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EDUCATION, POLITICAL INSTABILITY, AND GROWTH
James A. Kahn
Federal Reserve Bank of New York
Research Paper No. 9737
December 1997
This paper is being circulated for purposes of discussion and comment.
The views expressed are those of the author and do not necessarily reflect those
of the Federal Reserve Bank ofNew York of the Federal Reserve System.
Single copies are available on request to:
Public Information Department
Federal Reserve Bank of New York
New York, NY 10045
Education, Political Instability, and Growth
James A. Kahn
*
First draft September 1996, this version September 1997
Abstract
Empirical evidence suggests a positive association between income
levels and growth rates on the one hand, and political stability and
educational attainment on the other. This paper develops a simple
finite-horizon overlapping growth model that in the absence of
institutions for precommitment has a political equilibrium with
inefficiently low growth, low educational attainment, and high returns to
schooling. In the model, the laissez-faire growth rate is inefficient due to
an intergenerational externality in the decision to accumulate knowledge.
We then contrast the efficient growth rate with the outcome when there is
a sequence of governments with an objective that reflects the preferences
of the individuals currently alive. The result is an equilibrium in which
growth remains inefficiently low because future agents are unable to
reward those currently alive to induce them to accumulate knowledge.
The ability to achieve higher efficient growth hinges on either the
government's ability to set policies that cannot be undone by subsequent
governments, or on an alternative "trigger strategy" equilibrium in which
each government believes it will be punished by the next if it deviates
from the optimal policy.
*Domestic Research, Federal Reserve Bank of New York, 33 Liberty St., New York, NY
10045, e-mail: james.kahn@ny.frb.org. Colleagues at the University of Rochester, and Mark
Bils in particular, made helpful suggestions. The views expressed are those of the authors and
do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve
System.
The wide dispersion in both levels and growth rates of per capita income
across countries has received a great deal of attention in recent years. Among
many facts that researchers have uncovered is the association between low levels
of educational attainment and high measured returns to schooling on the one
hand, and low levels and growth rates of income on the other. Another is that
low growth is associated with measures of political instability. One natural
question to ask, then, is whether the political instability and low educational
attainments (despite the high return to schooling) might be related.
This paper explores that idea in the context of a simple overlapping
generations endogenous growth model. In the model, the accumulation of
knowledge is the engine of growth, but there is an intergenerational externality
that causes the laissez-faire outcome to exhibit suboptimal growth. While a
planner with an infinite horizon will choose choose efficient educational
attainment and growth, the presence of such farsightedness seems incongruous in
a model in which the agents all have finite horizons. The government itself is
presumably composed of agents who themselves have finite horizons, and-more
importantly-whose decisions reflect the preferences of their constituents. Hence
the main contribution of the paper is to address the question of how a
government whose decision-makers reflect the finite horizons of their
constituents would choose policies that affect the accumulation of knowledge.
Specifically we assume that each government maximizes a weighted sum of
utilities of those currently alive. Policy decisions are modeled as the outcome of
a non-cooperative dynamic game: Each period the government selects a policy
that takes into account any effect on subsequent policy decisions (and hence on
the welfare of the current young generation). It turns out that this political
equilibrium generally exhibits inefficiently low growth, and for plausible
1
parameters is quantitatively significantly inferior to the Pareto optimum. 1
1. Growth, Education, and Political Stability
This section briefly examines evidence of a link between education policies and
political stability. The data for this exercise come from Barro and Lee (1994),
and cover a total of 138 countries over the period 1960-1990. The motivation for
looking at political stability is as follows: The model will distinguish between
policymakers with an infinite horizon and those with a short horizon. One of the
ways a farsighted policymaker could implement an efficient policy is to enact a
law that is difficult to undo. That will almost certainly be more difficult to do in
an environment of political instability. The measure of inst.ability we use is the
number of coups and/ or revolutions experienced (per year) by each country over
the period 1960-1984.
We also do not have direct measures of education policy. We consider three
different types of variables: Government expenditures on education as a fraction
of GDP (denoted GEXPSH), primary and secondary emollment rates, and
average years of schooling in the population over 25. The latter really measures
a stock rather than a flow, but the panel structure of the data enables us to, for
example, use this stock as of the end of the time period, as a function of what
has occurred in the country over the prior 25 years. On the other hand, only the
first really measures something like a government policy variable. Also,
GEXPSH to some extent controls for income effects because it is expressed in
terms of a share of GDP.
