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on Econometrics |
| By: | Pang, Tianxiao; Du, Lingjie; Chong, Terence Tai Leung |
| Abstract: | Chong (1995) and Bai (1997) proposed a sample splitting method to estimate a multiple-break model. However, their studies focused on stationary time series models, where the identification of the first break depends on the magnitude and the duration of the break, and a testing procedure is needed to assist the estimation of the remaining breaks in subsamples split by the break points found earlier. In this paper, we focus on nonstationary multiple-break autoregressive models. Unlike the stationary case, we show that the duration of a break does not affect if it will be identified first. Rather, it depends on the stochastic order of magnitude of signal strength of the break under the case of constant break magnitude and also the square of the magnitude of the break under the case of shrinking break magnitude. Since the subsamples usually have different stochastic orders in nonstationary autoregressive models with breaks, one can therefore determine which break will be identified first. We apply this finding to the models proposed in Phillips and Yu (2011), Phillips et al. (2011) and Phillips et al. (2015a, 2015b). We provide an estimation procedure as well as the asymptotic theory for the model. |
| Keywords: | Change point, Financial bubble, Least squares estimator, Mildly explosive, Mildly integrated. |
| JEL: | C22 |
| Date: | 2018–08–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:92074&r=all |
| By: | Raffaella Giacomini (Institute for Fiscal Studies and cemmap and UCL); Toru Kitagawa (Institute for Fiscal Studies and cemmap and University College London) |
| Abstract: | This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in set-identified models by adopting a multiple-prior (robust) Bayesian approach. We propose new tools for Bayesian inference in set-identified models. We show that these tools have a well-defined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea is to construct a prior class that removes the source of the disagreement: the need to specify an unrevisable prior. The corresponding class of posteriors can be summarized by reporting the ‘posterior lower and upper probabilities’ of a given event and/or the ‘set of posterior means’ and the associated ‘robust credible region’. We show that the set of posterior means is a consistent estimator of the true identified set and the robust credible region has the correct frequentist asymptotic coverage for the true identified set if it is convex. Otherwise, the method can be interpreted as providing posterior inference about the convex hull of the identified set. For impulse-response analysis in set-identified Structural Vector Autoregressions, the new tools can be used to overcome or quantify the sensitivity of standard Bayesian inference to the choice of an unrevisable prior. |
| Keywords: | multiple priors, identified set, credible region, consistency, asymptotic coverage, identifying restrictions, impulse-response analysis |
| Date: | 2018–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:61/18&r=all |
| By: | Victor Chernozhukov (Institute for Fiscal Studies and MIT); Denis Chetverikov (Institute for Fiscal Studies and UCLA); Kengo Kato (Institute for Fiscal Studies) |
| Abstract: | This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters; a notable example is the market structure model of Ciliberto and Tamer (2009) where p = 2m+1 with m being the number of firms that could possibly enter the market. We consider the test statistic given by the maximum of p Studentized (or t-type) inequality-specifi c statistics, and analyze various ways to compute critical values for the test statistic. Speci fically, we consider critical values based upon (i) the union bound combined with a moderate deviation inequality for self-normalized sums, (ii) the multiplier and empirical bootstraps, and (iii) two-step and three-step variants of (i) and (ii) by incorporating the selection of uninformative inequalities that are far from being binding and a novel selection of weakly informative inequalities that are potentially binding but do not provide first order information. We prove validity of these methods, showing that under mild conditions, they lead to tests with the error in size decreasing polynomially in n while allowing for p being much larger than n; indeed p can be of order exp(nc) for some c > 0. Importantly, all these results hold without any restriction on the correlation structure between p Studentized statistics, and also hold uniformly with respect to suitably large classes of underlying distributions. Moreover, in the online supplement, we show validity of a test based on the block multiplier bootstrap in the case of dependent data under some general mixing conditions. |
| Keywords: | Many moment inequalities, moderate deviation, multiplier and empirical bootstrap, non-asymptotic bound, self-normalized sum |
| Date: | 2018–10–18 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:60/18&r=all |
| By: | Andrew Chesher (Institute for Fiscal Studies and University College London); Adam Rosen (Institute for Fiscal Studies and Duke University) |
| Abstract: | This chapter sets out the extension of the scope of the classical IV model to cases in which unobserved variables are set-valued functions of observed variables. The resulting Generalized IV (GIV) models can be used when outcomes are discrete while unobserved variables are continuous, when there are rich specifications of heterogeneity as in random coefficient models, and when there are inequality restrictions constraining observed outcomes and unobserved variables. There are many other applications and classical IV models arise as a special case. The chapter provides characterizations of the identified sets delivered by GIV models. It gives details of the application of GIV analysis to models with an interval censored endogenous variable and to binary outcome models ? for example probit models ? with endogenous explanatory variables. It illustrates how the identified sets delivered by GIV models can be represented by moment inequality characterizations that have been the focus of recently developed methods for inference. An empirical application to a binary outcome model of female labor force participation is worked through in detail. |
