352 research outputs found
Bayesian Inference in Cointegrated I (2) Systems: a Generalisation of the Triangular Model
No full textThis paper generalises the cointegrating model of Phillips (1991) to allow for I (0) , I (1) and I (2) processes. The model has a simple form that permits a wider range of I (2) processes than are usually considered, including a more flexible form of polynomial cointegration. Further, the specification relaxes restrictions identified by Phillips (1991) on the I (1) and I (2) cointegrating vectors and restrictions on how the stochastic trends enter the system. To date there has been little work on Bayesian I (2) analysis and so this paper attempts to address this gap in the literature. A method of Bayesian inference in potentially I (2) processes is presented with application to Australian money demand using a Jeffreys prior and a shrinkage prior.
Multivariate Stochastic Volatility with Co-Heteroscedasticity
No full texthttp://www.grips.ac.jp/list/jp/facultyinfo/leon_gonzalez_roberto/First version: October, 2018 [18-12] http://doi.org/10.24545/00001640This paper develops a new methodology that decomposes shocks into homoscedastic and heteroscedastic components. This specification implies there exist linear combinations of heteroscedastic variables that eliminate heteroscedasticity; a property known as co-heteroscedasticity. The heteroscedastic part of the model uses a multivariate stochastic volatility inverse Wishart process. The resulting model is invariant to the ordering of the variables, which we show is important for volatility estimation. By incorporating testable co-heteroscedasticity restrictions, the specification allows estimation in moderately high-dimensions. The computational strategy uses a novel particle filter algorithm, a reparameterization that substantially improves algorithmic convergence and an alternatingorder particle Gibbs that reduces the amount of particles needed for accurate estimation. We provide an empirical application to a large Vector Autoregression (VAR), in which we find strong evidence for co-heteroscedasticity and that the new method compares favorably to previous ones in terms of forecasting from horizon 3 onward. A Monte Carlo experiment illustrates that the new method estimates well the characteristics of approximate factor models with heteroscedastic errors.JEL Classification Codes: C11, C15Roberto Leon-Gonzalez acknowledges financial support from the GRIPS Policy Research Center under the grant "Multivariate Stochastic Volatility with Partial Homoscedasticity", from the Nomura Foundation (BE-004) and from JSPS (category C, 19K01588).Rodney Strachan acknowledges financial support from the GRIPS Policy Research Center for a research visit to GRIPS.technical repor
Bayesian Trace Statistics for the Reduced Rank Regression Model
No full textEstimation of the reduced rank regression model requires restrictions be imposed upon the model. Two forms of restrictions are commonly used. Earlier Bayesian work relied on the triangular method of identification which imposes an a priori ordering on the variables in the system, however, incorrect ordering of the variables can result in model misspecification. Bayesian estimation of the reduced rank regression model without ordering restrictions was presented in Strachan (1998) and follows the classical approach of Anderson (1951) and Johansen (1988). This method of estimation avoids placing restrictions on the space spanned by the reduced rank relations and simplifies testing of restrictions on that space. In this paper, a method for estimating approximate marginal likelihoods and Bayes factors is presented for this model, using Laplace approximations for integrals. These Bayes factors algebraically resemble the Johansen trace statistic (1995), hence the title. We consider the model with rank l and no restrictions on the reduced rank relations
Comment on ‘Jointness of growth determinants’ by Gernot Doppelhofer and Melvyn Weeks
No full textDoppelhofer and Weeks (2009) present a statistic designed to indicate the probability that pairs of regressors appear together or individually in a Bayesian model averaged linear regression. This comment presents an alternative measure that is designed to overcome some of the limitations of Doppelhofer and Weeks' statistic. Copyright © 2009 John Wiley & Sons, Ltd
Bayesian approaches to cointegration
No full textThe degree of empirical support of a priori plausible structures on the cointegration vectors has a central role in the analysis of cointegration. Villani (2000) and Strachan and van Dijk (2003) have recently proposed finite sample Bayesian procedures to calculate the posterior probability of restrictions on the cointegration space, using the existence of a uniform prior distribution on the cointegration space as the key ingredient. The current paper extends this approach to the empirically important case with different restrictions on the individual cointegration vectors. Prior distributions are proposed and posterior simulation algorithms are developed. Consumers' expenditure data for the US is used to illustrate the robustness of the results to variations in the prior. A simulation study shows that the Bayesian approach performs remarkably well in comparison to other more established methods for testing restrictions on the cointegration vectors
