Publications
Papers
Joint with Xinyue Bei, Marine Carrasco and Enrique Sentana
CEMFI Working Paper 2213, revised February 2024, forthcoming in the Journal of Econometrics
Testing normality against discrete normal mixtures is complex because some parameters turn increasingly underidentified along alternative ways of approaching the null, others are inequality constrained, and several higher-order derivatives become identically 0. These problems make the maximum of the alternative model log-likelihood function numerically unreliable. We propose score-type tests asymptotically equivalent to the likelihood ratio as the largest of two simple intuitive statistics that only require estimation under the null. One novelty of our approach is that we treat symmetrically both ways of writing the null hypothesis without excluding any region of the parameter space. We derive the asymptotic distribution of our tests under the null and sequences of local alternatives. We also show that their asymptotic distribution is the same whether applied to observations or standardized residuals from heteroskedastic regression models. Finally, we study their power in simulations and apply them to the residuals of Mincer earnings functions.
Joint with Gabriele Fiorentini and Enrique Sentana
CEMFI Working Paper 2103, revised January 2024, forthcoming in Econometrics and Statistics
The information matrix test for a normal random vector is shown to coincide with the sum of the moment tests for all third- and fourth-order multivariate Hermite polynomials. The statistic is decomposed as the sum of the marginal information matrix test for a subvector, the conditional information matrix test for the complementary subvector, and a third leftover component. It is also shown that exact finite sample distributions can be obtained by drawing spherical Gaussian vectors and orthogonalising them using sample moments. These tests are applied to assess the implications of Gibrat's law for US city sizes using the three most recent censuses.
Joint with Xinyue Bei and Enrique Sentana
CEMFI Working Paper 2302, revised January 2024, forthcoming in Econometrics and Statistics
Tests are developed for neglected serial correlation when the information matrix is repeatedly singular under the null hypothesis. Specifically, consideration is given to white noise against a multiplicative seasonal AR model, and a local-level model against a nesting UCARIMA one. The proposed tests, which involve higher-order derivatives, are asymptotically equivalent to the likelihood ratio test but only require estimation under the null. It is shown that the tests effectively check that certain autocorrelations of the observations are zero, so their asymptotic distribution is standard. Monte Carlo exercises examine finite sample size and power properties, with comparisons made to alternative approaches.
Joint with Martín Almuzara, Gabriele Fiorentini and Enrique Sentana
CEMFI Working Paper 2204, revised August 2023, forthcoming in the Journal of Business and Economic Statistics
We use the information in the successive vintages of GDE and GDI to obtain an improved timely measure of US aggregate output by exploiting cointegration between the different measures taking seriously their monthly release calendar. We also combine all existing overlapping comprehensive revisions to achieve further improvements. We pay particular attention to the Great Recession and the COVID-19 pandemic, which, despite producing dramatic fluctuations, did not generate noticeable revisions in previous growth rates. Our results suggest that revised GDE estimates, unlike GDI ones, are increasingly precise and receive higher weights, but early estimates retain some influence.
Joint with Gabriele Fiorentini and Enrique Sentana
SERIEs, 14 (3-4), pp. 253-300, December 2023
Arellano (1989a) showed that valid equality restrictions on covariance matrices could result in efficiency losses for Gaussian PMLEs in simultaneous equations models. We revisit his two-equation example using finite normal mixtures PMLEs instead, which are also consistent for mean and variance parameters regardless of the true distribution of the shocks. Because such mixtures provide good approximations to many distributions, we relate the asymptotic variance of our estimators to the relevant semiparametric efficiency bound. Our Monte Carlo results indicate that they systematically dominate MD, and that the version that imposes the valid covariance restriction is more efficient than the unrestricted one.
Joint with Xinyue Bei and Enrique Sentana
Journal of Applied Econometrics, 37 (7), pp. 1295-1313, November/December 2022
We propose a multivariate normality test against skew normal distributions using higher-order log-likelihood derivatives, which is asymptotically equivalent to the likelihood ratio but only requires estimation under the null. Numerically, it is the supremum of the univariate skewness coefficient test over all linear combinations of the variables. We can simulate its exact finite sample distribution for any multivariate dimension and sample size. Our Monte Carlo exercises confirm its power advantages over alternative approaches. Finally, we apply it to the joint distribution of US city sizes in two consecutive censuses finding that non-normality is very clearly seen in their growth rates.
