Back Matter
  • 1, International Monetary Fund

APPENDIX:I Military Expenditure Data

The primary data sources for military expenditures is the Stockholm International Peace Research Institute (SIPRI), supplemented by the US Arms Control and Disarmament Agency (ACDA). The data sources for the other variables are based upon published data by the IMF, the World Bank, the United Nations, the U.S. Central Intelligence Agency, and national accounts.

The SIPRI estimates of military expenditures were chosen because they are probably the most reliable and conform to a consistent definition. For the purposes of this study, two types of modification to the SIPRI data are made. First, the U.S.S.R. and China are among the countries omitted from the SIPRI data set. ACDA estimates for Chinese military expenditures are the only known time series source. In the case of the U.S.S.R., estimates of military expenditures are based on Steinberg (1990). Steinberg’s estimates are provided in local currency, his definition is comprehensive and compatible with SIPRI’s definition, and the latest estimates include an adjustment to account for price differentials within the U.S.S.R. The reader is cautioned that the military expenditure figures of both the U.S.S.R. and China are not as reliable as some of the other figures. However, it seems likely that they provide a credible estimate of the trend.

The SIPRI figures represent total government outlays on the military including military pensions, military interest payments, and paramilitary expenditures; they exclude police. SIPRI follows the NATO convention of including military aid to other nations in the military expenditures of the donating country, and does not include aid receipts from other nations in the military expenditures of the recipient countries,

SIPRI military expenditures -

  • Ministry of Defense budget

  • - non-military expenditures of the defense ministry

  • + military outlays of other ministries (including military pensions and interest payments)

  • + military aid to other nations

  • - military aid receipts from other nations.

Thus, the SIPRI military expenditures represent the domestic opportunity cost of military appropriations plus military aid to allies, or the total level of resources allocated for military purposes by a country, excluding expenditures funded by aid from foreign governments.

There are a number of potential problems with the SIPRI estimates. First, SIPRI explicitly does not include aid financed military spending. Second, military expenditures are often hidden in the budgets of other ministries. Third, off-budget expenditures financed through other means are often omitted. For instance, expenditures financed through foreign loans, direct earmarked payments to the military of mineral revenues, or funds obtained through asset sales or profits of public enterprises maybe omitted. SIPRI does make some adjustments to account for these factors. For instance, in several countries direct payments to the military of revenue from petroleum or copper sales are added to the military budget. In others, adjustments are made when high imports of military goods are detected without a corresponding change in the Ministry of Defense budget. In a few cases, an in-depth examination of the budget is carried out to reclassify expenditures. However, particularly for the small low profile countries, the budget estimate are used without modification.

The development index and form-of-government variables are constructed variables. The form-of-government variables are interdependent dummy variables constructed from descriptions in Sivard (1991), SIPRI Yearbooks, and the Europa World Yearbook. The benchmark is a multiparty democracy not engaged in internal or external conflict. In a monarchy, power is transferred through heredity. Where there is both multi-party democracy and a monarchy present, these are categorized as democracies. A military government refers to the means by which the authority gained power and the status of the ruler before taking power. A socialist government is one that does not fit into the other categories and where the self-proclaimed ideology of the leadership is consistent with socialist ideology. The category of others refers to states that do not unambiguously fit into one of the above groups, for instance, one-party states and politically unstable states. The number of countries in each category is listed in Table 9; certain countries change status over the time period under review.

The concept for the development index, DI, comes from the United Nations Development Programme (UNDP) human development index. Among the attractive features of the UNDP index is its reliance on purchasing power parity (PPP) rates instead of official exchange rates in cross-country comparisons and the use of other indicators of the quality of life. The development index used herein is constructed in the following manner. The ratio of PPP per capita GDP (1980 real prices) to $7000 is calculated, and a weight of 0.8 is applied. Next, the ratio of life expectancy to 70 years is calculated, and a weight of 0.2 is applied. As with the UNDP index, all countries with a per capita GDP above a certain level ($7000) are assigned a value of unity. Implicit in this formulation is that $7000 is the level at which a country is considered developed. The same is true of the health index.. An expected life span of 70 years is considered an indication of reasonable health standards. This index differs substantially from the UNDP index. The UNDP index is based upon the log of per capita GDP as a ratio to $5000, in 1987 prices; life expectancy as a ratio of 78 years; and the literacy rate. The variables are given equal weight. Since yearly estimates of literacy rates are not widely available for individual countries, this variable could not be used in the present analysis.

