Maximum likelihood estimation of sum-constrained linear models with insufficient observations

Boer, Paul M. C. de; Harkema, R.

doi:10.1016/0165-1765(86)90006-6

“…3 Finally, in the context of undersized samples, Chen (1995) uses a given demand system to investigate the performance of four different specifications of the covariance matrix of the error terms of the demand equations. He applies a timeseries version of Working's (1943) model and the covariance matrix is alternatively specified as (i) the ML estimate based on the residuals when the restriction of preference independence is imposed on the model; (ii) proportional to an augmented identity matrix (Deaton, 1975, Theil, 1987; (iii) such that the variances and covariances vary with the relative sizes of the commodities in question, as measured by the budget shares (Barten andTheil, 1964, S. Selvanathan, 1991); and (iv) that proposed by de Boer and Harkema (1986), with and without a bias correction. As Chen's analysis involves simulations revolving around a matrix with rows and columns corresponding to the true and estimated forms of the covariance matrix, this study can also be described as an application of MAS.…”

Section: •'mentioning

confidence: 99%

The matrix approach to evaluating demand equations

Clements¹,

Yang²,

Chen³

2001

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As there is a plethora of demand models, which one should be used to estimate income and price elasticities? The paper sheds light on this important practical problem by developing a matrix approach to simulating (MAS) demand equations to analyse their performance under idealized circumstances. Artificial data on the dependent variable are generated by one model, and these are then used for the estimation of another model. As an illustrative application, using four popular models, a 4 × 4 matrix is generated which gives all pair-wise comparisons. The performance of the models is then evaluated on the basis of the quality of the income and own-price elasticity estimates.

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“…3 Finally, in the context of undersized samples, Chen (1995) uses a given demand system to investigate the performance of four different specifications of the covariance matrix of the error terms of the demand equations. He applies a timeseries version of Working's (1943) model and the covariance matrix is alternatively specified as (i) the ML estimate based on the residuals when the restriction of preference independence is imposed on the model; (ii) proportional to an augmented identity matrix (Deaton, 1975, Theil, 1987; (iii) such that the variances and covariances vary with the relative sizes of the commodities in question, as measured by the budget shares (Barten andTheil, 1964, S. Selvanathan, 1991); and (iv) that proposed by de Boer and Harkema (1986), with and without a bias correction. As Chen's analysis involves simulations revolving around a matrix with rows and columns corresponding to the true and estimated forms of the covariance matrix, this study can also be described as an application of MAS.…”

Section: •'mentioning

confidence: 99%

The matrix approach to evaluating demand equations

Clements¹,

Yang²,

Chen³

2001

View full text Add to dashboard Cite

As there is a plethora of demand models, which one should be used to estimate income and price elasticities? The paper sheds light on this important practical problem by developing a matrix approach to simulating (MAS) demand equations to analyse their performance under idealised circumstances. Artificial data on the dependent variable are generated by one model, and these are then used for the estimation of another model. Using four popular models, a 4 x 4 matrix is generated which gives all pair-wise comparisons. The performance of the models is then evaluated on the basis of the quality of the income and own-price elasticity estimates. The overall results indicate that, among the four models, E. A. Selvanathan' s (1985) model performs the best, followed by Working's model under substitution independence (Keller, 1984).

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“…The algorithm was described by De Boer and Harkema (1986). Downloaded by [York University Libraries] at 02:07 20 November 2014…”

mentioning

confidence: 99%