The World Price System of Economic Analysis

Abstract

Chapter 5 discussed how all outputs and inputs in a project analysis can be valued at economic prices using what we have termed the domestic price numeraire. Economic analyses can be carried out using different units of account or numeraire. As with distance, which can be measured in miles or kilometres, the choice of different units makes the same calculation appear different, but provided the same information and equal accuracy are used, the results will be directly equivalent. This chapter shows how world prices can be a reference point for economic valuation in what we term a world price system or valuation at the world price level.

Appendices

Appendix 1: Semi-Input-Output (SIO) Analysis

This Appendix introduces SIO and gives a simplified illustration of an SIO model. The aim to construct a table linking a project with its supplier sectors and the rest of the economy, so that the impact of additional expenditure from a project can be traced. In terms of its coverage an SIO table can be comprehensive, in the sense of covering all production sectors in an economy, or it can be more limited, focusing on sectors which are linked closely with a new and large investment project. The aim is to establish the main economic effects of a new project, so that there is less need to incorporate sectors that are affected in only a minor way. Outputs from sectors covered in the table that are used as inputs into other economic activities can be termed produced inputs, in the sense that they come from sectors covered by the SIO system. This is in contrast with inputs supplied exogenously, either from abroad or from domestic activities not shown as productive sectors in the table. The illustration applies SIO analysis in a world price system, although in principle there is no reason why it cannot be applied in an equivalent domestic price analysis.¹¹

The SIO table is composed of two distinct matrices. What is conventionally termed the A matrix shows the produced inputs into sectors; what is termed the F matrix gives inputs of primary factors in our example labour, which are exogenous to the system, but which create value in the different sectors. To solve the system direct coefficient matrices are required which show inputs per unit of sector output. The structure of the direct coefficient matrix of a SIO table is illustrated in Fig. 6.1.

In Fig. 6.1 the table has n columns, so that the A matrix is n × n in size. There are g primary factor inputs, so that the F matrix is g × n. Since all entries are direct coefficients, each column in the table must total 1.0; a_ln, for example, is the value of inputs from sector 1 into one unit of sector n; f_gn is the value of primary factor input g per unit of sector n. Sectors 1–n will be productive sectors, both traded and non-traded, plus aggregate CFs that are weighted averages of the CFs for individual sectors in the table. Primary factors l-g can vary with the level of detail and assumptions adopted. However, as a minimum requirement there needs to be primary factors for foreign exchange, transfer payments (covering taxes, subsidies, and surplus profits), labour possibly distinguishing between skilled and unskilled workers, and capital inputs.¹²

Fig. 6.1

SIO table direct coefficients

The direct coefficients of the A matrix are given by expressing all entries in a column as a proportion of the value of output in each sector at financial prices. An important practical issue is what level of financial prices is used to value output. The chief alternatives are producers’ or purchasers’ prices. In practice most SIO analyses work with the latter and this example also uses purchasers’ prices as the reference price level. This means that for each sector financial prices include distribution margins, transport costs in moving goods from producers to purchasers, and retail and producer-level indirect taxes.

In an SIO analysis the aim is to assess the consequences of additional expenditure on each of the sectors in the table, with a project specified as a sector. For traded sectors the main effect will be in terms of foreign exchange, with more imports if the goods consumed are imported at the margin, and fewer exports if they are exported. The foreign exchange effects as a proportion of the financial price will be shown in the foreign exchange row of the F matrix. In addition, for all traded commodities there will be some costs incurred in non-traded sectors, since they have to be transported and distributed to users. These costs are shown in the relevant rows for non-traded sectors, such as transport and services.

The distinction between traded and non-traded sectors is crucial because output in each is valued differently. The principles discussed here and in other chapters are followed, with output from traded sectors valued at border prices plus adjustments for non-traded costs. Output from non-traded sectors poses a major complication, where it is valued at willingness to pay, rather than at cost of production. In the first case, a value of willingness to pay must be estimated externally to the model and the ratio of the willingness to pay price to the financial price will give the relevant coefficient. As willingness to pay is not derived internally in the system, the coefficient must be entered in the F matrix in a row for the project output. To convert this to world prices it must be multiplied by an aggregate conversion factor, either the CCF, as an average for consumption goods, or the SCF as the average for the economy.

For non-traded sectors producing inputs it is necessary to distinguish three possible situations:

• where output can be expanded in the short run owing to surplus capacity

• where in the short-run capacity is fully utilised, so that output can be expanded only in the longer run after new investment

• where no additional production is possible owing to rigid supply constraints.

