{"title":"AR(1)附加回归量时间序列模型的GMM估计","authors":"B. Chakalabbi, Sanmati Neregal, Sagar Matur","doi":"10.12785/IJCTS/060203","DOIUrl":null,"url":null,"abstract":"GMM estimators properties for panel data have been very well known in the econometric literature and it has been observed that for small sample cases, they perform well. The OLS (Ordinary Least Squares) is not applicable when lagged endogenous and exogenous variables are correlated with the error term. Hence, here an attempt is made to estimate AR(1) time series model with one additional regressor by considering First-difference GMM and Level GMM estimation methods proposed by Arellano and Bond (1991) and Arellano and Bover (1995) respectively. In order study the performances of the above mentioned estimators in comparison with the OLS estimator Monte Carlo simulation study is carried out. Further, a comparison among these estimators has been done in terms of bias and RMSE. Study disclose that for an autoregressive parameter, Level GMM estimator performs better than First-difference GMM and OLS estimators when T, the sample size is small and ρ, the autoregressive parameter is close to unity. Whereas for the parameter of additional regressor β, Level GMM estimator performs better than the other two mentioned estimators for all the values of ρ and T.","PeriodicalId":130559,"journal":{"name":"International Journal of Computational & Theoretical Statistics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"GMM Estimation of AR(1) Time Series Model with One Additional Regressor\",\"authors\":\"B. Chakalabbi, Sanmati Neregal, Sagar Matur\",\"doi\":\"10.12785/IJCTS/060203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"GMM estimators properties for panel data have been very well known in the econometric literature and it has been observed that for small sample cases, they perform well. The OLS (Ordinary Least Squares) is not applicable when lagged endogenous and exogenous variables are correlated with the error term. Hence, here an attempt is made to estimate AR(1) time series model with one additional regressor by considering First-difference GMM and Level GMM estimation methods proposed by Arellano and Bond (1991) and Arellano and Bover (1995) respectively. In order study the performances of the above mentioned estimators in comparison with the OLS estimator Monte Carlo simulation study is carried out. Further, a comparison among these estimators has been done in terms of bias and RMSE. Study disclose that for an autoregressive parameter, Level GMM estimator performs better than First-difference GMM and OLS estimators when T, the sample size is small and ρ, the autoregressive parameter is close to unity. Whereas for the parameter of additional regressor β, Level GMM estimator performs better than the other two mentioned estimators for all the values of ρ and T.\",\"PeriodicalId\":130559,\"journal\":{\"name\":\"International Journal of Computational & Theoretical Statistics\",\"volume\":\"61 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computational & Theoretical Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12785/IJCTS/060203\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computational & Theoretical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12785/IJCTS/060203","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
面板数据的GMM估计器属性在计量经济学文献中已经非常有名,并且已经观察到,对于小样本情况,它们表现良好。当滞后的内生变量和外生变量与误差项相关时,普通最小二乘法(OLS)不适用。因此,本文尝试通过考虑Arellano and Bond(1991)和Arellano and Bover(1995)分别提出的First-difference GMM和Level GMM估计方法,对带有一个额外回归量的AR(1)时间序列模型进行估计。为了研究上述估计器的性能,并与OLS估计器进行了蒙特卡罗仿真研究。此外,这些估计器之间的比较已经在偏差和RMSE方面完成。研究表明,对于自回归参数,当样本量T较小且自回归参数ρ接近于单位时,水平GMM估计量比一差GMM估计量和OLS估计量表现更好。而对于附加回归量β的参数,对于所有的ρ和T值,Level GMM估计器的性能都优于其他两种估计器。
GMM Estimation of AR(1) Time Series Model with One Additional Regressor
GMM estimators properties for panel data have been very well known in the econometric literature and it has been observed that for small sample cases, they perform well. The OLS (Ordinary Least Squares) is not applicable when lagged endogenous and exogenous variables are correlated with the error term. Hence, here an attempt is made to estimate AR(1) time series model with one additional regressor by considering First-difference GMM and Level GMM estimation methods proposed by Arellano and Bond (1991) and Arellano and Bover (1995) respectively. In order study the performances of the above mentioned estimators in comparison with the OLS estimator Monte Carlo simulation study is carried out. Further, a comparison among these estimators has been done in terms of bias and RMSE. Study disclose that for an autoregressive parameter, Level GMM estimator performs better than First-difference GMM and OLS estimators when T, the sample size is small and ρ, the autoregressive parameter is close to unity. Whereas for the parameter of additional regressor β, Level GMM estimator performs better than the other two mentioned estimators for all the values of ρ and T.