Efficient posterior simulation in cointegration models with priors on the cointegration space
No full textA message coming out of the recent Bayesian literature on cointegration is that it is important to elicit a prior on the space spanned by the cointegrating vectors (as opposed to a particular identied choice for these vectors). In this note, we discuss a sensible way of eliciting such a prior. Furthermore, we develop a collapsed Gibbs sampling algorithm to carry out efficient posterior simulation in cointegration models. The computational advantages of our algorithm are most pronounced with our model, since the form of our prior precludes simple posterior simulation using conventional methods (e.g. a Gibbs sampler involves non-standard posterior conditionals). However, the theory we draw upon implies our algorithm will be more efficient even than the posterior simulation methods which are used with identied versions of cointegration models
A study of the incidence of teacher absenteeism in the Dade County Public Schools for 1975- 76 and 1976- 77 years, 1977
No full textPurpose of Study The purpose of the study was to investigate the incidence of teacher absenteeism in the Dade County School System for the 197.5-76 and 1976-77 years. Specifically, the study sought to determine (1) the relationship of teacher absences between the secondary and elementary schools; (2) the relationship of teacher absences between secondary and elementary schools located in medium and low-income areas; (3) the relationship of absences among Black, White, and Hispanic teachers; (4) the performance between students taught in schools having a high or low absentee rate of teachers;and (.5) the causes of teacher absences between secondary and elementary schools. Methodology The procedure consisted of (0 a review of related literature; (2) identification of the prospective respondents for the study (40 principals and 800 teachers); (3) development and administration of a questionnaire to the study population; (4) use of a computer programmer (V06 and S02) for tabulating and coding the data furnished by the returned questionnaires; (.5) analysis of the data; and (6) report of the findings, conclusions, and ,recommendations. Summary of Findings Data provided by the respondents in this study indicated that: 1. The rate of teacher absences in secondary schools is as great as the rate of teacher absences in elementary schools. 2. Elementary and secondary schools located in low-income areas have the same rate of teacher absences as compared to secondary and elementary schools located lin medium-income areas. However, the rate of teacher absences is very low among the elementary schools in both groups. 3. It was found that Black teachers were absent less than White and Hispanic teachers, White teachers were absent less than Hispanic teachers in secondary schools only, and Hispanic teachers were absent less than both Black and White teachers in elementary schools. 4. The performance of students taught in schools identified as having a low absentee rate was average and above the national norm, while the performance of students taught in schools identified as having a high absentee rate was just the opposite. Additionally, student scores (Stanford Achievement Test) in schools located in medium, income areas were far greater than the student scores in schools located in low-income areas. 5. Findings indicated that teachers in the secondary schools were absent for the same reasons as teachers in the elementary schools. Conclusions The limitations of using a selected sample of only forty (40) schools and six hundred (600) teachers in the Dade County Public Schools must temper the conclusions. With this restraint, the following conclusions seem justified. Black, White, and Hispanic teachers were absent much more in the secondary schools than the elementary schools. Moreover, the average rate of teacher absences was considerably higher in the junior high schools than the senior high and elementary schools. Teachers assigned to secondary and elementary schools - located in the medium-income area - tended to have a better attendance record than those teachers assigned to schools located in low-income areas. When the teacher sample was isolated by race, the rate of absences of White teachers was greater in schools located in low-income areas rather than schools located in medium-income areas. Hispanic teachers recorded a much lower average rate of absences in selected schools than Black and White teachers in the same schools. The performance of students appeared not to be affected by the high average labsentee rate of teachers in the medium-income areas secondary and elementary schools, but the performance of students seemed to be affected in the low-income area secondary and elementary schools. Sample teachers responded to the following reasons for being absent: (1) illness self, (2) illness of relative, (3) illness of others, (4) approved meetings, (.5) vacation, :(6) size of school, (7) location of school, (8) salary, and (9) personal leave. Illness of self was ranked number one followed by personal leave, illness of others, and approved meetings. According to teachers' response, location of school was the least reason for I being absent. In other words, it simply indicated that the demographic location or distance to the school was not a major factor given for being absent from school. Finally, the study accepted Hypotheses 1, 2, 3, and .5 and rejected Hypothesis 4. Further, the study found the following factors to be major impediments to students' performance: 1. That White teachers assigned to low-income area schools were more frequently absent than Black and Hispanic teachers in the same schools. 