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on Econometrics |
| By: | Dakyung Seong; Won-Ki Seo |
| Abstract: | Functional linear regression gets its popularity as a statistical tool to study the relationship between function-valued response and exogenous explanatory variables. However, in practice, it is hard to expect that the explanatory variables of interest are perfectly exogenous, due to, for example, the presence of omitted variables and measurement errors, and this in turn limits the applicability of the existing estimators whose essential asymptotic properties, such as consistency, are developed under the exogeneity condition. To resolve this issue, this paper proposes new instrumental variable estimators for functional endogenous linear models, and establishes their asymptotic properties. We also develop a novel test for examining if various characteristics of the response variable depend on the explanatory variable in our model. Simulation experiments under a wide range of settings show that the proposed estimators and test perform considerably well. We apply our methodology to estimate the impact of immigration on native wages. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.12722&r= |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Igor Kheifets (HSE University) |
| Abstract: | A semiparametric triangular systems approach shows how multicointegration can occur naturally in an I(1) cointegrated regression model. The framework reveals the source of multicointegration as singularity of the long run error covariance matrix in an I(1) system, a feature noted but little explored in earlier work. Under such singularity, cointegrated I(1) systems embody a multicointegrated structure and may be analyzed and estimated without appealing to the associated I(2) system but with consequential asymptotic properties that can introduce asymptotic bias into conventional methods of cointegrating regression. The present paper shows how estimation of such systems may be accomplished under multicointegration without losing the nice properties that hold under simple cointegration, including mixed normality and pivotal inference. The approach uses an extended version of high-dimensional trend IV estimation with deterministic orthonormal instruments that leads to mixed normal limit theory and pivotal inference in singular multicointegrated systems in addition to standard cointegrated I(1) systems. Wald tests of general linear restrictions are constructed using a ï¬ xed-b long run variance estimator that leads to robust pivotal HAR inference in both cointegrated and multicointegrated cases. Simulations show the properties of the estimation and inferential procedures in ï¬ nite samples, contrasting the cointegration and multicointegration cases. An empirical illustration to housing stocks, starts and completions is provided. |
| Keywords: | Cointegration, HAR inference, Integration, Long run variance matrix, Multicointegration, Singularity, Trend IV estimation |
| JEL: | C12 C13 C22 |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2306&r= |
| By: | Carolina Caetano; Gregorio Caetano; Hao Fe; Eric R. Nielsen |
| Abstract: | We propose a simple test of the main identification assumption in models where the treatment variable takes multiple values and has bunching. The test consists of adding an indicator of the bunching point to the estimation model and testing whether the coefficient of this indicator is zero. Although similar in spirit to the test in Caetano (2015), the dummy test has important practical advantages: it is more powerful at detecting endogeneity, and it also detects violations of the functional form assumption. The test does not require exclusion restrictions and can be implemented in many approaches popular in empirical research, including linear, two-way fixed effects, and discrete choice models. We apply the test to the estimation of the effect of a mother's working hours on her child's skills in a panel data context (James-Burdumy 2005). |
| Keywords: | Bunching; Discrete-choice models; Endogeneity; Identification test; Linear models; Two-way fixed effects |
| JEL: | C12 C21 C23 C24 |
| Date: | 2021–10–18 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2021-68&r= |
| By: | Yanbo Liu (School of Economics, Shandong University); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | This paper explores predictive regression models with stochastic unit root (STUR) components and robust inference procedures that encompass a wide class of persistent and time-varying stochastically nonstationary regressors. The paper extends the mechanism of endogenously generated instrumentation known as IVX, showing that these methods remain valid for short and long-horizon predictive regressions in which the predictors have STUR and local STUR (LSTUR) generating mechanisms. Both mean regression and quantile regression methods are considered. The asymptotic distributions of the IVX estimators are new and require some new methods in their derivation. The distributions are compared to previous results and, as in earlier work, lead to pivotal limit distributions for Wald testing procedures that remain robust for both single and multiple regressors with various degrees of persistence and stochastic and ï¬ xed local departures from unit roots. Numerical experiments corroborate the asymptotic theory, and IVX testing shows good power and size control. The IVX methods are illustrated in an empirical application to evaluate the predictive capability of economic fundamentals in forecasting S\&P 500 excess returns. |
| Keywords: | IVX, Long horizon, LSTUR, Predictability, Quantile regression, Robustness, Short horizon, STUR |
| JEL: | C12 C22 G01 |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2305&r= |
| By: | Yuya Sasaki; Takuya Ura |
