Presence Of Heteroskedasticity Research Articles

Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity

We study the efficient estimation of nonparametric regression in the presence of heteroskedasticity. We focus our analysis on local polynomial estimation of nonparametric regressions with conditional heteroskedasticity in a time series setting. We introduce a weighted local polynomial regression smoother that takes account of the dynamic heteroskedasticity. We show that, although traditionally it is advised that one should not weight for heteroskedasticity in nonparametric regressions, in many popular nonparametric regression models our method has lower asymptotic variance than the usual unweighted procedures. We conduct a Monte Carlo investigation that confirms the efficiency gain over conventional nonparametric regression estimators in finite samples.

Heteroskedasticity in One-Way Error Component Probit Models

This paper introduces an estimation procedure for a random effects probit model in presence of heteroskedasticity and a likelihood ratio test for homoskedasticity. The cases where the heteroskedasticity is due to individual effects or idiosyncratic errors or both are analyzed. Monte Carlo simulations show that the test performs well in the case of high degree of heteroskedasticity. Furthermore, the power of the test increases with larger individual and time dimensions. The robustness analysis shows that applying the wrong approach may generate misleading results except for the case where both individual effects and idiosyncratic errors are modelled as heteroskedastic.

Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity

We derive an inference method that works in differences-in-differences settings with few treated and many control groups in the presence of heteroskedasticity. As a leading example, we provide theoretical justification and empirical evidence that heteroskedasticity generated by variation in group sizes can invalidate existing inference methods, even in data sets with a large number of observations per group. In contrast, our inference method remains valid in this case. Our test can also be combined with feasible generalized least squares, providing a safeguard against misspecification of the serial correlation.

A Model for Entrepreneurial Intention in University Students of Mexico

Background: Universities have shown to directly influence entrepreneurial activity in students [4-6], since they are concerned for the students to develop their entrepreneurial spirit [1-3], promoting Entrepreneurial Intention in University Students (EIUS). Objective: Therefore, the objective of this research is to determine a model of entrepreneurial intention of Mexican university students (EIUS), performing a multiple regression analysis, by the method of Ordinary Least Squares (OLS), on a sample of 538, with 4 independent variables (Personal and social features, innovative features, performance features and creativity) to determine the influence on the EIUS. Results and Conclusion: The results indicate that the four variables proposed in the model are relevant to explain the level of the EIUS, without problems of multicollinearity and discarding the presence of heteroskedasticity with the Breusch-Pagan test; and with the Kolmogorov-Smirnov normal distribution test it is determined that the predictor variable of the model does not require more independent variables; the contribution made with this research is of explanatory type, offering an elucidation of the empirical observations that characterize the university system in which the study was conducted.

Heteroskedasticity-consistent covariance matrix estimators for spatial autoregressive models

ABSTRACTIn the presence of heteroskedasticity, conventional test statistics based on the ordinary least squares (OLS) estimator lead to incorrect inference results for the linear regression model. Given that heteroskedasticity is common in cross-sectional data, the test statistics based on various forms of heteroskedasticity-consistent covariance matrices (HCCMs) have been developed in the literature. In contrast to the standard linear regression model, heteroskedasticity is a more serious problem for spatial econometric models, generally causing inconsistent extremum estimators of model coefficients. This paper investigates the finite sample properties of the heteroskedasticity-robust generalized method of moments estimator (RGMME) for a spatial econometric model with an unknown form of heteroskedasticity. In particular, it develops various HCCM-type corrections to improve the finite sample properties of the RGMME and the conventional Wald test. The Monte Carlo results indicate that the HCCM-type corrections can produce more accurate results for inference on model parameters and the impact effects estimates in small samples.

Modified Variance Ratio Test for Autocorrelation in the Presence of Heteroskedasticity

Given that autocorrelation tests do not perform well in the presence of heteroskedasticity and in variance-break cases, we present three modified weighted variance ratio tests of autocorrelation. The numerical results show that the proposed tests perform better for small samples. They provide a better approximation of asymptotic distributions and are more powerful when the lag length is mis-specified. The study also applies these tests to data on the daily returns of two companies listed on the Pakistan Stock Exchange.