| Date: | 2018–07–11 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:43/18&r=all |
| By: | Tiemen M. Woutersen (Institute for Fiscal Studies and John Hopkins University); Jerry Hausman (Institute for Fiscal Studies and MIT) |
| Abstract: | This paper shows how to increase the power of Hausman?s (1978) specification test as well as the difference test in a large class of models. The idea is to impose the restrictions of the null and the alternative hypotheses when estimating the covariance matrix. If the null hypothesis is true then the proposed test has the same distribution as the existing ones in large samples. If the hypothesis is false then the proposed test statistic is larger with probability approaching one as the sample size increases in several important applications, including testing for endogeneity in the linear model. |
| Keywords: | Specification test, Hausman test, Power of tests |
| Date: | 2018–07–20 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:46/18&r=all |
| By: | Dmitry Arkhangelsky; Susan Athey; David A. Hirshberg; Guido W. Imbens; Stefan Wager |
| Abstract: | We present a new perspective on the Synthetic Control (SC) method as a weighted least squares regression estimator with time fixed effects and unit weights. This perspective suggests a generalization with two way (both unit and time) fixed effects, and both unit and time weights, which can be interpreted as a unit and time weighted version of the standard Difference In Differences (DID) estimator. We find that this new Synthetic Difference In Differences (SDID) estimator has attractive properties compared to the SC and DID estimators. Formally we show that our approach has double robustness properties: the SDID estimator is consistent under a wide variety of weighting schemes given a well-specified fixed effects model, and SDID is consistent with appropriately penalized SC weights when the basic fixed effects model is misspecified and instead the true data generating process involves a more general low-rank structure (e.g., a latent factor model). We also present results that justify standard inference based on weighted DID regression. Further generalizations include unit and time weighted factor models. |
| JEL: | C01 |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:25532&r=all |
| By: | Vitaliy Oryshchenko (Institute for Fiscal Studies); Richard J. Smith (Institute for Fiscal Studies) |
| Abstract: | Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due to the systematic use of this extra information. The particular interest here is the estimation of the density or distribution functions of (generalised) residuals in semi-parametric models defined by a finite number of moment restrictions. Such estimates are of great practical interest, being potentially of use for diagnostic purposes, including tests of parametric assumptions on an error distribution, goodness-of-fit tests or tests of overidentifying moment restrictions. The paper gives conditions for the consistency and describes the asymptotic mean squared error properties of the kernel density and distribution estimators proposed in the paper. A simulation study evaluates the small sample performance of these estimators. |
| Keywords: | Moment conditions, residuals, mean squared error, bandwidth |
| JEL: | C14 |
| Date: | 2018–07–23 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:47/18&r=all |
| By: | Daniel Wilhelm (Institute for Fiscal Studies and cemmap and UCL) |
| Abstract: | This paper proposes a simple nonparametric test of the hypothesis of no measurement error in explanatory variables and of the hypothesis that measurement error, if there is any, does not distort a given object of interest. We show that, under weak assumptions, both of these hypotheses are equivalent to certain restrictions on the joint distribution of an observable outcome and two observable variables that are related to the latent explanatory variable. Existing nonparametric tests for conditional independence can be used to directly test these restrictions without having to solve for the distribution of unobservables. In consequence, the test controls size under weak conditions and possesses power against a large class of nonclassical measurement error models, including many that are not identifi ed. If the test detects measurement error, a multiple hypothesis testing procedure allows the researcher to recover subpopulations that are free from measurement error. Finally, we use the proposed methodology to study the reliability of administrative earnings records in the U.S., fi nding evidence for the presence of measurement error. |
| Date: | 2018–07–19 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:45/18&r=all |
| By: | Joel L. Horowitz (Institute for Fiscal Studies and Northwestern University) |
| Abstract: | The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap provides approximations to distributions of statistics, coverage probabilities of confidence intervals, and rejection probabilities of hypothesis tests that are more accurate than the approximations of first-order asymptotic distribution theory. The reductions in the differences between true and nominal coverage or rejection probabilities can be very large. In addition, the bootstrap provides a way to carry out inference in certain settings where obtaining analytic distributional approximations is difficult or impossible. This article explains the usefulness and limitations of the bootstrap in contexts of interest in econometrics. The presentation is informal and expository. It provides an intuitive understanding of how the bootstrap works. Mathematical details are available in references that are cited. |
| Keywords: | Resampling, confidence interval, hypothesis test, asymptotic refinement, bootstrap |
| Date: | 2018–09–18 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:53/18&r=all |
| By: | Nick James; Roman Marchant; Richard Gerlach; Sally Cripps |