APPENDIX:II A Public Choice Model of Demand for Military Expenditures

An econometric model designed to test the determinants of military expenditures in a cross-section of countries is developed in this Appendix. The model identifies the political, economic, financial, and geographical factors that are likely to influence government decisions on the level of military expenditures and provides a framework to test the relevant hypotheses. The model does not consider the interaction between military expenditures of allies and rivals. 1/

The model employs a public choice framework that analyzes how the government chooses the level of resources to allocate to the military. The primary assumption is that the leadership selects policies with the goal of maximizing its own welfare, subject to national economic and political constraints. This assumption does not imply that the political leadership is necessarily selfish or uninterested in the welfare of its citizens; any consideration can enter into the welfare calculation of the leadership. To the extent that the leadership is concerned about the welfare of citizens, the welfare function will reflect this concern.

In the model, the leadership of the country has to make two very important budgetary choices: (1) the size of the budget and therefore the ratio of private versus public use of resources in the economy, and (2) the mix of government expenditures between the military and others uses. The variables that enter the welfare function of the leadership are


where W the welfare level of the political leadership,

  • Ω the welfare function,

  • U utility derived from private consumption,

  • D the level of defense derived from military expenditure,

  • S social welfare derived from social expenditures (approximated by nondefense government expenditures).

The welfare function places relative weights on each of the three variables that determine welfare: private consumption, defense, and social expenditures. In order to keep the model simple and facilitate concentration on allocation of resources to the military, only two types of government expenditures are considered. While the other category includes interest payments, general government expenditures, and expenditures on economic services, for purposes of expositional ease it is referred to as social expenditures. The political variables are treated as state-of-nature factors that affect the environment in which the leadership operates or indicate the ideology of the leadership. Therefore, they determine the weights of the different elements in the welfare function.

The welfare function in its present form is not operational. A more convenient form can be obtained through transformations based on supply-cost relationships. Simple transformations will suffice for U and S since these are not the focus of the study,


where C private consumption,

  • SE the level of social expenditures.

A more careful consideration is warranted for defense. Defense, or the level of security, is influenced by a number of factors that affect the cost of obtaining security. It is hypothesized that the cost function for defense is


where ME the level of military expenditure,

  • POP population,

Geographical variables:

  • LA land area,

  • LB length of land borders,

  • CB length of coastal borders.

Equation (3) captures the notion that the effectiveness of military expenditure in providing security benefits will vary from country to country. For instance, larger countries are likely to be more costly to defend than small islands and therefore Chile is expected to have a higher defense budget than Mauritius, all other things being equal. The effect of population size is ambiguous. A larger population could be more costly to defend; however, a large population also acts as a deterrent to external attack.

The new welfare function, W, using equations (1), (2), and (3), is


The econometric specification uses a Cobb-Douglas functional form,


In this formulation the state variables, which describe political, demographic, and economic conditions, are assumed to influence the parameters of the equation: α1, α2, and α3; thus they determine the relative priority placed on C, ME, and S. Each parameters is also be assumed to take on a Cobb-Douglas functional form to arrive at equations (2A) and (2B) in the text.

The income constraint in this model is fixed by a number of interrelated equations. The government budget identities are,


where CGE is central government expenditure, T is government revenue, DF Is domestic financing, and FF is foreign financing. Since the government is seen as managing resource allocations within the economy, its budget constraint is determined by the total level of resources available to the economy,


Finally, since tax revenue is both a choice variable and a constraint,


where DI is a development index. Equation (5D) is a behavioral relationship. The level of development is hypothesized to affect the ease with which government can raise revenues; a higher level of development is generally associated with a higher tax base and greater administrative capacity to collect taxes. The form of government is also hypothesized to influence the ability to raise revenues; for instance, a socialist government may be In a better position to collect revenue than a nonsocialist government because a higher proportion of economic assets is gove rnment-owned.

