Does Income Distribution Matter for Effective Demand? Evidence from the U.S. Christopher Brown Arkansas State University

The issues Why, in theory, should a change in income distribution impinge on aggregate expenditure? Is it possible to formally demonstrate a nontrivial “income distribution” effect based on plausible assumptions about household spending behavior? Does the post-1978 evidence from the United States support the hypothesis that income distribution matters for effective demand? Does rising income mal-distribution create the need for greater reliance on debt to sustain aggregate consumption expenditure?

M. Kalecki’s Model 1 National income (Y) is divided between the wage share (w) and the profit share (P). The wage share is determined by the “degree of monopoly” and the the ratio of the materials bill to the wage bill (j). The degree of monopoly measured by the markup over unit prime costs (k). Kalecki derived the following equation for the wage share (w): Kalecki, M. (1954). “The Theory of Economic Dynamics,” in Collected Works of Michael Kalecki, Volume. 2, J. Osiatynski, ed. Oxford: Clarendon Press, 1991, pp [1]

To incorporate the relationship expressed by [1] into a theory of aggregate output, Kalecki posited total wage and salary income (V) as a function of total (private) income and output (Y): [2] The term (B) is a constant and  is the share of wages in national income that is determined independent of income  is the same thing as w and hence is determined by k and j. Assuming no taxes, V is the difference between Y and P. [3]

Rearranging [3]: [4] Note that: P is determined by investment and the propensity to consume out of profit income. An increase in the degree of monopoly (k), to the extent it diminishes the wage share (w), will reduce output (Y). An increase in k will increase the profit share, but not profits expressed in absolute terms.

Kalecki Summary: Assuming the propensity to consume out of wage and salary income is greater than the propensity to consume out of profit income, an increase in the degree of monopoly, by shifting the distribution of income in favor of profits at the expense of wages and salaries, would cause a decrease in the ratio of total spending to income.

Assumptions 1.Aggregate household income is fixed at $6 trillion million households 3.Perfect equality (or zero inequality) within income deciles. 4.Spending behavior of all households conforms to that of a representative agent. A Model to Simulate the Effects of Income Inequality on the Aggregate Propensity to Consume

Consumption function of a “representative agent.” Where C i is consumption of household i;  i is exogenous consumption; and Y i is income of household i. It is assumed that  i > 0 and 0 < a < 1. Thus total consumption (C) is given by: The aggregate propensity to consume (APC) is computed as:

The Theil Index (T ) where and Y i is income of agent i (individual, family,....) and n is the number of number of agents in the population. The Theil index is a monotonically increasing measure of inequality bounded by

Table 1—Theil Index = Notes: Column [3] was computed by multiplying average income by the number of households within the decile (100,000). Column [4] was computed by multiplying column [2] times 100,000.

Table 2—Theil Index = 0.0

Table 3: “Hard Budget Constraint “ (C  Y) Theil Index = 0.125

Specification1 1 st order autoregressive model specified as: Equation was estimated using nonlinear least squares C is consumption (seasonally-adjusted annual rate in billions of 1998 dollars); YD is disposable income (seasonally-adjusted annual rate in billions of 1998 dollars); Mood is the Michigan Index of Consumer Confidence (1966 = 100); and Theil is the Thiel Index (seasonally-adjusted).

Specification 2 Specification 3 Specification 4

Table 1—Theil Index = Decile Numbe r [1] Average Disposabl e Income (Dollars) [2] Average Consumption (Dollars) [3] Total Disposable Income (Billions of Dollars) [4] Total Consumption (Billions of Dollars) [5] = [4]  [3] APC 1$186,000$125,701.96$1,860$1, ,00078, , ,00064, ,00051, ,00047, ,00043, ,00040, ,00033, ,00029, ,00025,  = $6,000  = $5,408.1 Notes: Column [3] was computed by multiplying average income by the number of households within the decile (100,000). Column [4] was computed by multiplying column [2] times 100,000. Table 1—Theil Index = Decile Numbe r [1] Average Disposabl e Income (Dollars) [2] Average Consumption (Dollars) [3] Total Disposable Income (Billions of Dollars) [4] Total Consumption (Billions of Dollars) [5] = [4]  [3] APC 1$186,000$125,701.96$1,860$1, ,00078, , ,00064, ,00051, ,00047, ,00043, ,00040, ,00033, ,00029, ,00025,  = $6,000  = $5,408.1 Notes: Column [3] was computed by multiplying average income by the number of households within the decile (100,000). Column [4] was computed by multiplying column [2] times 100,000. Decile Numbe r [1] Average Disposabl e Income (Dollars) [2] Average Consumption (Dollars) [3] Total Disposable Income (Billions of Dollars) [4] Total Consumption (Billions of Dollars) [5] = [4]  [3] APC 1$186,000$125,701.96$1,860$1, ,00078, , ,00064, ,00051, ,00047, ,00043, ,00040, ,00033, ,00029, ,00025,  = $6,000  = $5,408.1 Decile Numbe r [1] Average Disposabl e Income (Dollars) [2] Average Consumption (Dollars) [3] Total Disposable Income (Billions of Dollars) [4] Total Consumption (Billions of Dollars) [5] = [4]  [3] APC 1$186,000$125,701.96$1,860$1, ,00078, , ,00064, ,00051, ,00047, ,00043, ,00040, ,00033, ,00029, ,00025,  = $6,000  = $5,408.1

Dependent Variable: log Consumption (see notes below) Period: 1978:1 to 2000:12 Observations: 270 Specification Parameter (1)(2)(3)(4) 2 (59.63) (3.93) (54.49) (44.37) 3 (2.617) (2.722) (2.38) (2.761) 4 (-3.662) (-2.73) (-3.448) (-4.08) R2R Inverted AR Roots Notes: t-ratios in parenthesis. The dependent variable for specification 2 is the year-over-year percentage change in consumption in month t. Table 4: Least Squares Estimates

Implications Development of broad domestic markets for the output of high value added industries is retarded when income distribution functions lack density. Income inequality can cause excessive macro- reliance on consumer debt to support consumption expenditure.

Ratio Consumer Debt to Personal Income Recessions are shaded Figure Includes installment and credit and loans outstanding. Does not include student or home equity loans. Source: Bureau of Economic Analysis