The subject of input-output tables and models is well beyond the scope of this paper. In this annex a few tentative observations are offered to help place them in perspective from a viewpoint of analysis in the agricultural sector. This annex is for the reader who has sane familiarity with input-output analysis and may wish to try to apply it to agricultural policy questions. Some comments are made about the nature of input-output data and the role of input-output based models, and then some suggestions are offered regarding simple, descriptive uses of the tables for agricultural analysis.
Agricultural Data in Input-Output Tables
A column of coefficients in an input-output table (an input-output column vector) for agriculture looks very much like a farm budget. It reports an output level and a long list of associated inputs. The differences are as follows: 1) In the input-output table, both the output and the inputs are reported in value terms, and prices are not given, so the input-output relationship in quantities is not known; 2) The input categories in the input-output table are not as specific as they are in farm budgets—instead of particular kinds of chemical fertilizers and pesticides and fungicides, the input-output table will list together all inputs from the chemical sector; 3) The input-output vectors are more aggregative—generally they deal with large aggregations of agricultural outputs, such as all crops, or all cereals, although occasionally there will be vectors for individual major crops (especially, it seems, in the rice-growing economies of Asia); 4) The input-output table adds together the wages paid to hired labor and the net economic rent accruing to family labor in one category of labor value added, whereas the farm budget lists labor costs and total farm profits separately (not attributing the profits to particular factors of production); 5) Similarly, the input-output table lumps together all returns to capital, while the farm budget may list land rents separately but the budget does not attempt to distinguish the components of the farm's net profits; 6) The input-output table may list separately the imported inputs, either in aggregate or by commodity, but the farm budgets do not specify the imported or domestic origin of the inputs; and 7) There is no seasonality in input-output data, while sometimes it is reported in the farm budgets.
Input-output tables provide the data necessary to link the agricultural sector and the rest of the economy, and likewise input-output based models are one kind of link between agriculture and the economy-wide level of analysis. Farm budget studies are used to build the columns of agricultural coefficients in the input-output tables; the ratios of value of input to value of output, for each group of inputs. The coefficients in the tables are then used by national income accountants to convert series on gross agricultural production into series on GDP (value added) in agriculture. When the input-output tables are reestimated at intervals of two to three years (as in South Korea) this procedure' leads to compatible series of gross production and GDP by sector. However, when the input-output tables are revised only every ten years, or even less frequently, then important changes in cropping patterns and technologies of input use can occur in the interim, making the production and GDP series less consistent with each other. Something like this appears to have occurred in Honduras, for the production data and the GDP data give very different pictures of the evolution of the agricultural sector in recent years.
In such a case, the analyst has little choice but to opt for use of the production series (and form his or her own indexes), given the limitations to the way the sectoral GDP series are constructed. Nevertheless, it is well to bear in mind that the GDP data have been reconciled with other aggregate economic accounts for the country, whereas the crop and livestock production data have not.
Agriculture in Input-Output Based Models
In the classical dynamic input-output models of an economy (Bruno, 1966; Manne, 1973) the treatment of agriculture was so stylized as to not be recognizable by most agricultural economists. Hence, while these models treated agriculture in some way in the economy-wide context, there was no feedback between the two levels of analysis. An attempt was made to overcome this problem in a methodological sense in Goreux and Manne (1973), and one conclusion was that the agricultural analysis enriched the economy-wide model more than vice-versa.
The reason for this finding was that the original input-output specification of the economy-wide model lacked aggregate production alternatives for the agricultural sector; from the center, as it were, it was impossible to predict how cropping patterns and agricultural input use patterns would change in response to say, changes in the wage rate or the exchange rate. Sensitivity analysis with an agricultural model (repeated solutions under different assumptions about the economy-wide price of labor, foreign exchange and capital) supplied this information to the economy-wide model. At the same time, it was a relatively simple matter to convey macro policy alter-natives to the agricultural model, via reasonable variations in interest rates, wage rates, and exchange rates, without necessarily having recourse to the economy-wide model.
More fruitful linkages between agriculture and the rest of the economy have been found in the input-output based general equilibrium models of recent years. Many of the studies, in fact, have used as their core set of data social accounting matrices, which embody input-output transactions (interindustry sales) within a broader set of institutional transactions. Among other things, these models have permitted assessment of the incidence by sector and household income level of the benefits of food aid (Norton and Hazell, 1986) and agricultural input subsidies (Suprapto, 1988). For Bangladesh, Norton and Hazell found that, after price responses were taken into account with the general equilibrium model, the bulk of the benefits of food aid in fact went to urban households.
However, it must be pointed out that, useful as these models are, they contain much less agricultural specificity in terms of crops and regions and technologies than do the sector-wide linear programming models. The latter, therefore, continue to be used as major vehicles for applying input-output production vectors to questions of pricing and subsidy policy within the sector.