In the first two cases additional expenditure induces additional production and opportunity cost is given by the resources that go into this production. In the first case, only variable costs are involved and there will be no primary factor input for capital. In the second case, however, both operating and capital inputs must be reflected in the opportunity cost. The third case, where supply is fixed, will be relatively rare. As with non-traded output such sectors are normally included as an additional row in the F matrix since their supply is not determined within the SIO system. In this approach, they are valued by an aggregate CF.

The logic of the SIO approach is that the value of a sector can be found by decomposing output at financial prices solely into primary factors. Total primary factor requirements in each sector are both the direct primary inputs shown in F plus the primary factors that go into the produced inputs from sectors in the table shown in A. Estimation of total primary factors per unit of output in each sector thus requires first identifying total (direct plus indirect) produced inputs into each sector, which involves inversion of a matrix based on the A matrix. Total produced inputs must then be decomposed into primary factors. The value of each sector is determined by the sum of the values of the primary factor inputs that are required directly and indirectly by the sector. This is expressed more formally in the Appendix 2.

The results of a SIO analysis are given typically as a set of conversion factors:

• for all sectors in the table

• for all primary factor inputs into these sectors

• for aggregate categories such as consumption expenditure or aggregate output.

Illustration of an SIO Application

To illustrate the approach, it is helpful to work at a simple level with a small table of only four productive sectors, one aggregate CF, and four primary factors. Although all actual calculations will involve a far larger table, this is sufficient for illustrative purposes. The purpose of the table is for an analysis of an agricultural project. In this example, the A matrix is composed of five entries:

• the agriculture project equipment

• other equipment

• services

• transport

• an aggregate conversion factor, the SCF that is a weighted average of the CFs for the four productive sectors.

The F matrix has four primary factors:

• transfers

• foreign exchange

• labour

• operating surplus.

All labour is assumed to be unskilled, and all operating surplus (profits before tax, interest, and depreciation) is assumed to represent opportunity costs associated with the use of capital, so that no surplus profits are involved. Transfers cover taxes and subsidies. Of the four sectors it is assumed that equipment and agriculture are traded, with significant imports of the former and exports of the latter. Services and transport are taken to be non-traded.

Table 6.8 gives the direct coefficients for this example. All row entries are proportions of the financial value of output at purchasers’ prices and columns sum to 1.00 as they show the composition of the financial price value of each sector/activity. As expected for the traded activities, equipment, and the agriculture project, output value is predominantly foreign exchange. For equipment—an importable—the cif value of output is 60% of the financial price, with an import tariff of 50% of the cif price; the foreign exchange entry is therefore 0.60 and transfers 0.30. There are small domestic costs of services and transport involved in moving the imported equipment to the project and other users and consumers; both are 5% of the financial price of output. These are shown in the services and transport rows, respectively.

Table 6.8 SIO table—direct coefficients

The table is constructed for the assessment of a project, which produces an exportable and does not provide inputs into any other domestic activity. The fob export price is 90% of the financial price, whilst there is an export subsidy of 10% of the fob price. Entries in the foreign exchange and transfer rows are 0.90 and 0.09, respectively. The only relevant transport and service costs will be any additional costs associated with the domestic consumption of agricultural output as compared with export. There is a small additional domestic transport cost of 1% of the financial price, so that the transport entry is 0.01.¹³

The non-traded sector services and transport use both produced inputs from other sectors and primary factors. For services produced inputs from industry, services itself, and transport are 10%, 20%, and 10%, respectively, of output at financial prices. Primary factors foreign exchange, labour, and operating surplus are 20%, 30%, and 10%, respectively, of output at financial prices. Similarly for transport produced inputs from industry and services are 15% and 5% of output, respectively, while primary factors of transfers, foreign exchange, labour, and operating surplus are 10%, 30%, 30%, and 10% of output, respectively.

In this example, the aggregate conversion factor used to revalue items where there is no direct world price is the SCF. This is calculated as a weighted average of the CFs for the four productive sectors. The weights used are 0.20, 0.45, 0.25, and 0.10, for equipment, agriculture, services, and transport, respectively, reflecting the relative value-added in the different sectors at financial prices.

Total primary factors are shown in Table 6.9. In all cases total primary inputs are greater than the direct inputs shown in Table 6.8, because of the primary factors that go into the produced inputs used in all sectors. This is most obviously the case for the labour and foreign exchange inputs into services and transport. For services, for example, whilst the direct labour input per unit of output is 0.30, the total labour input, allowing for the labour that goes into inputs used by services, rises to 0.42. Even the traded sectors, with no direct labour content, have a small indirect input through their use of non-traded transport and services inputs.

