Defense and Security

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This is the first application of mechanism design approach to model of conflict. The simple approach allows a non-linear, dynamic solution of defense burden. Defense burden is the required resources for defense. The model highlights the effects of population dynamics and technology of conflict. The dependence of defense on population introduces the dynamics of the logistic function. The rate of change of war making technology affects the dynamics of defense force. The result is chaotic defense requirement. Introduction Economics as a science Albert Einstein said that Science aims to explain the complex of our experience. Today Economics is defined as the science of allocating resources among alternatives. Since its break from Political Economy, mainly Economics has concentrated on Production and Distribution of goods. Game theory models competition and conflict. Yet, the interaction of the models of conflict with classical Economic theory is limited. Economics models should not abstract from reality to omit observables influences. Often, we observe appropriative behavior. Better economic models should account for the dynamics of rent seeking behavior.

“The Homo economicus of traditional economics is far from being completely self-interested, rational, or as individualistic as he is purported to be; he will haggle to death over price but will not take what he wants by force. Implicitly, he is assumed to behave ruthlessly within a well-defined bubble of sainthood.” Skaperdas 2003

The use of force is omitted in classical economic models. A model with omitted dimensions generates paradoxes. Economics is not a paradox free. Economics should strive to be a more complete model. Economics should study the Appropriation and defense of resources and Production and Distribution of goods. Economics will be a more complete model of the world and it would integrate better with other disciplines of social science. About the literature General literature Many areas of social science study conflict. The literature of economics, political science, and international relations discusses conflict and appropriation. While defense economics is concerned with conflict amongst nations, the general economic literature aims at the tradeoff between production and appropriation in a more generic and nation transcendent approach Game theoretic treatments consider abstract contests unconstrained optimization. International relations studies conflict among nations and how economic relations play a role in the dynamics of diplomacy . Finally, political science is concerned with domestic political conflict . Specific literature • Game theory • Contests • Skaperdas, Hirshliefer, and Garfinkle. • Other The literature above is mostly concerned with perfect information simultaneous optimization. About the model Let there be Amoral decision makers. They each have initial endowments of resources, population, and technology. All three endowments are changing in time. Each player can defend, produce and consume. Alternatively they can attack another player. The victorious attacker uses appropriated resources to produce and consume. This interaction is governed by a payoff function. It gives the payoff of one player attacking another. Given the intent to attack, the payoff depends on the resources of the defender and his strength. Contrast with other models In contrast with game theoretic models of conflict, this is a descriptive mechanism design model. This descriptive model analyzes the dynamics of the defense burden. The defense requirement is the amount of force that deters attackers. Deterrence is reducing attacking payoff to the point where attacking benefit is zero. Game theory Vs. Mechanism design Game theoretic treatments consider abstract contests unconstrained optimization. Often it assumes perfect information, symmetry. These are strong assumptions. In a tractable manner, this treatment models multiplayer defense requirement. The mechanism design approach of defining a set of player and method of interaction allows for a general dynamic treatment. An alternative scenario Suppose principalities have asymmetric information. They do not know the subjective probabilities of wining each is assigning to conflict. They also do not know the risk aversion of each other. See Aladhadh(2004)