2. That students' performance in the same schools showed a significant decline. Recommendations 1. Establishing by the administration, an effective accountability model, making teachers a part of that process. 2. Identifying master teachers in the system and paying (rewarding) them for their expertise, if assigned to schools reflecting high degrees of teacher absenteeism. This can be done with salary supplements, compensatory time, and improved working conditions. 3. Posting the lowest, highest, and average days absent of teachers monthly at ,each school, similar to the posting of student absences. 4. Analyzing data of teacher absenteeism should include the average days absent from each school instead of the percentages of absences. 5. Providing the school board and administration with special needs allocation to the schools reflecting poor achievement and teacher absentee trends to allow schools to improve and complement their efforts. 6. Conducting further nonstatistical and descriptive study as to allow the researcher to get into nuances of underlying factors behind teacher absenteeism
Bayesian Inference in Cointegrated I (2) Systems: A Generalization of the Triangular Model
No full textThis paper generalizes the cointegrating model of Phillips (1991) to allow for I (0), I (1) and I (2) processes. The model has a simple form that permits a wider range of I (2) processes than are usually considered, including a more flexible form of polynomial cointegration. Further, the specification relaxes restrictions identified by Phillips (1991) on the I (1) and I (2) cointegrating vectors and restrictions on how the stochastic trends enter the system. To date there has been little work on Bayesian I (2) analysis and so this paper attempts to address this gap in the literature. A method of Bayesian inference in potentially I (2) processes is presented with application to Australian money demand using a Jeffreys prior and a shrinkage prior.Cointegration, Bayesian, I (2) Analysis, Money demand,
Valid Bayesian estimation of the cointegrating error correction model
No full textTwo methods of identifying cointegrating vectors are commonly used linear restrictions and the nonlinear method of Johansen's maximum likelihood procedure. That the linear method can produce invalid estimates while the Johansen approach always produces valid estimates has been recognised in several recent articles. As all Bayesian studies to date have used linear restrictions, this article presents a Bayesian method for obtaining estimates of cointegrating vectors that will always be valid
Bayesian Estimation of the Reduced Rank Regression Model Without Ordering Restrictions
No full textEstimation of the parameters of the reduced rank regression model in a Bayesian method requires the solution of two identification problems: global or strong identification and local identification. Traditionally Bayesians, and to a large extent frequentists, have relied on zero-one identifying restrictions which require the researcher to impose an order on the variables to achieve global identification. Examples of this approach include Geweke (1996), Bauwens and Lubrano (1993), Kleibergen (1997), Kleibergen and Paap (1997), and Kleibergen and van Dijk (1994). This ordering relies on a, priori knowledge of which variables enter the reduced rank relations. For example, the cointegrating error correction model requires knowledge of which variables are 1(0) or cointegrate. Incorrect ordering may result in an estimated space for the cointegrating vectors that does not have the true cointegrating space as a subset, effectively misspecifying the model. In this paper, we present an estimation method which does not require a priori ordering by using restrictions similar to those used in maximum likelihood estimation by Anderson (1951) of the reduced rank regression model generally, and by Johansen (1988) in an error correction model specifically. As with much of the recent work, we focus on the cointegrating error correction model to show our approach. Local identification is achieved by nesting the reduced rank model within a full rank model with a well behaved posterior distribution. This approach is due to Kleibergen (1997) and is consistent with the principle of a "datatranslated likelihood" suggested by Box and Tiao (1973). In nesting the reduced rank model in a full rank model, we use a transformation from the potentially reduced rank matrix II to the matrices a, @ and A where A = 0 restricts II to a lower rank. Results from Roy (1952) enable us to derive the Jacobian for this transformation
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