Table 6.9 Total primary factors per unit of output in productive sectors

Once total primary factor requirements are known they must be revalued with CFs for each primary factor. In Appendix 2, it is shown that:

$$ C{F}_i=\sum \limits_g{b}_{gi}\cdotp C{F}_g $$

(6.9)

where

• CF_i is the conversion factor for sector i

• CF_g is the conversion factor for primary input g

• b_gi is the share of primary input g in a unit of output i

The weight b_gi placed on the conversion factor for a primary factor is the share of total requirements of that factor in output value of i at financial prices. In this example, therefore, Table 6.9 gives the weights for the different primary factors.

As far as CFs for primary factors are concerned, the example uses the following:

CF
Transfers	0
Foreign exchange	1.0
Labour	0.5 × Agriculture conversion factor (CFAG)
Operating surplus	1.0 × SCF

Transfers have no opportunity cost, so that their CF is 0. Foreign exchange has a CF of 1.0, since here world prices are used as the numeraire.¹⁴ For labour in this example, it is assumed that a worker’s output forgone at financial prices is 50% of the financial wage. This is additional information, external to the model, required to derive labour’s CF. However, a further step is also required since output forgone must be converted to world prices by a CF for the output workers would have produced. From (6.4) the shadow wage rate (SWR) can be expressed as:

$$ SWR=\sum \limits_i{a}_i{m}_i\cdotp CF $$

If for simplicity one single source of labour is assumed, a_i = 1.0, and ∑a_im_i can be re-written as M_i referring to one type of output forgone. Then:

$$ SWR=M\times C{F}_m $$

where

• M is output forgone from a worker’s alternative employment at financial prices

• CF_m is the conversion factor required to convert this output to world prices

The conversion factor for labour (CF_LAB) is the ratio of the shadow to the financial wage:

$$ C{F}_{LAB}=\frac{SWR}{FWR} $$

or, substituting

$$ C{F}_{LAB}=\frac{M.C{F}_m}{FWR} $$

In this example M/FWR is taken to be 0.50, while workers for new projects are assumed to be drawn from agriculture, so that the agriculture conversion factor (CF_AG) is used for CF_m:

$$ C{F}_{LAB}\mathrm{isthus}=\frac{M}{FWR}\times C{F}_{AG}\mathrm{or}0.50\times C{F}_{AG} $$

For simplicity, it is assumed that the project is representative of export agriculture, so its CF derived from the model, can be used to revalue labour’s opportunity cost. Labour is thus valued by a combination of external data, necessary for the ratio of output forgone at financial prices to the financial wage (M/FWR), and a sectoral CF derived from the model (CF_AG). The use of CF_AG in the valuation of a primary factor is an illustration of the interdependence of values in an SIO system, since CF_AG depends among other things on the value of labour, while in turn it is one of the two determinants of labour’s value.

Finally, operating surplus is taken to be resource costs reflecting the opportunity cost return on the capital committed to each sector, at financial prices. No surplus profits in excess of these resource costs are involved. Operating surplus must still be converted to world prices. It is assumed that capital is mobile within the economy and can thus be employed in any sector. It is therefore appropriate to use the SCF to revalue operating surplus, since the SCF is an average ratio of world to domestic prices for the whole economy. Interdependence also arises in the treatment of operating surplus since it is revalued by the SCF, whilst operating surplus itself is one of the influences on the CF for each sector, and the SCF is a weighted average of sectoral CFs.

Using this set of CFs for primary factors and the weights from Table 6.9 gives the results reported in Table 6.10.

Table 6.10 Full CF results

These results can be illustrated for the SCF. The former is an average of the CFs for the four productive sectors, using the weights from the last column of Table 6.8:

	Weight	CF	Weighted average
Equipment	0.2000	0.6664	0.1333
Agriculture	0.4500	0.9064	0.4078
Services	0.2500	0.6912	0.1703
Transport	0.1000	0.6476	0.0647
SCF	1.00		0.7761

1. SCF = 0.7761, or rounded to 0.78

Equipment at 0.67 is an average of the CFs for the total primary factors into the sector using the weights for equipment from Table 6.8:

	Weight	CF	Weighted average
Transfers	0.3103	0.0000	0.0000
Foreign exchange	0.6400	1.0000	0.6400
Labour	0.0373	0.4532	0.0169
Operating surplus	0.0124	0.7762	0.0096
	1.0000		0.6665

1. Equipment CF = 0.6665, or rounded to 0.67

These CFs from Table 6.10 can be used in the appraisal of, for example, an agricultural project. Its output value at financial prices would be revalued by the Agriculture CF of 0.9064 (or rounded to 0.90), its transport costs by the Transport CF of 0.6476 (rounded to 0.65), its equipment cost by the Equipment CF of 0.6664 (rounded to 0.67) and its services cost by the Services CF of 0.6912 (rounded to 0.69). Any minor items would be revalued by the SCF of 0.78.

