequencies they obtain a power distribution as a function of time and frequency that is consistent with the wold cramer evolutionary spectrum based on the model assumptions the authors develop the evolutionary periodogram ep for nonstationary signals an estimator analogous to the periodogram used in the stationary case they also derive the time frequency resolution of the new estimator the approach is free of some of the drawbacks of the bilinear distributions and of the short time fourier transform spectral estimates it is guaranteed to produce nonnegative spectra without the cross term behavior of the bilinear distributions and it does not require windowing of data in the time domain examples illustrating the new estimator are given

inference on structural parameters in instrumental variables regression with weak instruments we consider the problem of making asymptotically valid inference on structural parameters in instrumental variables regression with weak instruments using the localto zero asymptotics of staiger and stock 1997 we derive the asymptotic distributions of lr and lm type statistics for testing simple hypotheses on structural parameters based on maximum likelihood and generalized method of moments estimation methods in contrast to the nonstandard limiting behavior of wald statistics the limiting distributions of certain lm and lr statistics are bounded by a chi square distribution with degrees of freedom given by the number of instruments further we show how to construct asymptotically valid confidence sets for structural parameters by inverting these statistics

efficient estimation using panel data in an important recent paper hausman and taylor 1981 hereafter ht considered the instrumental variable estimation of a regression model using panel data when the individual effects may be correlated with a subset of the explanatory variables they provided a simple consistent estimator and an efficient estimator more recently amemiya and macurdy 1986 hereafter am have suggested an alternative estimator which is more efficient than the ht estimator under certain conditions and given stronger assumptions than ht made however the relationship between the ht and am papers is less clear than it might be in part because of notational differences between the two papers in this paper we clarify the relationship between the ht and am estimators and we show that the difference between these estimators lies in the treatment of the time varying explanatory variables which are uncorrelated with the effects ht use each such variable as two instruments means and deviations from means while am use such variables as t 1 instruments as deviations from means and also separately for each of the t available time periods this enables us to make clear the conditions under which the am estimator is more efficient than the ht estimator we also present each estimator in a form which allows it to be calculated using standard instrumental variables two stage least squares software following the am path one step further we then define a third bms estimator which under yet stronger assumptions is more efficient than the am estimator both ht and am use as instruments the deviations from means of the time varying variables which are correlated with the effects a more efficient estimator may be obtained by using separately the t 1 linearly independent values of these deviations from individual means consistency requires that these be legitimate instruments and whether this is so depends on why these time varying variables are correlated with the effects for example if such correlation arises solely because of a time invariant component which is removed in taking deviations from individual means these instruments are legitimate

robust inference in nonlinear models with mixed identification strength abstract the paper studies inference in regression models composed of nonlinear functions with unknown transformation parameters and loading coefficients that measure the importance of each component in these models non identification and weak identification present in multiple parts of the parameter space resulting in mixed identification strength for different unknown parameters this paper proposes robust tests and confidence intervals for sub vectors and linear functions of the unknown parameters in particular the results cover applications where some nuisance parameters are non identified under the null davies 1977 1987 and some nuisance parameters are subject to a full range of identification strength to construct this robust inference procedure we develop a local limit theory that models mixed identification strength the asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence a sequential argument is used to peel the criterion function based on identification strength of the parameters

on distributions of ratios a large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables if the denominator variable is positive then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random variables if in addition the joint characteristic function of numerator and denominator is known then standard fourier inversion techniques can be used to reconstruct the distribution function from it most research in this field has been based on this correspondence but which breaks down when both numerator and denominator are supported on the entire real line the present manuscript derives inversion formulae and saddlepoint approximations that remain valid in this case and reduce to known results when the denominator is almost surely positive applications include the iv est imator of a structural parameter in a just identified equation

a high resolution data adaptive time frequency representation a data adaptive time frequency representation is developed that overcomes some limitations of the short time fourier transform while avoiding the cross terms that make the wigner distribution and other bilinear representations difficult to interpret the adaptive time frequency representations uses gaussian basis functions but varies their time width and chirp rate with time and frequency to achieve high signal concentration everywhere a measure of local signal concentration allows fully automated determination of the optimal basis parameters the adaptive method is computationally expensive but may provide much better performance than any currently known technique

