Computing 3SLS Solutions of Simultaneous Equation Models with a Possible Singular Variance-Convariance Matrix

Algorithms for computing the three-stage least squares (3SLS) estimator usually require the disturbance convariance matrix to be non-singular. However, the solution of a reformulated simultaneous equation model (SEM) results into the redundancy of this condition. Having as a basic tool the QR decomposition, the 3SLS estimator, its dispersion matrix and methods for estimating the singular disturbance covariance matrix and derived. Expressions revealing linear combinations between the observations which become redundant have also been presented. Algorithms for computing the 3SLS estimator after the SEM have been modified by deleting or adding new observations or variables are found not to be very efficient, due to the necessity of removing the endogeneity of the new data or by re-estimating the disturbance covariance matrix. Three methods have been described for solving SEMs subject to separable linear equalities constraints. The first method considers the constraints as additional precise observations while the other two methods reparameterized the constraints to solve reduced unconstrained SEMs. Method for computing the main matrix factorizations illustrate the basic principles to be adopted for solving SEMs on serial or parallel computer

The pricing of risk factors and the UK insurance stocks' performance a nonlinear multivariate approach

The objective of the present study is to examine the impact of exchange and interest rate changes on the common stock returns of the insurance companies in the UK. All general and life insurance firms listed in the London Stock Exchange are selected for this purpose. An augmented market model with the additional variables of the interest and exchange rate indices is employed to test both the pricing question and the factor sensitivity of the particular sample. A seemingly unrelated regression (SURE) multivariate estimation with both cross–equation restrictions and within equation nonlinear constraints on the parameters is employed. This method eliminates the errors in variable (EIV) problem and the estimates are strongly consistent and asymptotically normal even without the assumption of normally distributed errors. The two main implications of this investigation are as follows. First both kinds of insurance companies are negatively and equally affected by unanticipated changes in interest rates. Second the changes in exchange rates seem to inversely affect the general insurance companies, while the life insurance firms seem to be insensitive.peer-reviewe

Computing 3sls solutions of simultaneous equation models with a possible singular variance-covariance matrix

Algorithms for computing the three-stage least squares (3SLS) estimator usually require the disturbance covariance matrix to be non-singular. However, the solution of a reformulated simultaneous equation model (SEM) results into the redundancy of this condition. Having as a basic tool the QR decomposition, the 3SLS estimator, its dispersion matrix and methods for estimating the singular disturbance covariance matrix are derived. Expressions revealing linear combinations between the observations which become redundant have also been presented. Algorithms for computing the 3SLS estimator after the SEM has been modified by deleting or adding new observations or variables are found not to be very efficient, due to the necessity of removing the endogeneity of the new data or by re-estimating the disturbance covariance matrix. Three methods have been described for solving SEMs subject to separable linear equalities constraints. The first method considers the constraints as additional precise observations while the other two methods reparameterized the constraints to solve reduced unconstrained SEMs. Methods for computing the main matrix factorizations illustrate the basic principles to be adopted for solving SEMs on serial or parallel computers

Solving the sequential accumulation least squares with linear equality constraints problem on a SIMD array processor

The solution of least squares subject to linear equality constraints (LSE), where the data is sequentially accumulated, has been considered using a SIMD array processor. The study is based on the method of constructing an orthogonal basis for the null space (BNS) of the constraints matrix. The implementation and performance of the BNS method on an array processor has been compared with that of direct elimination method and overall found to be less efficient