Growth, Political Instability, and the Defense Burden

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 436

October 1992

GROWTH, POLITICAL INSTABILITY, AND THE DEFENSE BURDEN

Stephen Brock Blomberg

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.

Abstract

This paper develops a model to examine the economic effects of political instability and military expenditure. In the model, “kleptocracies” use defense as “imperfect” insurance against the probability of being overthrown. Increasing defense has a secondary effect of augmenting the human capital stock (a spin-off effect). However, defense investment comes at the expense of consuming scarce resources (a crowding out effect). The paper’s central contribution is to model each of these effects and their relationship to one another. The resulting theory predicts that the equilibrium is Pareto inefficient and that increased political instability and increased defense can inhibit economic growth. Empirically, increases in political instability are found to decrease growth while increases in defense are found to decrease political instability. The paper also finds that increases in defense have a direct negative effect on growth, although the relation is weak. The weak relation implies the aforementioned crowding

out effect is largely mitigated by the spin-off effect.

Growth, Political Instability & Defense 1 Growth, f TO

Growth, Political Instability, and the Defense Burden

Stephen Brock Blomberg!

1 Introduction

The problem of lagging productivity in many countries has led to a reexamination of traditional theories of economic growth. As Seers points out, “The major inadequacies of conventional economics. . . are that the analysis focuses on the wrong factors, and the models do not fit at all closely to the way in which nonindustrial economies operate”.? In response to this characterization of conventional economics, this paper focuses on two factors rarely examined yet extremely important for growth-defense

and political instability.

Worldwide military expenditure topped the $ 1 trillion mark for the first time in 1987. This means worldwide military spending was greater than the entire Gross National Product (GNP) of Latin America and the combined GNP of Africa and the Middle East.* Worldwide political instability has also been pervasive in the recent past.* From 1950-82, insurrecting parties attempted to overthrow their governments

roughly every 8 years, with about one half of those attempts being successful.> Figure

‘The author is a student intern in the Division of International Finance. This paper represents the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System of other members of its staff. I have benefited greatly from discussions with Joseph Harrington, Gregory Hess, Louis Maccini, and Athanasios Orphanides. Special thanks also to P.K. Asea, Lisa Blomberg, Jon Faust, Rumana Khan, David Zervos and the participants of the Johns Hopkins and Federal Reserve Board seminars for their valuable comments. In addition, I thank William Carrington and Martin Gaynor for helpful discussions related to the empirical aspects of the paper and Holger Wolf & Phillip Swagel for providing me with the data sets used in the paper. All remaining errors are of course my responsibility.

Quote attributed to Seers in Belassa (1990), p I-2.

See World Military Expenditure and Arms Transfers, (1990).

*Political instability is defined throughout the paper as any irregular executive transfer of power. The figures are actually understated. Calculations were made by treating any year with at least one year as being one coup in that year.

See Londregan & Poole (1980).

Growth, Political Instability & Defense 2

A.1in the appendix emphasizes the importance of political instability, geographically. Countries in the sample that have experienced at least one coup from 1960-85 are highlighted. Note that 51 of 118 countries in the sample have experienced some form of political instability with the highest concentration being located in South America and Africa. Despite these facts, little attention has been given to analyzing

the economic effects of political instability and defense.

The research that has analyzed the relationship between defense, political instability, and growth has not yet coalesced. There are several lines of literature which have investigated the relationship between growth & political instability or defense & growth; however, there is no unifying theory which simultaneously relates growth, political instability and defense. One of the major goals of this paper is to “bridge” the gap in the literature by incorporating aspects from each of the theories into one school of thought.

The paper presents a brief overview of the literature with a schematic diagram provided in the appendix to aide in the exposition. The first line of research has been primarily concerned with analyzing the relationship between defense and growth. Originally, Benoit (1973) provided support for the view that increased military expenditure yields greater growth.® The result that defense enhances productivity is explained by assuming military spending is the conduit through which human capital, infrastructure, and discipline, etc. develop in society. However, an alternative hypothesis is that a country’s growing military burden (military spending as a percentage of GNP) crowds out investment and creates a large tax liability for future generations.’ Most recently, Chowdhury (1991), in his study of 55 developing countries, showed that either hypothesis can be true depending on the particular economy being investigated. The ambiguity in the results stems from the fact that this line of research has not considered the intimate relationship between defense, growth and

political instability.

The more recent lines of research do introduce political instability into the analy-

©The results were later corroborated by Benoit (1978), Kennedy (1974), and Whynes (1979) among others.

"For research supporting this hypothesis see Smith (1977, 1978, 1980b), Deger & Smith (1983), Deger & Sen (1983), and Leontief & Dutchin (1983) among others.

Growth, Political Instability & Defense 3

sis but focus largely on its partial relationship to defense or to growth. For example, Hess and Orphanides (1991) develop a model to analyze the relationship between defense and political instability. In their paper, they give the conditions necessary for an elected official to start an unnecessary war to increase his probability of reelection. But, their analysis concentrates largely on the political aspects involved without considering how political instability affects growth. Others, such as Alesina et al (1991) and Londregan & Poole (1990,1991a,b), have investigated the empirical relationship between political instability and growth but fail to link the relationship to defense. Grossman (1991) does link political events to economic activities in his positive theory of insurrections, but fails to provide a readily testable hypothesis. This paper unifies these approaches by examining how defense and political instability affect economic factors such as savings, investment, and economic growth, both

theoretically and empirically.

As a preliminary exercise, to help sort out the relationship between the relevant political and economic variables and establish the importance of the form of government, the paper provides data indexed by government.® Table 1 illustrates some differences in military spending and political instability between democratic and nondemocratic states. Notice that regardless of how it is defined (i.e. number of coups or

revolutions) political instability is significantly higher in the non-democratic states.

Table 1: Political and Economic Factors?

M/CDP

2.8% 2.97% 1.6% 2.99%

t1960-a5 Average Military Expenditures (M), Gross Domestic Product (GDP), Per Capita Growth (Growth), Coups (Coup) and Revolutions (Revolutions) Per Million. Source: Barro (1991) and author's calculations.

Type of Government

Democracies

Non-Democratic States

The correlation coefficients of the variables in question are reported in Table 2 and Table 3. It is important to note that the relationships between the variables differ dramatically in democracies as compared to dictatorships. Per capita growth,

8Countries are classified as non-democratic or democratic depending their classification in Alesina et al (1991) and Jodice & Taylor (1983) over the majority of years 1960-82.

Growth, Political Instability & Defense

Table 2: Correlation Coefficients For Democracies!

Const] Changes Govt Crises M/GDP

| Coups

| RevCoups Growth

Constl Ch. «ges

Govt Crises

1.000 —0.013

1.000

—0.055 0.265 1.000

0.771 0.100 0.029 1.000

RevCoup

ee t1 960-85 Average Military Expenditures (M), Gross Domestic Product (GDP), Per Capita Growth (Growth), Constitutional Changes (Constl Changes), Coups (Coups), Government Crises (Govt Crises) and Revolutions + Coups (RevCoups) Per Million. Source: Barro (1991) and

author's calculations.

Table 3: Correlation Coefficients For Non-Democratic States!

| Constl Changes Govt Crises M/GDP

Coups RevCoups Growth

Constl Changes | Govt Crises

1.000 0.067

1.000

0.029 —0.102

1.000

0.535 —0.192 1.000

Coups | RevCoup 0.461 0.371

Growth

0.629 —0.151 0.860 1.000

—0.128 —0.198

tigeo-a5 Average Military Expenditures (M), Gross Domestic Product (GDP), Per Capita Growth (Growth), Constitutional Changes (Conatl Changes), Coups (Coups), Government Crises (Govt Crises) and Revolutions + Coups (RevCoups) Per Million. Source: Barro (1991) and

author’s calculations.

Growth, Political Instability & Defense 5

coups and defense spending as a percentage of GDP are all positively correlated for

democracies but are negatively correlated for authoritarian governments.®

Given the preliminary results, the paper develops a theory for non-democratic

states.!°

The paper assumes that the role of defense in an authoritarian regime is threefold. First, there is an insurance effect. Intuitively, the military protects a dictator against being overthrown because of the military’s inherent ability and interest in defending her. Second, there is a crowding out effect. Obviously, purchasing this insurance comes at some cost to society. The cost is measured by the amount of resources “crowded out” by defense. Finally, there is a spin-off effect. Following early research by Benoit inter alia, the paper assumes time spent in the military makes the labor force better educated and disciplined. This labor augmenting effect makes the economy more productive. The purpose of the paper is to sort out which effects are

greater and how they relate to political instability and growth.

The paper finds empirical support for the view that increased political instability inhibits growth and increased military expenditure decreases political instability. The paper also finds that the defense burden decreases growth but not significantly. The weak relation implies the aforementioned crowding out effect is largely mitigated by the spin-off effect. None of these results are sensitive to the specification of the

empirical model.