natural conjugate priors for the instrumental variables regression model applied to the angrist krueger data we propose a natural conjugate prior for the instrumental variables regression model the prior is a natural conjugate one since the marginal prior and posterior of the structural parameter have the same functional expressions which directly reveal the update from prior to posterior the jeffreys prior results from a specific setting of the prior parameters and results in a marginal posterior of the structural parameter that has an identical functional form as the sampling density of the limited information maximum likelihood estimator we construct informative priors for the angrist krueger 1991 does compulsory school attendance affect schooling and earnings quarterly journal of economics 106 979 1014 data and show that the marginal posterior of the return on education in the us coincides with the marginal posterior from the southern region when we use the jeffreys prior this result occurs since the instruments are the strongest in the southern region and the posterior using the jeffreys prior identical to maximum likelihood focusses on the strongest available instruments we construct informative priors for the other regions that make their posteriors of the return on education similar to that of the us and the southern region these priors show the amount of prior information needed to obtain comparable results for all regions

a new specification test for the validity of instrumental variables we develop a new specification test for iv estimators adopting a particular second order approximation of bekker the new specification test compares the difference of the forward conventional 2sls estimator of the coefficient of the right hand side endogenous variable with the reverse 2sls estimator of the same unknown parameter when the normalization is changed under the null hypothesis that conventional first order asymptotics provide a reliable guide to inference the two estimates should be very similar our test sees whether the resulting difference in the two estimates satisfies the results of second order asymptotic theory essentially the same idea is applied to develop another new specification test using second order unbiased estimators of the type first proposed by nagar if the forward and reverse nagar type estimators are not significantly different we recommend estimation by liml which we demonstrate is the optimal linear combination of the nagar type estimators to second order we also demonstrate the high degree of similarity for k class estimators between the approach of bekker and the edgeworth expansion approach of rothenberg an empirical example and monte carlo evidence demonstrate the operation of the new specification test

further results on projection based inference in iv regressions with weak collinear or missing instruments we study a general family of anderson rubin type procedures allowing for arbitrary collinearity among the instruments and endogenous variables using finite sample distributional theory we show that the proposed procedures besides being robust to weak instruments are also robust to the exclusion of relevant instruments and to the distribution of endogenous regressors a solution to the problem of computing linear projections from general possibly singular quadric surfaces is derived and used to build finite sample confidence sets for individual structural parameters the importance of robustness to excluded instruments is studied by simulation applications to the trade growth relationship and to education returns are presented

multilevel modeling with correlated effects when there exist omitted effects measurement error and or simultaneity in multilevel models explanatory variables may be correlated with random components and standard estimation methods do not provide consistent estimates of model parameters this paper introduces estimators that are consistent under such conditions by employing generalized method of moments gmm estimation techniques in multilevel modeling the authors present a series of estimators along a robust to efficient continuum this continuum depends on the assumptions that the analyst makes regarding the extent of the correlated effects it is shown that the gmm approach provides an overarching framework that encompasses well known estimators such as fixed and random effects estimators and also provides more options these gmm estimators can be expressed as instrumental variable iv estimators which enhances their interpretability moreover by exploiting the hierarchical structure of the data the current technique does not require additional variables unlike traditional iv methods further statistical tests are developed to compare the different estimators a simulation study examines the finite sample properties of the estimators and tests and confirms the theoretical order of the estimators with respect to their robustness and efficiency it further shows that not only are regression coefficients biased but variance components may be severely underestimated in the presence of correlated effects empirical standard errors are employed as they are less sensitive to correlated effects when compared to model based standard errors an example using student achievement data shows that gmm estimators can be effectively used in a search for the most efficient among unbiased estimators

specification testing in panel data with instrumental variables i show that specification tests for correlated fixed effects developed by hausman and taylor extend in an analogous way to panel data sets with endogenous regressors given panel data different sets of instrumental variables can be used to construct the test for a simple class of models the test in many cases is asymptotically more efficient if an incomplete set of instruments is used however in small samples one may do better using the complete set of instruments monte carlo results demonstrate the likely gains for different assumptions about the degree of between and within variance in the data

problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak abstract we draw attention to two problems associated with the use of instrumental variables iv the importance of which for empirical work has not been fully appreciated first the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the iv estimates even if only a weak relationship exists between the instruments and the error in the structural equation second in finite samples iv estimates are biased in the same direction as ordinary least squares ols estimates the magnitude of the bias of iv estimates approaches that of ols estimates as the r 2 between the instruments and the endogenous explanatory variable approaches 0 to illustrate these problems we reexamine the results of a recent paper by angrist and krueger who used large samples from the u s census to estimate wage equations in which quarter of birth is used as an instrument for educational attainment we find evidence that despite huge sample sizes th

