Abstract
Considering the critique of existing research work as expressed in the previous pages, the model presented here should incorporate at least the following features.
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The purpose of our analysis is to relate changes in the structure of final demand to changes in the degree of (in)equality of income distribution. We are not concerned here with equity which is a concept requiring value judgments as to the welfare implications of (changes in) income distribution.
For a discussion, see for example, Wonnacott, 1974, pp. 348–352.
At least the simple version, when no capacity expansion matrix is included.
In addition, the data that are available for the empirical application in this paper are mostly cross-sectional and it would therefore require a number of fairly heroic assumptions to estimate the lag structures for a dynamic model.
This is more important than merely to achieve mathematical homogeneity.
Note, for example, the oddity in interpreting the heuristic dynamic income distribution model presented by Cline (1972): final demand is a function of level and distribution of income in the previous time period. Total output though is a function of final demand in the same period, in spite of the fact that the link between the two is the Leontief-inverse matrix. While formally this specification is correct (the Leontief-inverse is a static model component), economically, in the framework of an otherwise dynamic model, it seems inconsistent to claim a time-lag between income and spending, while claiming no lag between spending and production. Little confidence could be placed in the time-path of income distribution traced out by such a model. The distinction static vs. dynamic in mathematical sense does not always coincide with the same distinction when made in the real world. This point cannot be overlooked in the interpretation of model results.
Actually FD represents the sum of n column vectors, where n is the number of final demand components distinguished.
The reader will note that j represents both input-output sectors (see equation (1)) and spending categories. The nature of our model makes it necessary to group expenditure items into categories corresponding with input-output sectors. The adjustments and assumptions involved in this process are discussed in section III.2.1 of this paper.
The estimation procedure of the propensities to consume will be described in section III.2.1 of this paper; a discussion as to whether average or marginal propensities are most appropriate can be found in section II.4.
In addition to the conditions applying to the Leontief-inverse, the convergence of the propagation process is guaranteed if and only if for each socio-economic group the consumption coefficients add up to less than one (see Miyazawa, 1976, p.15–21).
It should be noted that, if one does not distinguish between socioeconomic groups, the linkages matrix reduces to (Math), where e is the aggregate marginal propensity to consume, which is, of course, the standard Keynesian multiplier (see Miyazawa, 1976, p.10–12).
This is in fact what we shall do in the empirical application in Chapter III, for reasons of data availability explained there.
It is assumed that there are no continuous redistribution programs which give, at the margin, the lower income quintiles each more than 20% of income. If there is such a program, inequality of income distribution could fall below the level predicted by the linkages matrix.
The normalization of the successive vectors d to s is not required in practice; one normalization after the nth iteration will produce the same result.
Although the steady state distribution will be arrived at from any initial distribution, the time needed to reach it may be affected by the starting point.
The selection of investment projects as a tool to influence income distribution is recognized by lending agencies such as the World Bank, especially when the government lacks the political power to directly alter the existing income distribution, as is the case in many LDC’s, See Lal (1972), Turnham and Hawkins (1973).
Equation (6) also takes saving out of incomes received because the consumption coefficients in matrix c have total household expenditures, rather than disposable income, as argument.
The Japanese input-output tables used in our empirical application treat imports this way (see Link Input-Output Tables, Explanatory Report, 1975, p.119–122) and we have simply taken over the methodology. Note that if imports are treated as noncompetitive, they form one or more additional rows to the matrix of technical coefficients.
See for example Arrow and Hoffenberg (1959); Chenery and Clark (1959), especially Chapter 6; Leontief (1953) especially Chapters 2 and 3.
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© 1983 Springer-Verlag Berlin Heidelberg
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Grootaert, C. (1983). An Equilibrium Model of Income Distribution. In: The Relation Between Final Demand and Income Distribution. Lecture Notes in Economics and Mathematical Systems, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51563-7_2
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DOI: https://doi.org/10.1007/978-3-642-51563-7_2
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