Estimating covariance matrices is an important part of portfolio selection, risk management, and asset pricing. This paper reviews the recent development in estimating high dimensional covariance matrices, where the number of variables can be greater than the number of observations. The limitations of the sample covariance matrix are discussed. Several new approaches are presented, including the shrinkage method, the observable and latent factor method, the Bayesian approach, and the random matrix theory approach. For each method, the construction of covariance matrices is given. The relationships among these methods are discussed.
{"title":"Estimating High Dimensional Covariance Matrices and its Applications","authors":"Jushan Bai, Shuzhong Shi","doi":"10.7916/D8RJ4SGP","DOIUrl":"https://doi.org/10.7916/D8RJ4SGP","url":null,"abstract":"Estimating covariance matrices is an important part of portfolio selection, risk management, and asset pricing. This paper reviews the recent development in estimating high dimensional covariance matrices, where the number of variables can be greater than the number of observations. The limitations of the sample covariance matrix are discussed. Several new approaches are presented, including the shrinkage method, the observable and latent factor method, the Bayesian approach, and the random matrix theory approach. For each method, the construction of covariance matrices is given. The relationships among these methods are discussed.","PeriodicalId":45810,"journal":{"name":"Annals of Economics and Finance","volume":"12 1","pages":"199-215"},"PeriodicalIF":0.4,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71367833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a stochastic endogenous aggregative growth model is constructed and two main results are established, based on endogenous horizon of the economy and endogenous terminal capital stock, which is also efficient capital accumulation in some sense. First, strong turnpike theorems under uncertainty and in the sense of uniform topology are obtained; second, inefficacy of temporary fiscal policy, which is chosen to be capital income taxation, has been demonstrated in comparatively weak conditions different from Yano (1998)'s.
{"title":"Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology","authors":"Darong Dai","doi":"10.2139/ssrn.2123745","DOIUrl":"https://doi.org/10.2139/ssrn.2123745","url":null,"abstract":"In this paper, a stochastic endogenous aggregative growth model is constructed and two main results are established, based on endogenous horizon of the economy and endogenous terminal capital stock, which is also efficient capital accumulation in some sense. First, strong turnpike theorems under uncertainty and in the sense of uniform topology are obtained; second, inefficacy of temporary fiscal policy, which is chosen to be capital income taxation, has been demonstrated in comparatively weak conditions different from Yano (1998)'s.","PeriodicalId":45810,"journal":{"name":"Annals of Economics and Finance","volume":"13 1","pages":"381-423"},"PeriodicalIF":0.4,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67924746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the behavior of short-term real and nominal rates of interest by combining consumption-based and production-based models into a single general equilibrium framework. Based on the theoretical nonlinear relationships that link interest rates to both the marginal rates of substitution and transformation in a monetary production economy, we develop an estimation and simulation procedure to generate historical time series of interest rates. We find that the predictions of interest rates based on a general equilibrium theory are partially consistent with US data.
{"title":"Measuring interest rates as determined by thrift and productivity","authors":"W. Choi, Y. Wen","doi":"10.20955/WP.2005.037","DOIUrl":"https://doi.org/10.20955/WP.2005.037","url":null,"abstract":"This paper investigates the behavior of short-term real and nominal rates of interest by combining consumption-based and production-based models into a single general equilibrium framework. Based on the theoretical nonlinear relationships that link interest rates to both the marginal rates of substitution and transformation in a monetary production economy, we develop an estimation and simulation procedure to generate historical time series of interest rates. We find that the predictions of interest rates based on a general equilibrium theory are partially consistent with US data.","PeriodicalId":45810,"journal":{"name":"Annals of Economics and Finance","volume":"309 1","pages":"167-195"},"PeriodicalIF":0.4,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67755153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a dynamic optimization model of durable good inventories to study the interactions between investment demand and production of capital goods. There are three major findings: First, capital suppliers' inventory behavior makes investment demand more volatile in equilibrium; Second, equilibrium price of capital is characterized by downward stickiness; Third, the responses of the capital market to interest rate and other environmental changes are asymmetric. All are the results of equilibrium interactions between demand and supply.
