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on Econometrics |
| By: | Christis Katsouris |
| Abstract: | In this paper, we study the estimation of the threshold predictive regression model with hybrid stochastic local unit root predictors. We demonstrate the estimation procedure and derive the asymptotic distribution of the least square estimator and the IV based estimator proposed by \cite{magdalinos2009limit}, under the null hypothesis of a diminishing threshold effect. Simulation experiments focus on the finite sample performance of our proposed estimators and the corresponding predictability tests as in \cite{gonzalo2012regime}, under the presence of threshold effects with stochastic local unit roots. An empirical application to stock return equity indices, illustrate the usefulness of our framework in uncovering regimes of predictability during certain periods. In particular, we focus on an aspect not previously examined in the predictability literature, that is, the effect of economic policy uncertainty. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.00860&r=ecm |
| By: | Xuan Leng; Yutao Sun |
| Abstract: | Panel data models often use fixed effects to account for unobserved heterogeneities. These fixed effects are typically incidental parameters and their estimators converge slowly relative to the square root of the sample size. In the maximum likelihood context, this induces an asymptotic bias of the likelihood function. Test statistics derived from the asymptotically biased likelihood, therefore, no longer follow their standard limiting distributions. This causes severe distortions in test sizes. We consider a generic class of dynamic nonlinear models with two-way fixed effects and propose an analytical bias correction method for the likelihood function. We formally show that the likelihood ratio, the Lagrange-multiplier, and the Wald test statistics derived from the corrected likelihood follow their standard asymptotic distributions. As a by-product, a bias-corrected estimator of the structural parameter can also be derived from the corrected likelihood function. We evaluate the performance of our bias correction procedure through simulations. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.03134&r=ecm |
| By: | Liang Chen; Minyuan Zhang |
| Abstract: | This paper focuses on estimating the coefficients and average partial effects of observed regressors in nonlinear panel data models with interactive fixed effects, using the common correlated effects (CCE) framework. The proposed two-step estimation method involves applying principal component analysis to estimate latent factors based on cross-sectional averages of the regressors in the first step, and jointly estimating the coefficients of the regressors and factor loadings in the second step. The asymptotic distributions of the proposed estimators are derived under general conditions, assuming that the number of time-series observations is comparable to the number of cross-sectional observations. To correct for asymptotic biases of the estimators, we introduce both analytical and split-panel jackknife methods, and confirm their good performance in finite samples using Monte Carlo simulations. An empirical application utilizes the proposed method to study the arbitrage behaviour of nonfinancial firms across different security markets. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.13199&r=ecm |
| By: | Pedro H. C. Sant'Anna; Qi Xu |
| Abstract: | This paper studies difference-in-differences (DiD) setups with repeated cross-sectional data and potential compositional changes across time periods. We begin our analysis by deriving the efficient influence function and the semiparametric efficiency bound for the average treatment effect on the treated (ATT). We introduce nonparametric estimators that attain the semiparametric efficiency bound under mild rate conditions on the estimators of the nuisance functions, exhibiting a type of rate doubly-robust (DR) property. Additionally, we document a trade-off related to compositional changes: We derive the asymptotic bias of DR DiD estimators that erroneously exclude compositional changes and the efficiency loss when one fails to correctly rule out compositional changes. We propose a nonparametric Hausman-type test for compositional changes based on these trade-offs. The finite sample performance of the proposed DiD tools is evaluated through Monte Carlo experiments and an empirical application. As a by-product of our analysis, we present a new uniform stochastic expansion of the local polynomial multinomial logit estimator, which may be of independent interest. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.13925&r=ecm |
| By: | David Bruns-Smith; Oliver Dukes; Avi Feller; Elizabeth L. Ogburn |