efficient two sided nonsimilar invariant tests in iv regression with weak instruments abstract as nelson and startz nelson c r startz r 1990a the distribution of the instrumental variable estimator and its t ratio when the instrument is a poor one journal of business 63 s125 s140 nelson c r startz r 1990b some further results on the exact small sample properties of the instrumental variables estimator econometrica 58 967 976 dramatically demonstrated standard hypothesis tests and confidence intervals in instrumental variables regression are invalid when instruments are weak recent work on hypothesis tests for the coefficient on a single included endogenous regressor when instruments may be weak has focused on similar tests this paper extends that work to nonsimilar tests of which similar tests are a subset the power envelope for two sided invariant to rotations of the instruments nonsimilar tests is characterized theoretically then evaluated numerically for five ivs the power envelopes for similar and nonsimilar tests differ theoretically but are found to be very close numerically the nonsimilar test power envelope is effectively achieved by the moreira moreira m j 2003 a conditional likelihood ratio test for structural models econometrica 71 1027 1048 conditional likelihood ratio test so that test is effectively uniformly most powerful invariant umpi we also provide a new nonsimilar test p which has 1 2 critical values is asymptotically efficient under strong instruments involves only elementary functions and is very nearly umpi

an alternative approach to obtaining nagar type moment approximations in simultaneous equation models this paper examines asymptotic expansions for estimation errors expressed explicitly as functions of underlying random variables taylor series expansions are obtained from which first and second moment approximations are derived while the expansions are essentially equivalent to the traditional nagar type the terms are expressed in a form which enables moment approximations to be obtained in a particularly straightforward way once the partial derivatives have been found the approach is illustrated by considering the k class estimators in a static simultaneous equation model where the disturbances are non spherical

bootstrap critical values for tests based on generalized method of moments estimators monte carlo experiments have shown that tests based on generalized method ofmoments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used this paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions particular attention is given to the case of dependent data it is shown that with such data the bootstrap must sample blocks of data and that the formulae for the bootstrap versions of test statistics differ from the formulae that apply with the original data the results of monte carlo experiments on the numerical performance of the bootstrap show that it usually reduces the errors in level that occur when critical values based on first order asymptotic theory are used the bootstrap also provides an indication of the accuracy of critical values obtained from first order asymptotic theory

on the exact small sample distribution of the instrumental variable estimator the purpose of this note is to point out that the bimodality is a consequence of the special case considered by n s the exact finite sample distribution of the iv estimator has been derived in the economic literature earlier but its tabulation or plotting involves some assumptions about the nuisance parameters in this note we plot the densities of the exact finite sample distribution of the iv estimator for several parameter values and show that the bimodality feature noted by n s is a consequence of a singular covariance matrix and not of a poor instrument

another look at the instrumental variable estimation of error components models this article develops a framework for efficient iv estimators of random effects models with information in levels which can accommodate predetermined variables our formulation clarifies the relationship between the existing estimators and the role of transformations in panel data models we characterize the valid transformations for relevant models and show that optimal estimators are invariant to the transformation used to remove individual effects we present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors finally we consider models with predetermined variables that have constant correlation with the effects and illustrate their importance with simulations

inference in structural vector autoregressions identified with an external instrument abstract this paper studies structural vector autoregressions in which a structural shock of interest e g an oil supply shock is identified using an external instrument the external instrument is taken to be correlated with the target shock the instrument is relevant and to be uncorrelated with other shocks of the model the instrument is exogenous the potential weak correlation between the external instrument and the target structural shock compromises the large sample validity of standard inference we suggest a confidence set for impulse response coefficients that is not affected by the instrument strength i e is weak instrument robust and asymptotically coincides with the standard confidence set when the instrument is strong