Simple Input-Output Exercises for Agriculture
Input-output tables contain some simple information pertinent to agriculture that can be drawn out constructing formal models. Since the focus of input-output is on intersectoral relationships, the tables provide a description of the relative importance of agricultural marketing and agroindustries, as compared to primary agriculture in a country. The agroindustrial sectors are tabulated explicitly as separate rows and columns in the table.
Agricultural marketing functions are subsumed in two cells of the table: the coefficients from the marketing (commerce) sector in the agricultural production vectors refer to the marketing margins associated with the purchase of agricultural inputs, and the marketing margins for agricultural outputs will be found in the corresponding marketing (commerce) entries in the agroindustrial columns and the final demand columns. To extract the agricultural marketing margins in particular out of the total marketing margins (for all classes of goods) in the final demand columns may require a little work and some assumptions, but normally it can be done.
When these exercises are completed, the role of agriculture in the total economy can be assessed. Some studies have found it to be much larger than is indicated by the ratio of the sector's GDP to total GDP. In the case of Colombia, it was found that under the broader definition, including agricultural marketing activities and agroindustries, agriculture's share of GDP was over 40 percent (versus 27 percent under the narrower definition).
The other simple and useful calculation that is performed frequently with input-output tables is to derive the multiplier effects, in all sectors, of an increase in either agricultural production or agricultural final demand (say, exports). The increased demand for outputs of all sectors that arises from an increment in agricultural exports depends on the strength of the interindustry -linkages in the economy? Is agricultural machinery produced locally? Is the steel that goes into the machinery produced locally? Or, more to the point in some cases, is the fertilizer produced locally? Is the phosphate that goes into fertilizer a national product, and are the bags for distributing the fertilizer produced locally? The total increase in demand for other sectors' outputs, from a unit increase in agricultural exports, is found from the relationship
| (A.1) | ΔX = (I - A)-1ΔE |
where ΔX is a column vector of incremental gross outputs by sector (of dimension nxl for n sectors), I is the identity matrix, A is the input-output coefficients matrix, and ΔE is the column vector of incremental exports (with zeros for those entries corresponding to nonagricultural sectors). Note that the coefficients of the inverse matrix (I - A) normally are published along the the input-output table itself.
The corresponding effect on incomes in each sector of the economy is given by
| (A.2) | ΔVj = vjΔXj |
where ΔVj is the increment in income (value added) in sector j, vj is the input-output coefficient for the ratio of value added to gross output in that sector, and ΔXj is the jth element of the vector ΔX in (A.1), that is, the calculated increment in the gross output of sector j as a consequence of the posited increase in agricultural exports.
The agricultural columns of the inverse matrix (I - A)-1 give the total direct and indirect increase in demand for the output of every sector (by row) that would arise from a unit increase in output of agri-cultural goods. In other words, agriculture demands a certain amount of chemical inputs per unit of output, and the chemical industries in turn demand other chemical inputs, and so forth. The infinite sequence of continuing rounds of demands is summarized in each coefficient of the inverse matrix.
What is missing in this kind of analysis, and other kinds as well, is an appreciation of the multi-sectoral nature of the agricultural labor force, and hence of rural incomes. As noted earlier, a rural household often has members working in agriculture and services, and sometimes in industry as well. In effect, the profession has not yet integrated the economic theory of rural households (a la Barnum and Squire, 1979, for example) into sector-wide and economy-wide empirical studies.
For the mathematically inclined reader, e is an irrational number that emerges naturally from the properties of mathematical series. It is defined as the least upper bond of the set of all numbers
Where n is a positive integer.
Natural logarithms are then defined so that
| (B.4) | ln ex = x, | x > 0, |
| or | ||
| (B.5) | eln x = x. |
This annex provides the derivation of the trend growth equation (2) in chapter 2. That equation defines, as a parameter to be estimated, the growth rate along the trend (that is, abstracting from fluctuations).
The starting point is the basic exponential growth equation for any variable X that changes over time:
| (B.1) | Xt = Xoert |
where e is the mathematical constant whose value, approximated to six decimal places, is 2.718282. The equation expresses the level of any variable at time t, denoted Xt, as a function of its initial value, Xo, the growth rate, r, and the number of periods elapsed, t. Taking logarithms of both sides of (B.1),
| (B.2) | 1n Xt = 1n Xo + rt |
But the expression In Xo is a constant, so the equation may be written in estimatable form as
| (B.3) | 1n xt + a + rt, |
which is the equation in chapter 2.
It should be noted that the logarithms here must be natural logarithms (base e) and not naperian logarithms (base 10); otherwise, the estimation will not yield a growth rate. For users of LOTUS and statistical computer packages, this means selecting the operator LN, and not LOG.
