The role of supply and use/input output tables in the perspective analysis of economic development of Rwanda with example

4.6. Challenges in information provided by Linear Model

From the analysis of SUT and IO-T and Linear Model, it is remarkable that Linear Model does not provide sufficient information necessary to measure the role of System of National Accounts in the perspective analysis of economic development of Rwanda. The main challenge encountered by the Linear Model is the lack of information in Intermediate Consumption by Product and by Industry. This information is the main intra in the so-called central equation system for input-output analysis which offers multiple approaches for analysis. Mathematically, this equation is defined as Z = B*(I-A)^-1F, where B is a matrix of input coefficients for a specific variable (intermediate uses, labor, capital, energy, emissions, etc.), (I-A)^-1 stands for the Leontief inverse, F represents a diagonal matrix for final demand and Z a matrix with results for direct and indirect requirements (intermediates, labor, capital, energy, emissions, etc.). Basically, this approach would provide quantitative assessment (José M. Rueda-Cantuche et al., 2005: 8; Eurostat, 2002).

The following analysis tried to estimate SUT and IO-T for Rwanda in 2007 basing on the main indicators provided by Linear Model. Information not provided by Linear Model are highlighted in order to show its deficiency and to demonstrate that with Linear Model it is not easy to perform central equation system for input-output analysis. In order to estimate those tables some assumption had been stated and some Ratios had been fixed in order to estimate attached indicators:

· The row and column items were computed basing on percentages of GDP decomposition by sectors [Services 46%, Industry 14%, and Agriculture 40 (John RWIRAHIRA, 2008: 11)].

· Each Product is produced in its own specific way, irrespective of the industry where it is produced.

· Each industry has its own specific way of production, irrespective of its product mix.

· Input in each sector and Production from each sector were estimated basing on that Intermediate consumption was 122.8 % of GDP and Production was 212.87% of GDP (AfDB-EIU-UNIDO Infobase-World Bank-Wold Economic Forum-World Factor Book, 2008: 1-2; htt://www.docstoc.com/docs/48810565/RWANDA--Kigali)

· The distribution of Intermediate Consumption and Production was based on percentage of GDP decomposition by Sectors (Agriculture, Industry, and Services).

Table 4.4. Estimated Simplified Supply and Use Framework of Rwanda in Billion Frw (in Constant 2006 Prices)

		Products					Industries					Final Uses				Total
		Agricult. Products	Industrial Products		Services		Agri-culture	Industry		Service Activities		Final Con- sumption	Gross Capital Formation		Exports
Products	Agricult. products						334	117		384		728	138		78	1778
	Industrial products						117	41		134		255	48		27	622
	services						384	134		442		837	158		89	2044
Industries	Agriculture	630		220		724										1574
	Industry	220		77		253										551
	Service Activities	724		253		833										1811
Value Added							740		259		851					1849
Imports		204		71		234										509
Total		1778		622		2045	1574		551		1811	1819		344	194	10738

The above Estimated simplified SUT shows the information which are not easily available in Rwanda, those information are: Input, Production, Final use, Value Added, and Import Matrices, even though they are available in single element for example, Import Total is available but import by products is not available, Export Total is available but Export by Product is not available in clean forms, Value Added Total is available but Value Added by Industry in not easily available because they are available in percentages of GDP. Those are the weakness of not using integrated SUT and IO-T. The part in yellow is not applicable.

Table4. 5. Estimated Simplified Symmetric input-output table (product by product) of Rwanda in Billion Frw (Constant Price)

Products	Products			Final Uses			Total
	Agricult. Products	Industrial Products	Services	Final Con- sumption	Gross Capital Formation	Exports
Agricult. products	334	117	384	728	138	78	1778
Industrial products	117	41	134	255	48	27	622
services	384	134	442	837	158	89	2044
Value Added	740	259	851				1849
Import	204	71	234				509
Supply	1778	622	2045	1819	344	194	6802

From SUT a Simplified Symmetric Input-Output Table was estimated, the information from this IO-T were used in the estimation of Input Coefficients in order to perform further analysis related to economic development, even though the analysis in this study was limited on the use of Input Coefficients further analysis for economic development may be based on those table and on the Input Coefficients Matrix through many techniques to evaluate the quality of life such as: Linkage, Activity Specification, and Dummy Sector Technique.

Apart from those techniques STU and IO-T are the basic steps in constructing SAM, because most of the details from those tables are carried over without modification to SAM, where there are reassembled in Matrix form (GRAHAM Pyatt, 1999: 365-386), and SAM has an important advantages on analyzing Economic development of an economy, among them: reduction of risk of confusion, and it emphases on consistence and the importance of complete articulation, both of which are the essence in trying to understand feedback systems, in general, and the interdependence of the distribution of income and the structure of income, in particular.

Table4.6 Input Coefficients

Products	Products
	Agricult. Products	Industrial Products	Services
Agricult. products	0.19	0.19	0.19
Industrial products	0.07	0.07	0.07
services	0.22	0.22	0.22
Import	0.11	0.11	0.11
Wages, Salaries etc. + Oper. Srplus	0.42	0.42	0.42
Supply	1	1	1

The Input Coefficients were computed in order to highlight the role of using Leontief inverse in the perspective economic analysis, its role is not only limited in the central equation system for input-output analysis but also it may be used to measure ecosystem structure and function, sensitivity, Cycling, dependence and contribution effects between compartments, loop analysis tropic dynamics, and self-organization (Manfred Lenzen, 2006: 334-342).

These analyses are efficient to measure economic development of an economy, but due to the non availability of that information in Rwanda, those depth analyses are not done, therefore its use in economic development is still under considered. The Leontief inverse can play a consolidated role in economic development of Rwanda as it has a multiple uses.

Through this study its consolidated role was shown in central equation system for input-output analysis to balance production by Products and by Industry and in output function to measure the impact of increasing or decreasing intensity of Input Coefficients in an economy.

Leontief inverse = (I-A)^-1

4.6.1. Use of central equation system for input-output analysis

Z = B*(I-A)^-1F

The above function is used as a central equation system for input-output analysis which offers multiple approaches for analysis. After verifying that the production provided using the above equation basing on Input Coefficient Matrix, Leontief Inverse Matrix, and Diagonal Matrix of Final Demand is equal to the production Matrix in the above Simplified Supply and Use Table, therefore further analysis may be made and (Z) Matrix can be useful when analyzing the impact of how the increase in Input will influence the Total production within the whole economy (José M. Rueda-Cantuche et al., 2005: 8).