Methodology This model is a descriptive model. Other models of conflict are normative. First a formulation of the benefits of attacking another player should be modeled. Then we will solve for the deterrence force. We have to define the dynamics of this paper. Let I = “The set n players.” Pi(t) = “ The population of i at time t.” Ri(t) = “ The total value of player I resources at time t.” Let Li(t) = “The number of laborers at time t.” Let Si(t) =”The number of soldiers at time t.” Fij(t, Si(t)) = “ The force of player i from Si soldiers at time t.” γi = “the per unit time cost “ Definitions Thus the cost of player Pi‘s conquest of Pj would depend on the “distance” between them and how much resistance the defender puts up. Note that the costs of both are in terms of r. Without loss of generality we will only consider the latter costs. The cost of producing the force lost in an attempt to acquire more resources. Formulation of cost function Attacking Benefit Adopting standard notation the total benefit of occupying payer j is the total value of the resources gained minus costs of take over. The costs of taking over are the value of casualties. Casualties are in two parts machinery and human. Human casualties are then expressed in terms of a function that yields troops in time. Then multiplied by cost per unit time. That makes the troop producing function similar to the population function with smaller carrying capacity. The carrying capacity will depend on the recruitment capabilities of the nation. Then The function T will be a the same as P with smaller carrying capacity. Then T takes time and gives troops. Its inverse takes troops and maps it back to time. Then T inverse is the value of casualties in term of time. Then, the per unit time cost of troops would give us the value of human casualties in resources. The effect of war technology on casualties is then accounted for by using F. F gives the fighting force of the number of Soldiers S. Then the function is.

ij= Rj(t) - γi T i-1 (Fijt(Sj)]

Without loss of generality let n=2. Proposition 1: Deterrence is achieved by minimizing the benefit of attacker

For player 1 to deter player 2 then:

12= 0 Then S1* = S : 12 = 0

Sj*: T i-1 [ Fijt(Sj) ] = Rj(t) / γi

Sj* = F ij-1 [T i (Rj(t) / γi )] let r(t) be Rj(t) / γi then

Sj* = F ij-1 [Ti (rji)]

Assumption P(.) is the population growth function. Logistic by choice of most population experts it. The logistic function is the classical chaotic function. Then T is a logistic function and T-1 is logit function. To illustrate the effects of that on the system we must first show the bifurcation, chaos, to order transformations of the function. Then we will discuss the consequences of that on Economics, security analysis and peace making. Then P is of the form and T is of the form Dynamic Results Consider S* and look at its dynamics in time. dSj*/dt = dF-1 /dt (T) dT/dt

It is comforting to see that the one major factor in the bifurcation of the system is warfare technology. One example is the invention of the chariot wheel in Assyria. Assyria dominated the Middle East after its invention of the chariot wheel. Before its invention conflict was largely limited to near by city sates. The result is very consistent with observation

Also notice that dT(r(t))/dt= T ’(r) dr/dt dr/dt= d [R(t) γi-1 ]=R’ *γi-1 +R* ln γi *dγi /dt Summary The model shows that the stability of deterrence is fragile and. Small changes in the system might push the system to bifurcation and chaos. Namely small advantages in military technology will alter the parameter of the logistic function pushing it over the edge.

"People have feelings about food and clothing that things cannot satisfy. Therefore, when they live together they do not share equally. If they do not get what they want, they fight. When they fight, the strong terrorize the weak, and the bold invade the timid." The Book of Leadership and Strategy, a Taoist classic

Abstract Peace building requires time and effort on the part of competitors. Peace is not guaranteed by cooperation or deterrence. Conflict readiness is on going and it affects economic behavior. Adversaries allocate resources between consumption and conflict management. The dynamics of forceful appropriation is important to include into the classical economic optimization problem. My model of conflict calculates an equilibrium defense burden. The defense burden causes chaotic behavior in the inputs market. Labor and capital carry over this dynamics into the product market. Introduction: The assumptions of classical economic analysis both Micro and Macro, speak only of managing resources among alternatives. Classically, Economics is the science of allocating scarce resources among alternatives for purposes of production and distribution. With few exceptions, the discipline as a whole ignores the problem of claiming and keeping securing resources. Economics should be redefined as the study of appropriation, defense, production, and distribution.

