Threshold Variables Research Articles

Climate Variability and the U.S. Corn Belt: ENSO and AO Episode-Dependent Hydroclimatic Feedbacks to Corn Production at Regional and Local Scales*

Abstract El Niño–Southern Oscillation (ENSO) and Arctic Oscillation (AO) climatology (1980–2010) is developed and analyzed across the U.S. Corn Belt using state climate division weather and historic corn yield data using analysis of variance (ANOVA) and correlation analysis. Findings provide insight to agroclimatic conditions under different ENSO and AO episodes and are analyzed with a perspective for potential impacts to agricultural production and planning, with findings being developed into a web-based tool for the U.S. Corn Belt. This study is unique in that it utilizes the oceanic Niño index and explores two teleconnection patterns that influence weather across different spatiotemporal scales. It is found that the AO has a more frequent weak to moderate correlation to historic yields than ENSO when correlated by average subgrowing season index values. Yield anomaly and ENSO and AO episode analysis affirms the overall positive impact of El Niño events on yields compared to La Niña events, with neutral ENSO events in between as found in previous studies. Yields when binned by the AO episode present more uncertainty. While significant temperature and precipitation impacts from ENSO and AO are felt outside of the primary growing season, correlation between threshold variables of episode-specific temperature and precipitation and historic yields suggests that relationships between ENSO and AO and yield are present during specific months of the growing season, particularly August. Overall, spatial climatic variability resulting from ENSO and AO episodes contributes to yield potential at regional to subregional scales, making generalization of impacts difficult and highlighting a continued need for finescale resolution analysis of ENSO and AO signal impacts on corn production.

Nonlinearity testing and modeling for threshold moving average models

In this paper, we suggest a simple test and an easily applicable modeling procedure for threshold moving average (TMA) models. Firstly, based on the fitted residuals by maximum likelihood estimate (MLE) for MA models, we construct a simple statistic, which is obtained by linear arrange regression and follows F-distribution approximately, to test for threshold nonlinearity and specify the threshold variables. And then, we use some scatterplots to identify the number and locations of the potential thresholds. Finally, with the statistic and Akaike information criterion, we propose the procedure to build TMA models. Both the power of test statistic and the convenience of modeling procedure can work very well demonstrated by simulation experiments and the application to a real example.

Property rights and the stock market-growth nexus

Using threshold estimation techniques, this study examines whether the growth effect of stock market development differs according to the different levels of property rights and minority shareholders protection in a cross-section of 85 jurisdictions during the post-crisis period. The results demonstrate that the impact of stock market liquidity on growth is positive and significant only in jurisdictions where there is high level of property rights protection. Similar effect is discerned in the case of strong minority shareholders protection. Using the market size as a measure of stock market development, the paper also documents a positive growth effect of market size when property rights and minority shareholders protection are strong. However, there is mixed evidence in the low to medium degrees of protection. Further analyses using other broader governance indicators as threshold variables and instrumental variable threshold regressions reaffirm the main findings. The study upholds the “better finance, more growth” proposition and contributes to the identification of thresholds above which institutional quality can positively shape the impact of stock market on economic growth.

Cash-Flow Based Dynamic Inventory Management

Small-to-medium size enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this paper, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm’s capital at the end of a finite planning horizon. Our study shows that the optimal ordering policy is characterized by a pair of threshold variables for each period as function of the initial state of the period. Further, upper and lower bounds for the threshold values are developed using two simple-to-compute ordering policies. Based on these bounds, we provide an efficient algorithm to compute the two threshold values. Since the underlying state space is two-dimensional which leads to high computational complexity of the optimization algorithm, we also derive upper bounds for the optimal value function by reducing the optimization problem to one dimension. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with numerical studies.