Section 2 of the paper describes the model in detail to include technology, endowments, preferences and scarcity. Section 3 provides the solution to the optimization problem and the various results derived. These results are tested in section 4. Finally,

section 5 sums up the paper and concludes with suggestions for future research.

°Note, that one cannot reject the null hypothesis that coups & defense and growth & defense are uncorrelated at any conventional level in democracies. However, in non-democratic states, growth & coups and defense & coups are significant at the .1 level. Defense & growth are significant at the .2 level. .

10The theory may be robust to democratic regimes, however, the model is better specified to

analyze the non-democratic case.

Growth, Political Instability & Defense 6

2 The Basic Model

The model presented here is an endogenous growth model of an economy with “political” preferences. The basic technology follows work by Lucas (1988) and Barro (1990). The political aspects of the model are related to work done by Nordhaus (1989) and Hess & Orphanides (1991), while preferences are a synthesis of Uzawa’s (1968) and Blanchard’s formulations (1985). Definitions of the notation are provided

in the appendix for the reader’s convenience.

2.1 Technology and Endowments

Consider an economy comprised of N identical households and an authoritarian government. Households employ physical capital, K,, and the quality adjusted labor force, Q,, to produce output, Q;, while the government provides for the common “defense”, G;.11 Defense is used by the government to insure itself from insurrections.

This point is discussed at length in Section 2.4.

Formally, the relationship between output and the factors of production are given by (1). a Qe = F(R, Qs) = AKE OF (1)

where A is a measure of the embodiment of capital into output. For simplicity, there

is assumed to be no physical depreciation of capital which implies that Q, is gross

rather than net output.!?

By introducing defense into the economy, the government also enhances output. To formally define the effect of defense on output, assume that the sum of total

defense investment, Jf, directly increases the quality of the labor force by making

‘Defense is a human capital augmenting consumption good. It is eaten by the government but augments human capital over time. The assumption that defense has both consumption and investment characteristics is made in response to empirical studies which suggest that both factors are necessary to explain the heterogeneous patterns across countries.

12The assumption will not effect the analysis if the depreciation rate is assumed to grow

exponentially.

Growth, Political Instability & Defense 7

it better educated, more disciplined, and better managed. Therefore the following relation holds:

$ | ' [Sdy = 6, (2)

where fj I,du is equal to the aggregate defense stock to date, G;, and ¢ measures the

amount that defense augments human capital. Substituting (2) into (1) yields:

Qt = F( Ki, Gt) = 6 AKE G2. (3)

Notice, the effect of defense, G;, on output comes through a spin-off effect on Q:.3 The assumption is made to support the belief that military expenditures foster

growth in developing countries.!*

Using the government budget restraint, G; = TQ;, rewrite (3) as (4).!5

Qe= F(K,) = pt Amalr (aK, (4)

Since the labor force is assumed to be constant, the analysis can be further sim-

plified by normalizing N to unity. Thus, the relationship in per capita terms is ae = I (ke) = GA Ta) (oa) (5) where lower case letters denote per capita values of these variables.

Finally, the economy is endowed with some initial physical capital which it uses to begin production, that is k, > 0.

13Historical studies, such as Rosenberg (1985) and Trebilcock (1969), show how military technology has stimulated productivity in various civilian industries. However, such an assumption is not

necessary for growth to be endogenous, only that production is linear in capital. 4See Benoit (1973), (1978), Kennedy (1974), and Whynes (1979) for support of such an

assumption. 15The government is assumed to finance defense contemporaneously by a flat rate income tax,

G, = TQ, so the government budget is balanced at every moment. Alternatively, one could assume

taxes are lump sum or that the government floats debt without changing the general results.

Growth, Political Instability & Defense 8

2.2 Preferences

Individuals’ welfare at time 0 is the present discounted value of the sum of their felicity functions, u(.). The function, u(.), is a continuously differentiable, increasing, concave function of c, per capita consumption. Individuals’ discount the present relative to the future by a constant sul, -ctive rate of time preference, 8, which is assumed to be strictly positive. The government derives utility by pleasing her constituency and from economic rents received while in power, 2;. Hence, her instantaneous felicity, v

P]

is a convex combination of individual welfare and personal welfare, w(z,).'®

u(ce, te) = (1 — p)u(ce) + pw(ze) (6)

The parameter p measures the selfishness of the dictator.!” In the limit, as p > 0, the dictator is concerning only with consumer welfare. In contrast, as p — 1, the

dictator cares only for herself.

2.3 Scarcity

After tax output net of rents is either consumed or invested. Investment takes the

form of accumulated physical capital. Formally, the dynamic budget constraint is?®

However, the constraint, in itself, is not sufficient to bind the economy. In order to

impose restrictions on borrowing, the following no-Ponzi-game condition must hold: t lim ke7 J (rst+7,)ds =Q. t—00

The condition is necessary to prevent the economy from borrowing indefinitely.

16For simplicity, assume w(.) is also a continuously concave increasing function of rents, z:. 17Since v is a positive linear transformation of u, it is also a continuously concave increasing

function of c;.

18The analysis is easily extended to allow for exogenous external aggression. For example, assume foreign countries take some percentage of output, vQ:, and that percentage depends on defense insurance. Since, the general qualitative results are not sensitive to such a specification, such an assumption is not made.

Growth, Political Instability & Defense 9 ee ee SSE ee

To close the model, substitute (5) into (7) to yield k= A* ke —Ce— Xe (8)

where A* = $%(1 — 7) Alia) (G2a),

2.4 Political Preferences

Assumption 1 Dictators face some instantaneous probability of being overthrown

because of their particular form of government.

To ensure that she remains in power, the government must consider the possibility that she could be ousted with probability 7, at any time. The probability is independent of the dictator’s age.’9 It can take any value between 0 and infinity because 7 is given as per unit time. Therefore, define a random variable, Z, as the “time until

death”, given by the following density function:

fe — ne ™ where EoZ = [ tre dt 0

and 7~ is an index of the dictator’s effective horizon. In the special case where 7 = 0, the dictator lives forever.” This is the only source of uncertainty considered in the

model.

Since individuals’ are assumed to discount the present relative to the future exponentially, the effect of including the probability of death in the problem is to increase the discount rate by 7.”) Hence, the dictator’s “political” rate of time preference is the sum of the subjective rate of time preference and the probability of death.

19This assumption allows the analysis to be tractable. However, considering the regularity in which dictators are overthrown in LDC’s, the assumption is not terribly restrictive. 20Dictators can alternatively be thought of as families of dictators, e.g. the Kim dynasty in South

Korea; the Duvallier dynasty in Haiti and Nicaragua. 21See Cass and Yaari (1967), for proof of the result.

Growth, Political Instability & Defense 10

Assumption 2 Defense provides “imperfect” insurance against the probability of be-

ing overthrown.

Unfortunately for the dictator, explicit insurance against the probability of being overthrown cannot be purchased.?* However, the dictator does provide imperfect “insurance” for herself through military production.?3 To incorporate this into the model, 7 is assumed to be a function of defense as a percentage of output, a: The motivation for the assumption is as follows: if the dictator produces a large amount of defense, she deters her rivals from attacking and increases her chances of remaining in power. Hence, her probability of death declines. It is necessary to deflate q by q& to show the extent to which an economy’s resources are devoted to defense insurance. The specification is important when testing the model. The formulation allows the model’s empirical results to be compared to earlier studies which regress economic growth on the defense burden, (#).?4 Formally, define the relation between 7 and a

Qt in the following way:?°

n=1(T)=6—£6r (9)

where the parameter § measures how effective defense is as an insurance against the probability of death. Political unrest, 6, measures the public level of dissatisfaction with the polity. A formal definition for 6, is difficult without reference to the empirical

results. Section 4.2 devotes itself to a more rigorous treatment of how 6 is measured.

22This differs from Blanchard (1985), where insurance companies insure agents against the probability of death.

?3Defense insurance is “imperfect” because it does not fully insure a dictator from being overthrown. This market imperfection is necessary as otherwise 7 = 0.

24There is also a technical consideration for the assumption. If 7 were a function of g; rather than the defense burden, 7 would no longer be stationary since it would depend on a variable which grows over time.

5 Alternatively, one could allow 7 to be quadratic in a without changing any of the general results in the paper. Motivation for such a specification would be supported by the preliminary data analysis in Table A.1 provided in the appendix.

