Updating and Estimating a Social Accounting Matrix Using Cross Entropy Methods

TLDR: A flexible 'cross entropy' (CE) approach to estimating a consistent SAM starting from inconsistent data estimated with error, which represents an efficient information processing rule-using only and all information available.

Abstract: The problem in estimating a social accounting matrix (SAM) for a recent year is to find an efficient and cost-effective way to incorporate and reconcile information from a variety of sources, including data from prior years. Based on information theory, the paper presents a flexible 'cross entropy' (CE) approach to estimating a consistent SAM starting from inconsistent data estimated with error, a common experience in many countries. The method represents an efficient information processing rule-using only and all information available. It allows incorporating errors in variables, inequality constraints, and prior knowledge about any part of the SAM. An example is presented, applying the CE approach to data from Mozambique, using a Monte Carlo approach to compare the CE approach to the standard RAS method and to evaluate the gains in precision from utilizing additional information.

Figures

Table 1. A National SAM

Figure 3. Adding information: 95% confidence interval for root mean square error of flows after balancing with entropy method (relative to unperturbed SAM) .

Figure 2. Basic Estimation: 95% confidence interval for root mean square error after balancing with entropy method (relative to unperturbed SAM).

Figure 1. Comparison of the root mean square deviation relative to the initial SAM (for flows and coefficients).

Figure 5. Adding information: Cross-Entropy comparison

Table 2. 1994 SAM for Mozambique (millions of 1994 Meticais)

Full text

TMD DISCUSSION PAPER NO. 58
Updating and Estimating a Social Accounting
Matrix Using Cross Entropy Methods
Sherman Robinson
Andrea Cattaneo
And
Moataz El-Said
International Food Policy Research Institute
Trade and Macroeconomics Division
International Food Policy Research Institute
2033 K Street, N.W.
Washington, D.C. 20006, U.S.A.
August 2000
TMD Discussion Papers contain preliminary material and research results, and are circulated prior to a
full peer review in order to stimulate discussion and critical comment. It is expected that most Discussion Papers
will eventually be published in some other form, and that their content may also be revised. This paper is
available at http://www.cgiar.org/ifpri/divs/tmd/dp.htm

Updating and Estimating a Social Accounting Matrix Using
Cross Entropy Methods
*
by
Sherman Robinson
Andrea Cattaneo
and
Moataz El-Said
1
International Food Policy Research Institute
Washington, D.C., U.S.A.
August 2000
Published in: Economic Systems Research, Vol. 13, No.1, pp. 47-64, 2001.
*
The first version of this paper was presented at the MERRISA (Macro-Economic Reforms and
Regional Integration in Southern Africa) project workshop. September 8 -12, 1997, Harare,
Zimbabwe. A version was also presented at the Twelfth International Conference on Input-
Output Techniques, New York, 18-22 May 1998. Our thanks to Channing Arndt, George Judge,
Amos Golan, Hans Löfgren, Rebecca Harris, and workshop and conference participants for
helpful comments. We have also benefited from comments at seminars at Sheffield University,
IPEA Brazil, Purdue University, and IFPRI. Finally, we have also greatly benefited from
comments by two anonymous referees.
1
Sherman Robinson, IFPRI, 2033 K street, N.W. Washington, DC 20006, USA. Andrea
Cattaneo, IFPRI, 2033 K street, N.W. Washington, DC 20006, USA. Moataz El-Said, IFPRI,
2033 K street, N.W. Washington, DC 20006, USA.

Abstract
The problem in estimating a social accounting matrix (SAM) for a recent year is to find an
efficient and cost-effective way to incorporate and reconcile information from a variety of
sources, including data from prior years. Based on information theory, the paper presents a
flexible “cross entropy” (CE) approach to estimating a consistent SAM starting from inconsistent
data estimated with error, a common experience in many countries. The method represents an
efficient information processing rule—using only and all information available. It allows
incorporating errors in variables, inequality constraints, and prior knowledge about any part of
the SAM. An example is presented applying the CE approach to data from Mozambique, using a
Monte Carlo approach to compare the CE approach to the standard RAS method and to evaluate
the gains in precision from utilizing additional information.
KEYWORDS: Entropy, cross entropy, social accounting matrices, SAM, input- output, RAS,
Monte Carlo simulations

Table of Contents
1. Introduction ............................................................................................................................... 1
2. Structure of a Social Accounting Matrix (SAM)....................................................................... 2
3. The RAS Approach to SAM Updating...................................................................................... 3
4. A Cross Entropy Approach to SAM estimation......................................................................... 4
4.1. Deterministic Approach: Information Theory..................................................................... 5
4.2. Types of Information .......................................................................................................... 7
4.3. Stochastic Approach: Measurement Error .......................................................................... 9
5. Updating a SAM: RAS and Cross-Entropy ............................................................................. 13
6. From Updating to Estimating Using the Cross-Entropy Approach.......................................... 15
7. Conclusion............................................................................................................................... 18