“The of traditional economics is far from being completely self-interested, rational, or as individualistic as he is purported to be; he will haggle to death over price but will not take what he wants by force. Implicitly, he is assumed to behave ruthlessly within a well-defined bubble of sainthood. Based on a simple model, I first examine what occurs when this assumption is relaxed and genuine, amorals interact. Productivity can be inversely related to compensation; a longer shadow of the future can intensify conflict; and more competition among providers of protection reduces welfare.” Skaperdas 2003

The model shows uncovers a source of chaotic perturbations in the economy. These perturbations are born from a constraint inherent to the process of securing economic resources such as land and capital. The chaos travels though the input market to the product market function. While I am not proposing that these inputs are the full source of fluctuation of the business cycle, I am however proposing that they might serve to explain the large margin of unpredictable errors in the study of the business cycle.

Given the importance of the consequences outlined above, we shall consider past treatment of the issue.

Literature review Both Keynes (1929,1939) and Pareto (1929) have written about war, peace and their effects on the economy. Marx (the intellectual Robin Hood) was one of the first to identify violent conflict as a force in the dynamics of wealth distribution. In fact, he advocates seizing control of resources from the poor by force. In his 1994 paper, Hirshleifer supports the importance of increasing our understanding of conflict and appropriation. Indeed our understanding of social structure and the requirements we should place on political systems are to be extracted out of our understanding of the causes of conflict between groups within the same state. There are three bodies of literature treating conflict. The literature of economics, political science, and international relations discusses conflict and appropriation. While defense economics is concerned with conflict amongst nations, the general economic literature aims at the tradeoff between production and appropriation in a more generic and nation transcendent approach Game theoretic treatments consider abstract contests unconstrained optimization. International relations also concerns itself with conflict amongst nations and how economic relations play a role in the dynamics of diplomacy . Finally, political science is concerned with domestic political conflict .

An Analysis of Hegemonic Dynamics In this paper I attempt to analyze an n player game with a general model that could explain the dynamics of interaction between players in a certain type of zero sum game . The main application is to use the model to understand real motivations of actions on the international scene, evaluate future repercussions of present changes of borders, foreign aid, and independence of nations from larger unions. Furthermore, evaluate the real consequences of the distribution of powers on the globe in terms of economic motivations and long run equilibrium tendencies. Also, this paper explains the economics that effect the formation of nations. Indeed, the context of this model allows for a complex method of computing equilibrium boundaries between nations in an era of national independence and the soviet breakup. we analyze this game in the context of acquiring resources protected by principalities and the means of overcoming opposition, relating these means to the players’ initial endowment of resources. Another application of this model could be the analysis of market place competition amongst companies in the same industry. While the analysis would have to be carries out in terms of market share and marketing campaigns, the applicability of this model still holds.

Initial formulation: Consider a setting where the number of players could be expressed as a function of time Let J(t) denote the set of all players Pi at time t. Let |J(0)|=n(t) , such that 0< n(0) < . Where | . | denotes the cardinality of a set . For each player Pi J(0) There is a vector such that the components are : • Let the strength of a player i be denoted si (0) R such that for any time t, Si(t)= si(0) + production + acquired strength with lag and si(0) • Let each player have a parametric set denoting the number of points in Rn that it holds at a certain point in the game. Ii(t) where the only point at t=0 is c R3 , and such that each Pi has a unique position. That is, Ii(0)  Ij(0) for all i j . Furthermore, When |Ii(t)|=0, then Pi is said to be out of the game. Likewise, let i(t) = ckIi(t) r(t,ck) . furthermore, 0  i(t) <  for all t and all Pi J(t. Also iJ(t) i(t) Associated with each cR3 a resource value of R0 (ck)  R that assign the initial resource endowment, such that 0  R0 (ck) <  and .Furthermore, 0  R(t,ck)  R <  is a non increasing function of time. Where R0 denotes initial endowment For example R could be:

  R(t,ck)= R0(ck) e-r(ck)t

Notice then that the individual player i could be made to seek to maximize the following utility function.

