Although many applications of the I-O model may not require the compilation of the I-O accounts annually, there is still a need for the generation of more current economic variables such as production and demand structures. Sectoral estimates of value added at current prices are generally derived from sectoral outputs and updated gross value added ratios. Analyses of repurcussive effects of changing factor and output prices often require quantitative determinations at current rather than at base-year prices.

This report presents the results of an empirical exercise conducted to provide researchers, local and international alike, with an updated set of I-O data. This study, which focused on Calendar year (CY) 1990, is the third attempt to construct updated Philippine I-O tables. Previous studies relate to CYs 1978 and 1983. The choice of 1990 as the update year was based solely on the availability of limited but more current information required during the course of the study.

As in previous exercises, this activity was undertaken as a collaborative effort between the Economic and Social Statistics Office (ESSO) of the National Statistical Coordiantion Board (NSCB) and the Industry and Trade Statistics Department of the National Statistics Office (NSO).

The basic table consists of 177 commodity sectors, six final demand and four primary inputs or value-added sectors. The commodity groupings were based on the 1988 benchmark I-O 230-sector classification scheme, with some sectors merged depending on the availability of data.

As in 1988 table, the intersectoral transactions are valued at producers' prices, i.e., net of distributive costs of trade mark-ups and transport/freight margins but gross of commodity taxes. Imports valued at producers prices include CIF plus customs duties and import taxes.

On the whole, the economic aggregates shown in the table are more or less consistent with the national accounts figures for the year under study.

Based on these assumptions, the general estimation methodology consisted of two successive operations. First, the latest available (1988) base-year input coefficients were adjusted to account for changes inprioces of outputs and inputs between CYs 1988 and 1990. These price-adjusted coefficients were then subjected to the modified RAS iterative procedure to account for possible shifts in production and demand structures from CYs 1988 to 1990.

To adjust the base-year input (1988) coefficients in terms of the prices of the current period (1990), two sets of price index numbers were specially constructed for 1990 (1988=100). One set was used to update the base-year matrix of domestic input coefficients, A₀^d. The other applied to the matrix of imported input coefficients, A₀^m.

If A₀^d is the 1988 domestic input coefficient matrix and if p_d is the domestic price vector in which 1990 prices are related to 1988 prices, then the 1988 domestic input coefficient matrix converted to 1990 (current) prices, A₁^d*, is calculated as:

A₁^d* = P_d A₀^d P _d ^-1                       (1)

where P_d is the diagonal matrix of the domestic price vector, P_d.

The 1988 imported input coefficient matrix converted to 1990 (current) prices A₁^m* is calculated as :

A₁^m* = P_m A₀^m P _m ^-1                       (2)

where P_m is the diagonal matrix of the imports vector, P_m.

The sum of these two price-adjusted coefficient matrices A₁^d* and A₁^m*, approximates the required total input coefficient matrix A₁^*.

On the assumption that there is no change in production technology, the resulting coefficient matrix, A₁^*, would have served the purpose of this exercise. That is , production cost structures change over time due solely to changing commodity prices. To be on the safer side however, the price updated matrix, A₁^*, was further adjusted to account for possible technological changes that might have occurred between 1988 and 1990.The updating exercise was carried out on the assumption that I-o coefficients change through time as a result of three factors, namely: (1) changes in price, (2) changes in the degree of substitution, and (3) changes in the degree of fabrication.

Based on these assumptions, the general estimation methodology consisted of two successive operations. First, the latest available (1988) base-year input coefficients were adjusted to account for changes inprioces of outputs and inputs between CYs 1988 and 1990. These price-adjusted coefficients were then subjected to the modified RAS iterative procedure to account for possible shifts in production and demand structures from CYs 1988 to 1990.

