Estimating large-scale general linear and seemingly unrelated regressions models after deleting observations

A new numerical method to solve the downdating problem (and variants thereof), namely removing the effect of some observations from the generalized least squares (GLS) estimator of the general linear model (GLM) after it has been estimated, is extensively investigated. It is verified that the solution of the downdated least squares problem can be obtained from the estimation of an equivalent GLM, where the original model is updated with the imaginary deleted observations. This updated GLM has a non positive definite dispersion matrix which comprises complex covariance values and it is proved herein to yield the same normal equations as the downdated model. Additionally, the problem of deleting observations from the seemingly unrelated regressions model is addressed, demonstrating the direct applicability of this method to other multivariate linear models. The algorithms which implement the novel downdating method utilize efficiently the previous computations from the estimation of the original model. As a result, the computational cost is significantly reduced. This shows the great usability potential of the downdating method in computationally intensive problems. The downdating algorithms have been applied to real and synthetic data to illustrate their efficiency

Gibbs Samplers for a Set of Seemingly Unrelated Regressions

Bayesian estimation of a collection of seemingly unrelated regressions, referred to as a ‘set of seemingly unrelated regressions’ is considered. The collection of seemingly unrelated regressions is linked by common coefficients and/or a common error covariance matrix. Gibbs samplers useful for estimating posterior quantities are described and applied to two examples – a set of linear expenditure functions and a cost function and share equations from production theory.

Efficient strategies for deriving the subset VAR models

Abstract.: Algorithms for computing the subset Vector Autoregressive (VAR) models are proposed. These algorithms can be used to choose a subset of the most statistically-significant variables of a VAR model. In such cases, the selection criteria are based on the residual sum of squares or the estimated residual covariance matrix. The VAR model with zero coefficient restrictions is formulated as a Seemingly Unrelated Regressions (SUR) model. Furthermore, the SUR model is transformed into one of smaller size, where the exogenous matrices comprise columns of a triangular matrix. Efficient algorithms which exploit the common columns of the exogenous matrices, sparse structure of the variance-covariance of the disturbances and special properties of the SUR models are investigated. The main computational tool of the selection strategies is the generalized QR decomposition and its modificatio

An alternative numerical method for estimating large-scale time-varying parameter seemingly unrelated regressions models

A novel numerical method for the estimation of large-scale time-varying parameter seemingly unrelated regression (TVP-SUR) models is proposed. The updating and smoothing estimates of the TVP-SUR model are derived within the context of generalised linear least squares and through numerically stable orthogonal transformations which allow the sequential estimation of the model. The method developed is based on computationally efficient strategies. The computational cost is reduced by exploiting the special sparse structure of the TVP-SUR model and by utilising previous computations. The proposed method is also extended to the rolling window estimation of the TVP model. Experimental results show the effectiveness of the new updating, rolling window and smoothing strategies in high dimensions when a large number of covariates and regressions are included in the TVP-SUR model, and in the presence of an ill-conditioned data matrix

Inflation Adjustment and Labour Market Structures: Evidence from a Multi-country Study..

The impact of labour market structures on the response of inflation to macroeconomic shocks is analysed empirically. Results based on a 20-country panel show that if labour market coordination is high, the effect on inflation of movements in unemployment, import prices, tax rates and productivity is dampened, both on impact and dynamically. In contrast, monopoly power in labour supply, measured by the percentage unionisation of the workforce, appears to amplify the response of inflation to its reduced-form determinants. These findings are attributed to the behaviour of wages following movements in demand-and supply-side conditions.

Feed grain imports and feed grain prices in importing countries

The effects of several variables on the feed grain sector of six importing countries were investigated in this study. The six countries were Greece, Israel, Japan, Portugal, Spain, and the United Kingdom. A simultaneous model with six equations was used to explain the domestic price of feed grains in the importing country and the quantity of feed grains imported by the country. Other endogeneous variables in the model were the price of livestock, the production of livestock products, the demand for livestock products, and the size of the livestock inventory in the importing country. The simultaneous model for each importing country allows the government of the importing country to control the domestic price of feed grains through the government’s manipulation of trade barriers for feed grains. Because of the existence of trade barriers, the domestic price of feed grains is allowed to differ from the cost of importing feed grains. The cost of importing feed grains incorporates ocean transportation costs and the exchange rate of the importing country

Estimating Fully Observed Recursive Mixed-Process Models with cmp

At the heart of many econometric models is a linear function and a normal error. Examples include the classical small-sample linear regression model and the probit, ordered probit, multinomial probit, Tobit, interval regression, and truncateddistribution regression models. Because the normal distribution has a natural multidimensional generalization, such models can be combined into multi-equation systems in which the errors share a multivariate normal distribution. The literature has historically focused on multi-stage procedures for estimating mixed models, which are more efficient computationally, if less so statistically, than maximum likelihood (ML). But faster computers and simulated likelihood methods such as the Geweke, Hajivassiliou, and Keane (GHK) algorithm for estimating higherdimensional cumulative normal distributions have made direct ML estimation practical. ML also facilitates a generalization to switching, selection, and other models in which the number and types of equations vary by observation. The Stata module cmp fits Seemingly Unrelated Regressions (SUR) models of this broad family. Its estimator is also consistent for recursive systems in which all endogenous variables appear on the right-hand-sides as observed. If all the equations are structural, then estimation is full-information maximum likelihood (FIML). If only the final stage or stages are, then it is limited-information maximum likelihood (LIML). cmp can mimic a dozen built-in Stata commands and several user-written ones. It is also appropriate for a panoply of models previously hard to estimate. Heteroskedasticity, however, can render it inconsistent. This paper explains the theory and implementation of cmp and of a related Mata function, ghk2(), that implements the GHK algorithm.econometrics, cmp, GHK algorithm, seemingly unrelated regressions

Measuring Oligopsony Power of UK Salmon Retailers

A significant increase of concentration in the UK salmon retail subsector has heightened concerns about retail firms’ ability to exercise market power in the purchase of supplies (oligopsony power). To assess the extent to which retail firms have exercised oligopsony power, we develop a dynamic error correction translog profit function to model the behaviour of retailers in the input market for smoke, fillet and whole salmon. Initial estimates indicated violations of monotonicity and convexity conditions as implied by economic theory. In order to ameliorate the problem, a Bayesian technique was used to impose inequality restrictions to correct the anomaly. The final estimated indices of market power in the models were low and statistically significant but sufficiently closer to the perfect competition benchmark to indicate that retailers as a whole behaved competitively during much of the period covered by this study.Salmon, market power, error correction model, translog profit function, Food Security and Poverty, JEL-I, JEL-J,