Table 1 displays the simple bivariate correlations between the educational
1 See,
for example, Persson and Svensson {1989), Persson, Persson, and Svenson (1987),
Cukierman and Meltzer {1989).
2
variables and the political instability. The emollment rate variable PSER is a
combined primary and secondary emollment rate, equal to 8x primary rate+
4 x secondary rate, and has the interpretation of number of years or primary
education (out of 12) the current school-age population is receiving on average.
The variable YS85 is average years of schooling in the over 25 population as of
1986. All three education variables are significantly negatively correlated with
political instability. Table 2 splits the sample into two groups: Those countries
with REVCOUP
= 0, and those with REVCOUP > 0. The conditional sample
means differ by economically meaningful amounts.
Of course these facts could be explained entirely by the fact that both
education and political stability are positively related to wealth or income. Even
government expenditure on education could have an income elasticity
significantly greater than one, which could account for the negative correlation
of GEXPSH and political stability. To explore this possibility, Table 3 reports
regression results of the education variabled on a constant, log(GDP) (where
GDP is averaged over 1960-1990), and REVCOUP. Similar results obtained
when REVCOUP was replaced with a dummy variable equal to one when
REVCOUP > 0, zero otherwise. Similar results also obtained for regressions run
separately for each time period in the sample (e.g. 1980-85 GEXPSH on 1980
log(GDP) and REVCOUP). Two sets of results are shown: Least squares
weighted by 1960 population, and ordinary least squares.
The differences between the weighted and unweighted results suggest that a
number of very small countries add a lot of noise to the OLS results, at least for
PSER and YS85. But overall the results point strongly to a negative impact of
political instability on educational attainment even after controlling for income
level. The interpretation of the WLS results, for example, is that a country
3
experiencing one coup or revolution per year (and there are such countries in the
Barro-Lee data set) would have government expenditures on education as a
share of GDP smaller by 2.1 percentage points (which is on the order of 50
percent of the mean!). The average years of schooling for the over age 25
population would be smaller by 2.7 years, and average primary-secondary
enrollments would be smaller by about 3.3 years.
An alternative explanation of these facts is that education is simply less
productive in poorer or less politically stable countries. Researchers have found,
however, that less developed countries have significantly higher returns to
schooling than developed countries (see Psacharopolous (1973)). 2 The
explanation offered in the model that follows is that the high returns in those
countries reflect endogenous policy decisions not to encourage human capital
accumulation to the same extent as in developed countries. Those decisions in
turn reflect a lack of incentive on the part each current generation to accumulate
human capital when the benefit falls primarily on subsequent generations,
together With the lack of stable political institutions that can achieve the desired
intergenerational cooperation.
2. The Model
This section presents a simple overlapping-generations model with endogenous
economic growth. Each generation (or "cohort") allocates time between labor
and the accumulation of knowledge when young, and consumes when both
young and old. Output is linear in effective labor and not storeable. Hence, as in
Samuelson's (1958) model, consumption of the old is zero in the absence of
2
Ljungqvist (1992) suggests a second-best insurance explanation for this stylized fact.
4
intergenerational transfers in their direction or of "money."
Knowledge is passed (at least to some degree) from one generation on to the
next. We assume only that a higher level of knowledge attained in one
generation makes it less costly for the next generation to attain the same level.
Thus the fact that the Wright brothers' generation discovered how to make
airplanes fly did not mean that the next generation was born with this
knowledge, only that it could attain that knowledge more easily, and without
fully rewarding their predecessors (hence the externality).
We assume that within each period knowledge accumulated by an individual
translates directly into his human capital, without any external spillovers. Hence
in what. follows we will speak of knowledge and human capital interchangeably.
There is, however, an intergenerational externalit.y, owing to the
nonexcludability of knowledge across generations. That is, the older generation
cannot sell its stock of knowledge to the young generation. In the model this is
simply assumed, but. even if it were technically possible to make the stock of
knowledge excludable, the young have nothing to offer the old in exchange for it.
Thus there are two reasons for intervention in this economy: To mitigate the
distortion in in the human capital market, and to keep the old from starving. 3
2.1. Laissez-Faire Growth
In this section the government's role is limited to making lump-sum
intergenerational transfers. Individuals live for two periods and are endowed
with one unit of time in their first period (when they are "young"). All
individuals within each cohort are identical. When young, they allocate their
3 Of
course in reality some knowledge is excludable. All that is required for the model is that
some knowledge not be inter-generationally excludable. Intra-generational excludability is just
a simplifying assumption.
