Magister Scientiae - MSc / In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as ‘mean-unbiased’ and ‘medianunbiased’ estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1). However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to  compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the ‘medianunbiased’ estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed; the ‘most-probably-unbiased’ estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed; (2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model; (3) the exact variance and MSE of LS estimator is determined; (4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort; (5) an exact method of evaluating the density of the three estimators is described; (6) their exact bias, mean, variance and MSE are determined and analysed; and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed. The discussion and results show that the estimators are still biased in the usual sense: ‘in expectation’. However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation. / South Africa

本研究目的在於探討投資等級債券信用價差是否存在外溢效果。信用價差是建構各種信用衍生性金融商品的基礎，惟目前學術界及業界都著眼在信用價差的拆解。信用價差可拆解成預期違約損失、稅的溢酬及信用風險溢酬。投資等級債券的信用價差來自於預期違約損失、稅的溢酬的部分較少，絕大多數來自於信用風險溢酬。信用風險溢酬係系統性影響信用價差的因素，此因素造成不同投資等級債券的信用價差間具有共整合的現象，進而引發外溢效果。然而並無人對於信用價差外溢效果作一深入探討。本研究利用目前學術界盛行的Panel模型的研究方法，對各種投資等級的債券的信用價差進行Panel Unit Root Tests、Panel Cointegration Tests及Panel Spillover Effect Tests，以求發現債券信用價差外溢效果存在與否的證據。 本文以iBoxx Index成份債券作為研究標的，利用Panel研究方法得到以下結論: 1.根據研究結果顯示，各種信評等級的債券的信用價差存在單根問題。 2.不同投資等級信評債券的信用價差擁有共整合關係。 3.不同投資等級信用評等的債券間信用價差外溢效果存在。且愈是相 鄰信評等級債券的外溢效果愈為顯著，例如BBB等級信用價差發生變動引發信評AAA等級信用價差變動的幅度便沒有AA等級信用價差變動引發AAA等級信用價差變動來得強烈。外溢效果係不對稱，當最高投資等級信評發生變動時，最低投資等級債券變動最為激烈;而最低投資等級信評發生波動時，最高投資等級債券發生變動的幅度就較小。 4.本研究支持不同債信評等的債券存在同向的外溢效果。 / This paper investigates the spillover effect in the investment grade bonds using the recently developed Panel Unit Root Tests, Panel Cointegrations Tests, Panel FMOLS and Panel DOLS techniques. Investment grade bonds’ credit spreads are found to be nonstationary and to be cointegrated in panels. This paper finds evidence of spillover effects.