| Abstract: | Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and dependency of financial time series in a non-parametric fashion assuming that the time series consists of a finite, but unknown number, of locally stationary processes, the locations of which are also unknown. The model allows a non-parametric estimate of the dependency structure by modelling the auto-covariance function in the spectral domain. All our estimates are made within a Bayesian framework where we use aReversible Jump Markov Chain Monte Carlo algorithm for inference. We study the frequentist properties of our estimates via a simulation study, and present a novel way of generating time series data from a nonparametric spectrum. Results indicate that our techniques perform well across a range of data generating processes. We apply our method to a number of real examples and our results indicate that several financial time series exhibit both long-range dependency and non-stationarity. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1902.03350&r=all |
| By: | Paulo Parente (Institute for Fiscal Studies); Richard J. Smith (Institute for Fiscal Studies) |
| Abstract: | This article introduces and investigates the properties of a new bootstrap method for time-series data, the kernel block bootstrap. The bootstrap method, although akin to, offers an improvement over the tapered block bootstrap of Paparoditis and Politis (2001), admitting kernels with unbounded support. Given a suitable choice of kernel, a kernel block bootstrap estimator of the spectrum at zero asymptotically close to the optimal Parzen (1957) estimator is possible. The paper shows the large sample validity of the kernel block bootstrap and derives the higher order bias and variance of the kernel block bootstrap variance estimator. Like the tapered block bootstrap variance estimator, the kernel block bootstrap estimator has a favourable higher order bias property. Simulations based on the designs of Paparoditis and Politis (2001) indicate that the kernel block bootstrap may be efficacious in practice. |
| Keywords: | Bias; Con fidence Interval; Resampling; Kernel function; Spectral density estimation; Time Series; Variance estimation |
| Date: | 2018–07–25 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:48/18&r=all |
| By: | Paolo Andreini (University of Rome "Tor Vergata"); Donato Ceci (University of Rome "Tor Vergata" & Bank of Italy) |
| Abstract: | In this paper, we study the predictive power of dense and sparse estimators in a high dimensional space. We propose a new forecasting method, called Elastically Weighted Principal Components Analysis (EWPCA) that selects the variables, with respect to the target variable, taking into account the collinearity among the data using the Elastic Net soft thresholding. Then, we weight the selected predictors using the Elastic Net regression coefficient, and we finally apply the principal component analysis to the new “elastically” weighted data matrix. We compare this method to common benchmark and other methods to forecast macroeconomic variables in a data-rich environment, dived into dense representation, such as Dynamic Factor Models and Ridge regressions and sparse representations, such as LASSO regression. All these models are adapted to take into account the linear dependency of the macroeconomic time series. Moreover, to estimate the hyperparameters of these models, including the EWPCA, we propose a new procedure called “brute force”. This method allows us to treat all the hyperparameters of the model uniformly and to take the longitudinal feature of the time-series data into account. Our findings can be summarized as follows. First, the “brute force” method to estimate the hyperparameters is more stable and gives better forecasting performances, in terms of MSFE, than the traditional criteria used in the literature to tune the hyperparameters. This result holds for all samples sizes and forecasting horizons. Secondly, our two-step forecasting procedure enhances the forecasts’ interpretability. Lastly, the EWPCA leads to better forecasting performances, in terms of mean square forecast error (MSFE), than the other sparse and dense methods or naïve benchmark, at different forecasts horizons and sample sizes. |
| Keywords: | Variable selection,High-dimensional time series,Dynamic factor models,Shrinkage methods,Cross-validation |
| JEL: | C22 C52 C53 |
| Date: | 2019–02–14 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:452&r=all |
| By: | Kanaya, S.; Bhattacharya, D. |
| Abstract: | In this note, we present some theoretical results useful for inference on a population Lorenz curve for income and expenditure distributions, when the population density of the distribution is not (uniformly) bounded away from zero, and potentially has thick tails. Our approach is to define Hadamard differentiability in a slightly nonstandard way, and using it to establish a functional delta method for the Lorenz map. Our differentiability concept is nonstandard in that the perturbation functions, which are used to compute the functional derivative, are assumed to satisfy certain limit conditions. These perturbation functions correspond to a (nonparametric) distribution function estimator. Therefore, as long as the employed estimator satis.es the same limit conditions, which we verify in this paper, the delta method and corresponding asymptotic distribution results can be established. |
| Date: | 2017–12–11 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1760&r=all |
| By: | Aknouche, Abdelhakim; Dimitrakopoulos, Stefanos; Touche, Nassim |
| Abstract: | We propose a novel class of count time series models, the mixed Poisson integer-valued stochastic volatility models. The proposed specification, which can be considered as an integer-valued analogue of the discrete-time stochastic volatility model, encompasses a wide range of conditional distributions of counts. We study its probabilistic structure and develop an easily adaptable Markov chain Monte Carlo algorithm, based on the Griddy-Gibbs approach that can accommodate any conditional distribution that belongs to that class. We demonstrate that by considering the cases of Poisson and negative binomial distributions. The methodology is applied to simulated and real data. |
| Keywords: | Griddy-Gibbs, Markov chain Monte Carlo, mixed Poisson parameter-driven models, stochastic volatility, Integer-valued GARCH. |
| JEL: | C13 C15 C32 C35 C58 |
| Date: | 2019–02–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91962&r=all |
| By: | Matteo Barigozzi; Marc Hallin; Stefano Soccorsi |