Combining the above equations yields the following maximization equation for the government leadership:


Assuming a Cobb-Douglas welfare function, equation (4), the solution is


Equation (7) is a simultaneous equations system that determines the level of central government expenditure in the economy and proportion of the budget allocated to military expenditures. In the first equation, military expenditures are a simple proportion of the government budget, based on the relative priority of defense vis-a-vis social expenditures. In the second equation, central government expenditures have two determinants. In part, a proportion of total national economic resources (GDP + FF) is allocated to CGE based on the relative priority accorded to social expenditures vis-á-vis private expenditure. The other part of the equation indicates that CGE is also a function of ME.

By dividing equations (7A) and (7B) by GDP and allowing for the state variables’ effect on the parameters of the function, the following general form of the simultaneous equations is obtained,


where HE military expenditures in local currency,

  • GDP GDP in local currency,

  • GDP$ real GDP in U.S. dollars, 1980 purchasing power parity prices,

  • POP population,

  • CGE central government expenditures in local currency,

  • FF foreign financing (in US dollars)

  • DI a development index (see below), and

form of government (mutually exclusive dummy variables, Appendix Table 3):

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political variables (mutually exclusive dummy variables):

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The formulation separates direct and indirect influences on the level of military expenditures. The indirect influences are transmitted through the central government budget. Among the determinants of the level of central government expenditures are military expenditures, which are expected to have a positive influence, a development index, the form of government variables, and foreign financing. For example, consider a nation that experiences an increase in its development index. Since it is now easier to raise revenues, both its central government spending and its level of military expenditures will rise, even with constant political preferences.

The direct influences on the level of military expenditures reflect the derived demand from the welfare function, which incorporates both the cost function and income constraints. For example, consider two identical countries that differ only in the length of their land borders. The larger country will have a higher value and will have higher demand for ME. Consequently, the larger country will have higher military expenditures and higher central government expenditures, even though the priority attached to defense is identical.

The direct influence of real GDP on ME/GDP is quite complicated and interesting. Military expenditures are often viewed as a pure public good. Therefore, a country with a larger GDP will have more defense for a given proportion of GDP spent on the military due to economies of scale. This implies a negative sign. Conversely, a higher GDP represents more resources available for financing military expenditures and a lower opportunity cost, and this implies a positive sign. Since the two effects have opposite signs, the expected sign is uncertain. Similarly, the coefficient on population could be either positive or negative. A larger population can be more costly to defend, particularly if the military is involved in domestic politics. On the other hand, a large population implies an automatic deterrent.

The financing variables present an interesting specification challenge. In the mechanical delineation of the model above, the level of foreign financing enters the determination of central government expenditures in the manner described in equation (8B). However, this formulation glosses over considerations of the cost of foreign financing and the ease of obtaining foreign financing. To account for this factor, a number of variables have been incorporated into the analysis that act as proxies for the cost of foreign financing. These variables are a dummy variable for the heavily indebted middle-income nations covering 1972-79, HD70; a dummy variable for heavily indebted nations covering 1980-90, HD80; a dummy variable for small low-income economies, SLIE; and the net flow of public and publicly guaranteed foreign financing as a ratio of GDP, PGFF. In order to avoid simultaneity problems, the lagged values of PGFF are used; in addition, since the variable can take on negative as well as positive values, the log transformation could not be applied to the variable. The hypothesized effect of the three dummy variables on the level of central government expenditure is negative while the effect of PGFF Is predicted to be positive. These four variables have also been incorporated into the military expenditures equation to determine whether the financing variables affect the mix of government expenditures. The hypothesis is that easier financing terms will allow governments to engage in the luxury of higher military expenditure, and therefore, HD70, HD80, and SLIE are expected to have negative signs and PGFF is expected to have a positive sign.

As indicated above, the 3SLS method was used to estimate the equations in Table 6. The 2SLS method was used in Tables 7 and 12 with data adjusted for autocorrelation and heteroskedasticity. Furthermore, one equation in Table 8 is based on the fixed effect technique and the other on country means.