| Abstract: | We provide a novel characterization of augmented balancing weights, also known as Automatic Debiased Machine Learning (AutoDML). These estimators combine outcome modeling with balancing weights, which estimate inverse propensity score weights directly. When the outcome and weighting models are both linear in some (possibly infinite) basis, we show that the augmented estimator is equivalent to a single linear model with coefficients that combine the original outcome model coefficients and OLS; in many settings, the augmented estimator collapses to OLS alone. We then extend these results to specific choices of outcome and weighting models. We first show that the combined estimator that uses (kernel) ridge regression for both outcome and weighting models is equivalent to a single, undersmoothed (kernel) ridge regression; this also holds when considering asymptotic rates. When the weighting model is instead lasso regression, we give closed-form expressions for special cases and demonstrate a ``double selection'' property. Finally, we generalize these results to linear estimands via the Riesz representer. Our framework ``opens the black box'' on these increasingly popular estimators and provides important insights into estimation choices for augmented balancing weights. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.14545&r=ecm |
| By: | Arindrajit Dube; Daniele Girardi; Òscar Jordà; Alan M. Taylor |
| Abstract: | Many of the challenges in the estimation of dynamic heterogeneous treatment effects can be resolved with local projection (LP) estimators of the sort used in applied macroeconometrics. This approach provides a convenient alternative to the more complicated solutions proposed in the recent literature on Difference-in-Differences (DiD). The key is to combine LPs with a flexible ‘clean control’ condition to define appropriate sets of treated and control units. Our proposed LP-DiD estimator is clear, simple, easy and fast to compute, and it is transparent and flexible in its handling of treated and control units. Moreover, it is quite general, including in its ability to control for pre-treatment values of the outcome and of other time-varying covariates. The LP-DiD estimator does not suffer from the negative weighting problem, and indeed can be implemented with any weighting scheme the investigator desires. Simulations demonstrate the good performance of the LP-DiD estimator in common settings. Two recent empirical applications illustrate how LP-DiD addresses the bias of conventional fixed effects estimators, leading to potentially different results. |
| JEL: | C1 C23 C5 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:31184&r=ecm |
| By: | Paulo M.M. Rodrigues; João Nicolau; Marian Z. Stoykov |
| Abstract: | This paper provides novel theoretical results for the estimation of the conditional tail index of Pareto and Pareto-type distributions in a time series context. We show that both the estimators and relevant test statistics are normally distributed in the limit, when independent and identically distributed or dependent data are considered. Simulation results provide support for the theoretical findings and highlight the good finite sample properties of the approach in a time series context. The proposed methodology is then used to analyze stock returns’ tail risk dynamics. Two empirical applications are provided. The first consists in testing whether the time-varying tail exponents across firms follow Kelly and Jiang’s (2014) assumption of common firm level tail dynamics. The results obtained from our sample seem not to favour this hypothesis. The second application, consists of the evaluation of the impact of two market risk indicators, VIX and Expected Shortfall (ES) and two firm specific covariates, capitalization and market-to-book on stocks tail risk dynamics. Although all variables seem important drivers of firms’ tail risk dynamics, it is found that overall ES and firms’ capitalization seem to have overall wider impact. |
| JEL: | C22 C58 G12 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w202306&r=ecm |
| By: | Jann Spiess; Guido Imbens; Amar Venugopal |
| Abstract: | Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parametrized models in causal inference, including synthetic control with many control units. In such models, there may be so many free parameters that the model fits the training data perfectly. As a motivating example, we first investigate high-dimensional linear regression for imputing wage data, where we find that models with many more covariates than sample size can outperform simple ones. As our main contribution, we document the performance of high-dimensional synthetic control estimators with many control units. We find that adding control units can help improve imputation performance even beyond the point where the pre-treatment fit is perfect. We then provide a unified theoretical perspective on the performance of these high-dimensional models. Specifically, we show that more complex models can be interpreted as model-averaging estimators over simpler ones, which we link to an improvement in average performance. This perspective yields concrete insights into the use of synthetic control when control units are many relative to the number of pre-treatment periods. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.00700&r=ecm |
| By: | Christian Bongiorno; Marco Berritta |
