What I learned from… Elisa Cavatorta


Cavatorta, E. (2010) Unobserved common factors in military expenditure interactions across MENA countries. Defence and Peace Economics, 21(4), 301-316.

What Elisa is interested in doing here is to go beyond the most typical variables used to explain military expenditure (monetary capacity, perception of external threats, perception of internal threats). Although I am using the word ‘beyond’ both as a consideration of granularity of known variables and, at once, an expression of existence of unknown variables.

The idea of there being unknown variables that matter toward how much a country spends in military is justified in the fact that perception is involved in this process. Perception is a type of phenomena for which measurement is very difficult. The more qualitative nuances are bound to be left out.

She gives the example of morale. Will a country with high morale invest the same as one with low morale? Or will high/low morale affect the perception of, say, threats? And if morale has a role, to what extent can one ‘observe‘ its influence if we cannot actually measure it – at least not accurately?

This issue seems to be particularly important for countries with strong inter-linkages due to either being enemies or allies (either way, they’re going to keep tabs on each other). Under these circumstances, qualitative nuances in one country (or those that affect them all) could potentially influence military expenditure across the region. A good example of one such region is the Middle East and North Africa (MENA) where Elisa believes considerations of legitimacy and the existence/absence of economic shocks arebound to affect military expenditure of many countries in similar ways.


As is typical of academic papers, the first section is a review of the most relevant literature. In this case, a review of literature about military interactions. Elisa notes this literature is broadly divided in two: military alliances and arms races.

She formalises this as

Military Expenditure (M) being a function of

national income (y),

price of one action (p),

total # of actions take by a country’s allies (M),

threat of enemies (T),

and environmental influences (E).

The key here is to recall that any and all functions entail an error coefficient (ε). This is necessary to account for any factors not covered by what can be measured. When many countries share similar allies, enemies, and/or environmental influences, the variables noted-above are going to also look alike and, by corollary, the ε‘s of each independent country will too. This does not mean, however, that the ε of a country will be exactly the same as the ε of another country. But the question of the extent to which all ε‘s will look like each other is open.


The next section deals with the measurement of M for the countries in the sample. It turns out that estimating the military expenditure of any country is wickedly difficult so imperfect estimates are bound to happen. Of particular concern is the fact that to compare different countries one needs to remain at the general level, which forbids Elisa from undertaken a thoroughly granular measure of each country’s military budget by herself. As such, she defaults to the most authoritative source of military expenditure estimates available: the Stockholm International Peace
Research Institute (SIPRI) database.


I continue to find that maybe I didn’t think this section out that well when I started it. The objective was to write about articles in a way that makes arguments by X type of scholars accesible to A, B, C, …., Z type of scholars.  However, some of these models I’m running require a lot of math-making. But OK, let’s try and find a middle ground.

Let’s talk about M again, and the fact that is has known factors and an ε. Assuming one can break down ε to more factors, one is bound to be able to reduce the size of ε. As such, M becomes a function of KNOWN + UNKNOWN variables + a smaller ε.

Since we cannot know the unknown factors a priori (because they are unknown), what Elisa wants to do is to start by finding how many there are, and then trying to piece out if what they are.


— Correlations and # of variables

Elisa notes that she can establish if the M’s that she has are directly explicable by known variables. If they are, well, that’s the end of the article.

If they are not, there are two possibilities, that she is consistently short (which, annoyingly, is called being ‘inconsistent’ – as it is measured as an aggregate so totals are actually not consistent if the parts are consistently short), or that estimates are all over the place (which is called ‘inneficiency’). The former indicates correlations (and thus opens room for the possibility of finding factors applicable to all), the latter does not (which would require a different type of analysis). If correlations are shown, given that the estimates are short, there will be some residuals (which in the terms given above would be made of both UNKNOWN variables + some remaining ε‘s). She can then take those residuals and  try piecing out the patterns.

Once the analysis is run, it is clear that there is evidence for the need of UNKNOWN variables. In addition, it also seems that correlations are centered on Egypt/Israel/Jordan and on Yemen/Oman/UAE. This is consistent with the idea that there are strong interlinkages between these countries (either positive or negative) due to the Arab/Israel conflict or the tensions in the entry to the Persian Gulf region (a very narrow strait of massive geopolitical importance due to the fact that all the oil in the region needs to be shipped through there).

All this leads Elisa to believe that there are at least two different unknown variables that do affect the ε‘s of many countries at once.

Open question - Why not 3?
Egypt and Oman, and Morocco and Oman showed to be correlated. Is this correlation covered by two regional unknown variables hypothesized?

— Can the unknown variables be known?

The short answer. No! But some informed guesses are possible.