• Let a production function Ti be considered where Ti: R+ R+. It turns resources into strength Ti(r)=strength. • Let a transportation or mobility function be denoted Mi,t(ck ,cm) M: R3 x R3R. where it differs with time as a result of technology. It expresses costs of attacking to acquire resources from a specific point in R3. This cost could be thought of as abstract “distance.” Distance in terms of a real number explained in the context of resources spent to move from one point to the other. It also must be invertible bounded and strictly positive. An example of this would be any simple metric such as the simple distance formula between two points. Notice that Mi,t(ck,cm)<  for all Pi in J(t). That is, all players have a position on a space wherein they are reasonably close.

Acquisition and anarchic competition:

Attack Defend Attack Defend

The analysis of cost :

Thus the cost of player Pi‘s conquest of Pj would depend on the “distance” between them and how much resistance the defender puts up. Note that the costs of both are in terms of r. Let Cost1 and Cost2 be the cost of distance and the cost of casualty consecutively. Certainly the cost of distance is a function of the player’s mobility M. While the latter cost is the cost of producing the force lost in an attempt to acquire more resources. Considering that shows us that the Cost1= Mi,t(ck,cm) and Cost2= γi T-1 (li(t,j))or more explicitly: Adopting standard notation the total benefit of occupying j for player i is:

       ij= rjt - [Mt,i(ck,cm)) + γi T i-1 (lit(Sj)]  

The Mobility function is a decreasing function that depends on the technology of transportation and the cost of mobilizing force.

Definition1: A class of the player Pi is the set i = j Xj. such that Ai(t)  Bi(t) =Xi (t) where:

• Ai (t) ={ j ; ij >0 } • Bi(t) = {  j ; ji >0}

In this way any state is given a class to which it belongs.

Definition2: Pi satisfies a regional power if : for all j  i

ji  0 

Static Equilibrium

Equilibrium defense burdens: For the system to be in equilibrium, the benefit of attacking should be zero for all players. Therefore the equilibrium condition is:

 I,j  J(t) ij =0

Dynamic Equilibrium

Now solving for the equilibrium defense forces :

ij= rjt - [Mt,i(ck,cm)) + γi T i-1 (lit(Sj)]

0= rjt - [Mt,i(ck,cm)) + γi T i-1 (lit(Sj)] [rjt -Mt,i(ck,cm))] = γi T i-1 (lit(Sj)) T[(rjt -Mt,i(ck,cm)/ γi] = T[T i-1 (lit(Sj))] lit(Sj)=T[(rjt -Mt,i(ck,cm)/ γi]

Consider (lit(Sj)) the function allocating a defense force. The function changes with time corresponding to new armament and war technology in time. The function also changes depending on the attacker to take into account some hidden costs. Consider for example the efforts in defending against a Mongol invasion as opposed to a Roman invasion. The perception of consequences of defeat changes the intensity of resistance. Thus we arrive at the following result:

 Sj* = lit-1 [T{( rjt -Mt,i(ck,cm))/ γi }] 

Let Ait (t) =[ rjt - Mt,i(ck,cm)] / γi Then

 Sj* = lit-1 [T(Ait (t)]………..Equation 1 is the equilibrium defense force needed in a multi-state anarchic competition system.

The lit(.) function could be assessed as linear as it has been by many military strategists such as Sun Tzu. He relates the coefficient to the risk averseness of the decision maker. Making the minimum damage calculated as 2 then 5 and finally 10. In World War II the technology gap between Germany and Russia and other European country was big. Every German soldier by virtue of technology was equal to several other European soldiers.

Ait (t) is a function depending on the speed of the resource depletion and the cost of force mobilization weighed by the cost of producing fighter per unit time. Consider however, depletion of rj(t) over time which might seem to be exponential with a negative rate of growth. Assumptions about the overall behavior of Ait (t) might be explored at later exposition because it seems promising.

And Finally T(.) is the population growth function. Logistic by choice of most population experts it yields the most interesting results. The logistic function is the classical chaotic function. To illustrate the effects of that on the system we must first show the bifurcation, chaos, to order transformations of the function. Then we will discuss the consequences of that to the security analysis and peace making.