Growth, Political Instability & Defense 11

3 Intertemporal Optimization

To analyze growth issues, felicity is assumed to be of the Constant Relative Risk Aversion variety (CRRA). The dictator chooses ¢, z:,k;,7 subject to the resource

constraint. The optimization problem is

rad

+ pw(ar)Je7 +9)" dt

max Eo f ((1 - p)

{ct,r¢,k+,7} l-o

s.t. k, given k= A* ky — Ce— Le

where o is the parameter which measures the intertemporal elasticity of substitution/relative risk aversion parameter. Notice, if the central planner is benevolent, p = 0, and the economy is politically stable, 7 = 0, the model collapses to the standard case with linear technology and CRRA utility.

For the more general case, optimality implies:”°

(1 — p)ul(ce) = (1 — pee? = At (10) pw'(xe) =r (11)

Mtn 46)— a (12)

lim Apkye~ +") = 0 (13)

At = wr, (14)

26See the mathematical appendix for the derivation.

Growth, Political Instability & Defense 12

where A* = $* Ata rina (20-7) —1]j,w =, anda, =—8.

r(1—a) 1

The relationship between the control and co-state variables are described by equation’s (10) and (11). If p = 0, the usual relation between marginal utility and the co-state variable holds, ie. c°’ = 7 = X. Equation (12) yields the growth path of the co-state variable. If ~* < (7 +6), the co-state variable grows overtime and

vice-versa.

Combining equation’s (10) and (11) yields

=? (15)

Equation (15) defines the ratio of the marginal utility of consumption to rents to be directly proportional to the selfishness of the dictator. The dictator trades off social welfare with her own welfare-the tradeoff being higher the higher her degree of

selfishness.

Equation (14) relates the marginal productivity of defense (i.e. At) to the marginal propensity to insure (i.e. 7,). To understand (14), one must first sort out the three individual effects of defense on productivity; (7) the spin-off effect: (it) the crowding out effect; and (22) the insurance effect. First, consider the spin-off effect. By assumption, any increase in defense increases the quality of the labor force. The extent to which this increase in labor quality spins off to production is seen in the amount of human capital employed in production, a. Hence, countries with a higher a gain

more from increases in defense than countries with a lower a, ceteris paribus.

Second, there is a crowding out effect. As the dictator allocates more output to defense, she devotes less to everything else. This effect is captured by the rate at

which defense is extracted from output, T.

Finally, there is an insurance effect which is captured by —@. This effect is alternatively thought of as the marginal propensity to insure (MPI). When the military insurance is high (high @), the dictator buys time in office through the discretionary use of force. In this case, increases in defense decrease the probability of being over-

thrown (i.e. m, < 0.).

Growth, Political Instability & Defense 13 EE SO Can Atastabity Oo Mertens

Consider how these effects interact with one another. If the crowding out effect is greater than the spin-off effect, the marginal product of defense (MPD) is negative. Conversely, if the spin-off effect is greater than the crowding out effect, the MPD is positive. From equation (14), notice the sign of the MPD fundamentally depends on preferences. When oc > 1, it must be true that the MPD is positive, given that the MPI is negative. Similarly, when o < 1, the MPD is negative. Hence, the equilibrium has the powerful implication that preferences ultimately decide the productivity of defense.

To analyze the implications derived from the equilibrium, first consider how the

degree of “kleptocracy” affects consumption.

Proposition 1 Dictators who are more selfish provide for less private consumption

or value additional capital less.

Proof:

From equation (10), optimality implies for any economy i = A, B

(1—p')(ch)"? =; or 1 — p* = Ai(ct)”

Let economy A be more selfish than B, i.e. p4 > p?. Ceteris paribus, this implies

1—p4<1-)%

or Aen)” < AP (ce)? Hence, AB > dB or

B A CG > cy.

Growth, Political Instability & Defense 14 ca cc a a

Logarithmically differentiating (10) with respect to time and combining (12) yields

Ct oO

Yeo=

(16)

where 7. is the growth rate of consumption. To ensure growth rates are positive and a solution exists, A* > 8+ 7 > A*(1 —c).?” Rewrite equation (16) as

A*=70+64 7. (17)

Notice, from equation (17), in the long run, the return to investment (the left hand side) equals the return to consumption (the right hand side). The return to consumption is greater than in the modified golden rule case because the dictator receives a

growth premium (oy) in addition to her political rate of time preference, (0 + 7).?8

Now that the growth rate of consumption has been defined, the next task is to define the growth rate of capital. Divide the budget constraint by the capital labor ratio to reveal ;

wegead (18) where 7% is the growth rate of capital and c* is aggregate consumption.”? Logarithmically differentiating equation (18) implies growth rates for capital and consumption

are equivalent given that +, is constant in the steady state.

Finally, by log differentiating equation (5), the growth rate of output is also shown to be equivalent to that of consumption and capital. Therefore, the results from a “politically” influenced program are that the rate of growth is identical, constant and

positive across all relevant macroeconomic variables.

Now that the relevant growth rates have been defined, consider the welfare impli-

cations derived from the model.

?7See the mathematical appendix for an explanation.

28The modified golden rule states that the steady state marginal product of capital is equal to the subjective rate of time preference. The powerful implication is that the productivity of capital is ultimately preference dependent.

?° Aggregate consumption is the sum of private consumption and the dictator’s consumption.

Growth, Political Instability & Defense 15

Proposition 2 An economy with “political preferences” is Pareto inefficient.

Define the private return to capital, A*, as r. In equilibrium, r > 8 + cy since m > 0. Therefore, the “growth-adjusted” modified golden rule (i.e. r = 6 + oy) does

not hold which implies the equilibrium is not pareto optimal.?°

In order to see why the equilibrium is pareto inefficient, notice that the interest rate in the economy, r = 6+ 7 + 07, is greater than the pareto optimal interest rate, r* = 6+ 07. High interest rates are assumed to stifle growth. The result is driven by the assumption made on government behavior. Because dictators are uncertain with regards to their probability of “death”, they behave differently than representative households. The government realizes its lifetime is finite and so it discounts the future by a greater amount. The increase in impatience implies an inefficient equilibrium

characterized by generations that invest less for the future.

In addition to consumer welfare, there are other areas affected by “political”

uncertainty. One such area is economic growth.

Proposition 3 An increase in the level of “political” unrest, 6, decreases the rate of

growth in an economy.

Recall from equation (9), = 6—{r. Substitute this into equation (16) and the new

reduced form equation for growth is

A*—60—6+6Fr y= - (19) o Therefore, 4 = i(2Atde _ onde _ 1) = 1/4*(1 — 1) — 1]. The sign of 2 is negative given that A* < 0. Intuitively, increases in political unrest decrease growth as long

as the resulting increase in defense does not greatly increase productivity.

30See Sala-i-Martin (1990b) for a detailed explanation.

Growth, Political Instability & Defense 16 eee OE ee

Proposition 4 An increase in the level of “political” instability, , due to an increase

the level of political unrest, 5, decreases the rate of growth in an economy.

oy > Ox

Recall from equation (16) = Side <Q),

6 dx 06

= —4. Since 7 is increasing in 6 (see equation 9), com

While the presence of political uncertainty has unfortunate welfare and growth implications, the use of defense by itself can actually stimulate economic growth. Before explaining how this can be so, to aide in the exposition, the paper defines certain conditions under which the economy may operate. It is necessary to define these conditions because the three effects of defense on technology and preferences

(i.e. crowding out, spin-off and insurance effects) may be offsetting.

The first condition characterizes a situation where the marginal propensity to

insure is negligible and the marginal product of defense is negative.

Case 1 The insurance effect is arbitrarily small (i.e. B = 0) and the crowding out effect is greater than the spin-off effect.

The second condition characterizes a situation where the marginal product of

defense is positive. Case 2 The spin-off effect is greater than the crowding out effect.

Proposition 5 An increase in the defense burden, r, decreases the rate of growth in

Case 1 but increases the rate of growth in Case 2.

Substitute equation (9) into equation (19) to yield A*(r)—0—6—Br , _ A) 6 2) a o° Atta psa a(l—r _

re If Case 1 < 0. However, if Case 2 holds, the

where A*(r) = 49(1 — r)A™3[r] 2, Note, 2 holds, then 6 = 0 and 7 > @ which implies =

sign inside [.] is positive causing 2% > 0.

Growth, Political Instability & Defense 17

The intuition behind the result is straight forward. If increasing defense sufficiently increases the quality of the labor force or makes the dictator behave prudently enough to mitigate the crowding out effect, productivity increases. If it does not, productivity declines. Such a result explains why the effect of defense on growth cannot be arbitrarily signed.

This illuminates one of the crucial aspects of the paper. It is not necessarily military expenditure that stifles growth per se; it is the political uncertainty usually associated with defense that harms productivity. Hence, previous research (see introduction) which solely examined the relationship between defense and growth has focused on the wrong factors. By empirically testing the correlation between defense and growth without considering political instability, researchers have left an important issue unexplored. A central contribution of this paper is to better define the

relationship between political instability, military expenditure, and growth.