5
time between labor and accumulation of knowledge. We will refer to the time
spent on accumulation as "schooling" , though a more apt interpretation is the
share of flexible resources (in this case time) that productive individuals allocate
to increasing their knowledge rather than producing. This could include
on-the-job training or time spent doing R&D.
The wage they earn for labor depends on their accumulated knowledge. The
government takes some lump-sum portion of their earnings and redistributes
them to the old. Taking the relevant sequence of redistributions into account
(with perfect foresight), each individual chooses
ft
to solve the problem
subject to
(2.1)
(2.2)
Czt+I
(2.3)
where
Wt
is the wage per unit of human capital, Ht is the individual's human
capital stock,
Ht
is the average human capital level of generation t, r, is the
lump-sum redistribution from young to old in period t per unit of fI, and
Ct E [0, 1] is the proportion of time allocated to labor. The remaining time 1 - £,
is allocated to human capital accumulation. We assume that g' :<:: 0, that
g(O) < oo, g(l) 2: 0, and that u' > 0, u" < 0. Since all individuals within a
cohort are assumed to be identical, we know that H, = H,, and the distinction is
between what is exogenous and endogenous to the individual.
6
The first order condition for the individual's maximization problem is
(2.4)
assuming an interior solution. Thus the individual simply chooses £, to
maximize his earnings w,R,,H,, given 2.1 and 2.3. The solution to 2.4-and
consequently the equilibrium growth rate-----is independent of
Output
f'I,_ 1 .
Yi. is produced from a linear production technology N,e,H,, where
N, is the number of individuals born in period t. We assume that
N, = N,_ 1 (l
+ n).
To keep the analysis interesting, we make one regularity
assumption on 9(£). First define
Al:
RLF
£LF
= argmax
Cg(£). Then we assume
< l.
The assumption that g(O) < oo already rules out £' = 0, so Al guarantees an
interior solution for 2.4
Equilibrium requires 2.1-2.4 and
(2.5)
or
(2.6)
where H,_ 1 is a state variables for period t. Since
l'.LF
is independent of the state
variables, we can fix g(€) and£ Vt. Consequently, H, c1, and c2 all grow at the
rate g( £) - 1. We shall see shortly, however, that the competitive outcome is
always Pareto inefficient.
7
2.2. A Planner's Problem
We first consider the solution of an infinitely lived social planner who discounts
the utility of generations at rate p. At time 1 he chooses a path {C1t, c2,, et}
4
from t
= 1 to
oo to solve the problem
subject to
(2.7)
and
(2.8)
given H 0 • and c21 . N, enters the objective for convenience, but does not affect
the analysis, since it just implies an effective discount factor of (1
+ n)/(1 + p).
Thus we will need to assume
A2: p > n.
Also, we will generally look for solutions under the assumption
A3: u(c)
c1-l/u /(1 - 1/a), if a f. 1
=
{ log(c) otherwise
We can set up the following Lagrangian:
£,
= I:~1(1 +
p)-t+ 1 (N,[u(c1t) + 1_;,,u(c2t+1)]+
>..,[H,N,e, - N,c1t - N,_1c2,]µt[Ht - H,_19(€,)])
4
+ (1 + p)u(c2t)
Equivalently, the planner could choose {r,, ft).
8
(2.9)
where At and µ, are multipliers associated with the two transition equations.
The first order conditions for the solution of the optimization problem in
{Ht,C1t,c2,,£,,>.,,µ,} given
B,_ 1 are
(2.10)
(2.11)
-µ,g 1(£,)H,_1
>.,N,H,
>.,N,£,
=
µ, - µt+1g(£1+1)/(l
(2.12)
+ p)
(2.13)
along with the two constraints 2. 7 and 2.8.
It is natural to conjecture given the structure of the problem that the choice
of£ will constant, so we will assume that and then verify it to be the case. First,
note 2.10 and 2.11 imply that the growth rates of C1t and
Czt
are the same, as
one would expect. So we have
(2.14)
We can get the levels of C1t and
Czt
directly from 2.7, 2.10, and 2.11:
From equation 2.12 and 2.14 we have µt+i/ µ,
9
= (1 + n)g(CJ- 1!~, which, after
some straightforward substitutions, yields:
1 + g'(C)C/g(C)
= (1 + n)g(C) 1 - 1/u /(1 + p).