| Abstract: | Ripple effects in financial markets associated with crashes, systemic risk and contagion are characterized by non-trivial lead-lag dynamics which is crucial for understanding how crises spread and, therefore, central in risk management. In the spirit of Diebold and Yilmaz (2014), we investigate connectedness among financial firms via an analysis of impulse response functions of adjusted intraday log-ranges to market shocks involving network theory methods. Motivated by overwhelming evidence that the interdependence structure of financial markets is varying over time, we are basing that analysis on the so-called time-varying General Dynamic Factor Model proposed by Eichler et al. (2011), which extends to the locally stationary context the framework developed by Forni et al. (2000) under stationarity assumptions. The estimation methods in Eichler et al. (2011), however, present the major drawback of involving two-sided filters which make it impossible to recover impulse response functions. We therefore introduce a novel approach extending to the time-varying context the one-sided method of Forni et al. (2017). The resulting estimators of time-varying impulse response functions are shown to be consistent, hence can be used in the analysis of (time-varying) connectedness. Our empirical analysis on a large and strongly comoving panel of intraday price ranges of US stocks indicates that large increases in mid to long-run connectedness are associated with the main financial turmoils. |
| Keywords: | Dynamic factor models, volatility, financial crises, contagion, financial connectedness, high-dimensional time series, panel data, time-varying models, local stationarity. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/283963&r=all |
| By: | Brigham R. Frandsen; Lars J. Lefgren; Emily C. Leslie |
| Abstract: | We propose a test for the identifying assumptions invoked in designs based on random assignment to one of many "judges.'' We show that standard identifying assumptions imply that the conditional expectation of the outcome given judge assignment is a continuous function with bounded slope of the judge propensity to treat. The implication leads to a two-part test that generalizes the Sargan-Hansen overidentification test and assesses whether implied treatment effects across the range of judge propensities are possible given the domain of the outcome. We show the asymptotic validity of the testing procedure, demonstrate its finite-sample performance in simulations, and apply the test in an empirical setting examining the effects of pre-trial release on defendant outcomes in Miami. When the assumptions are not satisfied, we propose a weaker average monotonicity assumption under which IV still converges to a proper weighted average of treatment effects. |
| JEL: | C26 K14 |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:25528&r=all |
| By: | Federico Bassetti (Politecnico of Milan, Italy); Roberto Casarin (University Ca' Foscari of Venice, Italy); Francesco Ravazzolo (Free University of Bolzano‐Bozen Faculty of Economics, Italy and BI Norwegian Business School) |
| Abstract: | This paper reviews different methods to construct density forecasts and to aggregate forecasts from many sources. Density evaluation tools to measure the accuracy of density forecasts are reviewed and calibration methods for improving the accuracy of forecasts are presented. The manuscript provides some numerical simulation tools to approximate predictive densities with a focus on parallel computing on graphical process units. Some simple examples are proposed to illustrate the methods. |
| Keywords: | Density forecasting, density combinations, density evaluation, boot-strapping, Bayesian inference, Monte Carlo simulations, GPU computing |
| JEL: | C10 C11 C15 C53 C63 |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:bzn:wpaper:bemps59&r=all |
| By: | Federico Carlini (Università della Svizzera italiana); Paolo Santucci de Magistris (LUISS University and Aarhus University and CREATES) |
| Abstract: | We study the theoretical properties of the model for fractional cointegration proposed by Granger (1986), namely the FVECM_{d,b}. First, we show that the stability of any discretetime stochastic system of the type Pi(L)Y_t = e_t can be assessed by means of the argument principle under mild regularity condition on Pi(L), where L is the lag operator. Second, we prove that, under stability, the FVECM_{d,b} allows for a representation of the solution that demonstrates the fractional and co-fractional properties and we find a closed-form expression for the impulse response functions. Third, we prove that the model is identified for any combination of number of lags and cointegration rank, while still being able to generate polynomial co-fractionality. In light of these properties, we show that the asymptotic properties of the maximum likelihood estimator reconcile with those of the FCVAR_{d,b} model studied in Johansen and Nielsen (2012). Finally, an empirical illustration is provided. |
| Keywords: | Fractional cointegration, Granger representation theorem, Stability, Identification, Impulse Response Functions, Profile Maximum Likelihood |
| JEL: | C01 C02 C58 G12 G13 |
| Date: | 2019–01–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2019-02&r=all |
| By: | Mingli Chen (Institute for Fiscal Studies and Warwick); Ivan Fernandez-Val (Institute for Fiscal Studies and Boston University); Martin Weidner (Institute for Fiscal Studies and cemmap and UCL) |
| Abstract: | Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifi cations. We establish that fi xed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer of incidental parameter bias. We show how models with factor structures can also be applied to capture important features of network data such as reciprocity, degree heterogeneity, homophily in latent variables and clustering. We illustrate this applicability with an empirical example to the estimation of a gravity equation of international trade between countries using a Poisson model with multiple factors. |
| Keywords: | Panel data, network data, interactive fixed effects, factor models, bias correction, incidental parameter problem, gravity equation |
| JEL: | C13 C23 |
| Date: | 2018–07–03 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:38/18&r=all |
| By: | Nicky L. Grant (Institute for Fiscal Studies); Richard J. Smith (Institute for Fiscal Studies) |