4 Testing the Model

There are three results derived in the paper that are tested. Namely, one tests whether (z) Political unrest, 6, hinders economic growth; (Proposition 3) (22) Political instability, 7, is associated with low economic growth; (Proposition 4) and (272) defense spending as a percentage of GDP, tt, is used to buffer political instability and hinders economic growth; (Proposition 5). To test these implications, parameter estimates for the relevant political and economic variables are examined in the empirical coun-

terparts of the growth and political instability equations [i.e. equations’ (16), (9)}.

4.1 Methodology and Data

As pointed out by Levine & Renelt (1992), cross-country growth regressions are extremely sensitive to the explanatory variables chosen in estimation. Therefore, the paper adopts a comprehensive approach by defining political and economic variables

in a variety of ways using a variety of data sets and specifications. The data sets

Growth, Political Instability & Defense 18

are taken from Barro (1991), Alesina et al (1991) and WMEAT (1991). The Barro data set selects data from a cross-section of 118 countries and provides time series averages for political and economic variables over the period 1960-85. The Alesina et al data set combines both cross-sectional and time-series data for 119 countries over the period 1950-82. WMEAT reports defense data for 144 countries over years 1967-90. For the purposes of the study, the paper selects a subsample of 69 countries defined to exhibit the characteristics described in the paper.*! All of the political and economic variables but defense as a percentage of GDP come from the Alesina et al data set. The “defense burden” data comes from WMEAT. The Barro data set is primarily used for the preliminary analysis described in the introduction. The individual data is collected from a variety of sources including Banks (1979), Gastil (1987), IMF Government and International Financial Statistics, Summers & Heston (1991), ILO, SIPRI and UNESCO Statistical Yearbooks, and the World Bank World Tables.

The methodology to test the model is fairly straight forward. Recall from section 3 that the model puts forth three predictions relating political instability, defense and growth.

Prediction 1 An increase in the level of “political” instability decreases the rate of

growth in an economy.

Prediction 2 The effect of the defense burden on growth is positive, negative, or neutral depending on the magnitude of the spin-off, crowding-out and insurance effects.

Prediction 3 An increase in the level of “political” unrest increases the level of po-

litical instability.

In order to test these predictions, the empirical counterparts of the growth and political instability equations [i.e. equations’ (16), (9)] are estimated.*? 31The countries are chosen because they are classified as non-democratic in Alesina ez al (1991)

and Jodice & Taylor (1983) over the majority of years 1967-82. 321t is also possible to estimate a three equation system, where the third equation relates variables

Growth, Political Instability & Defense 19 Oe = EE NTISU QD UY OC MCTENSC

; 5 Vit = Ao + a, Zit + OX it + Ss; ajZiit + agt yy + Ex (21) at j=3 Git 3 6 Tit = Bot am + > BrXorit + > BeZoie + Brvit + €% (22) wt A=? k=4

where a,,§; are constants, X is an identifying vector of variables, Z is a vector of exogenous variables, and € are errors whose variance-covariance matrix allow for crossequation correlations. The subscript 7 denotes country and the subscript t denotes time. The specification differs from Benoit inter alia because it allows Tit to enter into the problem and differs from Alesina inter alia because it introduces ** into the

problem. The null hypotheses are as follows: Ho, : ag > 0. If ag > 0, political instability is associated with higher not lower economic growth. Ho. : ay = 0. If a, = 0, the defense burden does not directly affect economic growth. Ho3 : Bi = 0. If 6, > 0, a higher defense burden increases political instability. Hoa: Ba < 0. If Bn < 0, increases in political unrest decrease political instability.* The model predicts the null hypotheses Ho1, Ho3, Hoa will be rejected. For sim-

plicity, the paper specifies Ho2 as such since the effect of defense on growth cannot be arbitrarily signed.

converge using maximum likelihood estimation. Furthermore, while estimating the system using three stage least squares does yield consistent estimates of the parameters, the variance-covariance

matrix is not efficient which implies low confidence for hypothesis testing. Hence, the paper analyzes Jit—h qit—h

the two equation system, but tests for the exogenity of reo Ok using Granger Causality tests.

Results from the test imply that political instability and growth do not “Granger-cause” defense. 32The identifying vector of variables, X21, in the political instability equation is political unrest, 6. This point is made in the following subsection.

Growth, Political Instability & Defense 20 4.2. Empirical Results

This section begins by discussing the different definitions employed in the empirical estimation. Political unrest, 6, is measured both through observed discontent with the polity and through standard of living measures.3? Unfortunately, 6 is an unobservable phenomenon despite its real consequences. It is possible, though, to observe the effects caused by political unrest. For example, if a society is unhappy with its polity, one expects that the dictator may “shake-up” her government by changing its composition. Therefore, executive adjustments may serve as a proxy for political unrest. To incorporate this into the empirical model, the paper considers a variety of definitions for 6 which include executive adjustments and economic growth (i.e. a proxy for reduced standard of living). In this way, 6 encompasses both political and

economic factors that are fundamental to political instability.

There is also ample empirical support for such a specification. Table 4 summarizes previous research which shows that economic growth and executive adjustments significantly impact political instability. Column one in Table 4 reports each of the explanatory variables used in previous research. Column’s 2 & 3 report the findings of Londregan & Poole while column 4 reports the findings of Alesina et al. Note that none of the authors have included the defense burden in the analysis which may imply a misspecification of the empirical model. Both groups of authors find that growth significantly inhibits the probability of a coup. This is seen by examining the sign and significance of the growth coefficient in each column. In each case, the coefficient is properly signed and significant at the .01 level. Alesina et al also show that lagged executive adjustments are a determinant of political instability. In this case, the coefficient on lagged executive adjustments is also properly signed and significant at all conventional levels. Hence, there is both empirical and theoretical support for specifying 6 as executive adjustments and reduced standard of living measures. An additional implication from this specification is that it identifies the political insta-

bility equation.

To identify the growth equation, the paper includes a measure of human capital

°°See Londregan & Poole (1990,1991a,b) for a detailed explanation of why decreased standard of living measures increase the probability of a coup.

Growth, Political Instability & Defense

21

Table 4: Previous Joint Estimation of Growth and Political Instabilityt

Authors Dependent Variable

L & P (1990) Growth Coups

Growth

Coups

Intercept

Recent Coups

Past Coups

Africa

Europe & North America

Latin America

Middle East

Lagged Income

Lagged Growth

Lagged Coups

Lagged Executive Adj

Lagged World Growth Human Capital

——_———}——

0.067*** 0.830*

0.189*** . 0.035 —0.017*** — 0.184 0.012*** — 0.052 —0.006* 0.533*** —0.359*** — 0.006*** —1.097 0.148***

Growth

. — 9.703***

0.077***

—0.023*** 0.011*** —0.008*** —0.003 —0.007*** 0.159***

L & P (1991a)

Coups

0.851* 0.171***

0.055*** — 0.246* — 0.290

0.376***

0.147 — 0.356***

A,O,R, & S (1991)

Growth Coups — 45.047***

—0.006***

—0.007*

— 1.530***

—0.009 — 0.239

—0.006** 0.100

0.118 4.465 0.559 0.227** 0.418*** 19.600***

0.009*

t source: Londregan & Poole (1990,1991a) and Alesina et al (1991). The data is in an annualised panel format where regions (e.g. Africa) are dummies, Lagged World Growth is the log weighted average of per capita growth for the G-7 countries lagged one period and Human Capital is primary school enrollment. “=significant at the .1 level, ““=significant at the .0B level, ***=significant at the .01 level.

Growth, Political Instability & Defense 22 eer SS ee eee

in equation (21). The motivation for the specification is both theoretical and empirical. The theoretical support comes from section 2, where output is assumed to depend on human capital. The empirical support comes from previous research done by Alesina et al (1991) and Barro (1991) among others. These results are reported in Table 5. Column one lists the various explanatory variables included in the regressions. The columns numbered (1) to (5) refer to various specifications which restrict certain variables to be zero. Note that the economic variables that are important to growth across each specification include initial Gross Domestic Product (GDP60), initial human capital measures (Prim60), and government consumption (Gov). Any of these measures would seem appropriate to identify the growth equation. However, including Gov is somewhat redundant since defense is also included in the regression. Furthermore, since the emphasis of the paper is not to examine the “convergence” hypothesis, there is little theoretical support for including GDP60 in the regression. The only consistently significant explanatory variable that remains is human capital. Therefore, the paper identifies the model by including annual primary school

enrollment in the growth equation.

