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For modelling the threshold effect in parameters of the quantile neural network models, this paper introduces a model called threshold quantile regression neural network (TQRNN), which allows a threshold effect in the quantile regression neural network (QRNN). We develop the estimation procedure of the proposed model and suggest test statistics for threshold effect and the linear setting used typically in the quantile regression framework. We conduct Monte Carlo simulations to assess the performance of estimation and testing procedures, and compare the forecasting performance of the TQRNN model relative to the QRNN model. Through Monte Carlo simulations, we show that the estimation and testing procedures work well in finite samples, and there is little loss in forecast accuracy by employing the suggested TQRNN model even when the true data is generated from a QRNN model; on the contrary, ignoring an existing threshold effect can deteriorate the forecast accuracy of the QRNN model. All the simulation results support the usefulness of the TQRNN model. [ABSTRACT FROM AUTHOR]

This paper introduces a panel threshold model with covariate-dependent and time-varying thresholds (PTCT), which extends the classical panel threshold model of Hansen, B. E. 1999. "Threshold Effects in Non-dynamic Panels: Estimation, Testing, and Inference." Journal of Econometrics 93: 345–68 to a framework with multiple covariate-dependent and time-varying thresholds. Based on the within-group transformation and Markov chain Monte Carlo (MCMC) technique, we develop methods for estimation and inference for threshold parameters in the proposed panel threshold model. We also suggest test statistics for threshold effect, threshold constancy, and for determining the number of thresholds. Monte Carlo simulations indicate that the estimation, inference and testing procedures work well in finite samples. Empirically, using the same data as in Hansen, B. E. 1999. "Threshold Effects in Non-dynamic Panels: Estimation, Testing, and Inference." Journal of Econometrics 93: 345–68 we revisit the cash flow/investment relationship and find quite different results. [ABSTRACT FROM AUTHOR]

This article introduces a panel threshold model with covariate-dependent and time-varying thresholds and unobserved individual-specific threshold effects (PTCDI). We develop methods for estimation and inference for threshold parameters in the proposed PTCDI model by employing the correlated random effects (CRE) device. We also suggest test statistics for linearity, threshold constancy, unobserved individual-specific threshold effects, and for determining the number of thresholds. We derive the asymptotic properties of the proposed estimator in the small-threshold-effect framework and establish the limiting distributions of the suggested test statistics. We also investigate the extension to dynamic panels and show that both the static and dynamic models can be handled uniformly in the CRE framework. Monte Carlo simulation results indicate that the estimation, inference, and testing procedures have the desired performance in finite samples. The model is illustrated with two empirical applications to the relationship between cash flow and investment and the nexus between inflation and economic growth. [ABSTRACT FROM AUTHOR]

This paper studies high-dimensional threshold models with a time-varying threshold approximated using a Fourier function. We develop a weighted LASSO estimator of regression coefficients as well as the threshold parameters. Our LASSO estimator can not only select covariates but also distinguish between linear and threshold models. We derive non-asymptotic oracle inequalities for the prediction risk, the l1 and l∞ bounds for regression coefficients, and provide an upper bound on the l1 estimation error of the time-varying threshold estimator. The bounds can be translated easily into asymptotic consistency for prediction and estimation. We also establish the variable selection consistency and threshold detection consistency based on the l∞ bounds. Through Monte Carlo simulations, we show that the thresholded LASSO works reasonably well in finite samples in terms of variable selection, and there is little harmness by the allowance for Fourier approximation in the estimation procedure even when there is no time-varying feature in the threshold. On the contrary, the estimation and variable selection are inconsistent when the threshold is time-varying but being misspecified as a constant. The model is illustrated with an empirical application to the famous debt-growth nexus. [ABSTRACT FROM AUTHOR]

This paper introduces a threshold mixed data sampling model with a covariate-dependent threshold (TMIDAS-CDT), which allows for a threshold effect in the relationship between dependent and independent variables sampled at different frequencies, and allows for threshold regimes depending on a time-varying threshold being modelled as a linear function of informative covariates. We develop the estimation procedure for the model, and suggest test statistics for threshold effect, threshold constancy and the equal weighting scheme in aggregating high-frequency data. We conduct Monte Carlo simulations to investigate the performance of the estimation and testing procedures. The simulation results support that the estimation procedure works well in finite samples, and the test statistics have good size and power properties. [ABSTRACT FROM AUTHOR]