maximum likelihood estimation and uniform inference with sporadic identification failure abstract this paper analyzes the properties of a class of estimators tests and confidence sets css when the parameters are not identified in parts of the parameter space specifically we consider estimator criterion functions that are sample averages and are smooth functions of a parameter this includes log likelihood quasi log likelihood and least squares criterion functions we determine the asymptotic distributions of estimators under lack of identification and under weak semi strong and strong identification we determine the asymptotic size in a uniform sense of standard t and quasi likelihood ratio qlr tests and css we provide methods of constructing qlr tests and css that are robust to the strength of identification the results are applied to two examples a nonlinear binary choice model and the smooth transition threshold autoregressive star model

bayesian and classical approaches to instrumental variable regression we establish relationships between certain bayesian and classical approaches to instrumental variable regression we determine the form of priors that lead to posteriors for structural parameters that have similar properties as classical 2sls and liml and in doing so provide some new insight especially in the context of weak instruments to the small sample behavior of bayesian and classical procedures using a reduced rank restriction on a multivariate linear model we determine the priors that give rise to posteriors that are identical in functional form to the sampling densities of the classical 2sls and liml estimators

higher moment estimators for linear regression models with errors in the variables abstract this paper proposes consistent instrumental variable estimators for linear regression models with errors in the variables that require no extraneous information these estimators are based on sample moments of order higher than two while similar estimators proposed previously in the literature seem to be quite erratic our experimental f findings suggest that our estimators perform better than ordinary least squares estimators in terms of root mean squared errors and also in terms of size of type i errors of standard tests in many typical situations of economic analyses tests for the presence of errors in the variables are also described

efficient estimation of panel data models with strictly exogenous explanatory variables abstract with panel data exogeneity assumptions imply many more moment conditions than standard estimators use however many of the moment conditions may be redundant in the sense that they do not increase efficiency if so we may establish the standard estimators efficiency we prove efficiency results for gls in a model with unrestricted error covariance matrix and for 3sls in models where regressors and errors are correlated such as the hausman taylor model for models with correlation between regressors and errors and with unrestricted error covariance structure we provide a simple estimator based on a gls generalization of deviations from means

efficient estimation and identification of simultaneous equation models with covariance restrictions this paper is a revision of an earlier version presented at the european econometric meetings 1982

approximating the distribution of the two stage least squares estimator when the concentration parameter is small this paper presents a new approximation to the exact sampling distribution of the instrumental variables estimator in simultaneous equations models it differs from many of the approximations currently available edgeworth expansions for example in that it is specifically designed to work well when the concentration parameter is small the approximation is remarkable in that simultaneously i it has an extremely simple final form ii in situations for which it is designed it is typically much more accurate than is the large sample normal approximation and iii it is able to capture most of those stylized facts that characterize lack of identification and weak instrument scenarios the development leading to the approximation is also novel in that it introduces techniques of some independent interest not seen in this literature hitherto

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

redundancy of moment conditions it is well known that adding moment conditions cannot decrease asymptotic efficiency however sometimes additional moment conditions are redundant in the sense that they do not increase the asymptotic efficiency of estimation for some or all of the parameters of interest this paper gives a general treatment of redundancy of moment conditions it provides necessary and sufficient conditions for redundancy in several equivalent forms the paper also provides interesting results for the case that there are three or more sets of moment conditions

gel statistics under weak identification abstract the central concern of this paper is the provision in a time series moment condition framework of practical recommendations of confidence regions for parameters whose coverage probabilities are robust to the strength or weakness of identification to this end we develop pearson type test statistics based on gel implied probabilities formed from general kernel smoothed versions of the moment indicators we also modify the statistics suggested in guggenberger and smith 2008 for a general kernel smoothing function importantly for our conclusions we provide gel time series counterparts to gmm and gel conditional likelihood ratio statistics given in kleibergen 2005 and smith 2007 our analysis not only demonstrates that these statistics are asymptotically conditionally pivotal under both classical asymptotic theory and weak instrument asymptotics of stock and wright 2000 but also provides asymptotic power results in the weakly identified time series context consequently the empirical null rejection probabilities of the associated tests and thereby the coverage probabilities of the corresponding confidence regions should not be affected greatly by the strength or otherwise of identification a comprehensive monte carlo study indicates that a number of the tests proposed here represent very competitive choices in comparison with those suggested elsewhere in the literature

robust confidence sets in the presence of weak instruments abstract this paper considers instrumental variable regression with a single endogenous variable and the potential presence of weak instruments i construct confidence sets for the coefficient on the single endogenous regressor by inverting tests robust to weak instruments i suggest a numerically simple algorithm for finding the conditional likelihood ratio clr confidence sets full descriptions of possible forms of the clr anderson rubin ar and lagrange multiplier lm confidence sets are given i show that the clr confidence sets have nearly the shortest expected arc length among similar symmetric invariant confidence sets in a circular model i also prove that the clr confidence set is asymptotically valid in a model with non normal errors

the generalized evolutionary spectrum evolutionary spectral theory defines a decomposition of signal energy jointly over time and frequency by assuming that processes are composed of sinusoidal components with time dependent amplitudes we expand this theory by allowing time variations in the frequency of the sinusoidal components examples are presented illustrating the advantages of this generalization