Fiscal Policies and Credit Regimes: A TVAR Approach

SUMMARY This work investigates how the state of credit markets affects the impact of fiscal policies. We estimate a threshold vector autoregression (TVAR) model on US quarterly data for the period 1984–2010. We employ the spread between BAA-rated corporate bond yield and 10-year treasury constant maturity rate as a proxy for credit conditions. We find that the response of output to fiscal policy shocks is stronger and more persistent when the economy is in the ‘tight’ credit regime. Fiscal multipliers are significantly different in the two regimes: they are abundantly and persistently higher than one when firms face increasing financing costs, whereas they are feebler and often lower than one in the ‘normal’ credit regime. The results appear to be robust to different model specifications, fiscal foresight, alternative threshold variables, different measure of variables and sample periods. Copyright © 2014 John Wiley & Sons, Ltd.

The role of macroeconomic stability in the finance-growth nexus. Threshold regression approach

In this paper we analyse the link between Finance and Growth and, in particular, if this link is variable in respect to changes in the Macroeconomic Stability. This topic was studied by many authors without any definite conclusion being reached. This paper considers the theoretical and the empirical problem in two ways: first, the evolution of the empirical literature, and a new empirical perspective to analyze that link. The research presented here attempts to answer this question using threshold methodology. It confirms previous analysis in respect to non-linearity of the relationship between finance and growth in international comparisons. The use of two different threshold variables confirms the complexity of this link and also the different mechanisms of transmission that operate inside different groups of countries. The use of the bank’s liquidity reserve ratio as a indicator suggests that probably the link between wealth and stability is not always enjoyed.

Modelling nonlinearities in commodity prices using smooth transition regression models with exogenous transition variables

This paper investigates the nonlinearities in commodity prices using smooth transition regression (STR) models. What distinguishes this paper from the majority of the studies in the smooth transition literature is its use of exogenous transition variables, in addition to the standard autoregressive lags of the dependent variable, in modelling the regime switching behavior of commodity prices. Two exogenous transition variables were found successful in capturing the regime switching behavior of commodity prices: inflation rate and oil price. Inflation rate was capable of capturing the early dynamics (between 1900 and 1950) of the commodity index whereas oil price captured the late ones (between 1970 and 2007). This result motivates the use of common exogenous threshold variables in regime switching models in general and, in particular, the use of inflation and oil price in the STR model when applied to an index of commodity prices. The paper also provides further insight on the issue of co-movement of commodity prices by classifying individual commodities into groups according to their border price (an issue that has been ignored in previous studies on commodity prices), and then trying to find the best common transition variable that can explain the dynamic behavior of each group. The results show that, for traded commodities, individual price series recorded on a free on board basis are driven by macroeconomic news in the exporting country. On the other hand, individual price series recorded on a cost and freight basis are driven by oil price and macroeconomic news variables in the importing country.

Threshold variable selection of asymmetric stochastic volatility models

A threshold stochastic volatility (SV) model is used for capturing time-varying volatilities and nonlinearity. Two adaptive Markov chain Monte Carlo (MCMC) methods of model selection are designed for the selection of threshold variables for this family of SV models. The first method is the direct estimation which approximates the model posterior probabilities of competing models. Using parallel MCMC sampling to estimate these probabilities, the best threshold variable is selected with the highest posterior model probability. The second method is to use the deviance information criterion to compare among these competing models and select the best one. Simulation results lead us to conclude that for large samples the posterior model probability approximation method can give an accurate approximation of the posterior probability in Bayesian model selection. The method delivers a powerful and sharp model selection tool. An empirical study of five Asian stock markets provides strong support for the threshold variable which is formulated as a weighted average of important variables.

Modeling OECD energy demand: An international panel smooth transition error-correction model

This study is the first to apply a newly developed panel smooth transition regression model with the error-correction term (PSECM) to estimate the non-linear relationship among energy consumption, real income and real energy prices for 24 OECD countries. Unlike the existing literature on non-linear estimation, we consider five “candidates” for the threshold variable including per capita real GDP, real energy prices, energy intensity, the ratio of gross capital formation to GDP, and error-correction term to explore which threshold variable is suitable for the non-linear energy demand model. Our empirical results demonstrate that energy consumption, real income and real energy prices can be cointegrated, and are in favor of the non-linearity for energy demand when the energy intensity and the ratio of gross capital formation to GDP are considered as the threshold variables. Furthermore, the results indicate that the adjustment speed toward long-run equilibrium of PSECM is small and approximately 7–17% in 1year.