| Abstract: | In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance matrices, without knowledge of the true covariance matrix. In this study, we demonstrate that this minimization problem is equivalent to minimizing the loss of information between the true population covariance and the rotational invariant estimator for normal multivariate variables. However, for Student's t distributions, the minimal Frobenius norm does not necessarily minimize the information loss in finite-sized matrices. Nevertheless, such deviations vanish in the asymptotic regime of large matrices, which might extend the applicability of random matrix theory results to Student's t distributions. These distributions are characterized by heavy tails and are frequently encountered in real-world applications such as finance, turbulence, or nuclear physics. Therefore, our work establishes a connection between statistical random matrix theory and estimation theory in physics, which is predominantly based on information theory. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.14098&r=ecm |
| By: | Konrad Menzel |
| Abstract: | We consider the problem of extrapolating treatment effects across heterogeneous populations (``sites"/``contexts"). We consider an idealized scenario in which the researcher observes cross-sectional data for a large number of units across several ``experimental" sites in which an intervention has already been implemented to a new ``target" site for which a baseline survey of unit-specific, pre-treatment outcomes and relevant attributes is available. We propose a transfer estimator that exploits cross-sectional variation between individuals and sites to predict treatment outcomes using baseline outcome data for the target location. We consider the problem of obtaining a predictor of conditional average treatment effects at the target site that is MSE optimal within a certain class and subject to data constraints. Our approach is design-based in the sense that the performance of the predictor is evaluated given the specific, finite selection of experimental and target sites. Our approach is nonparametric, and our formal results concern the construction of an optimal basis of predictors as well as convergence rates for the estimated conditional average treatment effect relative to the constrained-optimal population predictor for the target site. We illustrate our approach using a combined data set of five multi-site randomized controlled trials (RCTs) to evaluate the effect of conditional cash transfers on school attendance. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.01435&r=ecm |
| By: | Badi Baltagi (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244) |
| Abstract: | Mundlak (1978) shows that the fixed effects estimator is equivalent to the random effects estimator in the one-way error component model once the random individual effects are modeled as a linear function of all the averaged regressors over time. In the spirit of Mundlak, this paper shows that this result also holds for the two-way error component model once this individual and time effects are modeled as linear functions of all the averaged regressors across time and across individuals. Woolridge (2021) also shows that the two-way fixed effects estimator can be obtained as a pooled OLS with the regressors augmented by the time and individual averages and calls it the two-way Mundlak estimator. While Mundlak (1978) used GLS rather than OLS on this augmented regression, we show that both estimators are equivalent for this augmented regression. This extends Baltagi’s (2006) results from the one-way to the two-way error component model. The F test suggested by Mundlak (1978) to test for this correlation between the random effects and the regressors generate a Hausman (1978) type test that is easily generalizable to the two-way Mundlak regression. In fact, the resulting F-tests for the two-way error component regression are related to the Hausman type tests proposed by Kang (1985) for the two-way error component model. |
| Keywords: | Mundlak Regression, Panel Data, Fixed and Random Effects, Two-way error components model, Hausman test |
| JEL: | C33 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:max:cprwps:256&r=ecm |
| By: | Sung Hoon Choi; Donggyu Kim |
| Abstract: | In this paper, we develop a novel large volatility matrix estimation procedure for analyzing global financial markets. Practitioners often use lower-frequency data, such as weekly or monthly returns, to address the issue of different trading hours in the international financial market. However, this approach can lead to inefficiency due to information loss. To mitigate this problem, our proposed method, called Structured Principal Orthogonal complEment Thresholding (Structured-POET), incorporates structural information for both global and national factor models. We establish the asymptotic properties of the Structured-POET estimator, and also demonstrate the drawbacks of conventional covariance matrix estimation procedures when using lower-frequency data. Finally, we apply the Structured-POET estimator to an out-of-sample portfolio allocation study using international stock market data. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.01464&r=ecm |
| By: | Lutz Kilian; Michael D. Plante; Alexander W. Richter |