Now consider the recursive form of the logistic function so that we are better able to demonstrate the sensitivity of the equilibrium defense to initial conditions and changes in time. These changes might be represented by alliances independence of states or foreign aid. The recursive function is: at=m(1-(at-1 /K))at Where K =”carrying capacity” and m= ”rate of growth adjusted for starvation and birth” Then fixed points are at m(1-at-1 /K)=1. [T(Ait (t)]= γi a(Ait (t)] = γi mi [1- a(Ait (t) –1) /K]a(Ait (t) –1) with fixed points at : γi mi (1- a(Ait (t) –1) /K)=1 then K - a(Ait (t) –1) = K / γi mi

a(Ait (t) –1) = K - K / γi mi

= K(1-1 / γi mi) ……..Eq 2 are fixed points

As you can see the change in the model only includes the cost of producing fighting soldiers per unit time. This shows that races for armaments and the establishment of defense industries push the system away to bifurcation and chaos.

As you can see from the diagram below of the logistic function’s bifurcation and journey to chaos, order in some instances then chaos again.

• With m between 0 and 1, the population will eventually die, independent of the initial value a(Ai(0 ) between 0 and 1. • With m between 1 and 2, the population will quickly stabilize on a single value; this value depends on m but does not depend on the initial value a(Ai(0 ) • With m between 2 and 3, the population will also eventually stabilize on a single value, but first oscillates around that value for some time. Again, none of this deepens on the initial value a(Ai (0 ) • With m between 3 and 1+√6 (approximately 3.45), the population will oscillate between two values forever. These two values are again dependent on m but independent of the initial a(Ai (0 ) • With r between 3.45 and 3.54 (approximately), the population will oscillate between four values forever; again, this behavior does not depend on the initial value. • With m slightly bigger than 3.54, the population will oscillate between 8 values, then 16, 32, etc. The lengths of the parameter intervals which yield the same number of oscillations decrease rapidly; the ratio between the lengths of two successive such bifurcation intervals approaches the Feigenbaum constant δ = 4.669... All of these behaviors do not depend on the initial value. • At m = 3.57 (approximately) is the onset of chaos. We can no longer see any oscillations. Slightly varying the starting value a(Ai(0 ) of the equation yields dramatically different results over time, a prime characteristic of chaos. • Most values beyond 3.57 exhibit chaotic behavior, but there are still certain isolated non-chaotic ranges of m; for instance around 3.82 there is a range of parameters m which show oscillation between three values, and for slightly higher values of m oscillation between 6 values, then 12 etc. There are other ranges which yield oscillation between 5 values etc.; all oscillation periods do occur. These behaviors are again independent of the initial value. • Beyond m = 4, the value diverges for almost all initial values.

Now refer back to equation 1 and notice lit-1 (.) is an inverted armament function. Whether the function is linear or not the system remains chaotic. There have been suggestions in the security and strategic studies community that the function is itself chaotic without specifying the form. The argument was very heuristic and not very rigorous so we prefer not to use it. On the other hand the chaos in our system is based solely on the logistic form of population growth.

From the model above it is clear that the system is very sensitive. Furthermore, we get a good understanding of what it means for the security system to be stable i.e it should be within the interval of the parameters that keep the system within order and away from chaos. Politics might play a huge role in allocating foreign aid, or establishing alliances. However, the sensitivity of the system requires prudence or else the system is pushed to new fixed points or over the edge of chaos.

Effects on the macroeconomics.