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

a conditional likelihood ratio test for structural models this paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced form covariance matrix these tests are shown to be similar under weak instrument asymptotics when the reduced form covariance matrix is estimated and the errors are non normal the conditional test based on the likelihood ratio statistic is particularly simple and has good power properties like the score test it is optimal under the usual local to null asymptotics but it has better power when identification is weak

alternative approximations of the bias and mse of the iv estimator under weak identification with an application to bias correction abstract we provide analytical formulae for the asymptotic bias abias and mean squared error amse of the iv estimator and obtain approximations thereof based on an asymptotic scheme which essentially requires the expectation of the first stage f statistic to converge to a finite possibly small positive limit as the number of instruments approaches infinity our analytical formulae can be viewed as generalizing the bias and mse results of richardson and wu 1971 a note on the comparison of ordinary and two stage least squares estimators econometrica 39 973 982 to the case with nonnormal errors and stochastic instruments our approximations are shown to compare favorably with approximations due to morimune 1983 approximate distributions of k class estimators when the degree of overidentifiability is large compared with the sample size econometrica 51 821 841 and donald and newey 2001 choosing the number of instruments econometrica 69 1161 1191 particularly when the instruments are weak we also construct consistent estimators for the abias and amse and we use these to further construct a number of bias corrected ols and iv estimators the properties of which are examined both analytically and via a series of monte carlo experiments

nonparametric analysis of random utility models abstract this paper considers two sided tests for the parameter of an endogenous variable in an instrumental variable iv model with heteroskedastic and autocorrelated errors we develop the finite sample theory of weighted average power wap tests with normal errors and a known long run variance a typical weight choice yields tests with power near zero for parts of the parameter space we propose two boundary conditions that yield two sided tests with hac errors the locally unbiased lu condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness the strongly unbiased su condition is more restrictive than lu but the associated wap tests are easier to implement the wap su tests can outperform several tests under the weak iv asymptotics as they make use of the data beyond the anderson rubin and score statistics

bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models abstract this paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear iv models under weak assumptions the method provides a finite sample bound on the difference between the true and nominal probabilities of rejecting a correct null hypothesis the method is a non studentized version of the s test of stock and wright 2000 but is implemented and analyzed differently it does not require restrictive distributional assumptions linearity of the estimated model simultaneous equations or information about whether the instruments are strong or weak it can be applied to quantile iv models that may be nonlinear and can be used to test a parametric iv model against a nonparametric alternative it provides information about the relation between the degree of weakness of the instruments and the power of the test the bound presented here holds in finite samples regardless of the strength of the instruments

performance of conditional wald tests in iv regression with weak instruments abstract we compare the powers of five tests of the coefficient on a single endogenous regressor in instrumental variables regression following moreira 2003 a conditional likelihood ratio test for structural models econometrica 71 1027 1048 all tests are implemented using critical values that depend on a statistic which is sufficient under the null hypothesis for the unknown concentration parameter so these conditional tests are asymptotically valid under weak instrument asymptotics four of the tests are based on k class wald statistics two stage least squares liml fuller s some properties of a modification of the limited information estimator econometrica 45 939 953 and bias adjusted tsls the fifth is moreira s 2003 conditional likelihood ratio clr test the heretofore unstudied conditional wald cw tests are found to perform poorly compared to the clr test in many cases the cw tests have almost no power against a wide range of alternatives our analysis is facilitated by a new algorithm presented here for the computation of the asymptotic conditional p value of the clr test

