Do the rich save more? A revisit to the theories of the consumption function

Modern macroeconomic research on consumption/saving starts with Keynes (1936), who puts forward his well-known consumption function. The Keynesian consumption function can be written as follows, C = a + bY where C denotes consumption, Y denotes disposable income, a and b are both positive coefficient, and 0 < b < 1 . An important implication of the Keynesian consumption function is that saving rate increases with income. However, while this predication is consistent with cross-section evidence, it is not consistent with time-series evidence. For example, in a seminal contribution, Kuznets (1946) discovered that the saving rate in the United States was remarkably stable from 1869 to 1938, although people’s income increased significantly over this period. Thus, the long-run consumption function implies that saving rate is constant with economic development. Indeed, a key assumption of the Solow growth model that the saving rate of an economy is constant with economic development (Solow, 1956). More recently, an empirical contribution by Dynan, Skinner and Zeldes (2004) find a strong positive relationship between saving rates and lifetime income. This important empirical finding makes the old “consumption puzzle” more intriguing, because it shows that the average propensity to consume decreases not only with current income but also with lifetime income. This puzzle can be illustrated by the familiar international comparison of saving rates: If richer people have higher saving rates, why hasn’t the United States, which has been the most wealthy nation in the world, had a higher saving rate than many much poorer countries? The current paper attempts to provides a rigorous framework that helps resolve this puzzle. This model extends the related literature by examining individuals’ intertemporal choices with the consideration of intergenerational interactions. This extension is empirically important because intergenerational transfers account for an important part of aggregate saving. 1 This chapter is based on the same essential idea as Fan (2006), but it develops a different model. Our model implies that an individual is more concerned about her offspring’s well-being when the offspring’s future mean income is lower. In a Markovian game framework, the model shows that the bequests from parents to children decrease with the mean income of future generations. Meanwhile, ceteris paribus , an individual’s bequests to her children increase with her own wealth. Thus, the model has the following implications. First, at a given point in time, richer people have higher saving rates, because they are concerned that their children are likely to receive lower incomes than theirs. In other words, a household with higher lifetime income saves more in order to leave more bequests to its offspring, who are likely to be worse off. Second, over time, when an economy experiences economic growth and the mean income of the economy rises, individuals will reduce their bequests because their offspring are expected to be equally well off due to the economic growth. Consequently, the saving rate can be approximately constant over time if the impacts of the increase in one’s lifetime income and the increase in her offspring’s future mean income on her consumption cancel out each other. Thus, this model helps explain the consumption puzzle and reconcile the short-run and long-run consumption functions. This paper is closely related to Fan (2006), who studied a model that aims achieve the same purpose as the current paper. However, this paper builds model that is very different from Fan (2006). In Fan (2006), it is assumed parents get utility from their children’s future wealth. In contrast, the current paper is in line with Fan (2001), who assumes that parents get utility from quality of their grandchildren as well as their children. Consequently, the current paper studies a framework in which intergenerational conflicts and intergenerational commonality co-exist. Thus, while it is based on the same essential idea of Fan (2006), this paper examines this important issue from a different angle from Fan (2006). In what follows, Section 2 summarizes a framework on which the current model is based; Section 3 is the core of the paper, which examines the consumption functions both in the long run and in the short run and provides an explanation for the consumption puzzle; Section 4 further illustrates the intuition of the paper with an example; Section 5 offers the concluding remarks.