| Abstract: | The particular concern of this paper is the construction of a confidence region with pointwise asymptotically correct size for the true value of a parameter of interest based on the generalized Anderson-Rubin (GAR) statistic when the moment variance matrix is singular. The large sample behaviour of the GAR statistic is analysed using a Laurent series expansion around the points of moment variance singularity. Under a condition termed first order moment singularity the GAR statistic is shown to possess a limiting chi-square distribution on parameter sequences converging to the true parameter value. Violation, however, of this condition renders the GAR statistic unbounded asymptotically. The paper details an appropriate discretisation of the parameter space to implement a feasible GAR-based confidence region that contains the true parameter value with pointwise asymptotically correct size. Simulation evidence is provided that demonstrates the efficacy of the GAR-based approach to moment-based inference described in this paper. |
| Keywords: | Laurent series expansion; moment indicator; parameter sequences; singular moment matrix |
| JEL: | C13 C31 C51 C52 |
| Date: | 2019–01–30 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:05/19&r=all |
| By: | Richard Blundell (Institute for Fiscal Studies and Institute for Fiscal Studies and University College London); Joel L. Horowitz (Institute for Fiscal Studies and Northwestern University); Matthias Parey (Institute for Fiscal Studies and University of Surrey) |
| Abstract: | Berkson errors are commonplace in empirical microeconomics and occur whenever we observe an average in a specified group rather than the true individual value. In consumer demand this form of measurement error is present because the price an individual pays is often measured by the average price paid by individuals in a specified group (e.g., a county). We show the importance of such measurement errors for the estimation of demand in a setting with nonseparable unobserved heterogeneity. We develop a consistent estimator using external information on the true distribution of prices. Examining the demand for gasoline in the U.S., accounting for Berkson errors is found to be quantitatively important for estimating price effects and for welfare calculations. Imposing the Slutsky shape constraint greatly reduces the sensitivity to Berkson errors. |
| Keywords: | consumer demand, nonseparable models, quantile regression, measurement error, gasoline demand, Berkson errors. |
| Date: | 2018–11–29 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:67/18&r=all |
| By: | Masato Hisakado; Shintaro Mori |
| Abstract: | The probability of default (PD) estimation is an important process for financial institutions. The difficulty of the estimation depends on the correlations between borrowers. In this paper, we introduce a hierarchical Bayesian estimation method using the beta binomial distribution, and consider a multi-year case with a temporal correlation. A phase transition occurs when the temporal correlation decays by power decay. When the power index is less than one, the PD estimator does not converge. It is difficult to estimate the PD with the limited historical data. Conversely, when the power index is greater than one, the convergence is the same as that of the binomial distribution. We provide a condition for the estimation of the PD and discuss the universality class of the phase transition. We investigate the empirical default data history of rating agencies, and their Fourier transformations to confirm the correlation decay equation. The power spectrum of the decay history seems to be 1/f of the fluctuations that correspond to long memory. But the estimated power index is much greater than one. If we collect adequate historical data, the parameters can be estimated correctly. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1902.03797&r=all |
| By: | Ozer Karagedikli; Shaun P. Vahey; Elizabeth C. Wakerly |
| Abstract: | Many studies have found that combining forecasts improves predictive accuracy. An often-used approach developed by Granger and Ramanathan (GR, 1984) utilises a linear-Gaussian regression model to combine point forecasts. This paper generalises their approach for an asymmetrically distributed target variable. Our copula point forecast combination methodology involves fitting marginal distributions for the target variable and the individual forecasts being combined; and then estimating the correlation parameters capturing linear dependence between the target and the experts’ predictions. If the target variable and experts’ predictions are individually Gaussian distributed, our copula point combination reproduces the GR combination. We illustrate our methodology with two applications examining quarterly forecasts for the Federal Funds rate and for US output growth, respectively. The copula point combinations outperform the forecasts from the individual experts in both applications, with gains in root mean squared forecast error in the region of 40% for the Federal Funds rate and 4% for output growth relative to the GR combination. The fitted marginal distribution for the interest rate exhibits strong asymmetry. |
| Keywords: | Forecast combination, Copula modelling, Interest rates, Vulnerable economic growth |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2019-15&r=all |
| By: | Alexander Hanbo Li; Jelena Bradic |
| Abstract: | Random forests are powerful non-parametric regression method but are severely limited in their usage in the presence of randomly censored observations, and naively applied can exhibit poor predictive performance due to the incurred biases. Based on a local adaptive representation of random forests, we develop its regression adjustment for randomly censored regression quantile models. Regression adjustment is based on new estimating equations that adapt to censoring and lead to quantile score whenever the data do not exhibit censoring. The proposed procedure named censored quantile regression forest, allows us to estimate quantiles of time-to-event without any parametric modeling assumption. We establish its consistency under mild model specifications. Numerical studies showcase a clear advantage of the proposed procedure. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1902.03327&r=all |
| By: | Verena Monschang; Bernd Wilfling |
