Introduction
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We emphasize, first, that Piketty’s predictions are not mere extrapolations from past data but, instead, rest importantly on the use of economic theory. This is important, since for the predictions to be reliable, one would want to feel some comfort in the particular theory that is used. Our main point is to make clear that there are strong reasons to doubt the specific theory that Piketty advances.
We argue that one of the key building blocks in this theory—what he calls the second fundamental law of capitalism—is rather implausible, for two reasons. First, we demonstrate that it implies saving behavior that, as the growth rate approaches zero, requires the aggre- gate economy to save 100% of GDP each year. Such behavior is clearly hard to square with any standard theories of how individuals save, and it is inconsistent with the findings in the empirical literature on how individuals actually save.
Second, we look at aggregate U.S. data to try to compare Piketty’s assumption to stan- dard, alternative theories, and we find that the data speaks rather clearly against Piketty’s theory. Equipped with theories that we find more plausible, we show that even if the rate of economic growth were to decline all the way to zero, inequality would increase only very modestly, in fact so modestly that we would hesitate to use this argument to make a prediction of rising inequality. We think, in contrast, that future developments of other determinants of wealth inequality—such as educational institutions, skill-biased technical change, globalization, and changes in the structure of capital markets—are likely to be much more fundamental. ...
Concluding remarks
In conclusion, Piketty's "second fundamental law of capitalism" and the central theme of his book—that when growth goes to zero, the capital-income share increases dramatically— appear very difficult to justify, at least in light of our view of how savings decisions are made. These views are based, first, on the fact that we find a 100% gross saving rate—the implication of Piketty's model when growth approaches zero—implausible; and, second, on the large empirical literature studying individual consumption behavior. We also take a first look at U.S. postwar data and find, roughly speaking, that the optimal-saving model—that is, the model used in the applied microeconomics literature and by Cass and Koopmans in a growth context—seems to fit the data the best, somewhat better than the textbook Solow model. Piketty's model, on the other hand, does not appear consistent with this data. Equipped with the models we thus deem better capable of describing actual saving behavior, we then revisit Piketty's main concern: the evolution of inequality in the 21st century. Using these models as a basis for prediction, we robustly find very modest effects of a declining growth rate on the capital-output ratio, and hence on inequality. Thus, we find Piketty's second law quite misleading, and certainly not fundamental; we in fact think that the fundamental causes of wealth inequality are to be found elsewhere.
As a matter of history of economic thought, in making his assumptions on saving Piketty has respectable forerunners, to say the least. Solow's celebrated 1956 paper on economic growth, in fact, assumes from the outset that the net saving rate is constant (and positive), as do Swan's analysis from the same year and Domar's pioneering study in 1946. Later, in 1953, Domar posits two formulations of a growth model, one in terms of net savings rates and one in terms of gross rates, as does Johansen in 1959.14 Phelps (1961) develops his famous 'golden rule" in a model with a constant net savings rate, following Solow. Finally, to round out our quick (and surely incomplete) review of the early literature on growth models with fixed savings rates, Uzawa (1961) posits a capitalist-laborer model in which capitalists save all and laborers save none of their income; in this model he accounts explicitly for depreciation of the capital stock, unlike Solow (1956).
Turning to models of growth based on optimizing model, the pioneering studies of Cass (1965) and Koopmans (1965) both explicitly account for depreciation, as does their forerun- ner Uzawa (1964) in a model with linear utility.15 Drawing clear lessons from this whirlwind tour of the historical development of growth models would no doubt require much more detailed and careful study. But we conjecture that it was not until researchers started to take "microfoundations" seriously—in the sense of specifying explicitly the decision problem faced by savers and identifying the state variables, such as capital, upon which their decisions depend—that some of the confusions (apparent in our brief review of the literature) about how to specify saving rules began to clear up. Subsequently, the modern textbook version of the Solow growth model has universally assumed a constant gross savings rate, and we have argued that in an environment without growth in either population or technology this is the only assumption that makes sense.
Is Piketty's "Second Law of Capitalism" Fundamental? (PDF)
Per Krusell, Institute for International Economic Studies, CEPR, and NBER, and Tony Smith, Yale University and NBER
(h/t Tyler Cowen at Marginal Revolution)
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