{"title":"Production and inventory behavior of capital","authors":"Y. Wen","doi":"10.20955/WP.2005.044","DOIUrl":"https://doi.org/10.20955/WP.2005.044","url":null,"abstract":"This paper provides a dynamic optimization model of durable good inventories to study the interactions between investment demand and production of capital goods. There are three major findings: First, capital suppliers' inventory behavior makes investment demand more volatile in equilibrium; Second, equilibrium price of capital is characterized by downward stickiness; Third, the responses of the capital market to interest rate and other environmental changes are asymmetric. All are the results of equilibrium interactions between demand and supply.","PeriodicalId":45810,"journal":{"name":"Annals of Economics and Finance","volume":"8 1","pages":"95-112"},"PeriodicalIF":0.4,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67755234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we construct a simple model based on heterogeneity in workers' productivity and homogeneity in their working schedules. This simple model can generate unemployment, even if wages adjust instantaneously, firms are perfectly competitive, and firms can perfectly observe workers' productivity and effort. In our model, it is optimal for low-skilled workers to be unemployed because, on the one hand, firms do not find it optimal to hire low-skilled workers when labor hours must be synchronized across heterogeneous workers, and on the other hand, low-skilled workers do not find it attractive working for the same hours as high-skilled workers at competitive wages based on productivity. Thus our model offers an alternative explanation for why unskilled workers are a primary source of structural unemployment.
{"title":"Uniform working hours and structural unemployment","authors":"Haoming Liu, Y. Wen, Lijing Zhu","doi":"10.20955/WP.2005.045","DOIUrl":"https://doi.org/10.20955/WP.2005.045","url":null,"abstract":"In this paper, we construct a simple model based on heterogeneity in workers' productivity and homogeneity in their working schedules. This simple model can generate unemployment, even if wages adjust instantaneously, firms are perfectly competitive, and firms can perfectly observe workers' productivity and effort. In our model, it is optimal for low-skilled workers to be unemployed because, on the one hand, firms do not find it optimal to hire low-skilled workers when labor hours must be synchronized across heterogeneous workers, and on the other hand, low-skilled workers do not find it attractive working for the same hours as high-skilled workers at competitive wages based on productivity. Thus our model offers an alternative explanation for why unskilled workers are a primary source of structural unemployment.","PeriodicalId":45810,"journal":{"name":"Annals of Economics and Finance","volume":"8 1","pages":"113-136"},"PeriodicalIF":0.4,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67755390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Toutenburg, V. K. Srivastava, Shalabh, C. Heumann
This paper considers the estimation of coefficients in a linear regression model with missing observations in the independent variables and introduces a modification of the standard first order regression method for imputation of missing values. The modification provides stochastic values for imputation. Asymptotic properties of the estimators for the regression coefficients arising from the proposed modification are derived when either both the number of complete observations and the number of missing values grow large or only the number of complete observations grows large and the number of missing observations stays fixed. Using these results, the proposed procedure is compared with two popular proceduresiaone which utilizes only the complete observations and the other which employs the standard first order regression imputation method for missing values. It is suggested that an elaborate simulation experiment will be helpful to evaluate the gain in efficiency especially in case of discrete regressor variables and to examine some other interesting issues like the impact of varying degree of multicollinearity in explanatory variables. Applications to some concrete data sets may also shed some light on these aspects. Some work on these lines is in progress and will be reported in a future article to follow.
{"title":"Estimation of Parameters in Multiple Regression With Missing Covariates using a Modified First Order Regression Procedure","authors":"H. Toutenburg, V. K. Srivastava, Shalabh, C. Heumann","doi":"10.5282/UBM/EPUB.1437","DOIUrl":"https://doi.org/10.5282/UBM/EPUB.1437","url":null,"abstract":"This paper considers the estimation of coefficients in a linear regression model with missing observations in the independent variables and introduces a modification of the standard first order regression method for imputation of missing values. The modification provides stochastic values for imputation. Asymptotic properties of the estimators for the regression coefficients arising from the proposed modification are derived when either both the number of complete observations and the number of missing values grow large or only the number of complete observations grows large and the number of missing observations stays fixed. Using these results, the proposed procedure is compared with two popular proceduresiaone which utilizes only the complete observations and the other which employs the standard first order regression imputation method for missing values. It is suggested that an elaborate simulation experiment will be helpful to evaluate the gain in efficiency especially in case of discrete regressor variables and to examine some other interesting issues like the impact of varying degree of multicollinearity in explanatory variables. Applications to some concrete data sets may also shed some light on these aspects. Some work on these lines is in progress and will be reported in a future article to follow.","PeriodicalId":45810,"journal":{"name":"Annals of Economics and Finance","volume":"6 1","pages":"289-301"},"PeriodicalIF":0.4,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71095856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We find that the short-term deviations from long-run consumption-wealth relationship (cay) forecast stock market returns and serve as a conditioning variable in the capital asset pricing model (CAPM) for explaining the cross-section of stock returns for the United Kingdom and Japan. Our cross-sectional regressions using cay as a conditioning variable as opposed to using an alternative variable, tay, constructed using calendar time in place of consumption indicate that it is unlikely to be a spurious variable and provides useful information concerning the economic fundamentals. We show that both a consumption-based capital asset pricing model (CCAPM) and a human-capital-augmented capital asset pricing model (HC-CAPM) in conjunction with this conditioning variable can explain much of the cross-section of stock returns in each of the two countries; yet, in terms of relative performance, our results tend to favor the conditional HC-CAPM over the conditional CCAPM for pricing U.K. and Japanese cross-sectional returns.
