Strongly Consistent Determination of the Rank of Matrix

In this paper, we develop methods of the determination of the rank of random matrix. Using the matrix perturbation theory to construct or find a suitable bases of the kernel (null space) of the matrix and to determine the limiting distribution of the estimator of the smallest singular values. We propose a new rank test for an unobserved matrix for which a root-N-consistent estimator is available and construct a Wald- type test statistic (generalized Wald test). The test, based on matrix perturbation theory, enable to determine how many singular values of the estimated matrix are insignificantly different from zero and we fully characterise the asymptotic distribution of the generalized Wald statistic under the most general conditions. We show that it is chi- square distribution under the null. In particular case, when the asymptotic covariance matrix has a Kronecker product form, the test statistic is equivalent to likelihood ratio test statistic and to Multiplier Lagrange test statistic. Two approaches to be considered are sequential testing strategy and information theoretic criterion. We establish a strongly consistent of the determination of the rank of matrix using the two approaches.Rank Testing; Matrix Perturbation Theory; Rank Estimation; Subspace Methods; Singular Value Decomposition; Weighting Matrices; Sequential Testing Strategy; Information Theoretic Criterion.

Rank Test Based On Matrix Perturbation Theory

In this paper, we propose methods of the determination of the rank of matrix. We consider a rank test for an unobserved matrix for which an estimate exists having normal asymptotic distribution of order N1/2 where N is the sample size. The test statistic is based on the smallest estimated singular values. Using Matrix Perturbation Theory, the smallest singular values of random matrix converge asymptotically to zero in the order O(N-1) and the corresponding left and right singular vectors converge asymptotically in the order O(N-1/2). Moreover, the asymptotic distribution of the test statistic is seen to be chi-squared. The test has advantages over standard tests in being easier to compute. Two approaches are be considered sequential testing strategy and information theoretic criterion. We establish a strongly consistent of the determination of the rank of matrix using both the two approaches. Some economic applications are discussed and simulation evidence is given for this test. Its performance is compared to that of the LDU rank tests of Gill and Lewbel (1992) and Cragg and Donald (1996).Rank Testing; Matrix Perturbation Theory; Rank Estimation; Singular Value Decomposition; Sequential Testing Procedure; Information Theoretic Criterion.

Financial development and economic growth: evidence from West Africa

In this paper, we employ the Geweke (1982) decomposition method to examine the Granger causality between finance and growth in West Africa. Our sample contains twelve ECOWAS member countries (Economic Community of West African States) and we distinguish two subsamples: seven WAEMU countries which constitute an economic and monetary union (with the CFA Franc as their common currency) and five non-WAEMU countries. Data are from the World Bank (2008) and cover the period 1962-2006. The results show that:(1) finance leads economic growth in countries which have the common currency, (2) the reverse causation dominates in the other countries, (3) there is greater feedback between financial development and economic growth in countries sharing the common currency, (4) there is more instantaneous (contemporaneous) causality between finance and growth in WAEMU than in non-WAEMU countries suggesting that financial development affects growth and vice-versa in the short term in WAEMU countries. The first result can be explained by financial stability which suggests accelerating the process of creation of common currency for all West African countries. This paper highlights that the finance-growth nexus may vary across countries at similar stages of development and suggests that the existence of a stable monetary union may intensify the relationship between financial development and economic growth in developing countries.Finance; growth; Granger causality; monetary union; ECOWAS; Geweke decomposition test. 1

Rank Test Based On Matrix Perturbation Theory

In this paper, we propose methods of the determination of the rank of matrix. We consider a rank test for an unobserved matrix for which an estimate exists having normal asymptotic distribution of order N1/2 where N is the sample size. The test statistic is based on the smallest estimated singular values. Using Matrix Perturbation Theory, the smallest singular values of random matrix converge asymptotically to zero in the order O(N-1) and the corresponding left and right singular vectors converge asymptotically in the order O(N-1/2). Moreover, the asymptotic distribution of the test statistic is seen to be chi-squared. The test has advantages over standard tests in being easier to compute. Two approaches are be considered sequential testing strategy and information theoretic criterion. We establish a strongly consistent of the determination of the rank of matrix using both the two approaches. Some economic applications are discussed and simulation evidence is given for this test. Its performance is compared to that of the LDU rank tests of Gill and Lewbel (1992) and Cragg and Donald (1996).Rank Testing Matrix Perturbation Theory Rank Estimation Singular Value Decomposition Sequential Testing Procedure Information Theoretic Criterion