The paper also includes regional dummies for Africa and Latin America (Dum africa DumtatAmer) and lagged world growth in each equation. The inclusion of such dummy variables is supported by Lipset (1959), Londregan & Poole (1990,1991a,b) and Alesina et al (1991) who show that certain political and economic shocks are idiosyncratic to specific regions of the world. Lagged world growth is included to capture the idea of a “world business cycle”. In this case, the equation for growth is

Vit = A +Q, 7 + adie + a3Durma frica + A4DuMtatamer + O57”, + ast + eh. (23)

and the equation for political instability is

Tit = Bo+ Br + Brbezadi + Brbgrouth + B4Duma frica +65Dumtatamer + Bere +e}, (24) wt

where the subscript 1 = exadj, growth indicates which measure of 6; 1s chosen.

Initially, other instruments were included in preliminary estimation of (24) but were excluded from the final estimation because the other instruments failed to improve the log likelihood of the model. For example, both recent and lagged coups

were included in the regression. In each case, one fails to reject the null hypothesis

Growth, Political Instability & Defense

Table 5: Cross Section Regressions on Growth! Dependent Variable: Average Per Capita Growth 1960-85

Explanatory Variables Constant GDP60 Sec60 Prim60 Gov PPI60DEV Latin Africa RevCoup AssAss Instability Maj Instability

Democracy

Adjusted R? LN

thog per capita GDP (GDP60), 1960 secondary school enrollment rate, Average of the real government consumption net of defense and educat tor (PPI60DEV), Dummy for Latin America (Latin), Dummy for Africa (RevCoup), Average number of assassinations (AssAss), Average

(1) 0.035*** —0.007***

0.011 0.026*** —0.100*** —0.014*** —0.014*** —0.012*** —0.016***

—0.002

0.58

23

Q | @ | @ 0.066*** 0.062*** 0.031*** —0.001*** | —0.006*** | —0.006*** 0.015* 0.014* 0.010 0.031*** 0.028*** 0.030*** —0.093*** | —0.101*** | —0.083*** —0.017*** | —0.013*** | —0.018*** —0.021*** | —0.019*** | —0.016*** —0.024*** | —0.021*** | —0.011** ~—0.014** —0.112*** | —0.090**

0.58

0.60

—0.001 0.55

@)_| 0.054*** —0.006*** 0.015*

0.028*** —0.090*** —0.014** —0.001 —0.010**

—0.026**

0.57

*=aignificant at the .1 level, *“=significant at the .06 level, ***=significant at the .01 level.

(Sec60), 1960 primary school enrollment rate (Prim60), 1960-85 ion to GDP (GOV), Mean Deviation of PPP investment defla- (Africa), Average number of Revolutions + Coups per million Probability of government change per country ( probability of major government change per country (Maj Instability), Dummy variable for democracy, (the highe democratic), (Democracy) Source: Barro (1991), (1), and Alesina et al (1991) {(2), (3), (4), (5)).

Instability), Average r the number the less

Growth, Political Instability & Defense 24 a

that either variable matters separately or together. The values of the likelihood ratio

test statistic are insignificant at any reasonable level.34

4.2.1 Joint Reduced Form Estimation

As a baseline, the paper estimates the reduced form equations for political instability and growth. For a formal derivation of the econometric framework employed, see the appendix.*° The growth and the political instability equations are estimated by joint maximum likelihood and their results are reported in Table 6. Column one in Table 6 lists the explanatory variables in the regression. The second column reports the results for the growth equation while the third column reports the results for the

coup equation.

The results in Table 6 show that the African and Latin American experiences are not identical. Both African and Latin American countries experienced low growth relative to the other countries in the sample. The p-values associated with the coefficients are .002 for Africa and .012 for Latin America which imply statistically insignificance at most conventional levels. However, Latin American countries are more politically unstable as seen by the positive coefficient for the Latin American dummy in the coup equation. The coefficient for the African dummy is negative and significant in the coup equation. This implies that, on average, African countries are more stable than other non-democratic countries. These results are not terribly

surprising considering they duplicate the work of Londregan & Poole and Alesina et al. (See Table 4.)

Next, the paper examines Prediction 2-the effect of defense on growth. The parameter estimate of defense as a percentage of GDP is negative and significant which is not surprising considering what was found in the preliminary analysis in Table 3. One interpretation of the result is that the crowding out effect is greater than the spin-off effect in these economies. But, before accepting such an interpretation,

34]t should also be noted that one rejects the hypothesis that lagged executive adjustments do not matter at all conventional levels.

°5The appendix is an abridged version of Londregan & Poole’s appendix (1990). For a more formal description see Londregan & Poole (1990).

Growth, Political Instability & Defense 25

Table 6: Joint MLE of the Reduced Form Equations!

9: ~ Vit = Atay te +o2gieta3 Dumratamer +04 Duma fricat Os Yy" 1 +07bezadj—-1t+O8beradj—2 +E} it

Tit = Bo+ 8, 2

‘ +B2 Sexadj—1 +B3 bexadj— 2 +64Dumyatamer +B Dum africa + Ber. 1 +Badit +e? t

Dependent Variable Vit Tit

intercept 0.0150 ~—1.0392°**

t

Human Capital 0.0001** | —0.0075*** git —0.0013* —0.0048

dit Ex Adjy_y Ex Adje_2 Dumyatamer Duma frica | Yea

Covariatice

—0.0006 —0.0007 —0.0218*** —0.0210°* | —0.0781°° 0.4032%°* | 0.3084. p = —0.3018°** (.0585)

& = 0.0839"**

(.0032)

t1967-82 annual growth rates (7;;), number of coups (~), military spending as

0.0776*** —0.0618*** 0.3535°**

Parameters

& percentage of GDP ( Hit), primary school enrollment (Human Capital, Git) executive adjustments (Ex Adj), and the log weighted average of per capita growth for the G-7 countries lagged one period (vey ) for the 69 country sample. (Standard errors are in parentheses.) Source: WMEAT (1991) and Alesina et al. (1991)

“=significant at the .1 level, **=significant at the .05 level, ***=significant at the .01 level.

Growth, Political Instability & Defense 26

one must consider the simultaneity problems involved in reduced form estimation.

The paper next examines the effect of variables on political instability. Since 7 is a discrete variable, the political instability equation, (9), is estimated using PROBIT. To examine the effect of political unrest on political instability, the paper chooses a linear combination of executive adjustments and reduced economic growth as proxies for 6. The results support the conjectures made in the theoretical portion of the text.

In each case, the coefficient of political unrest is significant and properly signed.

More importantly, the coefficient on ae is properly signed in the coup equation. This may lead one to conclude that the model is empirically supported. But, before accepting such an interpretation, consider the technical problems associated with estimating the model in this manner. First, there is a fundamental problem if the error terms in the two equations are correlated. In that case, the dependent variables, 7, and +;, cannot be treated as predetermined. Failure to account for this joint endogeneity results in biased parameter estimates. Notice, in this case, the correlation coefficient is -0.3018 with a standard error of 0.0585 implying significance at the .99 significance level. (See Table 6) Hence, more advanced techniques, such as simultaneous equations systems, must be employed. Second, there may be a technically spurious problem. Since 7, and oe are negatively correlated with each other, (9), separating their individual effects on growth cannot be done without considering a

more complex system of equations.

4.2.2 Simultaneous Equations Estimation

The methodology to estimate the structural model [equations’ (23) and (24)] follows Alesina e¢ al (1991) and Londregan & Poole (1990, 1991a). Therefore, rather than concentrate on the technical complexities, the paper refers the reader to the appendix and the other authors for a detailed explanation. In summary, the structural parameters are extracted from the reduced form by employing GLS. Newey (1987) showed that such a procedure is asymptotically equivalent to maximum likelihood estimation

but more tractable.

The model’s predictions are tested using simultaneous equations methods and

Growth, Political Instability & Defense 27 a cc Ac

are reported in Table 7. Column one lists the explanatory variables in the system. Column two lists the values of the coefficients in the growth equation and column three lists the values of the coefficients in the coup equation. The results found in

Table 6 generally carry through to the simultaneous equations estimation.

Prediction 1 states that increased political instability decreases the rate of growth in an economy. The null hypothesis associated with the prediction implies that, in the growth equation, the coefficient on coups should be non-negative. Table 7 shows that such a hypothesis is indeed rejected. The coefficient is negative and significant at the .01 level. Hence, Prediction 1 holds—political instability hinders growth as was previously shown by Alesina et al (1991).

Prediction 2 describes the effect of defense on growth and political instability. First, examine the effect of defense on growth. Recall that the effect of defense on growth is positive, negative or neutral depending on the magnitude of the crowding out and spin-off effects. The null hypothesis I choose for simplicity implies, in the growth equation, the coefficient on defense should be zero. The null hypothesis is not rejected. Such a result confirms the paper’s conjecture that the true variable anathema to growth is political instability and not defense.

