Abstract
This paper details a method for estimating the unknown parameters of a regression model when the estimates of the dependent variable should be embedded in an input–output table with accounting constraints. Since in regression modelling the dependent variable is usually transformed either to achieve homoscedasticity of the residuals or for a better interpretation of the model, the estimating procedure becomes an optimization problem of an opportunely defined Lagrangian function with non-linear constraints. After detailing the algorithm and deriving the asymptotic distribution of the restricted estimator, the methodology is applied to estimate the flows of tourism within and between Italian regions with a gravity model. The procedure can be seen as an extension of Byron’s (J R Stat Soc Ser A 141:359–367, 1978) balancing method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aitchison J, Silvey SD (1958) Maximum-Likelihood estimation of parameters subject to restraints. Ann Math Stat 29:813–828
Anselin L (1988) Spatial econometrics: methods and models. Kluwer Academic, Boston
Byron RP (1978) The estimates of large social accounting matrices. J R Stat Soc Ser A 141:359–367
Fomby BT, Hill CR, Johnson SR (1984) Advanced econometric methods. Springer, New York
Fuller WA, Battese GE (1973) Transformations for estimation of linear models with nested-error structure. J Am Stat Assoc 68:626–632
Hsiao C (2003) Analysis of panel data, 2nd edn. Cambridge University Press, Cambridge
Magnus JR (1978) Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix. J Econ 7:281–312
Mercury (2004) Decimo Rapporto sul turismo italiano. Touring Club Italiano
Round JI (2003) Constructing SAMs for development policy analysis: lessons learned and challenges ahead. Econ Syst Res 15:161–183
Stone R, Champernowne DG, Meade JE (1942) The precision of national income estimates. Rev Econ Stud 9:111–125
Solomou S, Weale M (1993) Balanced estimates of national accounts when measurement errors are autocorrelated: the UK 1920-38. J R Stat Soc Ser A 156:89–105
Tinbergen J (1962) Shaping the world economy: suggestions for an international economic policy. The Twentieth Century Fund, New York
Weale M (1992) Estimation of data measured with error and subject to linear restrictions. J Appl Econ 7:167–174
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Falocci, N., Paniccià, R. & Stanghellini, E. Regression modelling of the flows in an input–output table with accounting constraints. Stat Papers 50, 373–382 (2009). https://doi.org/10.1007/s00362-007-0061-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-007-0061-8