Winter variability of aeolian sediment transport threshold on a cold-climate dune

Changes in surface conditions on cold-climate aeolian dunes are pronounced; during winter dunes are wet, snow covered, and/or frozen for extended periods of time. It is unknown how the critical wind speed for sediment transport (“threshold”) varies and how threshold may influence sediment transport predictions. Although the impact of surface conditions on threshold has been examined in synthetic experiments (wind tunnels), complicated feedbacks between threshold, sand transport, and surface conditions that occur in natural environments suggest that a ground-based empirical approach may provide enhanced insight. In this study we investigate threshold variability for 73days during fall–winter–spring surface conditions from 18 November 2008 to 30 May 2009 in the Bigstick Sand Hills of Saskatchewan, Canada. Simultaneous measurements of threshold and atmospheric variables (air temperature, relative humidity, solar radiation, wind speed and direction) were used to examine the extent to which surface erodibility was regulated by meteorology. Time‐lapse images of the surface from a co-located camera were used for quality control and interpreting changes in the surface affecting threshold. Results reveal that threshold varied throughout the deployment (25–75% quartiles: 6.92–8.28ms−1; mean: 7.79ms−1). Threshold variability was especially evident at two scales: (i) event timescale and (ii) seasonal timescale. Event-scale variability peaked during mid-winter; in one event the threshold varied by 6ms−1 in 2h with freezing and re-freezing of the surface and relatively constant atmospheric conditions. The causes of event-scale variability are complex though qualitatively related to changes of wind direction, antecedent meteorological conditions, and vertical variations of grain-scale bonding agents such as pore ice and moisture. Seasonal-scale changes manifested as an increase in threshold during fall, peaking in mid-winter, and decreasing in spring. Increased threshold in mid-winter was linked to lower insolation and air temperature, suggesting low erodibility due to the presence of pore ice. Correlation coefficients of threshold versus atmospheric variables yielded relatively weak correlations (air temperature: r=−0.322; relative humidity: r=0.388; solar radiation: r=−0.309) that also varied according to wind direction, suggesting that the link between atmospheric conditions and surface erodibility on cold‐climate dunes is complex. This contrasts with results from field-based studies in warmer climates and controlled wind tunnel experiments, which show a more direct link between atmospheric variables (temperature and humidity) and surface erodibility. Nevertheless, our results do show a seasonal pattern of threshold that could be important for modeling cold-climate aeolian sediment transport.

Searching for a better proxy for business cycles: with supports using US data

This study revises the original Current Depth of Recession (CDR) to prove that the Modified CDR (MCDR) is more suitable as a threshold variable than the CDR. We rebuild the CDR indicator and adjust its positive and negative ranges with the estimation results of the Threshold Autoregressive (TAR) model. We construct two TAR models utilizing CDR and MCDR as threshold variables, respectively. Estimation and test results of the root mean square error, Theil's inequality coefficient and the Diebold-Mariano (DM, 1995) test suggest that MCDR performs better as a threshold variable than CDR.

Theory and Applications of TAR Model with Two Threshold Variables

A growing body of threshold models has been developed over the past two decades to capture the nonlinear movement of financial time series. Most of these models, however, contain a single threshold variable only. In many empirical applications, models with two or more threshold variables are needed. This article develops a new threshold autoregressive model which contains two threshold variables. A likelihood ratio test is proposed to determine the number of regimes in the model. The finite-sample performance of the estimators is evaluated and an empirical application is provided.

