pwc-archive/papers-with-abstracts huggingface dataset:
Extremal points of Lorenz curves and applications to inequality analysis
Authors: Amparo Baíllo, Javier Cárcamo, Carlos Mora-Corral
Date: 2021-03-04 00:00:00

We find the set of extremal points of Lorenz curves with fixed Gini index and compute the maximal $L^1$-distance between Lorenz curves with given values of their Gini coefficients. As an application we introduce a bidimensional index that simultaneously measures relative inequality and dissimilarity between two populations. This proposal employs the Gini indices of the variables and an $L^1$-distance between their Lorenz curves. The index takes values in a right-angled triangle, two of whose sides characterize perfect relative inequality-expressed by the Lorenz ordering between the underlying distributions. Further, the hypotenuse represents maximal distance between the two distributions. As a consequence, we construct a chart to, graphically, either see the evolution of (relative) inequality and distance between two income distributions over time or to compare the distribution of income of a specific population between a fixed time point and a range of years. We prove the mathematical results behind the above claims and provide a full description of the asymptotic properties of the plug-in estimator of this index. Finally, we apply the proposed bidimensional index to several real EU-SILC income datasets to illustrate its performance in practice.
Prewhitened Long-Run Variance Estimation Robust to Nonstationarity
Authors: Alessandro Casini, Pierre Perron
Date: 2021-03-03 00:00:00
Tasks: valid

We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite-sample properties under nonstationarity (i.e., fixed-b methods), or are theoretically valid under the null hypothesis but lead to tests that are not consistent under nonstationary alternative hypothesis (i.e., both fixed-b and traditional HAC estimators). The proposed estimator accounts explicitly for nonstationarity, unlike previous prewhitened procedures which are known to be unreliable, and leads to tests with accurate null rejection rates and good monotonic power. We also establish MSE bounds for LRV estimation that are sharper than previously established and use them to determine the data-dependent bandwidths.
Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference
Authors: Alessandro Casini, Taosong Deng, Pierre Perron
Date: 2021-03-02 00:00:00
Tasks: Time Series Analysis

We establish theoretical results about the low frequency contamination (i.e., long memory effects) induced by general nonstationarity for estimates such as the sample autocovariance and the periodogram, and deduce consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We present explicit expressions for the asymptotic bias of these estimates. We distinguish cases where this contamination only occurs as a small-sample problem and cases where the contamination continues to hold asymptotically. We show theoretically that nonparametric smoothing over time is robust to low frequency contamination. Our results provide new insights on the debate between consistent versus inconsistent long-run variance (LRV) estimation. Existing LRV estimators tend to be in inflated when the data are nonstationary. This results in HAR tests that can be undersized and exhibit dramatic power losses. Our theory indicates that long bandwidths or fixed-b HAR tests suffer more from low frequency contamination relative to HAR tests based on HAC estimators, whereas recently introduced double kernel HAC estimators do not super from this problem. Finally, we present second-order Edgeworth expansions under nonstationarity about the distribution of HAC and DK-HAC estimators and about the corresponding t-test in the linear regression model.
Network Cluster-Robust Inference
Authors: Michael P. Leung
Date: 2021-03-02 00:00:00
Tasks: Clustering

Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster-robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network-dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster-robust methods control size better than HAC estimators. However, for important classes of networks lacking low-conductance clusters, the former can exhibit substantial size distortion. To determine the number of low-conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low-conductance clusters and spectral clustering to construct them.
Some Finite Sample Properties of the Sign Test
Authors: Yong Cai
Date: 2021-03-02 00:00:00

This paper contains two finite-sample results concerning the sign test. First, we show that the sign-test is unbiased with independent, non-identically distributed data for both one-sided and two-sided hypotheses. The proof for the two-sided case is based on a novel argument that relates the derivatives of the power function to a regular bipartite graph. Unbiasedness then follows from the existence of perfect matchings on such graphs. Second, we provide a simple theoretical counterexample to show that the sign test over-rejects when the data exhibits correlation. Our results can be useful for understanding the properties of approximate randomization tests in settings with few clusters.
Standing on the Shoulders of Machine Learning: Can We Improve Hypothesis Testing?
Authors: Gary Cornwall, Jeff Chen, Beau Sauley
Date: 2021-03-02 00:00:00
Tasks: BIG-bench Machine Learning, Econometrics, Time Series, Time Series Analysis