| Abstract: | In this paper we analyze the performance of supremum augmented Dickey-Fuller (SADF), generalized SADF (GSADF), and backward SADF (BSADF) tests, as introduced by Phillips et al. (International Economic Review 56:1043-1078, 2015) for detecting and date-stamping financial bubbles. In Monte Carlo simulations, we show that the SADF and GSADF tests may reveal substantial size distortions under typical financial-market characteristics (like the empirically well-documented leverage effect). We consider the rational bubble specification suggested by Rotermann and Wilfl ing (Applied Economics Letters 25:1091-1096, 2018) that is able to generate realistic stock-price dynamics (in terms of level trajectories and volatility paths). Simulating stock-price trajectories that contain these parametric bubbles, we demonstrate that the SADF and GSADF tests can have extremely low power under a wide range of bubble-parameter constellations. In an empirical analysis, we use NASDAQ data covering a time-span of 45 years and find that the outcomes of the bubble date-stamping procedure (based on the BSADF test) are sensitive to the data-frequency chosen by the econometrician. |
| Keywords: | Stock markets, present-value model, rational bubble, explosiveness, SADF and GSADF tests, bubble detection, date-stamping |
| JEL: | C15 C32 C58 G15 |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:cqe:wpaper:7819&r=all |
| By: | Roger Koenker (Institute for Fiscal Studies and UCL); Ivan Mizera (Institute for Fiscal Studies) |
| Abstract: | Shape constraints play an increasingly prominent role in nonparametric function estimation. While considerable recent attention has been focused on log concavity as a regularizing device in nonparametric density estimation, weaker forms of concavity constraints encompassing larger classes of densities have received less attention but offer some additional flexibility. Heavier tail behavior and sharper modal peaks are better adapted to such weaker concavity constraints. When paired with appropriate maximal entropy estimation criteria these weaker constraints yield tractable, convex optimization problems that broaden the scope of shape constrained density estimation in a variety of applied subject areas. In contrast to our prior work, Koenker and Mizera (2010), that focused on the log concave (a = 1) and Hellinger (a = 1/2) constraints, here we describe methods enabling imposition of even weaker, a = 0 constraints. An alternative formulation of the concavity constraints for densities in dimension d = 2 also signi cantly expands the applicability of our proposed methods for multivariate data. Finally, we illustrate the use of the Renyi divergence criterion for norm-constrained estimation of densities in the absence of a shape constraint. |
| Date: | 2018–09–18 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:54/18&r=all |
| By: | Spiliotis, Evangelos; Petropoulos, Fotios; Kourentzes, Nikolaos; Assimakopoulos, Vassilios |
| Abstract: | Achieving high accuracy in load forecasting requires the selection of appropriate forecasting models, able to capture the special characteristics of energy consumption time series. When hierarchies of load from different sources are considered together, the complexity increases further; for example, when forecasting both at system and region level. Not only the model selection problem is expanded to multiple time series, but we also require aggregation consistency of the forecasts across levels. Although hierarchical forecast can address the aggregation consistency concerns, it does not resolve the model selection uncertainty. To address this we rely on Multiple Temporal Aggregation, which has been shown to mitigate the model selection problem for low frequency time series. We propose a modification for high frequency time series and combine conventional cross-sectional hierarchical forecasting with multiple temporal aggregation. The effect of incorporating temporal aggregation in hierarchical forecasting is empirically assessed using a real data set from five bank branches, demonstrating superior accuracy, aggregation consistency and reliable automatic forecasting. |
| Keywords: | Temporal aggregation; Hierarchical forecasting; Electricity load; Exponential smoothing; MAPA |
| JEL: | C4 C53 D8 D81 L94 |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91762&r=all |
| By: | Harvey, A.; Liao, Y. |
| Abstract: | Score-driven models provide a solution to the problem of modelling time series when the observations are subject to censoring and location and/or scale may change over time. The method applies to generalized-t and EGB2 distributions, as well as to the normal distribution. A set of Monte Carlo experiments show that the score-driven model provides good forecasts even when the true model is parameterdriven. The viability of the new models is illustrated by fitting them to data on Chinese stock returns. |
| Keywords: | Censored distributions, dynamic conditional score model, EGARCH models, logistic distribution, generalized t distribution |
| JEL: | C22 C24 |
| Date: | 2019–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1913&r=all |
| By: | Victor Chernozhukov (Institute for Fiscal Studies and MIT); Vira Semenova (Institute for Fiscal Studies) |
| Abstract: | This paper provides estimation and inference methods for a structural function, such as Conditional Average Treatment Effect (CATE), based on modern machine learning (ML) tools. We assume that such function can be represented as a conditional expectation = of a signal , where is the unknown nuisance function. In addition to CATE, examples of such functions include regression function with Partially Missing Outcome and Conditional Average Partial Derivative. We approximate by a linear form , where is a vector of the approximating functions and is the Best Linear Predictor. Plugging in the fi rst-stage estimate into the signal , we estimate via ordinary least squares of on . We deliver a high-quality estimate of the pseudo-target function , that features (a) a pointwise Gaussian approximation of at a point , (b) a simultaneous Gaussian approximation of uniformly over x, and (c) optimal rate of convergence of to uniformly over x. In the case the misspeci cation error of the linear form decays sufficiently fast, these approximations automatically hold for the target function instead of a pseudo-target . The fi rst stage nuisance parameter is allowed to be high-dimensional and is estimated by modern ML tools, such as neural networks, -shrinkage estimators, and random forest. Using our method, we estimate the average price elasticity conditional on income using Yatchew and No (2001) data and provide uniform con fidence bands for the target regression function. |