| Abstract: | This paper clarifies the conditions under which the state-of-the-art approach to identifying TFP news shocks in Kurmann and Sims (2021, KS) identifies not only news shocks but also surprise shocks. We examine the ability of the KS procedure to recover responses to these shocks from data generated by a conventional New Keynesian DSGE model. Our analysis shows that the KS response estimator tends to be strongly biased even in the absence of measurement error. This bias worsens in realistically small samples, and the estimator becomes highly variable. Incorporating a direct measure of TFP news into the model and adapting the identification strategy accordingly removes this asymptotic bias and greatly reduces the RMSE when TFP news are correctly measured. However, the high variability of this alternative estimator in small samples suggests caution in interpreting empirical estimates. We examine to what extent empirical estimates of the responses to news and surprise shocks from a range of VAR models based on alternative measures of TFP news are economically plausible. |
| Keywords: | Structural VAR; total factor productivity (TFP); productivity shock; news; expectation |
| JEL: | C32 C51 C61 E32 |
| Date: | 2023–04–20 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddwp:96048&r=ecm |
| By: | Mohamed Hamdouche (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité); Pierre Henry-Labordere (Qube RT); Huyên Pham (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité) |
| Abstract: | We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We can estimate the drift function from data samples either by kernel regression methods or with LSTM neural networks, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with a toy autoregressive model, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal and temporal dependencies metrics. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets. Finally, we illustrate the SB approach for generating sequence of images. |
| Keywords: | generative models, time series, Schrödinger bridge, kernel estimation, deep hedging |
| Date: | 2023–04–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04063041&r=ecm |
| By: | Jean-Jacques Forneron; Liang Zhong |
| Abstract: | Generalized and Simulated Method of Moments are often used to estimate structural Economic models. Yet, it is commonly reported that optimization is challenging because the corresponding objective function is non-convex. For smooth problems, this paper shows that convexity is not required: under a global rank condition involving the Jacobian of the sample moments, certain algorithms are globally convergent. These include a gradient-descent and a Gauss-Newton algorithm with appropriate choice of tuning parameters. The results are robust to 1) non-convexity, 2) one-to-one non-linear reparameterizations, and 3) moderate misspecification. In contrast, Newton-Raphson and quasi-Newton methods can fail to converge for the same estimation because of non-convexity. A simple example illustrates a non-convex GMM estimation problem that satisfies the aforementioned rank condition. Empirical applications to random coefficient demand estimation and impulse response matching further illustrate the results. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.14386&r=ecm |
| By: | Carsten H. Chong; Viktor Todorov |
| Abstract: | We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the conditional characteristic function of the price increment until the options' expiration and we use these estimates to recover spot volatility. Our volatility of volatility estimator is then formed from the sample variance and first-order autocovariance of the spot volatility increments, with the latter correcting for the bias in the former due to option observation errors. The leverage effect estimator is the sample covariance between price increments and the estimated volatility increments. The rate of convergence of the estimators depends on the diffusive innovations in the latent volatility process as well as on the observation error in the options with strikes in the vicinity of the current spot price. Feasible inference is developed in a way that does not require prior knowledge of the source of estimation error that is asymptotically dominating. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.04137&r=ecm |
| By: | Luis J. Álvarez (Banco de España); Florens Odendahl (Banco de España) |
| Abstract: | We propose a method to adjust for data outliers in Bayesian Vector Autoregressions (BVARs), which allows for different outlier magnitudes across variables and rescales the reduced form error terms. We use the method to document several facts about the effect of outliers on estimation and out-of-sample forecasting results using euro area macroeconomic data. First, the COVID-19 pandemic led to large swings in macroeconomic data that distort the BVAR estimation results. Second, these swings can be addressed by rescaling the shocks’ variance. Third, taking into account outliers before 2020 leads to mild improvements in the point forecasts of BVARs for some variables and horizons. However, the density forecast performance considerably deteriorates. Therefore, we recommend taking into account outliers only on pre-specified dates around the onset of the COVID-19 pandemic. |