IV Estimation of a Panel Threshold Model of Tourism Specialization and Economic Development

The significant impact of international tourism in stimulating economic growth is especially important from a policy perspective. For this reason, the relationship between international tourism and economic growth would seem to be an interesting and topical empirical issue. The paper investigates whether tourism specialization was important for economic development in 159 countries over the period 1989–2008. The results from panel threshold regressions show a positive relationship between economic growth and tourism. Instrumental variable estimation of a threshold regression is used to quantify the contributions of tourism specialization to economic growth, while correcting for endogeneity between the regressors and error term. The significant impact of tourism specialization on economic growth in most regressions is robust to different specifications of tourism specialization, as well as to differences in real GDP measurement. However, the coefficients of the tourism specialization variables in the two regimes are significantly different, with a higher impact of tourism on economic growth found in the low regime. These findings do not alter with changes in the threshold variables. The empirical results suggest that tourism growth does not always lead to substantial economic growth.

Estimation of Panel Data Models with Parameter Heterogeneity when Group Membership is Unknown

This paper proposes two methods for estimating panel data models with group specific parameters when group membership is not known. The first method uses the individual level time series estimates of the parameters to form threshold variables. The problem of parameter heterogeneity is turned into estimation of a panel thresh- old model with an unknown threshold value. The second method modifies the K-means algorithm to perform condi- tional clustering. Units are clustered based on the devia- tions between the individual and the group conditional means. The two approaches are used to analyze growth across countries and housing market dynamics across the states in the U.S.

The determinants of international reserves in the emerging countries: a nonlinear approach

In this article, we adopt a nonlinear approach to examine the dynamics of the international reserves holdings by the emerging economies. To do so, we estimate the demand for international reserves with a Panel Smooth Transition Regression (PSTR) model that loosens two restricting hypotheses, homogeneity and time-stability. We find evidence for the presence of a nonlinear behaviour in the demand for international reserves, a result that is new to the literature. The coefficients are found to change smoothly, as a function of two threshold variables – out of five candidates tested in total. Our specification accounts for the acceleration of foreign exchange reserves accumulation that the linear specifications fail to explain.

The Effect of Three Different Start Thresholds on the Kinematics and Kinetics of a Countermovement Jump

Force plates are used to quantify kinematic and kinetic variables of countermovement jump (CMJ). The jump is initiated by an unloading phase resulting in the force-time curve to drop below body weight (BW). However, there is no consensus in the literature to determine the start of the analysis of the jump (i.e., start threshold). To determine the effects and reliability of 3 different start thresholds on the kinematics and kinetics of a CMJ, 10 soccer players performed 3 CMJs for maximal jump height 30 seconds apart. Initiation of the jump movement was defined as the point where the force-time curve dropped below a threshold of 2.5, 5, or 10% BW. Significant differences were found in all variables except eccentric and concentric peak force and force at zero velocity between 2.5 and 10%, and 5 and 10% thresholds. Similar results were found for the 2.5 and 5% threshold variables except that no significant difference was found in the concentric ground contact time. The different thresholds did not appear to influence the variability of the measurement and only concentric time to peak power was found to have high variability. These data suggest that the use of any of the start thresholds can be used to determine the starting point of a CMJ considering their reliability. However, the 2.5% BW threshold is preferable because most of the force-time signal can be considered for analysis, and significant differences in eccentric and concentric kinematic and kinetic variables were found when a higher threshold was used.

Optimal operation strategy development for fuel cell hybrid vehicle

An overall simulation model for fuel cell hybrid vehicle (FCHV) power train in parallel configuration using MATLAB/Simulink pro- gramming is constructed in this study. The model runs on power control strategy by using logic-threshold approach, achieved by the hybrid control unit (HCU) and fuel cell stack number. Using accelerator and decelerator pedal positions deduced from the driving sched- ule as the primary input, the simulation implements power flow and distribution under different vehicle operating modes. The HCU con- trol strategy also incorporates regenerative braking and recharge for battery capacity recovery. Using the D-optimality method for ex- periment points selection and sequential quadratic programming (SQP) algorithm for obtaining the optimal operational parameters, three control threshold variables of HCU and optimal stack cell number are selected for hydrogen fuel economy under certain driving cycles. The proposed method provides optimized configurations of the FCHV model and the fuel cell stack, which has the capability in satisfy- ing drive power request while satisfying vehicle driving schedule and battery state of charge (SOC) recovery with lower fuel consump- tion.