| Date: | 2018–07–04 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:40/18&r=all |
| By: | Marco Bottone; Mauro Bernardi; Lea Petrella |
| Abstract: | Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-linearity. Here we propose a unified Bayesian Conditional Autoregressive Risk Measures approach by using the Skew Exponential Power distribution. Further, we extend the proposed models using a semiparametric P-spline approximation answering for a flexible way to consider the presence of non-linearity. To make the statistical inference we adapt the MCMC algorithm proposed in Bernardi et al. (2018) to our case. The effectiveness of the whole approach is demonstrated using real data on daily return of five stock market indices. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1902.03982&r=all |
| By: | YAMAGUCHI Kazuo |
| Abstract: | This paper explains how to handle three issues that policy evaluators may face in using RCT (randomized controlled trials). The first issue concerns the sampling design that increases precision in the estimate of the average treatment effect under a given budget constraint. The second issue is the problem of noncompliance. This problem arises when the assignments of study subjects to treatment groups and control groups does not completely match the presence/absence of actual treatments, and initial randomness in selection of treatment and control groups is compromised. While there is a standard solution to this problem based on the instrumental variable method, the precision of this estimator is usually not high. This paper introduces a recent study by Black et al. (2015) regarding a test on the presence/absence of endogeneity in the treatment variable under the presence of noncompliance, and the use of a more precise estimator when the test result indicates the absence of endogeneity. The third issue concerns the estimation of the average treatment effect under RCT when a mediator variable that indicates the truncation of observation, and thereby the truncation-by-death problem exists. Discovering better solutions to this problem is one of the recent topics in statistical causal inference. This paper explains why certain methods, such as difference-in-differences (DID) estimator, cannot be applied to this situation even when the outcome before the treatment assignment is measurable, and why an estimate for the average treatment effect for the untreated (ATU) is desirable. The paper also introduces an estimator of the ATU for the truncation-by-death problem, based on an ignorability assumption. This paper also demonstrates that the idea of "principal stratification" based on certain assumptions of latent classes in behavioral patterns has been usefully employed in obtaining a causal understanding of both the noncompliance issue and the truncation-by-death issue. An illustrative application of empirical data for handing noncompliance with the Black et al.'s endogeneity test is also presented. |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:eti:rdpsjp:19003&r=all |
| By: | Serafin J. Grundl; Yu Zhu |
| Abstract: | In laboratory experiments bidding in first-price auctions is more aggressive than predicted by the risk-neutral Bayesian Nash Equilibrium (RNBNE) - a finding known as the overbidding puzzle. Several models have been proposed to explain the overbidding puzzle, but no canonical alternative to RNBNE has emerged, and RNBNE remains the basis of the structural auction literature. Instead of estimating a particular model of overbidding, we use the overbidding restriction itself for identification, which allows us to bound the valuation distribution, the seller's payoff function, and the optimal reserve price. These bounds are consistent with RNBNE and all models of overbidding and remain valid if different bidders employ different bidding strategies. We propose simple estimators and evaluate the validity of the bounds numerically and in experimental data. |
| Keywords: | Experimental findings ; First-price auction ; Partial identification ; Robust inference ; Structural estimation |
| JEL: | C14 D44 |
| Date: | 2019–02–07 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2019-06&r=all |
| By: | Susanne M. Schennach (Institute for Fiscal Studies and Brown University) |
| Abstract: | Many time-series exhibit “long memory”: Their autocorrelation function decays slowly with lag. This behavior has traditionally been modeled via unit roots or fractional Brownian motion and explained via aggregation of heterogenous processes, nonlinearity, learning dynamics, regime switching or structural breaks. This paper identifies a different and complementary mechanism for long memory generation by showing that it can naturally arise when a large number of simple linear homogenous economic subsystems with short memory are interconnected to form a network such that the outputs of the subsystems are fed into the inputs of others. This networking picture yields a type of aggregation that is not merely additive, resulting in a collective behavior that is richer than that of individual subsystems. Interestingly, the long memory behavior is found to be almost entirely determined by the geometry of the network, while being relatively insensitive to the specific behavior of individual agents. |
| Keywords: | Long memory, fractionally integrated processes, spectral dimension, networks, fractals. |
| Date: | 2018–07–27 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:49/18&r=all |
| By: | Kenichiro McAlinn; Knut Are Aastveit; Jouchi Nakajima; Mike West |
| Abstract: | We present new methodology and a case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the foundational BPS framework to the multivariate setting, with detailed application in the topical and challenging context of multi-step macroeconomic forecasting in a monetary policy setting. BPS evaluates– sequentially and adaptively over time– varying forecast biases and facets of miscalibration of individual forecast densities for multiple time series, and– critically– their time-varying interdependencies. We define BPS methodology for a new class of dynamic multivariate latent factor models implied by BPS theory. Structured dynamic latent factor BPS is here motivated by the application context– sequential forecasting of multiple US macroeconomic time series with forecasts generated from several traditional econometric time series models. The case study highlights the potential of BPS to improve of forecasts of multiple series at multiple forecast horizons, and its use in learning dynamic relationships among forecasting models or agents. |