The adjustment for autocorrelation and heteroskedasticity follows descriptions in Kmenta (1986) and Kelejian and Oates (1981). For each country an OLS estimate of military expenditures is carried out with the dependent variable ME/GDP and independent variables ln(GDP), ln(GDP) squared, PGFF, and CGE/GDP. If the Durbin-Watson statistic is below 1.57, autocorrelation is found to be present and the standard adjustment is made and the equation is re-estimated. The standard error of the equation for each country is then used to adjust for heteroskedasticity. Then a two staged least squares estimate is made with the adjusted data to derive the estimation results on the first equation. The process is then repeated to arrive at estimates for the second equation. The results produce much higher r-squares. However, since these r-squares are based on the transformed data, they are not subject to the normal interpretation.

APPENDIX:III Disaggregated Empirical Results

1. The fixed effects model and the means estimation

Alternative estimates using the fixed effect technique and the between country estimates provide a disaggregated view of the impact of the independent variables on military expenditure policies. The between estimates based on the mean values of each country, Table 12b, concentrate on the way in which country characteristics effect the average level of military expenditures between nations. The fixed effect technique, Table 12a, allows for a different constant (or intersect) for each country and therefore lumps differences between the countries into the constant. Only factors that vary within the countries will prove significant. Thus the two offer a disaggregated view of the main estimations in Table 7 where both differences between countries and within countries are examined simultaneously. When the two effects are disaggregated, many of the coefficients are found to be insignificant. This is expected because many of the independent factors vary both within countries and between countries.

The results indicate that GDP has a concave relationship which is significant in Table 12a (positive coefficient on log GDP and a negative coefficient on log GDP squared). An insignificant weak convex relationship is found in Table 12b (negative coefficient on log GDP and a positive coefficient on log GDP squared). This implies that at low levels of GDP, within individual countries, military expenditures displays the attributes of a superior good and at high levels of GDP it becomes an inferior good. However, when examining the different military expenditure policies between countries, the military expenditures appears to be a normal good.

Central government expenditures and population are found to have a positive and significant effect on military expenditures in the fixed effects model. The relationship is insignificant in the between estimates.

Among the political variables, war, civil war and other forms of governments have positive and significant coefficients in both the fixed effects and between estimations. Military governments are positive in both, but significant only in the fixed effects equation. Monarchy is positive but insignificant in both. The financial variables are insignificant in both, other than small low income economies which are found to spend less in the between estimation.

In the central government expenditure equation, military expenditures are found to induce higher spending in both. The development index is positive and significant in the fixed effects but insignificant in the between estimate. The financial variables are insignificant in both for the most part. Among the political variables, in the betweens estimate, international war, civil war, monarchies, and socialist governments from 1986-90 have negative and significant coefficients while socialist governments prior to 1986 have a positive and significant coefficient. In the fixed effects estimates, international war and civil war have negative and significant coefficients while the others are insignificant.

2. Country groups

The subsample estimates provide some insight into different demand relationships for military expenditures in different country groups. In general, however, the results are surprisingly similar among the different country group equations in Table 7. The second column in Table 6 and 7 provides estimates for the industrialized countries combined with the Eastern European countries (including the FSU) and the third column provides combined estimates for developing countries. For both groups, military expenditures is found to increase with population and central government expenditures.

For the industrial and Eastern European countries, the relationship with GDP appears to be concave. At low levels of GDP, ME/GDP falls as GDP rises. At higher levels of GDP, ME/GDP Is positively related to GDP. Both coastline and land borders appear to have a positive effect on military spending. Socialist countries appear to have a higher ME/GDP during the entire time period, as do other forms of government. PGFF appears to have a positive and significant impact on ME/GDP. Turning to the bottom of Tables 6 and 7, central government expenditures (CGE/GDP) are found to increase with military expenditures. The effect of the development index is uncertain. Among the political variables, other forms of government are foxind to have lower CGE, socialist governments are found to have higher CGE during 1972-85, while the relationship is uncertain during 1986-1990. Finally, the effect of PGFF on CGE is uncertain.

Among the developing countries, the relationship between military expenditures and GDP Is uncertain since the signs switch between Tables 6 and 7. The financial and political variables have coefficients that are virtually identical to those obtained in the entire sample. Among the determinants of CGE, military spending and PGFF are found to have positive effects. The configuration of the coefficients on the political variables and financial variables is similar to those in the entire sample.

