Change in Savings and Income Growth

New Result and Evidence in Consumption Theory 

By  Cheng  K.  Wu

      For many centuries, economists have made contributions to the savings (consumption) and growth theories.   In Adam Smith's Wealth of Nations (1776), Smith thought that  "it is not the actual greatness of national wealth, but its continual increase, which occasions a rise in the wages of labour."  

    Among the earliest saving contributors is Engel's law.  Formulated by German-born statistician Ernst Engel (1821-1896), Engel's Law states that as incomes increase, the proportion of income spent on food falls.   Engel's Law is accepted as a basic principle of income and consumption.   You can call it inertia or propensity to consume.

    In Keynes' General Theory, "a decline in income due to a decline in the level of employment, if it goes far, may even cause consumption to exceed income . . ..[p. 98]"  Clower argued that Keynes' General Theory had a Dual-Decision Hypothesis "at the back of his mind . . .."  That is, the difference between expected and actual income may cause errors in optimal consumption, which may require corrections on consumption.

     In analyzing consumption during a life time, Modigliani's Life Cycle Hypothesis (and Friedman's Permanent Income Hypothesis) reached the conclusion that income and consumption are based on an estimate of each consumer's life time financial and labor income.  Modigliani and Brumberg {1954, published 1980) theorized that "in the long run the proportion of aggregate income saved depends not on the level of income as such but, rather, on the rate of growth of income . . .."

    In sharp contrast with the above natural progression approach, Flavin (1977) and Hall  (1978) reached the false conclusion that permanent consumption should be independent of income.    The mathematical proof was less than rigorous and yet their work was published by the influential Journal of Political Economy (Robert Lucas, editor) and in 1981,  Hall (1978) article became essential part of the two volume, Rational Expectations and Econometric Practice (Lucas and Sargent, editors).   Clearly, Flavin's and Hall's conclusion was wrong in data.   Since the mid 1990's, many researchers have shown the correlation between growth and savings, including Modigliani.

    Based on his interest in international trade, around 1993, Wu (1997) made a rigorous mathematical proof that Flavin and Hall conclusion was indeed wrong and that changes in savings should be a function of labor income growth.   In the mid 1990s, Wu's result was reviewed by Angus Deaton and Flavin.     See their comments at:

    Wu's result is available for download at:

     Arguably, one would think that the relationship between savings and growth is obvious.  In effect, from Adam Smith to 1990s, it took over more than 200 years for Wu to prove that it is actually income growth that determines changes in savings.     

    Arguably, Modigliani and Brumberg's attempted proof (1954, published 1980) and Wu(1996) proof reach conclusions that are not exactly the same.  For instance, in Modigliani's Recent Declines in the Saving Rate (1990), "with zero growth, the saving [rate] will be zero, regardless of income or thrift habits . . .."   In Wu (1996), with zero growth, saving from one period to another may remain the same, not necessarily zero.  Only changes in saving will be zero. 

     Further, in Modigliani, only negative growth results in negative saving rate.  In Wu (1996), if change in savings is a partially a function of growth, depending on the intercept So, a slow but positive growth could result in negative saving (see line 3 below).   This helps explain why US saving rate can be negative while real growth is is between 1% to 3%.

Briefly, the relationship between change in savings and income growth shows:

  • The level of savings is irrelevant, all that matters is its change;
  • Savings can be negative if growth de-accelerates or turn negative (Modigliani); 
  • Optimal personal decisions on consumption can lead to savings and disavings (Keynes' disequilibrium)  if income expectation is wrong (Clower's Dual Decision Hypothesis);
  • All factors affecting income will contribute to changes in savings.  For instance,
    • Health costs;
    • Business (corruption/political, interest rates, tax, defense, etc) costs;
    • Infrastructure, financial markets, etc; 
    • Education and skilled labor;
    • Population growth, bequest, etc;
    • Currency and imports
     To illustrate the sharp decline in the U.S. saving rate and to show the relevance of the study of the causes of income growth, the charts below show the effect of imports (and trade deficit) on savings.   [I have not bothered to update them since the mid 1990s.  You may do easily with newer data from the Commerce Department]



Clower, R. W. (1965), "The Keynesian Counterrevolution: A Theoretical Appraisal," in The Theory of Interest Rates, ed. F.H. Hahn and F.P.R. Brechling, Macmillan, p. 103-25.

Flavin, M. A. (1981), "The Adjustment of Consumption to Changing Expectations about Future Income," Journal of Political Economy, vol. 89, no.5.

Flavin, M. A. (1992), "The Excess Smoothness of Consumption: Identification and Interpretation," Review of Economic Studies, forthcoming.

Friedman, M. (1957), A Theory of the Consumption Function, Princeton University Press.

Hall, R. E. (1978), "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, p. 971-87, October 1978.

Hall, R. E. and Mishkin, F. S. (1982), "The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households," Econometrica, 50, 461-481.

Harrod, R. F. (1957), International Economics, The University of Chicago Press.

Keynes, J. M. (1936), The General Theory of Employment, Interest, and Money, Hartcourt Brace Jovanovich.

Lucas, R. E. (1976), "Econometric Policy Evaluation: A Critique," in The Phillips Curve and Labor Markets, ed. K. Brunner and A. Meltzer, Carnegie-Rochester Conference on Public Policy 1, Amsterdam: North Holland.

Modigliani, F. (1975), "The Life Cycle Hypothesis of Saving Twenty Years Later," Contemporary Issues in Economics.

Modigliani, F. (1985), "Life Cycle, Individual Thrift and the Wealth of Nations," Nobel lecture.

Modigliani, F. (1988), "The Role of Intergenerational Transfers and Life Cycle Saving in the Accumulation of Wealth," Journal of Economic Perspectives.

Modigliani, F. and Brumberg R. (1954), "Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data," in K.K. Kurihara, ed., Post-Keynesian Economics. Rutgers University Press.

Modigliani, F. and Brumberg R. (unpublished manuscript 1952, published 1979), "Utility Analysis and Aggregate Consumption Functions: An Attempt at Integration," in The Collected Papers of Franco Modigliani, ed. A. Abel, Vol. 2, MIT Press.

Muth, J. F. (1960), "Optimal Properties of Exponentially Weighted Forecasts," Journal of the American Statistical Association, vol. 55, no. 290.

Muth, J. F. (1961), "Rational Expectations and the Theory of Price Movements," Econometrica, vol. 29, no. 6.

Sargent, T. J. (1987), Macroeconomic Theory, 2nd edition, Academic Press.

Smith, A. (1776), The Wealth of Nations, The University of Chicago Press 

Sraffa, P. (1961), Production of Commodities by Means of Commodities, Cambridge University Press.


 Copyright   2007   Cheng K. Wu