Download Exact answer to B.6, question e) and f)

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.
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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
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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.
–
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