Second, examine the effect of defense on political instability. The effect of defense on political instability should be negative given Table 3 and the theory. The null hypothesis implies the coefficient of defense in the coup equation should be positive. The data rejects the hypothesis. The coefficient of defense in the growth equation is not only negative but is associated with a p-value of .0005. Hence, there is empirical

evidence to support Predictions’ 1 and 2.

Prediction 3 states that political unrest decreases the rate of growth in an economy. The prediction means that decreased growth and increased executive adjustments should both increase the probability of a coup. The null hypothesis associated with the conjecture implies that, in the coup equation, the coefficient on growth should be nonnegative and the coefficient on executive adjustments should be nonpositive. Table 7 provides results to reject the null in favor of the paper’s predictions. However, in the case of lagged executive adjustments, the coefficient is not terribly

significant. The ¢ statistic associated with one period lagged executive adjustments

Growth, Political Instability & Defense 28 eee Eee eee

Table 7: Simultaneous Equations Estimation!

dit ~ w 1 Vit = Ao + 8 Oe + Arde + a3Dum rat Amer + a4Duma frica + as Ve-1 + AgMit + ett at

Tit = Bot hi * + B2beradj—~1+f3eradj—-2+B4Dumtat Amer +BsDum a fricat PoVe 1 +BrVie te 2. it

Dependent Variable Vit Tet intercept 0.0072 —0.4173 (0.0085) (0.2784) Human Capital 0.0001 (0.0001) . a —0.0013 —0.0595*** (0.0011) (0.0173) Dum tatamer —0.0189 —0.5652 (0.2743) (7.3098) Dum 4 frica —0.0216*** —0.9451*** (0.0065) (0.2893) Ex Adji_1 0.0522 (0.0437) Ex Adji_2 —0.0991 . (1.7707) Ve 4 0.4062*** 17.0005*** (0.1267) (5.3880) Wit —0.0075*** (0.0007) . —41.1887*** (10.5606) x? test of one overidentifying restriction

1967-82 annual growth rates (+,,), number of coups (7;,), military spending asa percentage of GDP (Bt), primary school enrollment (Human Capital, diz), executive adjustments (Ex Adj) and the log weighted average of per capita growth for the G-7 countries lagged one period (v1) for the 69 country sample. (Standard Errors are in Parentheses). Source: WMEAT (1991) and Alesina et al (1991). “=significant at the .1 level, “*=significant at the .05 level, **“=significant at the .01 level.

Growth, Political Instability & Defense Lot 29

is 1.193.

In addition, the paper does not reject the model at better than a .4 ‘significance level, using the x? test of one over-identifying restriction. While, one would be more comfortable with a higher p value, such a value is not too shabby given what has been previously reported. Furthermore, to underscore the importance of defense in the analysis, the paper excluded defense altogether and found the p value plummets to .009.

In summary, Predictions 1, 2 and 3 are empirically supported by the data. Defense provides insurance against political instability and political instability inhibits growth. The crowding out effect is found to be greater than the spin-off effect, but not significantly so. Therefore, the overall effect of defense on growth is positive and

the effect the political instability on growth is negative. 4.2.3 Sensitivity Analysis

Following Levine and Renelt (1992), the paper studies how sensitive the results are to alternative sample periods and the inclusion of other explanatory variables. Specifically, the paper reexamines the coefficient estimates under the assumption that economic and political decisions in non-democratic countries depend on different information. If the significance or sign of the relevant coefficients in section 4.2.2 are sensitive to the information set, one would consider such results “fragile.” The task

of this section is to see if the results in section 4.2.2 are fragile.

To incorporate this into the framework, the paper tests for sensitivity in three different ways. First, the paper reconsiders the basic model with a different set of explanatory variables. Second, the paper examines the model over different time periods. Third, the paper examines the model excluding certain countries that might

bias the results.

In the first case, the paper includes all lagged coups instead of executive adjust-

ments as additional explanatory variables in the coup equation. The new system

Growth, Political Instability & Defense 30 es eee

is t

Git ~ 1 Vit = Co + On — + O2git + A3Dumpatamer + C4DuMafrica + as ye, + a6 + Es tt

Tit = Bothy , +B 26coup-1t+836coup-2+64 Dum ,atAmer +9sDuma frica + Bo Ye_1 +Bryit +e? it

The sensitivity analysis works in the following way: the system of equations are reestimated. Then, the relevant coefficients, (e.g. ag, G,) are examined. If the coefficients remain the same sign and significant, then the results in the previous

section are robust.

The results from estimating the alternative model are reported in Table A.2 in the appendix and support the earlier conjectures. Replacing executive adjustments with coups does not harm the sign or significance of the relevant variables. Political instability in the growth equation is still significant at all conventional levels and defense is still significant in the coup equation at the .05 level. Hence, Prediction’s 1, 2 and 3 are robust to this alternative specification. However, the fit of the model

does appear to be a bit worse as the p value for over identifying restriction falls to

004.

In the second case, one finds similar results to support the model. Table A.3 reports the results over different time samples. Column one reports the results from 1970-82, while column two reports results from 1972-82.3° In each case, high political instability is significantly associated with low growth and low growth with high political instability. In addition, defense significantly decreases the probability of a coup but has no significant effect on growth.

In the third case, the paper excludes countries who actively engaged in external conflicts over the sample period. The rationale is as follows: the predictions in the paper are predicated on the assumption that defense exists primarily as a deterrent to internal rather than external aggression. However, it is possible that the level of defense could be more closely associated with wars rather than coups. In response to the criticism, the paper excludes all countries in the sample that were directly

ee °°The model was estimated over a broader range of samples with the general results remaining unchanged. For simplicity, only these two samples are reported.

Growth, Political Instability & Defense . __ — a 31

involved in an external conflict during the sample period. The results are reported in Table A.4 in the appendix. As in the other cases, the general results are not sensitive to this specification. However, in this case, defense is significantly negative in the growth equation. Hence, the MPD seems to be negative when controlling for‘external aggression.

4.2.4 Summary of Empirical Findings

The empirical results confirm the conjectures made in the model. Increases in political instability are found to decrease growth and increases in defense are found to decrease political instability. Any positive “spin-off” effect from defense spending is largely offset by the crowding out effect, leaving a weak direct relation between growth and

defense. These results are robust to alternative specifications and information sets.

5 Conclusions

When a dictator uses defense as insurance against the probability of being overthrown, the economy does not operate pareto efficiently. Both consumption and investment decisions are made inefficiently because the uncertainty associated with the probability of death causes the economy to move away from the growth-adjusted modified

golden rule levels of consumption and capital stock.

In addition, it is shown that political instability also effects growth. Higher levels of political instability mean lower growth rates for an economy. If a dictator insures herself against political instability by increasing the defense burden, some of this

effect is mitigated.

The empirical evidence also supports the hypotheses that political instability reduces growth and defense is used as an insurance against political instability. These findings are robust to alternative empirical specifications. Such results imply previous research which failed to incorporate both political instability and defense may have

left an important issue unresolved.

Growth, Political Instability & Defense gg Appendix A Appendix A.1 . Notational Definitions

Uppercase letters = actual values; Lowercase letters = per capita values A, A* = measurement of technologies Gig= defense E(.) = mathematical expectations operator F(.), F(.), f() = private production function f. =marginal density function of the time until death K,k = physical capital stock N = labor force Q,q = private output Q,¢= human capital stock r = “risk-free” interest rate u(.),v(.), w(.) = instantaneous “felicity” functions U(.) = social welfare function xz = rents ; Z,z = time until death a = share of defense in output

(1 — a) = share of physical capital in output

Growth, Political Instability & Defense 33

8 = effectiveness of defense as insurance against the probability of death. 6= level of political unrest ‘; = rate of growth of variable “i”

A=co-state variable

6 = subjective rate of time preference

II

mw = probability of being overthrown or “death” g@ = embodiment of defense in human capital p = selfishness of dictator

o = intertemporal elasticity of substitution/relative risk aversion parameter

T = marginal tax rate

Growth, Political Instability & Defense . 34 Appendix A.2 Solving the Optimization Problem

Consider the following optimization problem described in section 3.