Let HT ht ${\gamma } {t}={\gamma } {t}^{0}+\frac{w}{{a} {T}}$. Assumptions 1 and 3 above are needed to establish a limit theory for HT ht as in [3], [10], and [4]. [Extracted from the article]

This article extends the kink threshold regression model with a constant threshold to a panel data framework with a covariate-dependent threshold, where the threshold is modeled as a function of informative covariates. We suggest an estimator based on the within-group transformation and propose test statistics for kink threshold effect and threshold constancy. We establish the asymptotic joint normality of the slope and threshold estimators and derive the limiting distributions of the test statistics. Our asymptotic results show that the inclusion of a covariate-dependent threshold does not affect the asymptotic joint normality of the slope and threshold estimates in the kink threshold regression model. Monte Carlo simulations show that the finite-sample proprieties of the proposed estimator and test statistics are generally satisfactory. [ABSTRACT FROM AUTHOR]

Classical threshold models assume that threshold values are constant and stable, which appears overly restrictive and unrealistic. In this article, we extend Hansen's (2000) constant threshold regression model by allowing for a time‐varying threshold which is approximated by a Fourier function. Least‐square estimation of regression slopes and the time‐varying threshold is proposed, and test statistics for the existence of threshold effect and threshold constancy are constructed. We also develop the asymptotic distribution theory for the time‐varying threshold estimator. Through Monte Carlo simulations, we show that the proposed estimation and testing procedures work reasonably well in finite samples, and there is little efficiency loss by the allowance for Fourier approximation in the estimation procedure even when there is no time‐varying feature in the threshold. On the contrary, the slope estimates are seriously biased when the threshold is time‐varying but being treated as a constant. The model is illustrated with an empirical application to a nonlinear Taylor rule for the United States. [ABSTRACT FROM AUTHOR]

It is a popular method to deal with structural breaks using Fourier transformation, in which an integer frequency and a fractional frequency are respectively associated with transitory and permanent breaks, and hence is important in empirical applications. However, we still do not know how the integer and fractional frequencies affect the theoretical properties of unit root tests. This paper examines the properties of Dickey-Fuller tests when the true datagenerating process contains fractional Fourier-form breaks but ignored in testing procedures. We derive the limiting distributions by reparameterization, discuss the theoretical predictions of the limiting results on the properties of Dickey-Fuller tests, and give the conditions under which spurious rejection occurs. We use Monte Carlos simulations to confirm the predictions, finding that the theory is consistent with the simulation evidence. Our results imply that permanent breaks could more easily lead to spurious rejections than temporary breaks. Thus, ignoring a fractional frequency or specifying it as integer would cause misleading results. [ABSTRACT FROM AUTHOR]

This paper extends the cross-sectionally augmented panel unit-root test ( CIPS) developed by Pesaran et al. (2013, Journal of Econometrics, Vol. 175, pp. 94-115) to allow for smoothing structural changes in deterministic terms modelled by a Fourier function. The proposed statistic is called the break augmented CIPS ( BCIPS) statistic. We show that the non-standard limiting distribution of the (truncated) BCIPS statistic exists and tabulate its critical values. Monte-Carlo experiments point out that the sizes and powers of the BCIPS statistic are generally satisfactory as long as the number of time periods, T, is not less than fifty. The BCIPS test is then applied to examine the validity of long-run purchasing power parity. [ABSTRACT FROM AUTHOR]

Since the end of the Second World War, China, Japan and Korea have faced a challenge of protecting a national basic livelihood. However, the three countries have followed different development path of livelihood protection system due to different political system. Japan with an external influence of democracy established livelihood protection system immediately after the war. Korea established livelihood protection system in authoritarian governments. But it has not been implemented completely until the Kim Youngsam government established the national basic livelihood protection system under the careful guidance of the citizens. China with the impact of ideology established livelihood protection system, which is based on temporary social protection system for a few marginal groups. Since the Reform and Opening, China established the minimum livelihood protection system for urban residents under the pressure of the reform in the state-owned enterprises, which later on expanded to all the citizens in the country. There is certain difference in patterns of enjoying rights of livelihood protection because of the impact of political system. [ABSTRACT FROM AUTHOR]