Jeunes, accès au microcrédit et performance des microentreprises: une évidence au Mali

Le présent article s’intéresse au lien entre l’accès des jeunes au microcrédit et la performance de leurs activités en se demandant si la performance de leur microentreprise peut être expliquée par l’accès ou le non accès au microcrédit. Avec les données d’enquêtes réalisées par l’INSTAT et l’ODHD Mali auprès des bénéficiaires des services microfinanciers en 2007-2008, l’article mobilisera, d’abord, une approche descriptive pour analyser les conditions de financement des microentreprises puis les indicateurs de performance. La méthode de score de propension sera ensuite utilisée pour estimer à la fois les déterminants de l'accès au crédit et les effets de l'accès sur la performance des microentreprises

Regulation of Microfinance Institutions in Developing countries: an incentives theory approach

We analyze the optimal policy of regulation of microfinance institutions in developing countries, where investment funds are insured by the government and customer deposits. We used a mixed model, combining adverse selection and moral hazard to characterize a class of optimal incentive schemes applied in presence of government funds and in non-government funded. We also analyse the effects of prudential regulation of deposits on the profitability of MFI and social welfare, and we compare prudential and non-prudential regulation. The incentive scheme that we propose can be regarded as a "smart subsidy" mechanism that contributes to the economic and social development

Incentives, Supervision and Regulation of Microfinance Institutions in the developing countries

We analyze the optimal regulation of a MFI that has private information on the intrinsic quality of its loan portfolio (adverse selection) and where the MFI’s choice of effort to improve this quality cannot be observed by the regulator (moral hazard). In designing optimal contracts the regulator faces a tradeoff between inducing proper incentives for efficient MFI and costs of regulation in terms of leaving an informational rent for a high quality MFI. We identify conditions for the optimal incentive contract and show that, not surprisingly, these contracts depend on the accuracy of the supervisor’s signal, the likelihood of facing a high quality MFI, and the cost of supervision. However, since improving the accuracy of supervision is costly, even in the optimal monitoring scheme there generally exists a positive probability of MFI failure. The content of information disclosure is characterized by the optimal monitoring scheme

Regulation and supervision of microfinance institutions: an example of cooperative credit society

We study the optimal regulation of a cooperative credit society which has private information on the intrinsic quality of its loan portfolio (adverse selection) and where the cooperative’s choice of effort to improve this quality cannot be observed by the regulator (moral hazard). We characterize the optimal contracts offered by the regulator to the credit cooperatives. We have been able to show that the optimal contracts depend on 3 main factors namely: on the accuracy of the supervisor’s signal, the likelihood of facing a high quality credit cooperative, and the cost of supervision

Regulation and supervision of microfinance institutions: an example of cooperative credit society

We study the optimal regulation of a cooperative credit society which has private information on the intrinsic quality of its loan portfolio (adverse selection) and where the cooperative’s choice of effort to improve this quality cannot be observed by the regulator (moral hazard). We characterize the optimal contracts offered by the regulator to the credit cooperatives. We have been able to show that the optimal contracts depend on 3 main factors namely: on the accuracy of the supervisor’s signal, the likelihood of facing a high quality credit cooperative, and the cost of supervision

On approximate system dynamic

In this paper concepts and techniques from system theory are used to obtain state-space (Markovian ) models of dynamic economic processes instead of the usual VARMA models. In this respect the concept of state is reviewed as are Hankel norm approximations,and balanced realizations for stochastic models. We clarify some aspects of the balancing method for state space modelling of observed time series. This method may fail to satisfy the so-called positive real condition for stochastic processes. We us a state variance factorization algorithm which does not require us to solve the algebraic Riccati equation. We relate the Aoki-Havenner method to the Arun - Kung method