Forecasting the Volatilities of Philippine Stock Exchange Composite Index Using the Generalized Autoregressive Conditional Heteroskedasticity Modeling

This study was conducted to find an appropriate statistical model to forecast the volatilities of PSEi using the model Generalized Autoregressive Conditional Heteroskedasticity (GARCH). Using the R software, the log returns of PSEi is modeled using various ARIMA models and with the presence of heteroskedasticity, the log returns was modeled using GARCH. Based on the analysis, GARCH models are the most appropriate to use for the log returns of PSEi. Among the selected GARCH models, GARCH (1,2) has the lowest AIC value and also has the highest LL value implying that GARCH (1,2) is the best model for the log returns of PSEi.

Heteroskedasticity Consistent Covariance Matrix Estimators for Spatial Autoregressive Models

In the presence of heteroskedasticity, conventional test statistics based on the ordinary least square estimator lead to incorrect inference results for the linear regression model. Given that heteroskedasticity is common in cross-sectional data, the test statistics based on various forms of heteroskedasticity consistent covariance matrices (HCCMs) have been developed in the literature. In contrast to the standard linear regression model, heteroskedasticity is a more serious problem for spatial econometric models, generally causing inconsistent extremum estimators of model coefficients. In this paper, we investigate the finite sample properties of the heteroskedasticity-robust generalized method of moments estimator (RGMME) for a spatial econometric model with an unknown form of hetereoskedasticity. In particular, we develop various HCCM-type corrections to improve the finite sample properties of the RGMME and the conventional Wald test. Our Monte Carlo results indicate that the HCCM-type corrections can produce more accurate results for inference on model parameters and the impact effects estimates in small samples.

NONPARAMETRIC IDENTIFICATION AND ESTIMATION OF TRUNCATED REGRESSION MODELS WITH HETEROSKEDASTICITY

We consider nonparametric identification and estimation of truncated regression models with unknown conditional heteroskedasticity. The existing methods (e.g., Chen (2010,Review of Economic Studies77, 127–153)) that ignore heteroskedasticity often result in inconsistent estimators of regression functions. In this paper, we show that both the regression and heteroskedasticity functions are identified in a location-scale setting. Based on our constructive identification results, we propose kernel-based estimators of regression and heteroskedasticity functions and show that the estimators are asymptotically normally distributed. Our simulations demonstrate that our new method performs well in finite samples. In particular, we confirm that in the presence of heteroskedasticity, our new estimator of the regression function has a much smaller bias than Chen’s (2010,Review of Economic Studies77, 127–153) estimator.

Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models

In this paper we study high-dimensional correlated random effects panel data models. Our setting is useful as it allows including time invariant covariates as under random effects yet allows for correlation between covariates and unobserved heterogeneity as under fixed effects. We use the Mundlak–Chamberlain device to model this correlation. Allowing for a flexible correlation structure naturally leads to a high-dimensional model in which least squares estimation easily becomes infeasible with even a moderate number of explanatory variables.Imposing a combination of sparsity and weak sparsity on the parameters of the model we first establish an oracle inequality for the Lasso. This is valid even when the error terms are heteroskedastic and no structure is imposed on the time series dependence of the error terms.Next, we provide upper bounds on the sup-norm estimation error of the Lasso. As opposed to the classical ℓ1- and ℓ2-bounds the sup-norm bounds do not directly depend on the unknown degree of sparsity and are thus well suited for thresholding the Lasso for variable selection. We provide sufficient conditions under which thresholding results in consistent model selection. Pointwise valid asymptotic inference is established for a post-thresholding estimator. Finally, we show how the Lasso can be desparsified in the correlated random effects setting and how this leads to uniformly valid inference even in the presence of heteroskedasticity and autocorrelated error terms.

The value of transportation accessibility in a least developed country city – The case of Rajshahi City, Bangladesh

Little appears to be known about the capitalization of transportation accessibility in South Asian housing markets, which typically differ from those of industrialized countries. This study starts addressing this gap by providing empirical evidence about the nature and the magnitude of the value of accessibility as reflected by residential rents in Rajshahi City, Bangladesh. Results of our SARAR spatial hedonic model estimated on 526 observations from a random sample collected via in-person interviews indicate that the rent of a multi-unit dwelling decreases by 0.0239% for every 1% increase in network access distance to the nearest major road. Moreover, proximity (within 400m) to a primary school and to a healthcare facility commands rent premiums of respectively 93.55BDT ($1.40) and 109.45BDT ($1.64). Surprisingly, whether access roads are paved or not does not statistically impact rents, probably because of the dominance of walking, rickshaws use, and biking, combined with the rarity of personal cars. Likewise, proximity to bus stops and to train stations is not reflected in rents of multi-family dwellings, likely because buses and trains in Rajshahi City only provide regional and national service. Differences in estimates of our spatial models between maximum likelihood (ML) and generalized spatial two-stage-least-squares illustrate the danger of relying on ML in the presence of heteroskedasticity. These results should be useful for planning transportation infrastructure funding measures in least developed country cities like Rajshahi City.