The developing countries are partitioned into two groups, column four of Tables 6 and 7 provides estimates for the Sub-Saharan African countries and column five is the combined estimates for the other regions. Once again, the results are surprisingly similar. The signs and significance for population and CGE are approximately the same. For the sub-Saharan African countries, the effect of GDP is clearly convex. For countries with low levels of GDP, as GDP rises, military spending increases by a lower proportion. At higher levels of GDP, military expenditures are found to increase more rapidly than GDP. Net debtor countries, low income countries and democracies are found to spend less on the military. As for central government expenditures, higher military spending induces higher CGE. Military governments and other forms of government seem to have higher CGE, there appears to be a positive association with PGFF while small low income economies and high debt countries from 1972-1979 seem to have lower CGE. The effect of the development index is uncertain. In the equations covering Asia, Latin America, the Middle East, and North Africa, virtually identical results are obtained.

3. Individual country results

In order to carry out the transformation of the data to correct for autocorrelation and heteroskedasticity, OLS estimations for each individual country (except Angola and Lebanon for which not enough observations exist) were carried out. Only five variables were available in these equations since most of the others are dummy variables vary mostly between countries rather than within countries. For about three-fourths of the countries the r-squared exceeded 0.5, nonetheless, in most cases none of the coefficients were significant due to the relatively small number of observations for each country. To summarize the results, in 31 cases central government expenditures have a positive and significant coefficient while in 2 cases the sign is negative and significant. In 16 cases GDP has a concave relationship with military expenditures and in 4 cases the relationship is convex and significant. Finally, in 9 cases PGFF has a positive and significant coefficient while in 3 cases the sign is negative and significant. These results provide some further support for conclusions derived in the cross section analysis.

Table 11.

Country Rankings and Ratios of SIPRI Military Expenditure to GDP, 1980-90

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Sources: SIPRI Yearbook, IFS.
Table 12a.

Fixed Effects Estimations, Adjusted Data, 1972-90

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Table 12b.

Between Estimations (Means), Adjusted Data, 1972-90

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Table 13.

Means, Maxima, and Minima, 1972-90

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Sources: SIPRI, ACDA, Steinberg, published World Bank and IMF sources, Europa World Yearbook; staff estimates.


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The views expressed in this paper do not necessarily represent those of the International Monetary Fund. Thanks to Tarja Papavassiliou for data preparation and thanks to Boris Bravo-Ureta, Ke-young Chu, Shahbaz Khan, and Subhash Ray for their comments. All errors are solely the responsibility of the author.


Data on military expenditures is derived mostly from the Stockholm International Peace Research Institute (SIPRI), see Appendix I. Although the accuracy of this data is unknown, the trends in data are probably more reliable.


The dollar figures are derived using official exchange rate. The problems with this technique are well known, see Hewitt (1992) for a fuller analysis.


See the Kelejian and Oates (1981) Appendix “Autocorrelated Disturbance Terms in a Simultaneous-Equations Model” pages 296-299 and Kmenta (1986) pp. 616-633.


Thus, at low levels of GDP, military spending is an inferior good, at high levels of GDP military spending is found to be a superior good.


For Sub-Saharan Africa, this relationship is insignificant in Table 7, but is statistically significant in Table 6.


The growth figures in this section are taken from the October 1992 World Economic Outlook.


Among the countries that increased their military spending, a relatively high proportion also 60 percent experience a similar rise in PPP growth; in countries where the ratio of military spending to GDP remained the same, 50 percent also had a significant rise in PPP growth; while in countries that decreased their military spending in proportion to GDP, 42 percent had a significant increase in PPP.


This study does not provide the list of which countries fit into each category. The purpose of the political variables is to provide empirical insight into the determinants of military spending, rather than engage in categorizing different political regimes.


When a political change occurs, the country is placed in another political category in the following year. This is because the budget in force during the transition year was formulated by the preceding government. Clearly events preceding political changes can alter government policy. Furthermore, it is possible for a new government to immediately institute changes in budgetary allocations.


In the initial stages a number of variables for rival and allies were included, see Hewitt (1992). However, inconsistent results were obtained and for simplicity they were omitted from subsequent computer runs.

Military Expenditures 1972-1990: The Reasons Behind the Post-1985 Fall in World Military Spending
Author: Mr. Daniel P. Hewitt