Joint with Gabriele Fiorentini and Enrique Sentana
SERIEs, 13 (1-2), pp. 429-474, May 2022
We propose simple specification tests for independent component analysis and structural vector autoregressions with non-Gaussian shocks that check the normality of a single shock and the potential cross-sectional dependence among several of them. Our tests compare the integer (product) moments of the shocks in the sample with their population counterparts. Importantly, we explicitly consider the sampling variability resulting from using shocks computed with consistent parameter estimators. We study the finite sample size of our tests in several simulation exercises and discuss some bootstrap procedures. We also show that our tests have non-negligible power against a variety of empirically plausible alternatives.
Joint with Jesús Bueren and Julio A. Crego
Journal of Applied Econometrics, 36 (7), pp. 878-897, November 2021
We propose a methodology to classify individuals into few but meaningful health groups by estimating a panel Markov switching model that exploits rich information from panel household surveys. Using the HRS, we identify four persistent health groups, depending on individual's physical and mental disabilities. Our classification outperforms existing health measures at explaining entry in nursing homes, home health care, out-of-pocket medical expenses, and mortality for individuals in the HRS, ELSA, and SHARE. Through a workhorse model of savings, we recover an asset cost of bad health that is twice as big as when using self-reported health.
Joint with Marine Carrasco and Enrique Sentana
Journal of Econometrics, 218 (2), pp. 655-689, October 2020
We propose specification tests for parametric distributions that compare the potentially complex theoretical and empirical characteristic functions using the continuum of moment conditions analogue to an overidentifying restrictions test, which takes into account the correlation between influence functions for different argument values. We derive its asymptotic distribution for fixed regularization parameter and when this vanishes with the sample size. We show its consistency against any deviation from the null, study its local power and compare it with existing tests. An extensive Monte Carlo exercise confirms that our proposed tests display good power in finite samples against a variety of alternatives.
Joint with Enrique Sentana
Journal of Business and Economic Statistics, 38 (2), pp. 350-366, April 2020
We derive computationally simple and intuitive expressions for score tests of Gaussian copulas against Generalized Hyperbolic alternatives, including symmetric and asymmetric Student t, and many other examples. We decompose our tests into third and fourth moment components, and obtain one-sided Likelihood Ratio analogues, whose standard asymptotic distribution we provide. Our Monte Carlo exercises confirm the reliable size of parametric bootstrap versions of our tests, and their substantial power gains over alternative procedures. In an empirical application to CRSP stocks, we find that short-term reversals and momentum effects are better captured by non-Gaussian copulas, whose parameters we estimate by indirect inference.
Joint with Martín Almuzara and Enrique Sentana
Quantitative Economics, 10 (3), pp. 981-1017, July 2019
We exploit the rationale behind the Expectation Maximization algorithm to derive simple to implement and interpret LM normality tests for the innovations of the latent variables in linear state space models against generalized hyperbolic alternatives, including symmetric and asymmetric Student ts. We decompose our tests into third and fourth moment components, and obtain one‐sided likelihood ratio analogues, whose asymptotic distribution we provide. When we apply our tests to a common trend model which combines the expenditure and income versions of US aggregate real output to improve its measurement, we reject normality if the sample period extends beyond the Great Moderation.
Joint with Dacheng Xiu
Journal of Econometrics, 203 (2), pp. 297–315, April 2018
We introduce downward volatility jumps into a general non-affine modeling framework of the term structure of variance. With variance swaps and S&P 500 returns, we find that downward volatility jumps are associated with a resolution of policy uncertainty, mostly through statements from FOMC meetings and speeches of the Federal Reserve’s chairman. Ignoring such jumps may lead to an incorrect interpretation of the tail events, and hence biased estimates of variance risk premia. On the modeling side, we explore the structural differences and relative goodness-of-fits of factor specifications. We find that log-volatility models with at least one Ornstein–Uhlenbeck factor and double-sided jumps are superior in capturing volatility dynamics and pricing variance swaps, compared to the affine model prevalent in the literature or non-affine specifications without downward jumps.