{"title":"Aggregate consumption-wealth ratio and the cross-section of stock returns: some international evidence","authors":"Paul Gao, K. Huang","doi":"10.2139/SSRN.614151","DOIUrl":"https://doi.org/10.2139/SSRN.614151","url":null,"abstract":"We find that the short-term deviations from long-run consumption-wealth relationship (cay) forecast stock market returns and serve as a conditioning variable in the capital asset pricing model (CAPM) for explaining the cross-section of stock returns for the United Kingdom and Japan. Our cross-sectional regressions using cay as a conditioning variable as opposed to using an alternative variable, tay, constructed using calendar time in place of consumption indicate that it is unlikely to be a spurious variable and provides useful information concerning the economic fundamentals. We show that both a consumption-based capital asset pricing model (CCAPM) and a human-capital-augmented capital asset pricing model (HC-CAPM) in conjunction with this conditioning variable can explain much of the cross-section of stock returns in each of the two countries; yet, in terms of relative performance, our results tend to favor the conditional HC-CAPM over the conditional CCAPM for pricing U.K. and Japanese cross-sectional returns.","PeriodicalId":45810,"journal":{"name":"Annals of Economics and Finance","volume":"9 1","pages":"1-37"},"PeriodicalIF":0.4,"publicationDate":"2004-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2139/SSRN.614151","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67775639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-04-01DOI: 10.1142/9789812569257_0017
Xiaokai V Yang, DingSheng Zhang
This paper develops a general equilibrium model with transaction costs and endogenous and exogenous comparative advantages. The governments are allowed to choose between tariff war, tariff negotiation, and a {it laissez faire} regime. It shows that the level of the division of labor and trade increases as transaction conditions improve. When a high level of the division of labor occurs in general equilibrium, all countries prefer Nash tariff bargaining game that would result in multilateral free trade. If a medium level of the division of labor occurs in general equilibrium, then unilateral protection tariff in a less developed country and unilateral {it laissez faire} policies in a developed country would coexist. The results show that tariff negotiations are essential for achieving multilateral free trade. In addition, the model may explain the policy transition of some European governments from mercantilism to free-trade regime in the 18th and 19th century and policy changes in developing countries from protection tariff to tariff negotiation and trade liberalization.
{"title":"Endogenous Structure of the Division of Labor, Endogenous Trade Policy Regime, and a Dual Structure in Economic Development","authors":"Xiaokai V Yang, DingSheng Zhang","doi":"10.1142/9789812569257_0017","DOIUrl":"https://doi.org/10.1142/9789812569257_0017","url":null,"abstract":"This paper develops a general equilibrium model with transaction costs and endogenous and exogenous comparative advantages. The governments are allowed to choose between tariff war, tariff negotiation, and a {it laissez faire} regime. It shows that the level of the division of labor and trade increases as transaction conditions improve. When a high level of the division of labor occurs in general equilibrium, all countries prefer Nash tariff bargaining game that would result in multilateral free trade. If a medium level of the division of labor occurs in general equilibrium, then unilateral protection tariff in a less developed country and unilateral {it laissez faire} policies in a developed country would coexist. The results show that tariff negotiations are essential for achieving multilateral free trade. In addition, the model may explain the policy transition of some European governments from mercantilism to free-trade regime in the 18th and 19th century and policy changes in developing countries from protection tariff to tariff negotiation and trade liberalization.","PeriodicalId":45810,"journal":{"name":"Annals of Economics and Finance","volume":"1 1","pages":"211-230"},"PeriodicalIF":0.4,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64015030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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