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Micro-based Growth Models 29.11.2007. Exercise solutions Christian Groth Exact answer to B.6, question e) and f) B.6 The short answer to e) and f) is that since the bequest motive is operative in every period (also after the increase in π or temporary cut in σ, we assume), the dynasty will choose the same consumption path (c2t , c1t )∞ t=0 as it planned before the shift in fiscal policy. The reason is that any (non-confiscatory) change in the time profile of lump-sum transfers or lump-sum taxes will not make the dynasty feel richer or poorer. If for example the present value of the infinite stream of transfers goes up, then the present value of the infinite stream of taxes goes equally much up, because the government has to satisfy its intertemporal budget constraint. The conclusion is that aggregate consumption and saving in the economy will remain unchanged. A formal proof of this story goes as follows. Let the current period be period 0. Assume, for simplicity, that the number of dynasties in the economy is one (the actual number of dynasties is of no importance, because all dynasties are alike). Let the old generation in the dynasty in period 0 be of size 1. Thus, with L−1 = 1, we have Lt = (1 + n)t+1 . The dynasty must satisfy its intertemporal budget constraint. That is, the present value of the consumption stream can not exceed the total wealth of the dynasty. And in the optimal plan the present value of the consumption stream will exactly equal the total wealth. Thus, ∞ X (1 + n)t [c + (1 + n)c1t ] = A0 + H0 t+1 2t (1 + r) t=0 where A0 is initial (real) financial wealth of the dynasty and H0 is its (real) human wealth (after transfers and taxes). The financial wealth consists of capital, K0 , government bonds, B0 , and net foreign assets, Af0 . Thus, A0 + H0 = K0 + Af0 + B0 + H0 , where, from the information in the fourth line of p. 7 in Problem set B, B0 = (1 + n) ∞ ∞ X X (1 + n)t (1 + n)t π (σ − [(1 + n)σ t − π] , ) = t t+1 t+1 (1 + r) 1 + n (1 + r) t=0 t=0 1 (**) and ∞ X (1 + n)t [π + (1 + n)(wt − σ t )] . H0 = (1 + r)t+1 t=0 Now, since B0 and H0 are the only terms in (**) which depend on transfers and taxes, consider B0 + H0 = ∞ X (1 + n)t [(1 + n)σ t − π + π + (1 + n)(wt − σ t )] t+1 (1 + r) t=0 ∞ ∞ X X (1 + n)t 1 + n t+1 = (1 + n)wt = ( ) wt . t+1 (1 + r) 1+r t=0 t=0 We see that the time profiles of π and σ have vanished and can not affect B0 + H0 . Hence, the total wealth of the dynasty is unaffected. As a byproduct, we also see that higher initial debt has no effect on the sum, B0 + H0 , because H0 (which is after transfers and taxes) goes equally much down. This is what Barro meant by claiming that “governement debt is not net private wealth”. – Remark. This is an opportunity for me to emphasize that most macroeconomists (including myself, by the way) consider Barro’s Ricardian equivalence (or debt neutrality) result as an interesting and elegant theoretical result. And only that. In practice, temporary tax cuts and debt financing by the government seem to increase current consumption. Bernheim (NBER Macroeconomics Annual, vol. 2, 1987) reviews the empirical evidence. He concludes with the estimate, for the US, that private savings offset only roughly half the decline in government saving that results from a shift from taxes to deficit finance. Others find the empirical evidence somewhat more mixed. For a survey, see Elmendorf and Mankiw (Handbook of Macroeconomics, vol. 1C, 1999). The basic theoretical reason for not expecting Ricardian equivalence to hold is that the currently alive generations feel richer when there is a tax cut. Even if they rationally take into account that the taxes in the future will be higher (in order that the government can service the debt), the very fact that the higher taxes come in the future makes a difference. Some of us will be dead then. The currently alive know that future taxes partly will fall on future generations, whose interests the currently alive have not completely internalized. 2 Further aspects stressed by critics of the Ricardian equivalence hypothesis are: 1) Short-sightedness. Many people tend to be short-sighted and, therefore, do not respond to a tax cut by an increase in savings out of after-tax income. 2) Failure to leave bequests. Though the bequest motive is certainly of empirical importance, it is operative for only a fraction of the population (the wealthy families) and it need not have the form hypothesized by Barro. 3) Imperfections on credit markets. There are imperfections on the credit markets and those people who are credit rationed face a higher interest rate than that faced by the government. (However, there is also a counter argument to this, though probably not so important from an empirical point of view, see Romer, Advanced Macroeconomics, 2nd ed., 2001, p. 540). 4) The Keynesian view. Contrary to what the theory of Ricardian equivalence assumes, output and labour markets often do not clear (in the Walrasian sense), but are usually characterized by excess supply. Then, by stimulating the aggregate demand, government budget deficits may stimulate production and even investment. For example, if the economy is in a recession, a tax cut implying a budget deficit may stimulate both consumption and investment through a positive demand spiral: T ↓⇒ C ↑⇒ Y ↑⇒ I ↑⇒ K ↑. Thus, otherwise un-utilized resources are activated by a budget deficit. Instead of crowding out, there is crowding in. Sometimes this Keynesian view is claimed to be of relevance only for “the short run”. Other economists disagree and underline that “the long run is a succession of short runs”. One might add that in the real world taxes are not lump sum, but usually distortionary. But while this fact should, of course, always be kept in mind when discussing practical issues of fiscal policy, it is not an argument against the possible theoretical validity of the Ricardian equivalence proposition. This is so because Ricardian equivalence (in the proper sense of the word) refers to absence of real effects of deficit financing if taxes are lump sum. There is hardly disagreement that distortionary taxes and their timing may matter. To sum up, there are good reasons to believe that Ricardian equivalence fails. Of course, this could in some sense be said about nearly all theoretical abstractions. But Ricardian equivalence systematically fails in one direction: it over-estimates the offsetting reaction of private saving in response to budget deficits. The important issue is: how 3 important − empirically − are the departures from Ricardian equivalence? For differ- ing views about this, see “Symposium on the Budget Deficit” in Journal of Economic Perspectives, vol. 3, 1989. – 4