Joint with Yacine Aït-Sahalia and Elena Manresa
Journal of Econometrics, 187 (2), pp. 418-435, August 2015
We propose a method for estimating stochastic volatility models by adapting the HJM approach to the case of volatility derivatives. We characterize restrictions that observed variance swap dynamics have to satisfy to prevent arbitrage opportunities. When the drift of variance swap rates are affine under the pricing measure, we obtain closed form expressions for those restrictions and formulas for forward variance curves. Using data on the S&P500 index and variance swap rates on different time to maturities, we find that linear mean-reverting one factor models provide inaccurate representation of the dynamics of the variance swap rates while two-factor models significantly outperform the former both in and out of sample.
Joint with Gabriele Fiorentini and Enrique Sentana
Journal of Econometrics, 177 (2), pp. 233-249, December 2013
Sequential maximum likelihood and GMM estimators of distributional parameters obtained from the standardised innovations of multivariate conditionally heteroskedastic dynamic regression models evaluated at Gaussian PML estimators preserve the consistency of mean and variance parameters while allowing for realistic distributions. We assess their efficiency, and obtain moment conditions leading to sequential estimators as efficient as their joint ML counterparts. We also obtain standard errors for VaR and CoVaR, and analyse the effects on these measures of distributional misspecification. Finally, we illustrate the small sample performance of these procedures through simulations and apply them to analyse the risk of large eurozone banks.
Joint with Enrique Sentana
Journal of Econometrics, 154 (1), pp. 16-34, January 2010
We analyse the asymptotic properties of mean–variance efficiency tests based on generalised methods of moments, and parametric and semiparametric likelihood procedures that assume elliptical innovations. We study the trade-off between efficiency and robustness, and prove that the parametric estimators provide asymptotically valid inferences when the conditional distribution of the innovations is elliptical but possibly misspecified and heteroskedastic. We compare the small sample performance of the alternative tests in a Monte Carlo study, and find some discrepancies with their asymptotic properties. Finally, we present an empirical application to US stock returns, which rejects the mean–variance efficiency of the market portfolio.
Joint with Mark W. Watson
Journal of Business and Economic Statistics, 25 (1), pp. 91-96, January 2007
Bai and Ng proposed a consistent estimator for the number of static factors in a large N and T approximate factor model. This article shows how the Bai–Ng estimator can be modified to consistently estimate the number of dynamic factors in a restricted dynamic factor model. The modification is straightforward: The standard Bai–Ng estimator is applied to residuals obtained by projecting the observed data onto lagged values of principal-components estimates of the static factors.
Comments and Contributions to Volumes
Joint with Gabriele Fiorentini and Enrique Sentana
In J.J. Dolado, L. Gambetti and C. Matthes (eds.) Essays in honour of Fabio Canova, Advances in Econometrics 44B, pp. 1-35, Emerald 2022
Joint with Enrique Sentana and Zhanyuan Tian
In A. Chudik, C. Hsiao and A. Timmermann (eds.) Essays in honor of M. Hashem Pesaran: Panel Modeling, Micro Applications and Econometric Methodology, Advances in Econometrics 43B, pp. 269-306, Emerald 2022
We study the statistical properties of Pearson correlation coefficients of Gaussian ranks, and Gaussian rank regressions - OLS applied to those ranks. We show that these procedures are fully efficient when the true copula is Gaussian and the margins are non-parametrically estimated, and remain consistent for their population analogues otherwise. We compare them to Spearman and Pearson correlations and their regression counterparts theoretically and in extensive Monte Carlo simulations. Empirical applications to migration and growth across US states, the augmented Solow growth model, and momentum and reversal effects in individual stock returns confirm that Gaussian rank procedures are insensitive to outliers.
Joint with Enrique Sentana
Journal of Financial Econometrics, 14 (2), pp. 248–252, Spring 2016