Let us define Si*= Si; ji  0 for all j i and if L+Si= population W then let Si+ =Si; a production function P(L,K)/L =0 and 2P(L,K)/L2 <0 The effects of such the difference between the optimal resource protection force and that of optimal production may be described as follows: If Si*-Si+ >0 then since L+Si=W then the economy will not be operating at its optimum and will be below its maximum production. Thus, the economy will operate within it possibility frontier and growth is stumped. If Si*-Si+ <0 then the economy will be operating at maximum capacity and the resources would be protected, but there will be excess labor. It is under these conditions that the marginal returns of one more warrior is more than the marginal return of one fighter is higher than the return of one more worker. As mentioned in Findlay(1995.) This is where a specific country begins to out grow its neighbors in military size. There are two way to realize this potential force return. One is to increase capital and use more workers. The second is to acquire more resources by force and put the fighters to work. Then the acquisition would acquire just enough resources to make Si*=Si+. Economic Growth Under the Constraints of defense: If W=W0 at then Si should be such that : • P(L,K)/L =0 or P(W0 at –si ,K)/L =0 by the chain rule……..(1a)

P(L(t),K)/L=   [P(L,K)/L]*(dL/dt))=0……………………………(1b)

• 2P(L,K)/L2 <0…………………………………………………...(2) • Si Ti(j-M(.))/beta ………………………………………………..(3)

The dynamics of change and convergence of growth rate As one can clearly see from the above equations, the conditions clearly outline a space wherein optimality and thus a form of equilibrium is maintained. Equation 3 explains the convergence in growth rate observed empirically. From the form of the rate of change of labor with respect to time which is exponential we see why growth rate slows down in mature economies. Mature economies observe common traits of a slow down in growth rate and increasing unemployment like Japan. At this juncture I would like to point out why this convergence takes place. It is simply explained by pointing out that labor is increasing while resources are not. The mere fact that we are unable to surpass it is our commitment to a non anarchic system of resource acquisition. Without that classical economic assumption

Cooperation Possibilities

Core analysis Shapely value Achievable through binding agreements Consider a two player game Normative approach would drive both sides to optimize. Consider the cost function, Min costi s.t si 0 Boundary point solution at si = sj = 0. Notice this is the same as contest solutions. Then these two can agree not to arm to minimize the cost of defense.

Incentive to cheat The incentive to cheat would be too high for wither of them. Because the payoff of making sj an epsilon and seizing their resources would be strictly greater. So the incentive to cheat is too strong in a two player game.

Consider an n player game Then cheating would cause the cheater to pay defense burdens against all the other because their agreements are not credible. Then The payoff of production with ri and rj summed and discounted would be affected by paying defense expenditure. Finite horizons and increasing scaricty Consider a time tfi =t when ri =0. This could happen if ri = ri(0) e-rt . Or even easier if tfi =t when rt <g (w(t)) where g is some sort of a need function.Then at tf there is no doubt that the MRS> MRL. Then cheating is definitely better because: j(Cheating) = tfi ri e-rt + tfj rj e-rt j(inevitable conflict) = tfi ri e-rt + tfi tfj rj e-rt

Blocking forces Say we have 3 players such that : ij >0 and ik >0. Then there is a possibility of cooperation between j and k so that in a coalition between them would render both their forces as sj+sk. Then ij 0. and ik 0. Conditions on coalitions it has to be optimal for both fo them to keep their word:

Possible scenarios.

Appendices:

Appendix 1:

Interrelation of social science Social science is a system. That is, social science is set of independently interacting parts that produce an observable result. Therefore, it is very important that we keep in mind that any attempt to specialize in studying these interacting parts independently must not keep us from piecing the dynamics of the interaction. Once we are able to see both pictures, we are close to producing advances in social science. Social science as a whole is a system based on man’s problem, scarcity. Based on the nature of our physical existence we are faced with needs and while the structure of these needs is an issue of Biology and Psychology, Economics is certainly the science that most directly deals with the way humans deal with scarcity. Thus, Economics is the first step to understanding the dynamics of the social sciences. If we are to use Economics as our starting point in a venture to better understand social science, we must first realize that the discipline of Economics has set aside the first step in combating scarcity, namely, securing resources.