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The RAS method is used to update existing I-O tables to relate to a year for which intermediate input (column) sums are known but not the intermediate deliveries themselves. The simple RAS method consists of finding a set of multipliers to adjust the rows of the existing matrix, in this case the price-adjusted coefficient matrix, A₁^*, and a set of multipliers to adjust the columns so that the cells in the adjusted matrix will add up to the given row and column totals relating to the chosen update year. It is assumed that each element, a_ij, of the coefficient matrix being estimated, i.e., A₁, is the subject to two effects, namely:  (1) the effect of substitution, measured by the extent to which commodity i has been replaced by, or used as substitute for, other commodities in industrial production; and  (2) the effect of fabrication, measuring the extent to which commodity j has come up to absorb a greater or smaller ratio of intermediate to total inputs used in production. It is further assumed that each effect works unformly, i.e., commodity i increases or decreases at the same rate as an input to all sectors, and that any change in the ratio of intermediate to total inputs of a commodity has the same effect on all commodities used as inputs.

The substitution multipliers which operate along the rows are denoted as vector r and the fabrication multipliers which operate on the columns as vector s. Each cell in the base matrix, in this case, A₁^*, will be subject to these two effects and the new matrix, A₁, can thus be written as:

A₁ = R A₁^* S             

or       A₁ = R P A₀ P ^-1 S                                          (3)

            where R and S are diagonal matrices with vector r and s in the diagonals, respectively.

It can be observed from equation (3) that the whole updating exercise took into account not only price effects but also substitution and fabrication effects, which then quantified, are actually measures of structural changes. Sectors with high values of r, usually greater than unity, are those which tend to replace sectors with low r values as inputs into intermediate demands. Sectors with high values of s are subject to higher fabrication effects, i.e. they are using more intermediate inputs in their production processes.

The estimation procedure for getting the values of r and s is as follows:

Let u₁ stand for the intermediate demand vector for (update) year 1, derived by subtracting the estimated vector of final demand, Y₁, from the output vector, q₁ and v₁ for the intermediate input vector which is equal to q₁ less the given vector of gross value added. These estimated vectors of final demand and gross value added are consistent with available national income accounts data. Also, let x₁ be the unknown matrix of interindustry transactions for year 1, in this case 1990. Then,

X₁ = A₁ q₁                                            (4)

Substitution eq. (3) into eq. (4), we have

X₁ = (r  A₁^*  s)  q₁                                 (5)

The row totals of equation (5) will be:

u₁ = X₁  i                                                (6)

     [1]

where i = [1]

               [:]

               [1]

Substituting equation (5) into (6), we have:

u_i = r  (A₁^* q) s                                 (7)

The column totals will be:

v₁ = X₁' i

v₁' = i' X₁

v₁' = r' (A₁* q₁) s                              (8)

Equations (7) and (8) contain all the information desired: the price-adjusted base-year coefficient matrix, A₁*: the derived row and column contraints, u₁ and v₁; and the current output levels q₁. If these values are solved simultaneously, the values of the vectors r and s will be obtained which in turn will be used to calculate A₁, and eventually, X₁. The most usually and conveniently adopted solution to the equations in an iterative one. The estimation process of obtaining X₁ from X₀, thus in effect, amounts to nothing more than a bi-proportional adjustment of the base-year matrix along its rows and columns until convergence is reached.

The resulting r and s multipliers measure the degrees of substitution and fabrication, respectively.

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The availability of the 1990 ASE results during the course of this study allows for the modification of the simple RAS method by excluding some predetermined transactions from the bi-proportional adjustment process, thus enhancing the reliability of the estimates. These transactions include updated data on fuel and electricity costs by using sector.

In adopting the modified RAS method, the initial step undertaken was to compute for the new row and column contraints, u₁^* and v₁^*, respectively, by subtracting those predtermined transactions from the original u₁ and v₁ values. the next step was to set at zero all the cells in the base matrix, A₀^* for which current values have been firmly estimated. Subsequently, the normal RAS iteration process was carried out. When a solution has been reached, the zero entries were replaced by their corresponding known values.

With this modified procedure, however, computed r and s multipliers could not be used as measures of technological change.

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The final step in the updating exercise was to combine the resulting intersectoral transactions matrix, X₁, with the given final demand and gross value added matrices to obtain the desired 1990 USE Table.

Derived analytical tables such as the direct as well as the total (direct plus indirect) input coefficients are also appended in this report, together with computed indices of total structural interdependencies such as the forward and backward linkage effects.

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