| Keywords: | COVID-19 pandemic, outliers, Bayesian VARs, forecasting, euro area |
| JEL: | C11 C32 C51 E37 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:2239&r=ecm |
| By: | Cantone, Giulio Giacomo; Tomaselli, Venera |
| Abstract: | Multiverse analysis is a paradigm for estimation of the uncertainty regarding the veracity of a scientific claim, through a systemic not random sampling of a massive set of specifications of a model, which is the multiverse. Specifications, once fit on a sample, result in statistics. Observation of the variability of result statistics across groups of specifications is considered useful for checking the robustness of the claim or for better understanding its premises. However, the assumptions behind these procedures are not explicit and not always univocal: generally, the proprieties of a multiversal sample hold uniformly only for non-parametric assumptions. A new formal categorisation of the analytical choices in modelling is proposed. It helps to make the assumption of the multiverse more transparent and to check the parametric assumption. These theories are applied to the panel dataset. The analytical process is documented from the design of the hypothesis to the computation of the distribution of estimates for the same generalised linear effect. The analysis highlights the sensitivity of the model to the estimation of fixed covariates in the panel and how these results are so sensitive to this decision to twist the estimates of the linear effect. In the conclusion, the theory of multiversal sampling is related to the debate on how to weigh a multiverse. |
| Date: | 2023–05–10 |
| URL: | http://d.repec.org/n?u=RePEc:osf:metaar:ukvw7&r=ecm |
| By: | Silvia Goncalves; Ana María Herrera; Lutz Kilian; Elena Pesavento |
| Abstract: | Do state-dependent local projections asymptotically recover the population responses of macroeconomic aggregates to structural shocks? The answer to this question depends on how the state of the economy is determined and on the magnitude of the shocks. When the state is exogenous, the local projection estimator recovers the population response regardless of the shock size. When the state depends on macroeconomic shocks, as is common in empirical work, local projections only recover the conditional response to an infinitesimal shock, but not the responses to larger shocks of interest in many applications. Simulations suggest that fiscal multipliers may be off by as much as 40 percent. |
| Keywords: | local projections; business cycle; state-dependence; impulse response; multiplier; nonlinear structural model; potential outcomes model |
| JEL: | C22 C32 H20 C51 E32 E52 E60 E62 |
| Date: | 2023–04–19 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddwp:96045&r=ecm |
| By: | Cheng Zhang; Nilam Nur Amir Sjarif; Roslina Binti Ibrahim |
| Abstract: | Forecasting financial time series has long been a challenging problem that has attracted attention from both researchers and practitioners. Statistical and machine learning techniques have both been explored to develop effective forecasting models in the past few decades. With recent developments in deep learning models, financial time series forecasting models have advanced significantly, and these developments are often difficult to keep up with. Hence, we have conducted this literature review to provide a comprehensive assessment of recent research from 2020 to 2022 on deep learning models used to predict prices based on financial time series. Our review presents different data sources and neural network structures, as well as their implementation details. Our goals are to ensure that interested researchers remain up-to-date on recent developments in the field and facilitate the selection of baselines based on models used in prior studies. Additionally, we provide suggestions for future research based on the content in this review. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.04811&r=ecm |
| By: | Andrew Na; Meixin Zhang; Justin Wan |
| Abstract: | In this paper, we propose a generative adversarial network (GAN) approach for efficiently computing volatility surfaces. The idea is to make use of the special GAN neural architecture so that on one hand, we can learn volatility surfaces from training data and on the other hand, enforce no-arbitrage conditions. In particular, the generator network is assisted in training by a discriminator that evaluates whether the generated volatility matches the target distribution. Meanwhile, our framework trains the GAN network to satisfy the no-arbitrage constraints by introducing penalties as regularization terms. The proposed GAN model allows the use of shallow networks which results in much less computational costs. In our experiments, we demonstrate the performance of the proposed method by comparing with the state-of-the-art methods for computing implied and local volatility surfaces. We show that our GAN model can outperform artificial neural network (ANN) approaches in terms of accuracy and computational time. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.13128&r=ecm |