(2.15)
which implicitly expresses the optimal C as a function of the parameters p, n,
and a. Alternatively, we can express this in terms of the intertemporal marginal
+ a)- 1 u'(c 2,+ 1 )/u'(c1t) = g- 1/u /(1 + p) which has
interpretation of an implicit real interest factor 1/(1 + r). We have
rate of substitution (1
1 + g'(C)C/g(e)
the
= (1 + n)g(C)/ (1 + r)
Either of these expressions determines the planner's choice of e, denoted
€'~which in turn determines the optimal growth rate g(f')~as a function of p
or the intertemporal marginal rate of substitution. It equates the marginal
foregone output from additional work to the discounted value of the resulting
increased output the following period, in utility terms.
We can compare 2.15 with the laissez-faire equilibrium condition implied
by 2.4, 1 + g'(eLF)CLF/g(CLF)
p
= oo,
= 0. The two conditions coincide only when
as one might expect. The optimal and laissez-faire growth rates also
coincide when a, the intertemporal elasticity of substitution, is zero. Except for
such extreme cases, however, we have C* < CLF, which means that the optimal
growth rate generally exceeds the equilibrium growth rate for any p < oo.
The remainder of the paper will drop the assumption that governments
necessarily implement efficiency, and replace it with an assumption that
governments have the same time horizon as their constituents, and act
sequentially and in an uncoordinated fashion to maximize their welfare.
10
3. Political Economy
The normative implications of the model for government policy are
straight.forward, as we have seen. In particular, with the ability to make
lump-sum transfers between individuals, government policy can in principle
attain any point on the Pareto frontier. As a positive matter as well it would
seem that a rational government ought to be interested in efficiency, regardless
of how it chooses to split the rents. When distortions arise from the fact that
individuals have finite horizons, however, it is less obvious that. governments
composed of such individuals will necessarily opt for efficiency. First, it might be
necessary that. those currently alive collectively appropriate the full gains froin
increased efficiency, or else they will lack the incentive to pursue it. Second, the
gains must. be distributed among those alive in accordance with the
government's preferences. Otherwise the government could face a tradeoff
between efficiency and the distribution of wealth.
In this part of the paper the political system is assumed each period to
maximize a weighted sum of the utilities of those currently alive, taking into
account the fact that the same decision process will take place in the next
period, and that the choice today will in principle influence next period's choice
through its influence on the state variables of the economy. 5 Thus political
choice is depicted as a dynamic Stackelberg game between governments at
different time periods. We assume that the political system chooses C and the
size and direction of intergenerational transfers.
In general the inability to coordinate with subsequent governments gives rise
to inefficiency in the steady state. It turns out that the government improves
5 Majority
voting would not be very interesting in this context with only two types of agents.
11
upon the competitive equilibrium, but does not achieve Pareto efficiency. There
exists a steady state policy that would make everyone better off by increasing
growth (at the expense of current output) and decreasing transfers to the old.
That policy is not selected, however, because each government cannot coordinate
with subsequent governments to carry out the transfer that results in the Pareto
improvement. In equilibrium some of the gains from growth spill over to those
not yet alive. Consequently governments opt for inefficiently low growth.
The model economy is the same as in Section 1. The political system at
time t is assumed to choose
Tt
and
0
Max --u(c2t)
e,,r, 1 + a
to solve
Ct
+ (1 -
0)[u(c1t)
1
+ --u(c2t+i)]
1 +a
(P2)
given fI,_ 1 , given 2.1-2.3 and 2.5, and knowing that at t + 1 the same decision
process will determine Ct+ 1 and
Ti+i .
6
Thus it follows that the political decision
at t would take into account any effect it might have on all future political
decisions, since the decision at t
+l
takes into account its effect on t
+ 2,
and so
forth. The parameter 0 represents a welfare weight on the old relative to the
young that is assumed for simplicity to be constant from one period to the next.
The result is a decision for (Tt, Ct) = rt that in general could depend directly
only on
Ht-I
and next period's decision
(T1+1 ,C,+1)
= r,+ 1 (Ht; ... ).
Consequently
we have rt(fft_ 1 ; rt+ 1 (fI,;rt+2(Ht+1; ... ), ... )). Note, however, that the
homothetic structure of the model ensures that the policy choice will in fact be
independent of ff. Moreover, we will limit attention to symmetric equilibria in
which
T
and P are the same in all time periods. As a result, finding the solution
6
Although some types of intergenerational altruism in which agents effectively have an infinite horizon-such as in Barro (1974)-would make this problem completely uninteresting, the
results that follow are not sensitive to the inclusion of a conventional bequest motive.