| Abstract: | Panel data often contain stayers (units with no within-variations) and slow movers (units with little within-variations). In the presence of many slow movers, conventional econometric methods can fail to work. We propose a novel method of robust inference for the average partial effects in correlated random coefficient models robustly across various distributions of within-variations, including the cases with many stayers and/or many slow movers in a unified manner. In addition to this robustness property, our proposed method entails smaller biases and hence improves accuracy in inference compared to existing alternatives. Simulation studies demonstrate our theoretical claims about these properties: the conventional 95% confidence interval covers the true parameter value with 37-93% frequencies, whereas our proposed one achieves 93-96% coverage frequencies. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.12041&r= |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | New methods are developed for identifying, estimating and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit root (UR), local unit root (LUR), mildly integrated (MI) and mildly explosive (ME) speciï¬ cations in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME speciï¬ cations and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade. |
| Keywords: | Cauchy limit distribution, Local to unity, Localizing rate sequence, Mild integration, Mildly explosive process, Unit root |
| JEL: | C22 |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2304&r= |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Ying Wang (Renmin University of China) |
| Abstract: | Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or ï¬ xed. In such cases, the limit theory of FC kernel regression is shown to depend intimately on functional shape in ways that affect rates of convergence, optimal bandwidth selection, estimation, and inference. The paper develops new asymptotics that take account of shape characteristics of the function in the locality of the point of estimation. Both stationary and integrated regressor cases are examined. Locally flat behavior in the coefficient function has, as expected, a major effect on bias and thereby on the trade-off between bias and variance, and on optimal bandwidth choice. In FC cointegrating regression, flat behavior materially changes the limit distribution by introducing the shape characteristics of the function into the limiting distribution through variance as well as centering. Both bias and variance depend on the number of zero derivatives in the coefficient function. In the boundary case where the number of zero derivatives tends to inï¬ nity, near parametric rates of convergence apply for both stationary and nonstationary cases. Implications for inference are discussed and simulations characterizing ï¬ nite sample behavior are reported. |
| Keywords: | Boundary asymptotics, Functional coefficient regression, Limit theory, Locally flat regression coefficient, Near-parametric rate |
| JEL: | C14 C22 |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2307&r= |
| By: | Alessandra Luati (University of Bologna); Francesca Papagni (Free University of Bozen); Tommaso Proietti (CEIS & DEF, Università di Roma "Tor Vergata") |
| Abstract: | This paper provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalized autocovariance function of a stationary random process. The generalized autocovariance function is the inverse Fourier transform of a power transformation of the spectral density and encompasses the traditional and inverse autocovariance functions as particular cases. A nonparametric estimator is based on the inverse discrete Fourier transform of the power transformation of the pooled periodogram. The general result on the asymptotic efficiency is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. Finally, we illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalized autocovariance estimator. |
| Keywords: | Cramér-Rao lower bound; Frequency Domain; Minimum Contrast Estimation; Periodogram |
| Date: | 2021–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:515&r= |
| By: | Abhishek K. Umrawal; Joshua C. C. Chan |
| Abstract: | We propose a new quadratic-programming-based method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved components models involving inequality constraints on the parameters. For instance, Chat et al. (2016) propose a new model of trend inflation with linear inequality constraints on the stochastic trend. We implement the proposed new method for this model and compare it to the existing approximation. We observe that the proposed new method works as good as the existing approximation in terms of the final trend estimates while achieving greater gains in terms of sample efficiency. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.12149&r= |
| By: | Tommaso Proietti (CEIS & DEF, Università di Roma "Tor Vergata"); Federico Maddanu (Università di Roma "Tor Vergata") |
| Abstract: | The paper proposes a novel model for time series displaying persistent stationary cycles, the fractional sinusoidal waveform process. The underlying idea is to allow the parameters that regulate the amplitude and phase to evolve according to fractional noise processes. Its advantages with respect to popular alternative specifications, such as the Gegenbauer process, are twofold: the autocovariance function is available in closed form, which opens the way to exact maximum likelihood estimation; secondly the model encompasses deterministic cycles, so that discrete spectra arise as a limiting case. A generalization of the process, featuring multiple components, an additive `red noise' component and exogenous variables, provides a model for climate time series with mixed spectra. Our illustrations deal with the change in amplitude and phase of the intra-annual component of carbon dioxide concentrations in Mauna Loa, and with the estimation and the quantification of the contribution of orbital cycles to the variability of paleoclimate time series. |