The New Field of Defense Economics I am by no means the first that has voiced the above suggestions. In the (1996,) book, The Political Economy of Conflict and Appropriation, Skaperdas, and other authors like Ronald Findlay of Columbia, point out that changing the classical assumptions of Economics with regards to considering conflict and appropriation is essential. On the other hand, no real work has been done to build on what they have pioneered to change to the classical assumptions of economic analysis. I believe that the change such study make will be no less than the change Debreu made by considering dynamic rather than static market price equilibrium decades ago. As an outline and an excellent up to date reference I found Keith Hartley’s edited volume titled The Handbook of Defense Economics. On the other hand, the only paper that spoke of the effect of defense and appropriation on the classical production model was Ronald Findlay’s (1996) Towards A Model of Territorial Expansion And The Limits of Empire. The Size of Defense Economics “The estimate by the US arms and Disarmament control and Disarmament Agency [US ACDA](1994,p.47)] indicates that the total world military expenditure exceeded one trillion dollars in 1991. In the developing world military expenditure constituted about 4.5 percent of GNP and over 18% of all central government expenditure.” Similar reports by the United Nations Development Program [UNDP(1994,pp.170-171)] abut sustained military spending exceeding health and education budgets from 1960s until the early nineties were quoted by a Rati Ram[chapter10, H.D.E] Thus, we add that even though economic growth seems to be a universal goal, large defense spending is almost as universal as growth by both developed and growing countries.

The effect on Macroeconomics Despite the size and importance of the defense sector, the effects of defense on Macroeconomic conditions are left to practical economists and purely empirical studies. Although empirical studies such as that of Benoit’s (1973,1978) work provided an initiative for a variety of empirical studies of the effects of defense spending on economic growth for the latter half of the last century. According to Ram of Illinois state university, there is has been a wide spectrum of methodologies in the empirical study of the effects of defense outlays and economic growth using different ad hoc and theoretical models and proxies of variables used in these studies. Nevertheless, there has been no explanation for the reason of the evidently contradicting statistical evidence. My attempt to incorporate defense economics and understand its real effects on Macro economics through careful mathematical modeling will provide theoretical support for the empirical work of Ram(1994) . As Ram points out most these empirical studies use ad hoc modeling and numerous doubtable proxies in their analysis. Therefore, with the lack of proper theoretical basis, we are left with inconclusive evidence regarding the effects of defense outlays on economic growth. Furthermore, Ram states: “In traditional models, one can find positive as well as negative effects of defense spending by using different periods and groups of countries.” The model proposed shows the sampling methods in both time series and cross sectional studies are the source of such conflicting results. What drives econometricians to pool countries together is the assumption that the data generating process of growth is the same and that weakens estimates at best and some cases takes us to the realm of misspecification errors and omitted variable biases. The model proposed herein would show the specific differences in the data generating processes that are usually pooled and thus clarify the ambiguity in the usual results and will back the results given by Ram’s more comprehensive and careful work. Perhaps it is hard to see how the market of widgets in the classical economic example is affected by the conflict and appropriation. However, it is not at all unreasonable to see the importance of such a large segment of the economy and this impact on the widgets market by taking away resources and limiting the supply of widgets in the market. The price of widgets increases in reaction with the shortage in supply. The consumer henceforth is left with less disposable income once adjusting for inflation caused by the increase in money supply chasing non appropriative goods. After this example it is very easy to see the error of any theory that does not take into account the effects of conflict and appropriation.

References

• Ronald Findlay (1995), “Towards a Model of Territorial Expansion and the Limits of Empire” chapter The political Economy of conflict and appropriation Michelle R. Garfinkel (Editor), Stergios Skaperdas (Editor.), (1996)Cambridge University Press;

• Skaperdas, Stergios(2003), "Restraining the Genuine Homo Economicus: Why the Economy Cannot be Divorced from its Governance" . Economics & Politics, Vol. 15, pp. 135-162

• Rati Ram (1995), “Defense Spending and Economic Growth.” Chapter 7 Hartley, K., and Sandler, T. (Eds.), (1995), Handbook of Defense Economics, Cambridge Univers