In this paper we have updated the hypothesis testing framework by drawing upon modern computational power and classification models from machine learning. We show that a simple classification algorithm such as a boosted decision stump can be used to fully recover the full size-power trade-off for any single test statistic. This recovery implies an equivalence, under certain conditions, between the basic building block of modern machine learning and hypothesis testing. Second, we show that more complex algorithms such as the random forest and gradient boosted machine can serve as mapping functions in place of the traditional null distribution. This allows for multiple test statistics and other information to be evaluated simultaneously and thus form a pseudo-composite hypothesis test. Moreover, we show how practitioners can make explicit the relative costs of Type I and Type II errors to contextualize the test into a specific decision framework. To illustrate this approach we revisit the case of testing for unit roots, a difficult problem in time series econometrics for which existing tests are known to exhibit low power. Using a simulation framework common to the literature we show that this approach can improve upon overall accuracy of the traditional unit root test(s) by seventeen percentage points, and the sensitivity by thirty six percentage points.
The Kernel Trick for Nonlinear Factor Modeling
Authors: Varlam Kutateladze
Date: 2021-03-01 00:00:00
Tasks: Time Series, Time Series Analysis

Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and widespread use for various applications ranging from genomics to finance, this methodology has predominantly remained linear. This study estimates factors nonlinearly through the kernel method, which allows flexible nonlinearities while still avoiding the curse of dimensionality. We focus on factor-augmented forecasting of a single time series in a high-dimensional setting, known as diffusion index forecasting in macroeconomics literature. Our main contribution is twofold. First, we show that the proposed estimator is consistent and it nests linear PCA estimator as well as some nonlinear estimators introduced in the literature as specific examples. Second, our empirical application to a classical macroeconomic dataset demonstrates that this approach can offer substantial advantages over mainstream methods.
Structural models for policy-making: Coping with parametric uncertainty
Authors: Philipp Eisenhauer, Janoś Gabler, Lena Janys, Christopher Walsh
Date: 2021-03-01 00:00:00
Tasks: counterfactual, Decision Making, Decision Making Under Uncertainty

The ex-ante evaluation of policies using structural econometric models is based on estimated parameters as a stand-in for the true parameters. This practice ignores uncertainty in the counterfactual policy predictions of the model. We develop a generic approach that deals with parametric uncertainty using uncertainty sets and frames model-informed policy-making as a decision problem under uncertainty. The seminal human capital investment model by Keane and Wolpin (1997) provides a well-known, influential, and empirically-grounded test case. We document considerable uncertainty in the models's policy predictions and highlight the resulting policy recommendations obtained from using different formal rules of decision-making under uncertainty.
United States FDA drug approvals are persistent and polycyclic: Insights into economic cycles, innovation dynamics, and national policy
Authors: Iraj Daizadeh
Date: 2020-12-16 00:00:00
Tasks: Time Series, Time Series Analysis

It is challenging to elucidate the effects of changes in external influences (such as economic or policy) on the rate of US drug approvals. Here, a novel approach, termed the Chronological Hurst Exponent (CHE), is proposed, which hypothesizes that changes in the long-range memory latent within the dynamics of time series data may be temporally associated with changes in such influences. Using the monthly number the FDA Center for Drug Evaluation and Research (CDER) approvals from 1939 to 2019 as the data source, it is demonstrated that the CHE has a distinct S-shaped structure demarcated by an 8-year (1939-1947) Stagnation Period, a 27-year (1947-1974) Emergent (time-varying Period, and a 45-year (1974-2019) Saturation Period. Further, dominant periodicities (resolved via wavelet analyses) are identified during the most recent 45-year CHE Saturation Period at 17, 8 and 4 years; thus, US drug approvals have been following a Juglar-Kuznet mid-term cycle with Kitchin-like bursts. As discussed, this work suggests that (1) changes in extrinsic factors (e.g., of economic and/or policy origin ) during the Emergent Period may have led to persistent growth in US drug approvals enjoyed since 1974, (2) the CHE may be a valued method to explore influences on time series data, and (3) innovation-related economic cycles exist (as viewed via the proxy metric of US drug approvals).
Forecasting high-frequency financial time series: an adaptive learning approach with the order book data
Authors: Parley Ruogu Yang
Date: 2021-02-27 00:00:00
Tasks: Time Series, Time Series Analysis

This paper proposes a forecast-centric adaptive learning model that engages with the past studies on the order book and high-frequency data, with applications to hypothesis testing. In line with the past literature, we produce brackets of summaries of statistics from the high-frequency bid and ask data in the CSI 300 Index Futures market and aim to forecast the one-step-ahead prices. Traditional time series issues, e.g. ARIMA order selection, stationarity, together with potential financial applications are covered in the exploratory data analysis, which pave paths to the adaptive learning model. By designing and running the learning model, we found it to perform well compared to the top fixed models, and some could improve the forecasting accuracy by being more stable and resilient to non-stationarity. Applications to hypothesis testing are shown with a rolling window, and further potential applications to finance and statistics are outlined.
Simultaneous Bandwidths Determination for DK-HAC Estimators and Long-Run Variance Estimation in Nonparametric Settings
Authors: Federico Belotti, Alessandro Casini, Leopoldo Catania, Stefano Grassi, Pierre Perron
Date: 2021-02-26 00:00:00
Tasks: parameter estimation