12
will involve merely solving for a single number rather than for an entire
function. 7
The question is whether this political system, with its finite horizon, will
choose an efficient solution. It will turn out that the political equilibrium is
characterized by underaccumulation of knowledge. That is, the growth rate is
too low relative to the size of intergenerational transfers. The intuition behind
this result. is that although starting from the equilibrium it would be possible to
lower f; and more than compensate the current young for their sacrifice with
additional consumption the next period, there is no way for the political system
to bring about the compensation. Consequently, although the equilibrium with
the short.sighted political system is an improvement over laissez-faire, the
non-cooperative nature of the system leads to inefficiency relative to a system
that binds current and future policy to the cooperative or efficient solution.
If we again deflate by f'l,_ 1, the resource constraint facing the government
at time tis:
(3.1)
Consequently we have
(3.2)
(3.3)
Assuming perfect foresight, and taking as given the policies (Tt+J, €,+1), the
7 Kahn-Lim (1996) solve the model with both physical and human capital, in which the
equilibrium policies are state-dependent. In that case finding the equilibrium involves solving
for functions rather than numbers.
13
current government would solve the problem
0
Max - -u(Tt(l + n)g(C1)) + (1- 0)[u(g(f1)[ft
lt ,Tt 1 + Qt
])+
- T1
(P3)
The first-order condition from differentiation with respect to Tt (given fl,) yields
the equilibrium policy directly as a function of e,:
0(1 + n)u'(T,(l + n)g(£,)) = (1 - 0)(1 + a)u'(g(t\)[£, - T,])
(3.4)
For the CES preferences given by assumption A3 this implies
(3.5)
where~=
[(l!~~~~e)r.
As for £1 , we have the first-order condition
(3.6)
Making these substitutions yields
(3.7)
14
Hence the equilibrium policy Re is characterized by
(3.8)
Recall that the optimal policy can be expressed as
l+g'(R')R'/g(R*) = (l+n) u'(c21+1) (£*).
1+ a
u'(c1t) g
The ratio of the right-hand side of 3.8 to that of 3.9 is
be less than one for any P such that ig'(P,)IPt/.9(£1)
:','.
(3.9)
(l~~~'g;eJ.), which has to
1, which is to say for any
£ :','. £u·. Consequently the sacrifice of current output for growth is smaller
(relative to the intertemporal marginal rate of substitution) for the equilibrium
policy than under the efficient policy, which means that. growth is inefficiently
low. 8
If the governments could fix for all time (r, P) policies that satisfied 3.9,
everyone could be better off: There exists a cooperative policy that would lead
to a higher growth rate without any sacrifice in utility by any generation. The
fact that 1 + g'(P)P/g(P) is smaller in equilibrium than under the efficient policy
implies that a marginal sacrifice of current output for growth would yield more
than enough gains in the next period to compensate the current young (who
would then be old), while leaving the next and all future generations no worse
off. The problem is that the next government will not make that compensation.
The equilibrium policy fails to internalize the benefits of human capital
It may be possible to find, given some value for p and the corresponding efficient growth rate,
some value for 0 that produces the same or higher growth rate with a much higher marginal rate
of substitution. But conditioning on the MRS is the natural way to evaluate the growth rate,
especially since in a more realistic model (e.g. Kahn-Lim, 1996) the MRS would be constrained
by technology or by world capital markets.
8
15
accumulation. Consequently although the equilibrium
eis smaller than under
laissez-faire (since the equilibrium policy does internalize some of the benefits),
it is still too large.
The problem here is somewhat subtler than might first appear. In moving
away from the laissez-faire outcome by reducing f! below f!LF, current output is
reduced. For given values of current
T
and future (r, f!), the current young are
harmed and the current old benefit. Thus a Pareto improvement among those
currently alive requires a transfer from old to young (or, rather, a smaller
transfer from young to old). The political equilibrium can accomplish this. But
what it cannot. accomplish is a further reduction in £ that could make both old
and young better off provided next period's policies were similarly altered. In
other words, the movement from the political equilibrium to the efficient
equilibrium requires redistribution from the next generation's young (in the form
of choosing lower f!) to the current young when the latter become old. Unless
that can be guaranteed, the current generation is unwilling to invest any further
in accumulating knowledge beyond what the political equilibrium implies.
3.1. The Returns to Schooling
As mentioned earlier, researchers have found that returns to schooling are higher
in poorer, low-growth countries. It is straightforward to see that in this model
the return to schooling is also higher in the political equilibrium than in the
efficient allocation. The usual definition of the return to schooling is the
derivative of the log of earnings on years of school. In the model, earnings are
H,f!, = fl,_ 1 g(€,)€,. "Schooling" would correspond to 1 schooling R, is
16
e, and the return to
This is increasing in£ over the relevant range (i.e. 0 < £ :<:: fu•), which implies
that R would be higher in the political equilibrium (and higher still under
laissez-faire) than under the efficient allocation.