Impact of Currency Futures on Volatility in Exchange Rate

The present study has been carried out to study the impact of currency futures on the exchange rates volatility with respect to “euro”. The daily exchange rate values of euro vis-à-vis Indian rupee (INR) have been obtained for a period commencing from 1 January 2006 up to 30 September 2014. The time series data used in the study have been tested for stationarity by applying augmented Dicky and Fuller (ADF) test of unit root. The presence of heteroskedasticity in the residuals of return series of underlying data has been verified with autoregressive conditional heteroskedasticity Lagrange multiplier (ARCH LM) test. The volatility of the exchange rate return has been modelled with the help of generalized autoregressive conditional heteroskedasticity GARCH (1, 1) and Glosten–Jagannathan–Runkle (GJR) GARCH models. The results of GARCH models confirm that volatility is persistent and good news is causing more volatility than bad news. The difference in the volatility in the exchange rate returns during pre- and post-currency futures period has been examined with the help of various statistical tests and the results have been found to be significantly different and volatility has reduced in the post-futures period.

Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets

Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should co-integrate with a unit slope on futures prices, does not hold. However, these statistical methods are known to be unreliable if the data are fractionally integrated. Moreover, spot and futures price data tend to display clear patterns of time-varying volatility which also has the potential to invalidate the use of these methods. Using new tests constructed within a more general heteroskedastic fractionally integrated model we are able to find a body of evidence in support of the efficient market hypothesis for a number of commodities. Our new tests are wild bootstrap implementations of score-based tests for the order of integration of a fractionally integrated time series. These tests are designed to be robust to both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that the asymptotic tests do not admit pivotal asymptotic null distributions in the presence of heteroskedasticity, but that the corresponding tests based on the wild bootstrap principle do. A Monte Carlo simulation study demonstrates that very significant improvements in finite sample behaviour can be obtained by the bootstrap vis-à-vis the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments.

Inference Problems Under a Special Form of Heteroskedasticity

In the presence of heteroskedasticity, conventional standard errors (which assume homoskedasticity) can be biased up or down. The most common form of heteroskedasticity leads to conventional standard errors that are too small. When Wald tests based on these standard errors are insignificant, heteroskedasticity robust standard errors do not change inference. On the other hand, inference is conservative in a setting with upward-biased conventional standard errors. We discuss the power gains when using robust standard errors in this case and also potential problems of heteroskedasticity tests. As a solution for the poor performance of the usual heteroskedasticity tests in this setting, we propose a modification of the White test which has better properties. We illustrate our findings using a study in labor economics. The correct standard errors turn out to be around 15 percent lower, leading to different policy conclusions. Moreover, only our modified test is able to detect heteroskedasticity in this application.

Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality

In the presence of heteroskedasticity, Lin and Lee (2010) show that the quasi-maximum likelihood (QML) estimator of the spatial autoregressive (SAR) model can be inconsistent as a ‘necessary’ condition for consistency can be violated, and thus propose robust GMM estimators for the model. In this paper, we first show that this condition may hold in certain situations and when it does the regular QML estimator can still be consistent. In cases where this condition is violated, we propose a simple modified QML estimation method robust against unknown heteroskedasticity. In both cases, asymptotic distributions of the estimators are derived, and methods for estimating robust variances are given, leading to robust inferences for the model. Extensive Monte Carlo results show that the modified QML estimator outperforms the GMM and QML estimators even when the latter is consistent. The proposed methods are then extended to the more general SARAR models.

Time Series Analysis of the Relationship between Macroeconomic Factors and the Stock Market Returns in Pakistan