| Keywords: | Agent opinion analysis, Bayesian forecasting, Dynamic latent factors models, Dynamic SURE models, Macroeconomic forecasting, Multivariate density forecast combination, |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:bny:wpaper:0073&r=all |
| By: | Frank Windmeijer |
| Abstract: | This paper is concerned with the …findings related to the robust …first-stage F-statistic in the Monte Carlo analysis of Andrews (2018), who found in a heteroskedastic design that even for very large values of the robust F-statistic, the standard 2SLS con…dence intervals had large coverage distortions. This …finding appears to discredit the robust F-statistic as a test for underidenti…fication. However, it is shown here that large values of the robust F-statistic do imply that there is …first-stage information, but this may not be utilised well by the 2SLS estimator, or the standard GMM estimator. An estimator that corrects for this is a robust GMM estimator, with the robust weight matrix not based on the structural residuals, but on the …first-stage residuals. For the grouped data setting of Andrews (2018), this estimator gives the weights to the group speci…fic estimators according to the group specific concentration parameters in the same way as 2SLS does under homoskedasticity, which is formally shown using weak instrument asymptotics. This estimator is much better behaved than the 2SLS estimator in this design, behaving well in terms of relative bias and Wald test size distortion at more ‘standard’ values of the robust F-statistic. We further derive the conditions under which the Stock and Yogo (2005) weak instruments critical values apply to the robust F-statistic in relation to the behaviour of this GMM estimator. |
| Keywords: | weak instruments, heteroskedasticity, F-test, Stock-Yogo critical values. |
| Date: | 2019–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:bri:uobdis:19/708&r=all |
| By: | Oliver Kley; Claudia Kl\"uppelberg; Sandra Paterlini |
| Abstract: | We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account the Pareto tails of losses and the heterogeneous dependence structures between them. We then derive estimators for individual as well as aggregated tail risk, measured in terms of Value-at-Risk and Conditional-Tail-Expectation for very high confidence levels, and provide also an asymptotically full capital allocation method. Estimation methods for such tail risk measures and capital allocations are also proposed and tested on simulated data. Finally, by having access to real-world operational risk losses from the Italian banking system, we show that even with a small number of observations, the proposed estimation methods produce reliable estimates, and that quantifying dependence by means of the empirical network has a big impact on estimates at both individual and aggregate level, as well as for capital allocations. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1902.03041&r=all |
| By: | Maria Bolboaca (Institute of Economics, University of St. Gallen); Sarah Fischer (State Secretariat for Economic Affairs SECO) |
| Abstract: | This paper investigates the nonlinearity in the effects of news shocks about technological innovations. In a maximally fl exible logistic smooth transition vector autoregressive model, state-dependent effects of news shocks are identified based on medium-run restrictions. We propose a novel approach to impose these restrictions in a nonlinear model using the generalized forecast error variance decomposition. We compute generalized impulse response functions that allow for regime transition and find evidence of state-dependency. The results also indicate that the probability of a regime switch is highly infl uenced by the news shocks. |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:szg:worpap:1901&r=all |
| By: | Charles F. Manski (Institute for Fiscal Studies and Northwestern University) |
| Abstract: | The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data => decision]. An SDF need not perform statistical inference; that is, it need not use data to draw conclusions about the true state of nature. Inference-based SDFs have the sequential form [data => inference => decision]. This paper offers remarks on the use of statistical inference in statistical decisions. Concern for tractability may provide a practical reason for study of inference-based SDFs. Another practical reason may be necessity. There often is an institutional separation between research and decision making, with researchers reporting inferences to the public. Then planners can perform the mapping [inference => decision], but they cannot perform the more basic mapping [data => decision]. The paper first addresses binary choice problems, where all SDFs may be viewed as hypothesis tests. It next considers as-if optimization, where one uses a point estimate of the true state as if the estimate is accurate. It then extend this idea to as-if decisions using set estimates of the true state, such as confidence sets. |
| Date: | 2019–01–30 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:06/19&r=all |
| By: | Charles D. Kolstad; Frances C. Moore |
| Abstract: | This paper reviews methods that have been used to statistically measure the effect of climate on economic value, using historic data on weather, climate, economic activity and other variables. This has been an active area of research for several decades, with many recent developments and discussion of the best way of measuring climate damages. The paper begins with a conceptual framework covering issues relevant to estimating the costs of climate change impacts. It then considers several approaches to econometrically estimate impacts that have been proposed in the literature: cross-sections, linear and non-linear panel methods, long-differences, and partitioning variation. For each method we describe the kind of impacts (short-run vs long-run) estimated, the type of weather or climate variation used, and the pros and cons of the approach. |
| JEL: | H41 Q51 Q54 |
| Date: | 2019–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:25537&r=all |