APPENDIX: Technical Note on the Model
The constant term, d0, in equation (2.7) can be shown to be:
whereas, the constant term, d1, in equation (2.8):
The former is a negative function of
If α1=α2=β=0, equations (2.7)′ and (2.8)′ are reduced to the conventional results:
Equation (2.7)″ indicates that the unskilled labor share of aggregate income is a3; this equation is identical with the equation in footnote 1 on page 10 of this paper, where
In the aggregate supply function (3.1), the constant term
where d1 and d0 are as defined above. The constant term
and the constant term
These coefficients are all complicated functions of
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Presented at the Third Annual Inter-American Seminar on Economics, Public Sector, and Labor Markets in Latin America, organized by the National Bureau of Economic Research and Pontífica Universidade Católica do Rio de Janeiro, March 16-17, 1990. We thank Vito Tanzi, Eliana Cardoso, Kenneth Miranda, and other Fund colleagues and the seminar participants for their helpful suggestions on an earlier draft. Any remaining errors are ours.
The extent to which social programs increase aggregate production would also depend on the structure of the labor force, particularly its age composition. See the discussion in the following section.
The surveys of literature by Scrimshaw (1986) and McGuire and Austin (1987) suggest that aerobic capacity has been shown to affect labor productivity among lumberjacks, sugarcane workers, construction workers, and other manual workers in Australia, Brazil, Colombia, Ethiopia, Guatemala, and India. A World Bank review of public work programs in developing countries indicates that 30 percent of those invited to participate in a food-for-work program in Bangladesh had to decline the offer as they were too weak to carry out any meaningful physical work (Burki and Weaving (1976)). See also Strauss (1986, 1990) and Deolalikar (1988).
Cornia (1988) indicates that millions of workdays are lost every year through the incidence of malaria. McCuire and Austin (1987) estimate that at least 140-280 million workdays are lost annually to the care of about 140 million malnourished children.
This implies that the supply of unskilled labor is elastic with respect to wages, not because of the effect of higher wages on work efforts but because of their effect on the capacity to work.
The demand for labor services may be expressed as a function of, among other variables, capital services and skilled labor services employed, rather than of output (QS). This formulation of labor demand function, using QS, is aimed at illustrating the relationship between the real wage rate and output (see the following discussion).
This type of expenditure includes spending on nutrition and health for the poor (e.g., primary health clinics, food stamps, and child care).
One could conceive of an upward-sloping demand curve for unskilled workers when α1>1; for this condition to hold, b2 should be greater than 0.5. The unskilled labor market would still be stable as far as the slope of the unskilled labor supply exceeds the slope of the unskilled labor demand.
This model does not explicitly consider the possibility that a larger number of self-employed workers in the informal market constitute major poor groups. However, the unskilled labor market could be taken as representing the informal market and the unskilled wage rate could be taken as representing the level of self-employed earnings. Results will not be altered by this alternative interpretation.
The constant terms, d0 and d1, in equations (2.7) and (2.8) are complicated nonlinear functions of several variables and coefficients, including Ns and Nu, and the quantity of skilled and unskilled workers, respectively. See the Appendix for a derivation.
Note that if α1 = α2 = β = 0, equation (2.7) reduces to
Aggregate production would be a negative function of g and wu only if 1-a2+βa3 < 0, that is, 1 < a2-βa3, which is an unlikely condition to be met under normal circumstances.
The condition for a positive relationship between a3 and α1a3/(1-a2+ βa3) can be shown to be 1-a2>0, which is easily satisfied in the model.
In Figure 2 (Case B), the differential effects of an expansion of capital stock in Cases A and B are compared. In the conventional Case A, the new equilibrium is E1a; in this case, the new equilibrium is E1b. The additional output and wage effects are denoted by ΔQS and Δwu, respectively.
For a discussion of the longer-term implications of targeted social expenditure for stable growth, see Tanzi and Chu (1989).
The specific (log-linear) nature of the functional form for the aggregate demand function is not critical for the analysis; the substantive part of the conclusions would not change even if we assumed an alternative functional form.
For simplicity, no external factors are specifically considered. Opening the system will change the process of adjustment as well as the magnitude of the effects, but not the qualitative conclusions reached here.
The coefficient θ = (1+α1)(1-a2)+a3(β-α1) is unlikely to be negative in the normal situation in which a1, a2, and a3 are all positive and less than unity.
We again assume that β=0. In other words, for this purpose, the existence of unemployed skilled workers spilled over to unskilled labor markets is disregarded.
Tax financing of the increase in g may raise other problems (e.g., distortionary effects), as well as the distributionary effects of taxation. Foreign financing will increase the debt service burden.