Estimating Nonnegative Matrices from Marginal Data

Bacharach, Michael

doi:10.2307/2525582

Cited by 136 publications

(96 citation statements)

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“…The method was first given formal mathematical treatment by Deming and Stephan (1940), based on a restricted least-squares criterion, in the context of the adjustment of sample estimates to fixed census marginal totals in the construction of contingency tables. It was subsequently taken up in the construction of economic input-output tables (Bacharach 1965;1970), where it has had extensive application over the years under the name RAS Method. (See Lahr and de Mesnard 2004, for a history of RAS applications.)…”

Section: The Male Fertility Rate and Associated Implicationsmentioning

confidence: 99%

Immigration and the rate of population mixing: explorations with a stylized model

Denton

Spencer

2017

IZA J Develop Migration

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The integration or mixing of immigrants with non-immigrants is an important issue in many countries. There are various forms of mixing. We consider here crossparenting, the bearing of children with one immigrant parent and one nonimmigrant. Our objective is to model cross-parenting as a demographic process and investigate the rate at which such mixing could occur. We identify three populations within an overall total: non-immigrant, immigrant, and mixed. A model is constructed to track the three as they change and interact through cross-parenting. The populations evolve by simulation in accordance with a common stable projection matrix. However, as cross-parenting between immigrants and non-immigrants occurs, the progeny are transferred to the mixed population; the immigrant and non-immigrant populations are thus depleted by the transfers and the mixed population augmented in each generation. The transfers are governed by underlying preferences, but the preference pattern must be modified to recognize constraints imposed by differences in population size. A restricted leastsquares procedure effects the modification so that the actual pattern is as close as possible to the preferred one. Simulations are carried out with alternative preferential patterns and rates of immigration. Of particular interest is the proportion of mixed population in the total in each generation and the final steady state. The paper develops a new framework and model to show the rate at which population mixing could occur under alternative assumptions about the immigration rate and preferences for cross-parenting. JEL Classification: J10, J15

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Section: The Male Fertility Rate and Associated Implicationsmentioning

confidence: 99%

Immigration and the rate of population mixing: explorations with a stylized model

Denton

Spencer

2017

IZA J Develop Migration

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“…Therefore, the second (RAS) algorithm (Bacharach 1965) is used to balance the scaled prior in order to achieve row and column sum equality. In essence, the exogenously given marginal row and column sums act as constraints on the solution of the RAS algorithm.…”

Section: Methodsmentioning

confidence: 99%

“…It is the aim and also the novelty of this work to demonstrate a semi-survey method for constructing enterprise input-output tables solely from marginal totals. In this respect, our method resembles early matrix balancing methods described by Deming and Stephan (1940), Stephan (1942), Friedlander (1961, and Bacharach (1965), and in fact, our work makes use of the widely known RAS matrix balancing technique (Bacharach 1970).…”

Section: Aim Of This Workmentioning

confidence: 99%

Constructing enterprise input-output tables - a case study of New Zealand dairy products

Lenzen

Lundie

2012

Economic Structures

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We describe an efficient method for estimating enterprise input-output tables for cases when only information on marginal totals is available. In order to estimate the production structure of enterprises, we utilize engineering knowledge to construct a qualitative prior containing 1 wherever an output may require an input, and 0 otherwise. This qualitative prior is then scaled by the total enterprise turnover, and subsequently reconciled using the RAS method in order to meet accounting rules. We demonstrate the usefulness of this method in an application to dairy product manufacturing in New Zealand, where we estimate the input-output tables for 22 production sites. Our analysis is carried out in units of mass, and hence the accounting rules are mass balance requirements.Keywords enterprise input-output tables · RAS matrix balancing · qualitative prior · dairy industry JEL Classification Q560 · C650 · L660

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“…We estimated weights for 1,494 records (women whose M3 records did not indicate fetal demise) using a raking procedure, which iteratively adjusts the poststratification weights so the adjusted (weighted) distribution of the analytic sample matches the distribution of the target population on each covariate included in the model (Bacharach, 1965). Estimation took place in the R package using the rake command and the weights controlled for maternal age, race, education, and income.…”

Section: Approach To Weighting the Candle Samplementioning

confidence: 99%

The Urban Child Institute CANDLE Study: Methodological Overview and Baseline Sample Description

Sontag-Padilla¹,

Shih²,

Griffin³

et al. 2015

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Limited Print and Electronic Distribution RightsThis document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited. Permission is given to duplicate this document for personal use only, as long as it is unaltered and complete. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial use. For information on reprint and linking permissions, please visit www.rand.org/pubs/permissions.html.The RAND Corporation is a research organization that develops solutions to public policy challenges to help make communities throughout the world safer and more secure, healthier and more prosperous. RAND is nonprofit, nonpartisan, and committed to the public interest.RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.Support RAND Make a tax-deductible charitable contribution at www.rand.org/giving/contribute www.rand.org For more information on this publication, visit www.rand.org/t/rr1336Published by the RAND Corporation, Santa Monica, Calif.

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Estimating Nonnegative Matrices from Marginal Data

Cited by 136 publications

References 1 publication

Immigration and the rate of population mixing: explorations with a stylized model

Immigration and the rate of population mixing: explorations with a stylized model

Constructing enterprise input-output tables - a case study of New Zealand dairy products

The Urban Child Institute CANDLE Study: Methodological Overview and Baseline Sample Description

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