Of course in practice there would have to be exogenous variation in £ across
individuals within a country to produce actual estimates of return to schooling,
whereas we have assumed that individuals are identical and all choose the same
£. The point here is that the evidence suggests that there is underinvestment in
schooling in low-ineome/low-growth countries, as contrasted with just
endogenously low investment because of a lower payoff, and that is what the
model implies as well. 9
3.2. Some Numerical Results
Results were computed for a variety of parameter settings with little qualitative
variation in the outcomes. Figure 1 plots the equilibrium and efficient
annualized growth rates (assuming a 30-year generation), assuming the marginal
= 1,
and v = 2. Note that having n = 0.3
rate of substitution from the political equilibrium, for the parameters a
a= n
= 0.3, and with g(R.) = 2(1 -
cv)lfv,
corresponds to approximately 1 percent population growth for a 30-year
generation. Also note that for each value 0 there is a corresponding value of
p
from the planner's problem that can be backed out from the marginal rate of
substitution. Values of 0 near 1 correspond to very large values of p, which
explains why there is little difference between the political equilibrium and the
optimum. For values of 0 sufficiently low, the corresponding value of p falls
9 Note that in the model the return actually equals zero for the laissez-faire choice off, and
is negative for f, and f'. This is simply because the private decision problem for f is essentially
static, and there is no direct cost of schooling. It would be easy to modify the model to generate
positive returns.
17
below n and consequently the planner's problem has no solution.
The main finding is that the for moderate values of 0 and
p
the equilibrium
growth rate falls substantially short of the efficient growth rate given any
marginal rate of substitution. In fact, except for very large values of p and very
small values of 0, the political equilibrium growth rate is globally smaller than
the efficient growth rate, i.e. smaller than any efficient growth rate,10 For the
above parameters, the laissez-faire equilibrium annual growth rate (again
assuming a 30-year generation) is 1.16 percent, the equilibrium growth rate
hovers at about 1.4-1.5 percent, while the efficient rate ranges as high as 2.34
percent. For 0 = 0.6 (which corresponds top= 0.62), for example, the efficient
growth rate is 2.04 percent, while the political equilibrium growth rate is 1.40
percent. Going in the other direction, the 0 corresponding to p = 0.4 is 0.578.
For that value the equilibrium growth rate is 1.41 percent, while the efficient
growth rate is 2.22 percent. For 0 < 0.567 the marginal rate of substitution
implies p < 0.3, so no efficient growth rate is shown.
Thus the political equilibrium, despite involving a planner who is assumed
to maximize the welfare of those currently alive, achieves a modest improvement
over the laissez-faire outcome, but is still substantially below the efficient
growth rate for reasonable welfare weights. In a more general model where there
is a state variable such as a physical capital stock, each generation could in
principle exert some influence on subsequent policy decisions through the state
variables of the economy. It turns out, however (see Kahn and Lim,1996) that
this generalization-while greatly complicating the analysis-does not alter the
results. The basic outline of this model is provided in the Appendix, along with
10 1n
the figure, the smallest value of p for which the efficient growth rate is below the highest
equilibrium growth rate is 2 (i.e. 1/(1 + p) = 0.33).
18
numerical results depicted in Figure 2.
3.3. Trigger Strategy Equilibria
As an alternative to the Markovian equilibrium, we can consider the possibility
of a more efficient "trigger strategy" equilibrium. Specifically, suppose the
period t planner believes that if he chooses an efficient policy, the period t
+l
planner will also choose an efficient policy, whereas if he chooses any inefficient
policy, the t
+l
planner will revert to the Markovian equilibrium. There will
clearly exist a trigger strategy equilibrium that is efficient. For any suboptimal
allocation there must. by definition exist. an allocation that. yields a higher value
of the planner's objective. Since planner t believes he can count on planner t + l
carrying on the efficient allocation, and further that if he deviates, planner t
+l
will revert to the Markov equilibrium (in which case the best possible deviation
would also be the Markov equilibrium), the beliefs of planner t will sustain the
efficient equilibrium. Of course, once we allow for this equilibrium, it must be
noted that there are undoubtedly infinitely many such equilibria, some of which
may be efficient and some of which may be not. But this equilibrum does
provide an alternative interpretation of the data: The more successful countries
•
are either playing a different game (one in which the planner effectively has an
infinite horizon) or they are simply in a better equilibrium of the same game.
