A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

Índices antecedentes e coincidentes da atividade econômica brasileira:uma aplicação da análise de correlação canônica

This paper uses canonical correlation analisys to identify leading and coincident indicators of economic activity in Brazil. ln contrast with the traditional literature on the subject, no restrictions are made regarding the number of common cycles that are necessary to explain the complete cyclical behavior of the coincident variables. For the brazillian data, it is found that three common cycles exhaust all the cyclical pattern of economic activity. Based on the methodology developed here, it is also sugested an alternative chronology of the recent brazillian recessions.

Essays on the relationship between the equity and the forward premium puzzles

Our research agenda consists in showing this strong relation between these puzzles based on evidences that both empirical failures are related to the incapacity of the canonical CCAPM to provide a high volatile intertemporal marginal rate of substitution with reasonable values for the preferences parameters.

The missing link: using the NBER recession indicator to construct coincident and leading indices economic activity

We use the information content in the decisions of the NBER Business Cycle Dating Committee to construct coincident and leading indices of economic activity for the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We establish that our index performs better than other currently popular coincident indices of economic activity.

The missing link: using the NBER recession indicator to construct coincident and leading indices economic activity

We use the information content in the decisions of the NBER Business Cycle Dating Committee to construct coincident and leading indices of economic activity for the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We establish that our index performs better than other currently popular coincident indices of economic activity.

The missing link: using the NBER recession indicator to construct coincident and leading indices economic activity

We use the information content in the decisions of the NBER Business Cycle Dating Committee to construct coincident and leading indices of economic activity for the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We compare the performance of our index with other currently popular coincident indices of economic activity.

Sequential cost-reimbursement rules

This paper studies cost-sharing rules under dynamic adverse selection. We present a typical principal-agent model with two periods, set up in Laffont and Tirole's (1986) canonical regulation environment. At first, when the contract is signed, the firm has prior uncertainty about its efficiency parameter. In the second period, the firm learns its efficiency and chooses the level of cost-reducing effort. The optimal mechanism sequentially screens the firm's types and achieves a higher level of welfare than its static counterpart. The contract is indirectly implemented by a sequence of transfers, consisting of a fixed advance payment based on the reported cost estimate, and an ex-post compensation linear in cost performance.

Testing consumption optimality using aggregate data

The objective of this paper is to test for optimality of consumption decisions at the aggregate level (representative consumer) taking into account popular deviations from the canonical CRRA utility model rule of thumb and habit. First, we show that rule-of-thumb behavior in consumption is observational equivalent to behavior obtained by the optimizing model of King, Plosser and Rebelo (Journal of Monetary Economics, 1988), casting doubt on how reliable standard rule-of-thumb tests are. Second, although Carroll (2001) and Weber (2002) have criticized the linearization and testing of euler equations for consumption, we provide a deeper critique directly applicable to current rule-of-thumb tests. Third, we show that there is no reason why return aggregation cannot be performed in the nonlinear setting of the Asset-Pricing Equation, since the latter is a linear function of individual returns. Fourth, aggregation of the nonlinear euler equation forms the basis of a novel test of deviations from the canonical CRRA model of consumption in the presence of rule-of-thumb and habit behavior. We estimated 48 euler equations using GMM, with encouraging results vis-a-vis the optimality of consumption decisions. At the 5% level, we only rejected optimality twice out of 48 times. Empirical-test results show that we can still rely on the canonical CRRA model so prevalent in macroeconomics: out of 24 regressions, we found the rule-of-thumb parameter to be statistically signi cant at the 5% level only twice, and the habit ƴ parameter to be statistically signi cant on four occasions. The main message of this paper is that proper return aggregation is critical to study intertemporal substitution in a representative-agent framework. In this case, we fi nd little evidence of lack of optimality in consumption decisions, and deviations of the CRRA utility model along the lines of rule-of-thumb behavior and habit in preferences represent the exception, not the rule.

Testing consumption optimality using aggregate data

This paper tests the optimality of consumption decisions at the aggregate level taking into account popular deviations from the canonical constant-relative-risk-aversion (CRRA) utility function model-rule of thumb and habit. First, based on the critique in Carroll (2001) and Weber (2002) of the linearization and testing strategies using euler equations for consumption, we provide extensive empirical evidence of their inappropriateness - a drawback for standard rule- of-thumb tests. Second, we propose a novel approach to test for consumption optimality in this context: nonlinear estimation coupled with return aggregation, where rule-of-thumb behavior and habit are special cases of an all encompassing model. We estimated 48 euler equations using GMM. At the 5% level, we only rejected optimality twice out of 48 times. Moreover, out of 24 regressions, we found the rule-of-thumb parameter to be statistically significant only twice. Hence, lack of optimality in consumption decisions represent the exception, not the rule. Finally, we found the habit parameter to be statistically significant on four occasions out of 24.