Savings and Growth

Changes in Savings and Growth - Theory and Evidence



Why is the U.S. personal savings so low? What determines our saving rate? What to do? Back in the 1980’s and early 1990’s, many economists voiced their concern on the very low U.S. saving rate. In mid 1990’s, thanks to internet, I was able to publish a mathematical proof showing that change in savings has to be a function of labor income growth. This result refuted the established view on consumption theory. Arguably, it is the only theory that could help explain the behavior of personal savings in fast and slow growing countries and be able to explain why positive growth can result in negative saving rates. Finally, I also tried to relate the effect of imports on growth and by extension on change in savings.


   For many centuries, economists have tried to understand the relationship between savings (consumption/income) and growth.   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.”  [We will see that it is actually the other way around]

   Engel was among the earliest saving contributors.  German-born statistician Ernst Engel (1821-1896) stated 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.  [We will see that, though we make optimal decisions, Keynes’ disequilibrium approach is more relevant than ever]

     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 savings 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 positive, let’s say between 1% to 3%.

     Let’s say growth (g) is +2% and saving at intercept (So) is -5%.  Assuming S – So = g then S = -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.  If you take into account the three to six months lags then the curves below will approach to a straight line.   [I have not bothered to update them since the mid 1990s.  You may do easily with newer data from the Commerce Department]


    1. I believe that Milton Friedman used to say that a good model is one that can fit historical data and also should make accurate future forecasts.  The above theory and data show changes in savings in the U.S. for short and long run with quarterly precision (plus and minus the lags).  Most theories cannot even attempt to explain yearly (or decade) changes in savings.  Since 1996, when I first published my work in the internet, I’ve got 12 years of track record. 

    2. When I first started working on savings in late 1980s, all the news, from Financial Times, Economist, Wall Street Journal, Business week, etc, was about the need for higher personal savings as they would magically drive up investments.  Curiously, in the mid 1990s, after my paper was published, the discussion slowly died down but few knows why.  

    3. Ricardo’s comparative advantage and many untested trade theories must be taken with high doses of skepticism.  As the above chart shows, trade affects your job and income and eventually your savings.  I prefer the Adam Smith’s view that good opportunities are rather scarce.  For the U.S. manufacturing industry to concede important markets, such as TV and other consumer electronics, to other countries is irresponsible and helps explain the decline in growth of income.

    4. Arguably, essential regulations are important as we can see from the recent failures of the finance and insurance, oil, refining and energy, transportation, and drug industries, to name just a few ones.  For instance, the drug industry tries to avoid, at all cost, serious research in vaccine, which generates little revenue.  Worse, drugs in the U.S. are approved without cost considerations.  In general, what is lost in Washington is that a more comprehensive coverage and lower health care cost is strategically more important to the growth of jobs (and the increase in income and savings).  An obvious fact understood in most developed countries.  It is heath care and its cost!

    5. How to handle the trade deficit?  The problem starts with trade and goes to income and then to consumption and savings (and investment).  Weak dollar strategy has helped U.S. exports in short run but recent rise in oil prices and inflation has exposed the efficacy of this policy.  So we need a long term solution dealing with some of the issues mentioned above, which will allow the country to continue growing in a more sustainable way.

    6. In some corners, “quants” in Wall Street  are being partially blamed for applying esoteric models to financial markets and the resulting crash of 2008.  It seems quants were allowed to develop equations without sufficient knowledge of economics and its underlying trends so they often miss recessions (see also CAPM vs CCAPM). But, even with the knowledge of the above correlation between change in savings and growth, macroeconomic models are still dependent on the forecast of growth of income.


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