4. Discussion and Conclusions
This paper has developed a model of non-cooperative sequential government
decision-making in a finite-horizon setting, and applied it to a simple
endogenous growth model. The approach yields explicit policy outcomes in
19
equilibrium, and we suspect that it could be useful for a variety of policy
questions beyond those addressed here. Each government's objective mirrors the
objectives of the individuals currently alive. Attention has been focused on
Markovian solutions, i.e. those in which policies only depend on the state of the
economy, as a possible explanation for why low-growth economies appear to be
underinvesting in knowledge accumulation. There are, of course,
trigger-strategy equilibria that achieve optimal growth. Thus the observation of
relatively successful economies could be interpreted within the general
framework of this paper as either "good" trigger-strategy equilibria or as
economies that somehow managed to set up durable institutions that implement
efficient. policies. 11 The main finding is that in the Markovian equilibrium
governments will choose policies that involve systematic underinvestment in
"schooling" (or more generally in the accumulation of knowledge). A Pareto
improvement involving higher growth would be possible if governments could set
up stable institutions that would guarantee the current young that their sacrifice
today will definitely get rewarded when they are old with a comparable sacrifice
by the next generation.
11 See,
for example, Kotlikoff, Persson, and Svensson (1988).
20
Appendix : The Model with Physical Capital
Each individual solves the problem
subject to
(Al)
(A2)
where the only difference is the wage per efficiency unit of labor Wt, and the
interest rate
rt+ 1 .
Output is produced from a constant returns to scale
production technology F(Kt, NtftHt), Defining kt
= Ktf (NtftHt), and
J(kt) = F(kt, 1), profit maximization implies
(A3)
and
f(kt) - ktf'(kt)
= Wt,
(A4)
The government is again assumed to solve P2, but now kt is a state variable, and
the government's choice of r and C will not only depend on kt, but it will also
affect kt+i, which will in turn affect the next government's choice of r and C.
These spillover effects matter to the current government because the current
young will still be alive in t + 1. As one would expect, the direct effect of a
21
transfer from young to old is normally to decrease the saving of the young (i.e.
dkt+i/dTt < 0), while the effect of increased time working relative to
accumulating knowledge is to increase saving (i.e. dkt+i/dft > 0).
Let 1 + 'Yt+1 - (1
+ n)g(£1+1)
and q,
= 9 (£,)/9(€,).
1
The first-order
conditions for turn out to be (see Kahn-Lim (1996) for details):
(A5)
and
+ n)u1 (C2t)[(l + q,ft)kt(l + J'(kt)) + Ttq,] =
(1- 0)u'(c2t+1){(l + J'(k1+1))[-(l + qtft)Ut - k,f'(kt)) + Ttq,]1
(1 + 'Yt+l) [qt7t+l + d~~-;- (71+1qt+1~::: + £t+1kt+d"(k,+1) + ~~:::)]}
0(1
where the various derivatives such as
(A6)
d~[,' 1 can be derived from the individual's
maximization problem. Given k, and 71+i(kt+1) and £1+1(kt+ 1), we can solve for
the optimal 7t and£,. An equilibrium is a pair of policy functions T(k), £(k)
such that if Tt+1 = 7(k1+1) and £,+1
= £(kt+ 1),
then the Tt and ft values that
satisfy (A5) and (A6), given that k1+1 comes from the consumer's maximization
problem, are 7(k,) and £(k,).
Kahn and Lim (1996) use numerical methods to compute equilibrium policy
functions. Figure 2 provides a diagram of laissez-faire, equilibrium, and efficient
growth rates as a function of 0 for comparison to Figure 1 in this paper.
22
References
[l] Azariadis, C. and A. Drazen, "Threshold Externalities in Economic
Development," Quarterly Journal of Economics 105 (1990), 501-526.
[2] Barro, R., "Are Government Bonds Net Wealth?" Journal of Political
Economy 82 (1974).
[3] Barro, R., and J.-W. Lee, "Data Set for a Panel of 138 Countries," mimeo,
1994.
[4] Cukierman, A. and A. Meltzer, "A Political Theory of Government Debt.
and Deficits in a Neo-Ricardian Framework," American Economic Review
79 (1989), 713-732.
[5] Kahn, J. and J.-S. Lim, "Finite Horizons, Political Economy, and Growth,"
Rochester Center for Economic Research Working Paper No. 433, October
1996.