Data Issues

In an economy with a relatively up-to-date national input-output table, construction of an SIO table will be more straightforward, since data on the average cost structure of produced inputs will already be available. Where possible this data should be adjusted to derive estimates of marginal costs, where constant costs cannot be assumed. However, sector classifications from a national table will usually be far too aggregate to be helpful for an SIO table built around a project and additional information from varying sources will have to be put together.

For traded activities the main data required will be on tariffs and quotas and on transport and distribution margins. For non-traded activities, however, more detailed data will be required to decompose their cost structure. For manufacturing, periodic censuses of enterprises provide one source; for public utilities project documents and sector surveys may be available. For services often relatively little data are available; one source may be the information used to construct the national accounts, where this type of activity has to be quantified, even if approximately. The limitations of data derived from such varying sources must not be overlooked when the consistency and relative rigour of the approach is acknowledged.

Classification of sectors as either traded or non-traded can also be a problem. There may be situations where output of a sector is insufficiently homogeneous to be wholly traded or non-traded, so that it is necessary to distinguish between the traded and non-traded components, showing its traded and non-traded elements as separate columns in the SIO table. Another problem relates to the choice of reference price level, normally either producer or purchaser prices. It is essential to use a single reference price level for financial prices. This is necessary for consistency so that for all activities financial prices at one price level can be compared with economic prices at the same price level. However, whatever level is adopted requires data on distribution and transport costs, and indirect taxes, as a proportion of the financial price. Estimation of capital charges in non-traded sectors is usually a problem. In principle, they can be calculated as an annuity by applying a capital recovery factor, based on the estimated economic discount rate and length of life of the assets, to the value of capital assets. Any profit in excess of this charge will be surplus profit, not an opportunity cost and will therefore not be included in economic costs. Each item of the information required will be subject to varying degrees of uncertainty. The value of capital assets is a particular problem, since historical book values will rarely be a useful guide to current values.

For large projects where linkages within the economy are important in principle, SIO analysis offers a means of introducing greater detail and consistency into the project analysis, although it is still subject to qualifications regarding data availability and the assumptions required to apply the approach.

Appendix 2: Semi-Input-Output System

Formally in matrix terms the calculation requires the Leontief inverse of the A matrix to give total produced inputs per unit of sector output. One must then post-multiply the direct primary factor matrix F by the Leontief inverse to give total primary factor inputs per unit of output, so that:

$$ M=F{\left[1-A\right]}^{-1} $$

(6.10)

where

• M is the matrix of total primary factor requirements

• F is the direct coefficient matrix of primary factors

• A is the direct coefficient matrix of produced inputs

• [1 − A]⁻¹ is the Leontief inverse.

Once sector output is broken down into only primary factors for sector i producing commodity i:

$$ {P}_i=\sum \limits_g{C}_{gi}\cdotp {P}_g $$

(6.11)

where

• P_i is the financial price of a unit of output i

• C_gi is the number of units of primary factor g per unit of i

• P_g is the value of a unit of g, at financial prices

The economic value of a sector is given as the sum of the primary factors that go into the sector, with each primary factor itself valued at opportunity costs. For sector i, economic value (V_i) is given as:

$$ {V}_i=\sum \limits_g{C}_{gi}\cdotp {V}_g $$

(6.12)

where

• V_g is the economic price of primary factor g

• C_gi is as in (6.11)

As it is conventional to give information on economic prices in the form of ratios, or conversion factors (CFs):

$$ C{F}_i=\frac{V_i}{P_i} $$

(6.13)

To derive a CF for a particular sector requires an economic valuation of the primary inputs into that sector. It can be shown that CF_i can be derived as a weighted average of the conversion factors of each of the primary inputs that go into i, so that:

$$ C{F}_i=\sum \limits_g{b}_{gi}\cdotp C{F}_g $$

(6.14)

where

b_gi is the share of primary factor g in the value of output of i, where both g and i are at financial prices, so that

$$ {b}_{gi}=\frac{C_{gi}\cdotp {P}_g}{P_i} $$

CF_g is the conversion factor for primary factor input g

The model is solved for the set of CFs by multiplying the total primary requirements for each sector by the CFs for different primary factors. Formally in matrix terms M must be multiplied by the vector of CFs for primary factors, so that:

$$ {P}_n={P}_f.M $$

(6.15)

where

• P_n is the vector of final CF results

• P_f is the vector of CFs for primary factors