We consider the derivation of data-dependent simultaneous bandwidths for double kernel heteroskedasticity and autocorrelation consistent (DK-HAC) estimators. In addition to the usual smoothing over lagged autocovariances for classical HAC estimators, the DK-HAC estimator also applies smoothing over the time direction. We obtain the optimal bandwidths that jointly minimize the global asymptotic MSE criterion and discuss the trade-off between bias and variance with respect to smoothing over lagged autocovariances and over time. Unlike the MSE results of Andrews (1991), we establish how nonstationarity affects the bias-variance trade-o?. We use the plug-in approach to construct data-dependent bandwidths for the DK-HAC estimators and compare them with the DK-HAC estimators from Casini (2021) that use data-dependent bandwidths obtained from a sequential MSE criterion. The former performs better in terms of size control, especially with stationary and close to stationary data. Finally, we consider long-run variance estimation under the assumption that the series is a function of a nonparametric estimator rather than of a semiparametric estimator that enjoys the usual T^(1/2) rate of convergence. Thus, we also establish the validity of consistent long-run variance estimation in nonparametric parameter estimation settings.
General Bayesian time-varying parameter VARs for predicting government bond yields
Authors: Manfred M. Fischer, Niko Hauzenberger, Florian Huber, Michael Pfarrhofer
Date: 2021-02-26 00:00:00
Tasks: Model Selection

Time-varying parameter (TVP) regressions commonly assume that time-variation in the coefficients is determined by a simple stochastic process such as a random walk. While such models are capable of capturing a wide range of dynamic patterns, the true nature of time variation might stem from other sources, or arise from different laws of motion. In this paper, we propose a flexible TVP VAR that assumes the TVPs to depend on a panel of partially latent covariates. The latent part of these covariates differ in their state dynamics and thus capture smoothly evolving or abruptly changing coefficients. To determine which of these covariates are important, and thus to decide on the appropriate state evolution, we introduce Bayesian shrinkage priors to perform model selection. As an empirical application, we forecast the US term structure of interest rates and show that our approach performs well relative to a set of competing models. We then show how the model can be used to explain structural breaks in coefficients related to the US yield curve.
Quasi-maximum likelihood estimation of break point in high-dimensional factor models
Authors: Jiangtao Duan, Jushan Bai, Xu Han
Date: 2021-02-25 00:00:00

This paper estimates the break point for large-dimensional factor models with a single structural break in factor loadings at a common unknown date. First, we propose a quasi-maximum likelihood (QML) estimator of the change point based on the second moments of factors, which are estimated by principal component analysis. We show that the QML estimator performs consistently when the covariance matrix of the pre- or post-break factor loading, or both, is singular. When the loading matrix undergoes a rotational type of change while the number of factors remains constant over time, the QML estimator incurs a stochastically bounded estimation error. In this case, we establish an asymptotic distribution of the QML estimator. The simulation results validate the feasibility of this estimator when used in finite samples. In addition, we demonstrate empirical applications of the proposed method by applying it to estimate the break points in a U.S. macroeconomic dataset and a stock return dataset.
Overnight GARCH-Itô Volatility Models
Authors: Donggyu Kim, Minseok Shin, Yazhen Wang
Date: 2021-02-24 00:00:00

Various parametric volatility models for financial data have been developed to incorporate high-frequency realized volatilities and better capture market dynamics. However, because high-frequency trading data are not available during the close-to-open period, the volatility models often ignore volatility information over the close-to-open period and thus may suffer from loss of important information relevant to market dynamics. In this paper, to account for whole-day market dynamics, we propose an overnight volatility model based on It\^o diffusions to accommodate two different instantaneous volatility processes for the open-to-close and close-to-open periods. We develop a weighted least squares method to estimate model parameters for two different periods and investigate its asymptotic properties. We conduct a simulation study to check the finite sample performance of the proposed model and method. Finally, we apply the proposed approaches to real trading data.
Misguided Use of Observed Covariates to Impute Missing Covariates in Conditional Prediction: A Shrinkage Problem
Authors: Charles F Manski, Michael Gmeiner, Anat Tamburc
Date: 2021-02-22 00:00:00
Tasks: Imputation