[6] Kotlikoff, L., T. Persson, and L. Svensson, "Social Contract as Assets: A
Possible Solution to the Time Consistency Problem," American Economic
Review 78 (1988), 662-667.
[7] Lucas, R., "On the Mechanics of Economic Development," Journal of
Monetary Economics 22 (1988), 3-42.
[8] Ljungqvist, L., "Economic Development, Wage Structure and Implicit
Insurance on Human Capital," University of Wisconsin-Madison, mimeo,
1992.
23
[9] Persson, M., T. Persson, and L. Svensson, "Time-Consistency of Fiscal and
Monetary Policy," Econometrica 55 (1987), 1419~1432.
[10] Persson, T. and L. Svensson, "Why a Stubborn Conservative \\/ould Run a
Deficit: Policy with Time-Inconsistent Preferences," Quarterly Journal of
Economics 104 ( 1989), 325-346.
[11] Persson, T. and G. Tabellini, "Politico-Economic Equilibrium Growth,"
mimeo, 1990.
[12] Psacharopolous, G., Returns to Education: An International Comparison,
San Francisco: Elsevier (1973).
[13] Samuelson, P., "An Exact Consumption Loan Model of Interest with or
without the Social Contrivance of Money," Journal of Political Economy 66
(1958), 1002-1011.
[14] Uzawa, H., "Optimal Technical Change in an Aggregative Model of
Economic Growth," International Economic Review 6 (1965), 18-31.
24
Table 1: Correlations between Education Variables and Political
Instability
PSER
YS85
-0.339 -0.336
GEXPSH
-0.337
Table 2: Sample Means Conditional on REVCOUP
PSER YS85
GEXPSH(%)
REVCOUP > 0
6.993
4.290
3.370
REVCOUP = 0
9.925
7.723
4.789
25
Table 3: Education Variable Cross-Section Regression Results Table
3a: WLS Results
PSER
YS85
GEXPSH
log(GDP)
REVCOUP
R2
#obs
1.384
-3.275
0.996
98
(0.050)
(0.544)
2.549
-2.720
0.971
98
(0.091)
(1.052)
0.0090
-0.021
0.983
89
(0.0004)
(0.005)
Table 3b: OLS Results
PSER
YS85
GEXPSH
log(GDP)
REVCOUP
R2
#obs
2.302
-0.388
0.738
98
(0.149)
(0.589)
2.455
-1.102
0.759
98
(0.154)
(0.607)
0.0066
-0.013
0.321
89
(0.0014)
(0.005)
26
Figure 1: Equilibrium versus Efficient Growth Rates
p
00
0.3
~ r---r--...---...---...---....--.,..--...---.,..--....--.,..----',--,--,--,--,--,--,---.-,--,
N
N
N
0
N
co I
Efficient '
\
\
~Utic
al
Equlllbrlwn
~r- - - - - - - - - -
::~
----
N
f
-----
-
--::
~
I
Lalssez--Falre
__;;>\
0
~
0.0
0. 1
0.2
0.3
0.4
0.5
(}
0.6
0.7
0.8
0.9
1.0
Figure 2: Equlllbrlum versus Efficient Growth Rates, Model with Capital
--q-
Nr---,---,.---,----,---.----,c----.---.----,---..-----,--....,.---,---..---.----,
\
\
N
N
\
\
0
\
N
\
co
~
co
~
Efficient,
\"f
Polltlcal
Equilibrium
f
"' """
-q~
'--..
-....._
...._
N
~
.
Laissez-Faire
0
~
.
.. .
. . . . . . .
.
.
. . . .
.
. .
..
. . . . . .
..
. . . .
..
.. .. . .
___:;,i
-----~-------~-------....._
__ __.____.___ _
0.1
,__
0.2
0.3
0.5
0.4
0
,__
0.6
0.7
_._
. .
.
. . .
__ _____._
0.8
0.9
FEDERAL RESERVE BANK OF NEW YORK
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1997
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9703. Antzoulatos, Angelos. "On the Determinants and Resilience of Bond Flows to LDCs,
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from Foreign Exchange Options and Historical Data." September 1997.
9731. Jayaratne, Jith, and Don Morgan. "Information Problems and Deposit Constraints at
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9732. Steindel, Charles. "Measuring Economic Activity and Economic Welfare: What Are We
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9733. Campbell, John, and Sydney Ludvigson. "Elasticities of Substitution in Real Business
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9734. Harrigan, James. "Cross-Country Comparisons oflndustry Total Factor Productivity:
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9735. McConnell, Margaret, and Gabriel Perez Quiros. "Output Fluctuations in the United
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