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

power enhancement in high dimensional cross sectional tests we propose a novel technique to boost the power of testing a high dimensional vector h 0 against sparse alternatives where the null hypothesis is violated only by a couple of components existing tests based on quadratic forms such as the wald statistic often suffer from low powers due to the accumulation of errors in estimating high dimensional parameters more powerful tests for sparse alternatives such as thresholding and extreme value tests on the other hand require either stringent conditions or bootstrap to derive the null distribution and often suffer from size distortions due to the slow convergence based on a screening technique we introduce a power enhancement component which is zero under the null hypothesis with high probability but diverges quickly under sparse alternatives the proposed test statistic combines the power enhancement component with an asymptotically pivotal statistic and strengthens the power under sparse alternatives the null distribution does not require stringent regularity conditions and is completely determined by that of the pivotal statistic as specific applications the proposed methods are applied to testing the factor pricing models and validating the cross sectional independence in panel data models

practical estimation of correlation functions of nonstationary gaussian processes corresp the preponderance of gaussian processes among random signals encountered in practical situations has provided the motivation for developing a practical method for the estimation of correlation functions of nonstationary gaussian processes the practicality of the method lies in the fact that only a single data record is required to obtain unbiased and consistent estimates of the correlation functions thus effectively waiving the strict requirements of the ergodic hypothesis

three stage least squares with different instruments for different equations abstract the standard treatments of 3sls assume that the same instrument set is valid for every equation when this is not so a generalized method of moments estimator proposed by amemiya is available this paper compares amemiya s estimator to three estimators based on fitted values of the endogenous variables two of these estimators are inconsistent when the instrument set varies across equations the third estimator based on fitted values for the dependent variable as well as the endogenous explanatory variables is consistent but inefficient relative to the generalized method of moments estimator

estimating systems of equations with different instruments for different equations abstract for applications where different instruments are required for different equations this paper offers a relatively primitive set of assumptions under which the nonlinear three stage least squares estimator is the asymptotically efficient generalized method of moments estimator these conditions can be verified for a general class of panel data models under reasonable assumptions about the dynamics in the model on the other hand the 3sls estimator is necessarily inefficient for models such as hedonic price systems and for certain simultaneous equations models with measurement error or omitted variables in some equations

panel data and unobservable individual effects abstract an important purpose in pooling time series and cross section data is to control for individual specific unobservable effects which may be correlated with other explanatory variables e g latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions using instrumental variables and the time invariant characteristics of the latent variable we derive 1 1 a test for the presence of this effect and for the over identifying restriction we use 2 2 necessary and sufficient conditions for identification of all the parameters in the model and 3 3 the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within groups estimator we calculate efficient estimates of a wage equation from the michigan income dynamics data which indicate substantial differences from within groups and balestra nerlove estimates particularly a significantly higher estimate of the returns to schooling

some further results on the exact small sample properties of the instrumental variable estimator we present new results on the exact small sample distribution of the instrumental variable estimator in particular we compare the small sample distribution to the asymptotic distribution

data adaptive evolutionary spectral estimation we present a novel data adaptive estimator for the evolutionary spectrum of nonstationary signals we model the signal at a frequency of interest as a sinusoid with a time varying amplitude which is accurately represented by an orthonormal basis expansion we then compute a minimum mean squared error estimate of this amplitude and use it to estimate the time varying spectrum at that frequency all while minimizing the interference from the signal components at other frequencies repeating the process over all frequencies we obtain a power distribution that is consistent with the wold cramer evolutionary spectrum and reduces to capon s 1969 method for the stationary case our estimator possesses desirable properties in terms of time frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data we also propose a new estimator for the autocorrelation of nonstationary signals this autocorrelation estimate is needed in the data adaptive spectral estimation we illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time frequency distribution with exponential kernels

the finite sample properties of simultaneous equations estimates and estimators bayesian and non bayesian approaches abstract after discussing the need for good finite sample estimation procedures for simultaneous equations models and showing the inadequacies of asymptotically justified estimators it is shown how the bayesian method of moments bmom provides an exact finite sample analysis of unrestricted reduced form systems then optimal finite sample estimates of structural coefficients are derived using three standard loss functions and they are compared to traditional bayesian optimal estimates monte carlo experimental evidence from four studies on the relative performance of bayesian and non bayesian estimators is reviewed with the finding that the performance of bayesian estimators is better