Researchers regularly perform conditional prediction using imputed values of missing data. However, applications of imputation often lack a firm foundation in statistical theory. This paper originated when we were unable to find analysis substantiating claims that imputation of missing data has good frequentist properties when data are missing at random (MAR). We focused on the use of observed covariates to impute missing covariates when estimating conditional means of the form E(y|x, w). Here y is an outcome whose realizations are always observed, x is a covariate whose realizations are always observed, and w is a covariate whose realizations are sometimes unobserved. We examine the probability limit of simple imputation estimates of E(y|x, w) as sample size goes to infinity. We find that these estimates are not consistent when covariate data are MAR. To the contrary, the estimates suffer from a shrinkage problem. They converge to points intermediate between the conditional mean of interest, E(y|x, w), and the mean E(y|x) that conditions only on x. We use a type of genotype imputation to illustrate.
Cointegrated Solutions of Unit-Root VARs: An Extended Representation Theorem
Authors: Mario Faliva, Maria Grazia Zoia
Date: 2021-02-21 00:00:00

This paper establishes an extended representation theorem for unit-root VARs. A specific algebraic technique is devised to recover stationarity from the solution of the model in the form of a cointegrating transformation. Closed forms of the results of interest are derived for integrated processes up to the 4-th order. An extension to higher-order processes turns out to be within the reach on an induction argument.
Assessing the Sensitivity of Synthetic Control Treatment Effect Estimates to Misspecification Error
Authors: Billy Ferguson, Brad Ross
Date: 2020-12-30 00:00:00
Tasks: counterfactual, Sensitivity

We propose a sensitivity analysis for Synthetic Control (SC) treatment effect estimates to interrogate the assumption that the SC method is well-specified, namely that choosing weights to minimize pre-treatment prediction error yields accurate predictions of counterfactual post-treatment outcomes. Our data-driven procedure recovers the set of treatment effects consistent with the assumption that the misspecification error incurred by the SC method is at most the observable misspecification error incurred when using the SC estimator to predict the outcomes of some control unit. We show that under one definition of misspecification error, our procedure provides a simple, geometric motivation for comparing the estimated treatment effect to the distribution of placebo residuals to assess estimate credibility. When we apply our procedure to several canonical studies that report SC estimates, we broadly confirm the conclusions drawn by the source papers.
A Novel Multi-Period and Multilateral Price Index
Authors: Consuelo Rubina Nava, Maria Grazia Zoia
Date: 2021-02-21 00:00:00
Tasks: regression

A novel approach to price indices, leading to an innovative solution in both a multi-period or a multilateral framework, is presented. The index turns out to be the generalized least squares solution of a regression model linking values and quantities of the commodities. The index reference basket, which is the union of the intersections of the baskets of all country/period taken in pair, has a coverage broader than extant indices. The properties of the index are investigated and updating formulas established. Applications to both real and simulated data provide evidence of the better index performance in comparison with extant alternatives.
Estimation and Inference by Stochastic Optimization: Three Examples
Authors: Jean-Jacques Forneron, Serena Ng
Date: 2021-02-20 00:00:00
Tasks: regression, Stochastic Optimization

This paper illustrates two algorithms designed in Forneron & Ng (2020): the resampled Newton-Raphson (rNR) and resampled quasi-Newton (rqN) algorithms which speed-up estimation and bootstrap inference for structural models. An empirical application to BLP shows that computation time decreases from nearly 5 hours with the standard bootstrap to just over 1 hour with rNR, and only 15 minutes using rqN. A first Monte-Carlo exercise illustrates the accuracy of the method for estimation and inference in a probit IV regression. A second exercise additionally illustrates statistical efficiency gains relative to standard estimation for simulation-based estimation using a dynamic panel regression example.
Deep Structural Estimation: With an Application to Option Pricing
Authors: Hui Chen, Antoine Didisheim, Simon Scheidegger
Date: 2021-02-18 00:00:00
Tasks: parameter estimation

We propose a novel structural estimation framework in which we train a surrogate of an economic model with deep neural networks. Our methodology alleviates the curse of dimensionality and speeds up the evaluation and parameter estimation by orders of magnitudes, which significantly enhances one's ability to conduct analyses that require frequent parameter re-estimation. As an empirical application, we compare two popular option pricing models (the Heston and the Bates model with double-exponential jumps) against a non-parametric random forest model. We document that: a) the Bates model produces better out-of-sample pricing on average, but both structural models fail to outperform random forest for large areas of the volatility surface; b) random forest is more competitive at short horizons (e.g., 1-day), for short-dated options (with less than 7 days to maturity), and on days with poor liquidity; c) both structural models outperform random forest in out-of-sample delta hedging; d) the Heston model's relative performance has deteriorated significantly after the 2008 financial crisis.