Bo [ v(cx, ee“ tat (edhe, Mo f, Vico )e

s.t. k, given

k= A*ky — ce — fe. The Hamiltonian is given by

H = ((1 — p)u(ce) + pw(ae) + AL(A* hy — ce — 2 )JeW (7 *),

The following first order conditions are due to Pontryagin’s maximum principle:

AH, = 0;(1 — p)ep? =v. = rt (A.1) H, = 0; pw'(ae) = rz (A.2) dd de .

v(ce, Zt) ke H, => : A* = 1, —— —

where At = *AT-a7i=a(20=7) _ 1] and x, = —f.

r(1-a)

Substituting the definition for societal and the dictator’s consumption and (A.1) into (A.4) yields

l-o l-o Tv —o + “=o + k l-o

Growth, Political Instability & Defense 35

or . Ce + Zet+ ky oO k,(1 — a) — =)

Using the resource constraint and the definition for growth implies

At = n,(

7

* Al =wnt,

where w = S42. l-o

Logarithmic differentiation of (A.1) and substitution of (A.3) yield

= = 4 = Ct oO

Appendix A.3 Proof of Existence

In order for a solution to exist in section 3, the objective function must be bounded, given the continuity of U on a closed technology. To prove this, take the limits of Up as t — oo and show that the function goes to zero. Therefore, the limits of the term

in the integral must satisfy?’

l-o

lim(1 — p)(——) + pw(a))e“** = 0.

t—00 l-—o By definition, c, = coe7’. Substitute this above. Therefore,

(1-0 )—(4+6)t lim (1 — p)(2=

t—+0o l _

y+ pw(a,)e7 ("+9 = 0.

Hence, if 6+ 7 > (1 —@) or rewritten 6+ 7 > A*(1 — oc) in the limit, then Up is bounded. 7

37For simplicity, let w(.) also be of the CIES variety, then an analogous argument can be made for w(.)

Growth, Political Instability & Defense 36

Appendix A.4 Estimation of the Model

This section is an abridged discussion of Londregan & Poole (1990). For a more detailed description see Londregan & Poole (1990). Consider the system of equations described in section 4. Define the vector of dependent variables as Y;; the vector of variables that enter either equation as X,; the J by 2 vector of errors by &4; and the

vector of coefficients, as Jit.

Using the notation in section 4.1, let E(éé’) = 9 and define the vector functions

T'(Gi) and A(Bx) as

(8) = | a | (A.5)

= Qo, 1, A2, a; A(By = A.6 ?) here (A) Therefore, the system of equations is rewritten as: Yul (Bit) = Xi A(Bit) + Ect. (A.7) The reduced form of (A.7) is Yi = XiTl(Bit) + Ext (A.8)

where II(Bz) = A(Gi)[T(G)]“* is the matrix of reduced form parameters and é, is

the vector of disturbances which satisfies é = €(I'(G;)|7?.

Denote the variance-covariance matrix of the reduced form parameters as

= (A(Bie)*)'O[A(Bx)~*] (A.9)

For notational convenience, let w,; and o;; denote the (z,7)’* elements of 2 and x. This implies

2.2 2 Woo = I — 28706 + Brag — 2agwy2 — agwrz

Growth, Political Instability & Defense | 37

x -|° "| (A.10)

where p is the correlation between the disturbances and a? is the variance of the error

and

in the first equation.

Assume each (€,) is normally distributed. Therefore, the disturbances are dis-

tributed as a bivariate normal with joint density*®

z) — ~3(@)/E-* (2) é) = ———re ? . A.11 f= (A.11) or f(@) = ——2 ear inyes (tovertn 0728) (A.12) 2no(I — p2)3 . The equation is further simplified by completing the square, I -——1 2(I- v2 —pé f(@) = mel ‘Hrmetyat (ETP) +(e 981)"), (A.13)

By appealing to conditional normal theory, the above equation is factored into two multiplicative arguments, each conditional on the parameters of the other. Hence, f(é) is

i 2

f(® = fale) fle - PrN] — p?)2). (A.14)

Considering that the product of densities across states makes up the likelihood

function, the corresponding log-likelihood function is

InL = rin( |

—oo

XT2(8) . ; fle—E (Ie? F aera yin fe

where 7* is a function that assumes a value of “I” if m is positive, and equals zero

°° I 2

fe—E(el(1—9)# )dé+ in flee)

otherwise.

Substitute the reduced form equation for €; and change the appropriate variables

to yield

Ge taint — (ES) + nfl)

38For simplicity, suppress the time subscripts from the immediate discussion.

InL = n*ln®(

Nin q

Growth, Political Instability & Defense 38

where ® is the cumulative density function corresponding to the marginal density

functions.

Having defined the likelihood function, the paper could proceed using maximum likelihood estimation. However, due to the inherent non-linearities in the problem, it is more practical to employ Amemiya’s generalized least squares (GLS). Direct application of GLS is possible because GLS is asymptotically equivalent to Full Information Maximum Likelihood (FIML) estimation. See Newey (1987).

Therefore, proceed as follows: e Step One:

Estimate the first reduced form equation using OLS, where the estimator is given by: (Bors = (X,%1) "XN.

Next, collect the residual, € from the estimation and estimate a probit model with

é and X as independent variables and ~ as the dependent variable where yp=l

if there is a probability of being overthrown and y=0

if not.

The argument of the cdf is taken from the earlier

XTI2(8) — (1-3)? — e Step Two:

Once Step One is completed, one has the maximum likelihood estimates of the

reduced form parameters, Il, 6 and p. To recover the structural parameters from IL,

Growth, Political Instability & Defense 39

the paper could employ minimum x? estimation. (See Rothemberg (1973).) However,

for simplicity, the paper chooses to use GLS.

‘To accomplish this, denote a matrix of zeros corresponding to the number of

independent variables by O. Then, consider the following equations:

3. = a | (A.15) and

Define the identity matrix as I[a : 6], where a, b denote the relevant columns, and let H,,; = Ifa: 3]

for 1 = 1,2 equations and 7 = 1,..., K independent variables.

Once the preceding is accomplished, use OLS to estimate the following equation:

2 K-2 vec(II) = grag + 9287 + > > Ai, 8"

j where vec(II) is the column vector consisting of the columns of II stacked one atop the other, beginning with the first column on top, ending with the last column at the

bottom. This means that §* is the matrix of structural parameters minus ag and 7.

Next, estimate the variance-covariance matrix of vec(II), A,, using the bootstrap

technique pioneered by Efron (1979).

Then, using the OLS estimates, Gg and Br, redefine the matrix T as I. Now, estimates of the following variance-covariance matrix of the entire model are the true values.

D, =(@ljA,(, ary

From Newey (1987), it is shown that the estimate of # is fully efficient, and the

standard errors from the GLS estimator are the true standard errors.

Growth, Political Instability & Defense 40

One further advantage to estimating the model in this manner is that the predicted value of vec(II) given by E[vec(II)] is easily manipulated to test model specification.

If there are m overidentifying restrictions, (Elvec(II)] — vec(I1))'A,(E[vec(II)] — vec(I1))

is asymptotically x? distributed with m degrees of freedom. Hence, the specification

of the model is tested by comparing the tested value to the actual value.

Growth, Political Instability & Defense 41

Appendix A.5 Additional Tables and Figures

Table A.1: Political & Economic Factors by Defense Burden Quintilet

Lowest .128

Second Lowest

Middle

Second Highest

Highest

tig60-85 Average Defense Burden, Per Capita Growth (Growth), end Coups (Coups) Per Million of non-democratic states with at least one coup. Source: Barro (1991) and author’s calculations. Lowest is defined as less than 1.4%; Second Lowest is between 1.41% and 1.98%; Middle is between 1.99% and 2.5%; Second highest is between 2.51% and 3.58%; and Highest is at least 3.59%. Standard Errors are in parenthesis.

Table A.1 shows that for non-democratic countries the relationship between defense, coups and growth is non-linear. Column one in Table A.1 divides the sample of countries into five quintiles-lowest to highest. The secoud and third columns report the average incidence of coups and the rate of growth for the countries in each quintile. Table A.1 shows that the incidence of coups rises at the lower tail of the defense burden distribution but falls after the second quintile. It also shows that growth rates fall at the lower end of the distribution but rise after the third quintile.

Growth, Political Instability & Defense 42

Table A.2: Simultaneous Equations Estimation for Alternative Modell

Jit ~ 1 Vit = Ao + rm + a2git + a3Dumyatamer + G¢Duma frica + Ose 1 + AeMit + EX st :

at

Mt = Bo +B; t, +Bo2beradj—1 +636eradj—2 +84DumtatAmer +5 Duma frica +Beve 4 +Brvit +e},

Dependent Variable

intercept —0.6797* Human Capital . ae —0.0553** Dum atAmer —0.4629 Duma frica —0.0212*** —0.8307** Tit-1 0.3514* Tit-2 . 0.8491 Vt 4 0.4050*** 14.4656*** Tit —0.010***

—35.1296**

x? = 4.089 p = 0.043

ti967-62 annual growth rates (+;;), number of coups (7,4), average military spending as a percentage of GDP ( #), primary school enrollment (Human Capital, 4j,), executive adjustments (Ex Adj) and the log weighted average of per capita growth for the G-7 countries lagged one period (W234) for the .69 country sample. (Standard Errors are in Parentheses). Source: WMEAT (1991) and Alesina et al (1991).