The purpose of this research is to investigate the relationship between Karachi stock market 100 index and macroeconomic variables, i.e., inflation, industrial production, money supply, exchange rate and interest rate. The long term relationship between macroeconomic variables and stock market returns has been analyzed by using Johnson Cointegration test, Augmented Dicky Fuller (ADF) and Phillip Perron (PP) tests. The Autoregressive Conditional heteroskedasticity Lagrange Multiplier (ARCH LM) test provided prudent evidence about the presence of heteroskedasticity in the data. The Generalized Autoregressive Conditional heteroskedasticity (GARCH) model was used to find out the relationship between stock returns and the variance of the squared error terms as there was heteroskedastic trend in the data. The results show that the cointegrating relationship exists between stock prices and the macroeconomic variables in Pakistani stock market. The GARCH model showed the significant relationships after mitigating the heteroskedasticity. The consumer price index (CPI), money supply (MS), exchange rates (ER) and interest rates (IR) proved to be negatively associated with the stock returns (SR), while industrial production index (IPI) was found to be positively associated with the stock returns. All the variables were significantly associated to stock market returns except inflation. The investors can use the GARCH results for investment decisions that is the returns are volatile not only due to any happening today but also on the past. The findings suggest that in the long run, the Pakistani stock market is reactive to macroeconomic indicators

A Comparison of Sequential and Information‐based Methods for Determining the Co‐integration Rank in Heteroskedastic VAR Models

AbstractIn this article, we investigate the behaviour of a number of methods for estimating the co‐integration rank in VAR systems characterized by heteroskedastic innovation processes. In particular, we compare the efficacy of the most widely used information criteria, such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) , with the commonly used sequential approach of Johansen [Likelihood‐based Inference in Cointegrated Vector Autoregressive Models(1996)] based around the use of either asymptotic or wild bootstrap‐based likelihood ratio type tests. Complementing recent work done for the latter in Cavaliere, Rahbek and Taylor [Econometric Reviews(2014) forthcoming], we establish the asymptotic properties of the procedures based on information criteria in the presence of heteroskedasticity (conditional or unconditional) of a quite general and unknown form. The relative finite‐sample properties of the different methods are investigated by means of a Monte Carlo simulation study. For the simulation DGPs considered in the analysis, we find that the BIC‐based procedure and the bootstrap sequential test procedure deliver the best overall performance in terms of their frequency of selecting the correct co‐integration rank across different values of the co‐integration rank, sample size, stationary dynamics and models of heteroskedasticity. Of these, the wild bootstrap procedure is perhaps the more reliable overall as it avoids a significant tendency seen in the BIC‐based method to over‐estimate the co‐integration rank in relatively small sample sizes.

Conditional Score Tests for Heteroscedasticity in the Two-Way Error Components Model

This paper extends the one-way heteroskedasticity score test of Holly and Gardiol (2000, In: Krishnakumar, J, Ronchetti, E (Eds.), Panel Data Econometrics: Future Directions, North-Holland, Amsterdam, pp. 199–211) to two conditional Lagrange Multiplier (LM) tests of heteroskedasticity under contiguous alternatives within the two-way error components model framework. In each case, the derivation of Rao's efficient score statistics for testing heteroskedasticity is first obtained. Then, based on a specific set of assumptions, the asymptotic distribution of the score under contiguous alternatives is established. Finally, the expression for the score test statistic in the presence of heteroskedasticity and related asymptotic local powers of these score test statistics are derived and discussed.

Binary Choice Model with Endogeneity: Identification via Heteroskedasticity

The idea of identifying structural parameters via heteroskedasticity is explored in the context of binary choice models with an endogenous regressor. Sufficient conditions for parameter identification are derived for probit models without relying on instruments or additional restrictions. The results are extendable to other parametric binary choice models. The semi- parametric model of Manski (1975, 1985), with endogeneity, is also shown to be identifiable in the presence of heteroskedasticity. The role of heteroskedasticity in identifying and estimating structural parameters is demonstrated by Monte Carlo experiments.

A panel data analysis of trade creation and trade diversion effects: The case of ASEAN–China Free Trade Area

This study uses a theoretically justified gravity model of trade to examine the impact of the ASEAN–China Free Trade Agreement (ACFTA) on exports, focusing on trade creation and diversion effects. The model is tested on a sample of 31 countries over the period dating from 1995 to 2010 using aggregated and disaggregated export data for agricultural and manufactured goods and within manufactures for chemical products, as well as for machinery and transport equipment. In order to obtain unbiased estimates, multilateral resistance terms are included as regressors and the endogeneity bias of the FTA variables is addressed by controlling for the unobserved specific heterogeneity that is specific to each trade flow. A multinomial PML is also applied to solve the zero trade issue and the presence of heteroskedasticity. The results indicate that ACFTA leads to substantial and significant trade creation. Using disaggregated data, the significant and positive relationship between exports and ACFTA is confirmed in the case of both agricultural and manufactured goods, as well as in the case of the most important manufacturing industries, namely, chemical products and machinery and transport equipment.