1
1. Introduction
There is a continuing need to use recent and consistent multisectoral economic data to
support policy analysis and the development of economywide models. A Social Accounting
Matrix (SAM) provides the underlying data framework for this type of model and analysis. A
SAM includes both input-output and national income and product accounts in a consistent
framework. Estimating a SAM for a recent year is a difficult and challenging problem. Input-
output data are usually prepared only every five years or so, while national income and product
data are produced annually, but with a lag. To produce a more disaggregated SAM for detailed
policy analysis, these data are often supplemented by other information from a variety of
sources; e.g., censuses of manufacturing, labor surveys, agricultural data, government accounts,
international trade accounts, and household surveys. The problem in estimating a disaggregated
SAM for a recent year is to find an efficient (and cost-effective) way to incorporate and reconcile
information from a variety of sources, including data from prior years.
A standard approach is to start with a consistent SAM for a particular prior period and
“update” it for a later period, given new information on row and column totals, but no
information on the flows within the SAM. The traditional RAS approach, discussed below,
addresses this case. However, in practice, one often starts from an inconsistent SAM, with
incomplete knowledge about both row and column sums and flows within the SAM.
Inconsistencies can arise from measurement errors, incompatible data sources, or lack of data.
What is needed is an approach to estimating a consistent set of accounts that not only uses the
existing information efficiently, but also is flexible enough to incorporate information about
various parts of the SAM.
In this paper, we propose a flexible “cross entropy” (CE) approach to estimating a
consistent SAM starting from inconsistent data estimated with error. The method is very flexible,
incorporating errors in variables, inequality constraints, and prior knowledge about any part of
the SAM (not just row and column sums). The next section presents the structure of a SAM and
a mathematical description of the estimation problem. The following section describes the RAS

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Updating and estimating a social accounting matrix using cross entropy methods" ?

Based on information theory, the paper presents a flexible “ cross entropy ” ( CE ) approach to estimating a consistent SAM starting from inconsistent data estimated with error, a common experience in many countries. An example is presented applying the CE approach to data from Mozambique, using a Monte Carlo approach to compare the CE approach to the standard RAS method and to evaluate the gains in precision from utilizing additional information. 

Q2. What is the common way to estimate a new set of coefficients?

Treating the column coefficients as analogous to probabilities, assuming known column sums in equation (11) is equivalent to knowing averages of the column sums, weighting by the coefficients—or first moments of the distributions. 

Q3. How many runs were generated by sampling from a set of normal distributions?

The perturbed values were generated by sampling from a set of normal distributions with increasing standard deviations: the values starting from 1% and increasing up to 10% in 1% increments every 100 samples, making for a total of one thousand runs. 

Q4. What is the procedure used for the Monte Carlo simulations?

The procedure adopted for the Monte Carlo simulations is as follows: three row totalswere randomly perturbed relative to the balanced Macro SAM, and the perturbed values were imposed as the new row and column totals in the updating process. 

Q5. What is the significance of the estimation problem?

Most importantly, the estimation problem is set in the context of information theory and the procedure generates measures of the “importance” of different data used in the estimation process. 

Q6. What is the way to deal with negative expenditures?

A simple approach to dealing with this issue is to treat a negative expenditure as a positive receipt or anegative receipt as a positive expenditure. 

Q7. What is the purpose of this paper?

In this paper, the authors propose a flexible “cross entropy” (CE) approach to estimating aconsistent SAM starting from inconsistent data estimated with error. 

Q8. What are the arguments of Byron and Schneider?

Byron (1978) and Schneider and Zenios (1990) also argue in favor of a constrained maximization approach, and are also skeptical of imposing strong statistical assumptions. 

Q9. What is the analogy to Bayes’ Theorem?

The analogy to Bayesian estimation is that the approach can be seen as an efficient Information Processing Rule (IPR) whereby the authors use additional information to revise an initial set of estimates (Zellner, 1988, 1990). 

Q10. What is needed to estimate a consistent set of accounts?

What is needed is an approach to estimating a consistent set of accounts that not only uses the existing information efficiently, but also is flexible enough to incorporate information about various parts of the SAM. 

Q11. How much is the RMSE on the coefficients reduced?

one can see that if the column totals are assumed known with error (with the weights on the error term appearing in the objective), then the RMSE on the coefficients is reduced by as much as 50% in their example (see Figure 4b). 

Q12. What is the significance of knowing the column totals?

This result highlights the importance of knowing the row or column totals, and in an environment where these totals are not known with certainty, the cross entropy specification with error can be extremely useful from an operational standpoint. 

Q13. What is the problem in estimating a disaggregated SAM for a recent?

The problem in estimating a disaggregated SAM for a recent year is to find an efficient (and cost-effective) way to incorporate and reconcile information from a variety of sources, including data from prior years. 

Q14. How can one limit the value of a cell in a SAM?

it is also straightforward in the CE approach to allow zero elements in the prior to become nonzero in the estimated SAM, and vice versa. 

Q15. What are the arguments of Harrigan and Buchanan?

Harrigan and Buchanan (1984) argue persuasively for the advantages of a constrained maximization estimation approach in terms of flexibility, but are aware of the statistical problems.