“=significant at the .1 level, **=significant at the .06 level, ***=significant at the .01 level.

‘Jit x? test of one over-

identifying restriction

Growth, Political Instability & Defense 43

Table A.3: Simultaneous Equations Estimation for Varying Sample Periods!

Git ~ 1 Vit = Ao + a1 — + A2Gie + A3DuMzctAmer + A4DuM Africa + O5Ve-1 + HeTit + Ey it

Mit = Bot fi qt Pbecadi—1 +f3beradj—2 +B4DumtatAmer +Bs Dum africa +Be%e1 +Bryiete?, at

Sample Period 1970-82 | Sample Period 1972-82 Dependent Variable Vit Tit Vit Tit

intercept 0.0056 —0.5230*** 0.0101 —0.7689*** Human Capital 0.0001** . 0.0001** .

a —0.0015 —0.0595** —0.0016 —0.0676*** Dum zatAmer —0.0178 — 0.7000 —0.0110 — 0.2016 Duma frica —0.0217*** —0.8005*** | —0.0197*** — 0.6064*** Ex Adje-1 . 0.0462 . 0.0875** Ex Adje_2 . — 0.0988 . — 0.0720 Ve-1 0.4489*** = 14.5533** 0.4091*** =13.9420** Tit —0.0092*** . —0.0046*** . “it . — 37.6607*** . — 40.8555***

x? test of one over-

identifying restriction Tannual growth rates (7;4), number of coups (*;¢), average military spending as a percentage of GDP (Bt), primary school é enrollment (Human Capital, 9;,), executive adjustments (Ex Adj), and the log weighted average of per capits growth for the G-7

countries lagged one period (We) for the 69 country sample. Source: WMEAT (1991) and Alesina et al (1991). "=significant at the .1 level, **=significant at the .06 level, ***=significant at the .01 level.

Growth, Political Instability & Defense 44

Table A.4: Simultaneous Equations Estimation Excluding War Datal

Jit ~ 1 it = Ao + A — + Q2git + @3DUM Lat amer + A4DuMa frica + ASI, + AeTMit + E%, it

Tit = Bot Pi , +B26ezadj-1+P3beradj—-2+84Dumzatamer + 0s Duma fricat Beye 1 +P7vit +e, it

Dependent Variable Tit intercept 0.0018 —0.7839*** Human Capital 0.0001 .

a --0.5005** —0.1459* DumtatAmer —0.0149 —0.2889 Duma frica —0.0142** —0.5532*** Ex Adjy_1 . 0.1090* Ex Adjr_2 . 0.0338 yt 4 0.4459*** 15.2225 Tit —0.0081*** . Vit . —32.1757*

x? test of one over-

identifying restriction

t1967-82 annual growth rates (y,;), number of coups (*;4), average military spending as a percentage of GDP (#), primary school enrollment (Human Capital, 4:4), executive adjustments (Ex Adj) and the log weighted average of per capita growth for the G-7 countries lagged one period (yey) for the 69 country sample. (Standard Errors are in Parentheses). Source: WMEAT (1991) and Alesina et al (1991).

“=significant at the .1 level, “*=significant at the .06 level, ***=significant at the .01 level.

Growth, Political Instability & Defense

Table A.5: Listing of Non-Democratic Countries

Algeria

Angola Argentina Bangladesh Somolia

Benin

Bolivia

Brazil

Burma

Burundi

CAR

Chad

Congo, Peop. Rep. Ecuador

Egypt, Arab Rep. El Salvador Ethiopia

Gabon

Gambia

Ghana

Guinea

Guatemala

Senegal

Haiti Honduras Hong Kong Indonesia Iran

Iraq

Ivory Coast Jordan Kenya Korea, South Lesotho Liberia Madagascar Malawi Sudan Mauritania Mauritius Morocco Kuwait Sierra Leone Mozambique Nepal

Sri Lanka

Nicaragua Niger Nigeria Pakistan

Panama

Paraguay Peru Philippines Saudi Arabia Swaziland Syria Taiwan Tanzania Thailand Togo

Tunisia Uganda Papua New Guinea Suriname Rwanda Zaire

Zambia

Zimbabwe

45

Growth, Political Instability & Defense

Table A.6: Listing of Democratic Countries

Australia Austria Barbados Belgium Botswana

Canada

Columbia

Costa Rica

Cyprus

Denmark

Finland

France

Gambia

Germany, Fed. Rep

Greece

Iceland

India

Ireland Israel Italy Jamaica

Japan Luxembourg Mexico Netherlands

New Zealand Norway

Singapore

Sweden Switzerland Trinidad & Tobago United Kingdom United States

Venezuela

46

47

Growth, ponlede stability & Defense

TV 21n3iy

(1661) Oleg :a2unos "$8-0961 Woy 110,p dnod suo jse9] ye YIM somUNOD

Growth, Political Instability & Defense 48

Figure A.2: Schematic Diagram of the Literature

Benoit, Kennedy, Whynes

Military Economic

Spending

Deger Duthin Leontief Sen, Smith Growth

Chowdhury

<>

Grossman,Hess ,Orphanides

Alesina ,Ozler Roubini,Swagel

—_—_—_——

Political Londregen,Poole Economic

Instability —_——————) Growth

Growth, Political Instability & Defense 49

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IFDP NUMBER

436

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427

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International Finance Discussion Papers TITLES 1992

Growth, Political Instability, and the Defense Burden

Foreign Exchange Policy, Monetary Policy, and Capital Market Liberalization in Korea

The Political Economy of the Won: U.S.-Korean Bilateral Negotiations on Exchange Rates

Import Demand and Supply with Relatively Few Theoretical or Empirical Puzzles

The Liquidity Premium in Average Interest Rates

The Power of Cointegration Tests

The Adequacy of the Data on U.S. International Financial Transactions: A Federal Reserve Perspective

Whom can we trust to run the Fed? Theoretical support for the founders views

Stochastic Behavior of the World Economy under Alternative Policy Regimes

Real Exchange Rates: Measurement and Implications for Predicting U.S. External Imbalances

Central Banks’ Use in East Asia of Money Market Instruments in the Conduct of Monetary Policy

Purchasing Power Parity and Uncovered Interest Rate Parity: The United States 1974 - 1990

Fiscal Implications of the Transition from Planned to Market Economy

Does World Investment Demand Determine U.S. Exports?

55

AUTHOR(s

Stephen Brock Blomberg

Deborah J. Lindner

Deborah J. Lindner

Andrew M. Warner

Wilbur John Coleman II Christian Gilles Pamela Labadie Jeroen J.M. Kremers Neil R. Ericsson Juan J. Dolado

Lois E. Stekler Edwin M. Truman Jon Faust

Joseph E. Gagnon Ralph W. Tryon

Jaime Marquez

Robert F. Emery

Hali J. Edison William R. Melick

R. Sean Craig Catherine L. Mann

Andrew M. Warner

Please address requests for copies to International Finance Discussion Papers, Division of International Finance, Stop 24, Board of Governors of the

Federal Reserve System, Washington, D.C.

20551.

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International Finance Discussion Papers

TITLES 1992

The Autonomy of Trade Elasticities: Choice and Consequences

German Unification and the European Monetary System: A Quantitative Analysis

Taxation and Inflation: A New Explanation for Current Accor+ Balances

1991

A Primer on the Japanese Banking System

Did the Debt Crisis Cause the Investment Crisis?

External Adjustment in Selected Developing Countries in the 1990s

Did the Debt Crisis or the Oil Price Decline Cause Mexico’s Investment Collapse?

Cointegration, Exogeneity, and Policy Analysis: An Overview

* The Usefulness of P Measures for Japan and Germany

Comments on the Evaluation of Policy Models

Parameter Constancy, Mean Square Forecast Errors, and Measuring Forecast Performance: An Exposition, Extensions, and Illustration

Explaining the Volume of Intraindustry Trade: Are Increasing Returns Necessary?

How Pervasive is the Product Cycle? The Empirical Dynamics of American and Japanese Trade Flows

Anticipations of Foreign Exchange Volatility and Bid-Ask Spreads

A Re-assessment of the Relationship Between

Real Exchange Rates and Real Interest Rates: 1974 - 1990

Argentina’s Experience with Parallel Exchange Markets: 1981-1990

56

AUTHOR(s)

Jaime Marquez

Gwyn Adams Lewis Alexander Joseph Gagnon

Tamim Bayoumi Joseph Gagnon

Allen B. Frankel Paul B. Morgan

Andrew M. Warner

William L. Helkie David H. Howard

Andrew M. Warner

Neil R. Ericsson

Linda S. Kole Michael P. Leahy

Clive W.J. Granger Melinda Deutsch

Neil R. Ericsson

Donald Davis

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Shang-Jin Wei

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Steven B. Kamin