symmetry based inference in an instrumental variable setting we describe exact inference based on group invariance assumptions that specify various forms of symmetry in the distribution of a disturbance vector in a general nonlinear model it is shown that such mild assumptions can be equivalently formulated in terms of exact confidence sets for the parameters of the functional form when applied to the linear model this exact inference provides a unified approach to a variety of parametric and distribution free tests in particular we consider exact instrumental variable inference based on symmetry assumptions the unboundedness of exact confidence sets is related to the power to reject a hypothesis of underidentification in a multivariate instrumental variables context generalizations of anderson rubin confidence sets are considered

efficient estimation of models for dynamic panel data abstract in this paper we consider a dynamic model for panel data we show that under standard assumptions there are more moment conditions than are currently exploited in the literature some of these are linear but others are quadratic so that nonlinear gmm is required we also show that exogenous regressors generate a larger number of relevant moment conditions in a dynamic model than they would in a static model

the zero information limit condition and spurious inference in weakly identified models abstract in many econometric models the asymptotic variance of a parameter estimate depends on the value of another structural parameter in such a way that the data contain little information about the former when the latter is close to a critical value this paper introduces the zero information limit condition zilc to identify such models where weak identification leads to spurious inference we find that standard errors tend to be underestimated in these cases but the size of the asymptotic t test may either be too great the intuitive case emphasized in the weak instrument literature or too small as in two cases illustrated here

consistent estimation with a large number of weak instruments this paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables iv regression when the available instruments are weak and the number of instruments k n goes to infinity with the sample size we show that consistent estimation depends importantly on the strength of the instruments as measured by r the rate of growth of the so called concentration parameter and also on k n in particular when k n the concentration parameter can grow even if each individual instrument is only weakly correlated with the endogenous explanatory variables and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature hence the use of many weak instruments may actually improve the performance of certain point estimators more specifically we find that the limited information maximum likelihood liml estimator and the bias corrected two stage least squares b2sls estimator are consistent when k n r n 0 while the two stage least squares 2sls estimator is consistent only if k n r n 0 as n these consistency results suggest that liml and b2sls are more robust to instrument weakness than 2sls

efficiency bounds for semiparametric regression efficiency bounds for conditional moment restrictions with a nonparametric component are derived there is a given function of the data a random sample from a distribution f and a parameter the restriction is that a conditional expectation of this function is zero at some point in the parameter space the parameter has two parts a finite dimensional component and a general function evaluated at a subset of the conditioning variables an example is a regression function that is additive in parametric and nonparametric component as arises in sample selection models copyright 1992 by the econometric society

tests with correct size when instruments can be arbitrarily weak abstract this paper applies classical exponential family statistical theory to develop a unifying framework for testing structural parameters in the simultaneous equations model under the assumption of normal errors with known reduced form variance matrix the results can be divided into the limited information and full information categories in the limited information model it is possible to characterize the entire class of similar tests in a model with only one endogenous explanatory variable in the full information framework this paper proposes a family of similar tests for subsets of endogenous variables coefficients for both limited and full information models there exist power upper bounds for unbiased tests when the model is just identified the anderson rubin score and pseudo conditional likelihood ratio tests are optimal when the model is over identified the pseudo conditional likelihood ratio test has power close to the power envelope when identification is strong

a lagrange multiplier test for cross sectional dependence in a fixed effects panel data model abstract it is well known that the standard breusch and pagan 1980 lm test for cross equation correlation in a sur model is not appropriate for testing cross sectional dependence in panel data models when the number of cross sectional units n is large and the number of time periods t is small in fact a scaled version of this lm test was proposed by pesaran 2004 and its finite sample bias was corrected by pesaran et al 2008 this was done in the context of a heterogeneous panel data model this paper derives the asymptotic bias of this scaled version of the lm test in the context of a fixed effects homogeneous panel data model this asymptotic bias is found to be a constant related to n and t which suggests a simple bias corrected lm test for the null hypothesis additionally the paper carries out some monte carlo experiments to compare the finite sample properties of this proposed test with existing tests for cross sectional dependence

initial conditions and moment restrictions in dynamic panel data models estimation of the dynamic error components model is considered using two alternative linear estimators that are designed to improve the properties of the standard first differenced gmm estimator both estimators require restrictions on the initial conditions process asymptotic efficiency comparisons and monte carlo simulations for the simple ar 1 model demonstrate the dramatic improvement in performance of the proposed estimators compared to the usual first differenced gmm estimator and compared to non linear gmm the importance of these results is illustrated in an application to the estimation of a labour demand model using company panel data