| Keywords: | Mixed Spectrum. Cyclical long memory. Paleoclimatic data |
| Date: | 2021–10–19 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:518&r= |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d ≥ 1 2: Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d |
| Keywords: | Discrete Fourier transform, Fractional Brownian motion, Fractional integration, Log periodogram regression, Nonstationarity, Operator decomposition, Semiparametric estimation, Whittle likelihood |
| JEL: | C22 |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2303&r= |
| By: | Matias D. Cattaneo; Luke Keele; Rocio Titiunik |
| Abstract: | The Regression Discontinuity (RD) design is a widely used non-experimental method for causal inference and program evaluation. While its canonical formulation only requires a score and an outcome variable, it is common in empirical work to encounter RD implementations where additional variables are used for adjustment. This practice has led to misconceptions about the role of covariate adjustment in RD analysis, from both methodological and empirical perspectives. In this chapter, we review the different roles of covariate adjustment in RD designs, and offer methodological guidance for its correct use in applications. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.08410&r= |
| By: | Morgan Kelly |
| Abstract: | Historical persistence studies and other regressions using spatial data commonly have severely inflated t statistics, and different standard error adjustments to correct for this return markedly different estimates. This paper proposes a simple randomization inference procedure where the significance level of an explanatory variable is measured by its ability to outperform synthetic noise with the same estimated spatial structure. Spatial noise, in other words, acts as a treatment randomization in an artificial experiment based on correlated observational data. Combined with Müller and Watson (2021), randomization gives a way to estimate credible confidence intervals for spatial regressions. The performance of twenty persistence studies relative to spatial noise is examined. |
| Keywords: | Historical persistence; Spatial data; Randomization inference; Spatial noise |
| JEL: | N0 |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:ucn:wpaper:202124&r= |
| By: | Blanka Horvath; Zacharia Issa; Aitor Muguruza |
| Abstract: | The problem of rapid and automated detection of distinct market regimes is a topic of great interest to financial mathematicians and practitioners alike. In this paper, we outline an unsupervised learning algorithm for clustering financial time-series into a suitable number of temporal segments (market regimes). As a special case of the above, we develop a robust algorithm that automates the process of classifying market regimes. The method is robust in the sense that it does not depend on modelling assumptions of the underlying time series as our experiments with real datasets show. This method -- dubbed the Wasserstein $k$-means algorithm -- frames such a problem as one on the space of probability measures with finite $p^\text{th}$ moment, in terms of the $p$-Wasserstein distance between (empirical) distributions. We compare our WK-means approach with a more traditional clustering algorithms by studying the so-called maximum mean discrepancy scores between, and within clusters. In both cases it is shown that the WK-means algorithm vastly outperforms all considered competitor approaches. We demonstrate the performance of all approaches both in a controlled environment on synthetic data, and on real data. |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2110.11848&r= |
| By: | Bhattacharya, Rudrani (National Institute of Public Finance and Policy); Bhandari, Bornali (National Council of Applied Economic Research); Mundle, Sudipto (National Council of Applied Economic Research) |
| Abstract: | Governments, central banks, private firms and others need high frequency information on the state of the economy for their decision making. However, a key indicator like GDP is only available quarterly and that too with a lag. Hence decision makers use high frequency daily, weekly or monthly information to project GDP growth in a given quarter. This method, known as nowcasting, which started out in advanced country central banks using bridge models. Nowcasting is now based on more advanced techniques, mostly dynamic factor models. In this paper we use a novel approach, a Factor Augmented Time Varying Coefficient Regression (FA-TVCR) model, which allows us to extract information from a large number of high frequency indicators and at the same time inherently addresses the issue of frequent structural breaks encountered in Indian GDP growth. One specification of the FA-TVCR model is estimated using 19 variables available for a long period starting in 2007-08:Q1. Another specification estimates the model using a larger set of 28 indicators available for a shorter period starting in 2015-16:Q1. Comparing our model with two alternative models, we find that the FA-TVCR model outperforms a DFM model in terms of both in-sample and out-of-sample RMSE. The RMSE of the ARIMA model is somewhat lower than the FA-TVCR model within the sample period but is higher than the out-of-sample of the FA-TVCR model. Further, comparing the predictive power of the three models using the Diebold-Mariano test, we find that FA-TVCR model out-performs DFM consistently. In terms of out-of-sample forecast accuracy both the FA-TVC model and the ARIMA model have the same predictive accuracy under normal conditions. However, the FA-TVCR model outperforms the ARIMA model when applied for nowcasting in periods of major shocks like the Covid-19 shock of 2020-21. |
| Keywords: | Nowcasting ; Quarterly Year-on-Year GDP growth ; State-Space Model, India |
| JEL: | C52 C53 O40 |
| Date: | 2021–10 |
| URL: | http://d.repec.org/n?u=RePEc:npf:wpaper:21/357&r= |