Evolutionary procedure based model to predict ground–level ozone concentrations

This study aims to predict the next day hourly average ozone (O3) concentrations using threshold autoregressive (TAR) models in which the threshold value and the threshold variable are defined by genetic algorithms. The procedure is also able to generate models with statistically significant regression parameters. The performance of TAR models was then compared to the one obtained with autoregressive (AR) and artificial neural network (ANN) models. Different TAR models were generated, corresponding to different threshold variables and values. For the training period, ANN model presented better results than TAR and AR models. However, in the test period, AR and one of the TAR models achieved better predictions of O3 concentrations than the ANN model. The distinction between the applied models became greater when they were evaluated in the prediction of the extreme values, for which the TAR model presented the best performance. The performance with respect to extreme values is a useful implication for the protection of public health as this model can provide more reliable early warnings about high O3 concentration episodes.

The influence of a fast ramp rate on peak cardiopulmonary parameters during arm crank ergometry

The influence of a very fast ramp rate on cardiopulmonary variables at ventilatory threshold and peak exercise during a maximal arm crank exercise test has not been extensively studied. Considering that short arm crank tests could be sufficient to achieve maximal oxygen consumption (VO₂), it would be of practical interest to explore this possibility. Thus, this study aimed to analyse the influence of a fast ramp rate (20 W min⁻¹) on the cardiopulmonary responses of healthy individuals during a maximal arm crank ergometry test. Seventeen healthy individuals performed maximal cardiopulmonary exercise tests (Ultima CardiO2; Medical Graphics Corporation, St Louis, USA) in arm ergometer (Angio, LODE, Groningen, The Netherlands) following two protocols in random order: fast protocol (increment: 2 w/6 s) and slow protocol (increment: 1 w/6 s). The fast protocol was repeated 60-90 days after the 1st test to evaluate protocol reproducibility. Both protocols elicited the same peak VO₂ (fast: 23.51 ± 6.00 versus slow: 23.28 ± 7.77 ml kg⁻¹ min⁻¹; P = 0.12) but peak power load in the fast ramp protocol was higher than the one in the slow ramp protocol (119 ± 43 versus. 102 ± 39 W, P < 0.001). There was no other difference in ventilatory threshold and peak exercise variables when 1st and 2nd fast protocols were compared. Fast protocol seems to be useful when healthy young individuals perform arm cardiopulmonary exercise test. The usefulness of this protocol in other populations remains to be evaluated.

IV Estimation of a Panel Threshold Model of Tourism Specialization and Economic Development

The significant impact of international tourism in stimulating economic growth is especially important from a policy perspective. For this reason, the relationship between international tourism and economic growth would seem to be an interesting and topical empirical issue. The purpose of this paper is to investigate whether tourism specialization is important for economic development in 159 countries over the period 1989-2008. The results from panel threshold regressions show a positive relationship between economic growth and tourism. Instrumental variable estimation of a threshold regression is used to quantify the contributions of tourism specialization to economic growth, while correcting for endogeneity between the regressors and error term. The significant impact of tourism specialization on economic growth in most regressions is robust to different specifications of tourism specialization, as well as to differences in real GDP measurement. However, the coefficients of the tourism specialization variables in the two regimes are significantly different, with a higher impact of tourism on economic growth found in the low regime. These findings do not change with changes in the threshold variables. The empirical results suggest that tourism growth does not always lead to substantial economic growth.