The long answer. Elisa analyses the data with a technique known as Principal Component Analysis. This is a graphical multi-variate approach that takes a table of existing observations, maps them on an X/Y chart, and establishes the minimum number of factors needed to acccount for most them – which are called the principal components (PCs). The idea is that the more correlated the data is, the less PCs will be found.

She does this in two ways. First, to the shares of GDPs as such. Second, to the residuals found in the previous section (i.e. the bits not acccounted for by known variables, including UNKNOWN variables and remaining ε‘s).


Elisa finds that 4 factors account for as much as 87% of the military shares, with the two first factors being particularly strong indicators. She also finds that PCA supports the idea of strong regionally-centred correlations between countries in a manner similar to that found earlier, Yemen/Oman/Morroco on the one hand and Israel and a bunch of other guys on the other.

Since PCA does not tell you what the factors are, what follows is speculation. Very informed and very reasonable speculation, but still speculation.

External shocks (in particular, Gulf War & Algerian civil war). This is because whilst most countries are similarly influenced by the largest factor, Algeria and Kuwait behave very differently. The most plausible explanation of one such thing is that Algerian and Kuwait experienced large increases in military expenditure due to the particular shocks being in their territories (shocks that then go to affect the rest of the region in similar manners).

Resource availability. The second largest component seems to break the region in two types of countries. Those with negative or null effect: Bahrain, Kuwait, UAE and Egypt present (negative effects), and Oman, Tunisia, and Saudi Arabia (null effect). Those with positive effect: Algeria, Iran, Israel, Morocco, Syria, Turkey and Yemen. With the exception of Israel, this can be explained by the availability/lack of internal resources. This idea is supported by the fact that there is significant deviation from normal patterns in 1979 and in 1991, two years that correspond to very significant oil crises (Iran’s revolution & Gulf War).

* Residuals

The second PCA analysis is performed only on residuals. In here, five factors are found to explain 79% of data, also with two of these factors being particularly strong.

The first factor has a relatively similar effect to all countries except for Bahrain, Iran, Kuwait, Jordan, Tunisia and Turkey. Whilst not definitely, as it is unclear why Iran and Turkey are in this list, this can be explained by the existence of internal conflicts in these countries. The ensuing rationale would support the shock-driven explanation given earlier.

The second component has a particular strong effect to Jordan, Syria, Israel and Kuwait, a negative effect to Turkey, Tunisia, UAE, Morocco and Algeria, and most of the Gulf countries are in the vicinity of zero. This also supports the idea of regional clusters of allies/enemies. The Arab-Israeli conflict grouping the first set of countries. The interlinkages between Maghreb countries homogenising military expenditure in North West Africa. Iran’s quest for hegemony and subsequent struggle for acccess to maritime ways as significant to most of the Gulf countries.

A robustness test

Since the considerations about the specific factors are speculatory, Elisa takes the PCA analysis into a second round by performing a robustness test with another tool called a ‘multiple-indicator multiple-cause ‘ (MIMIC) model. I will, however, skip this bit because I think I reached my personal limit of weekly mathematics already.


Elisa finds that, in MENA, two unobserved variables seem to have fairly homogeneous impact to the military expenditure of many countries. Of this, there seems to be little doubt. There are at least two factors that do tie together the military expenditure of these countries.

Where there is some room for doubts is on the explanation of what the specific factors are, because the tools used do not given certainty on the matter (not that any other tool would). That said, it is reasonable to think that the two factors come down to the existence of external shocks and the regional clusterisation of military expenditure due to geopolitical concerns.

In addition, there are also some interesting general notes that can be done.

Firstly, I am amazed at Elisa’s ability to stick to the evidence. I cannot find a single superflous consideration in the entire article. Whilst this may sound basic given that it should be the norm of academic research, it actually is very difficult to achieve (and relatively rare).

Secondly, I loved the fact that, exception made of the inevitable use of math (it is, after all, a quant. paper), the argument is very easy to follow.

Thirdly, I am particularly impressed about Elisa’s willigness to engage in such an ambitious analysis upon knowledge of the fact that military expenditure statistics are very innacurate. Academics can be timid about using imperfect datasets in their work (I suppose because they fear their work later being problematised as a result). By definition, however, most of the difficult questions in modern times are bound to be related to complex and rather difficult to measure issues. Ergo, Elisa’s willigness to engage is exemplary.

Fourthly, although this is not mentioned in the article, I loved the fact that the article can be linked to risk management literature. This is because Elisa ultimately explaines the region as a system with relatively low levels of slack in between the parts. In these type of systems, shocks spread more easily across the components. Definitely not a happy thought given the topic of the essay, but a very interesting one I think.