# Estimating National Power

Over the last seventy years, there have been numerous efforts to quantify national power. Here we propose a definition that derives from the ideas of quantitative realism.

## Definition

In quantitative realism, power is the ability to affect the power of another state either constructively or destructively. When applied to international relations, how does this correspond to real world quantities?

### Constraints

There are several constraints this correspondence should satisfy:

1. The measured quantities should allow for absolute increases in power, since the model allows for absolute growth. This breaks with many definitions of national power, which are based on states' shares of the world total of some quantity, such as GDP.
2. Quantities that are combined into a composite metric should have compatible units of measure. The common method of using shares of world total sidesteps this problem, but due to #1, that is not available to us. We will use U.S. dollars baselined to some relevant year.
3. There should be a coherence between the quantities used for power in motion and power at rest. Power at rest is what is possessed by agents at a point in time; power in motion constitutes transactions of trade, exchange, and violence that occur over some interval of time. The various quantities used for these activities should be commensurable. Ideally, they would be based on some sort of accounting identity that is true by definition.
4. Quantitative realism assumes an immediate fungibility between constructive and destructive power, in that each agent has a single bucket of power that can be used for either purpose. In the real world, this is obviously not the case. A state with immense wealth but no military would have a limited ability to apply destructive power. So when estimating expenditures of positive and negative power in the context of international relations, we should take into account each state's capacity for these two activities. The two primary dimensions of interest are overall economic strength and military capacity. While there are numerous indicia of positive and negative relations among states, we assume that destructive power is based primarily upon military capacity, and constructive power is based primarily upon trading capacity.

### Definition

One formulation which meets the above criteria is to define national power in terms of national wealth. National wealth is a stock quantity, estimated at a point in time, and it has a standardized definition in the United Nations System of National Accounts, section 13.4 (2008). By explicitly separating out the military and non-military components, we could define power at rest as:

$\displaystyle{ s = m + c }$

where m is the value of a state's military assets and c is the value of its non-military (civilian) assets. The amount m represents the limit of a state's destructive capacity.

Destructive action could then be measured as state A's military expenditure on a particular conflict with state B over some time interval. In other words, state A expends some amount of its resources on violence towards state B, and state B's wealth is reduced accordingly. This expenditure, when multiplied by the destructive multiplier μ, would be equal to state B's reduction in wealth over that same time period, ceteris parabus. This reduction would have to be apportioned over state B's military and non-military assets, the simplest approach being to reduce each by the same factor. If we allow the parameter μ to vary by situation, which is reasonable due to technological and other differences, we will have established an accounting identity per constraint #3 above.

Constructive action could be measured in terms of the trade volume between states A and B over some time interval. Since for our purposes there is no qualitative difference between imports and exports, the average of the two should be used. One-way transfers of foreign assistance could also be included. When state A transfers this outgoing amount, it reduces A's national wealth accordingly, and increases the national wealth of state B by that amount times the constructive multiplier β. State B's military and non-military assets would increase by the same factor. This multiplier effect is arguably not instantaneous; state B's economy may need time to productively metabolize the new assets, thereby increasing its wealth, but this effect is presumed to occur within the relevant time interval. The parameter β can float to satisfy constraint #3.

What happens when a bilateral relationship entails simultaneous trade and conflict, the alternative formulation of the law of motion is apt. That way, when two nations engage in trade and conflict at the same time, the positive and negative effects partially cancel each other out.

One consequence of using wealth, military expenditure, and trade is that it obviates the need to arbitrarily set the self-allocation percentage ρ. Instead, the percentage of power allocated by a state will be

(total dyadic military expenditures + total trade volume) / national wealth.

The conception above could be extended to non-state actors: power at rest would correspond to wealth, destructive action would correspond to the amount of assets expended on violence, and constructive action would correspond to commercial activity.

### Example

In 2019 the national wealth of the U.S. was approximately $92T (World Inequality Database), military assets were worth around$2.9T (Dept. of Defense Financial Report 2019, p. 34), and the average of imports plus exports was \$2.8T (Census Dept.). If all military assets had been directed towards a single conflict, it would represent an expenditure of 3% of national power. Since not all assets can be deployed toward a single enemy, this figure is an upper ceiling, with less than 1% of national power being a more likely magnitude for a dyadic conflict. In this example, trade flows constitute a constructive transfer of 3% of national power.

## Availability of Data

Given the above, the data we need (by year) is:

• National wealth, preferably separated into military and non-military components
• Military expenditure per dyadic conflict

Unfortunately, the availability of this data is rather limited at present. Currently known sources include:

Variable Source Data set Years Units
National wealth World Inequality Lab World Inequality Dataset Varies by country 2019 USD
Military expenditure
Trade volume Correlates of War Trade data set v4.0 1870-2014 Current USD (millions)
Foreign assistance David Roodman Net Aid Transfers data set 1960-2016 Current USD (millions)

If the variables listed above are indeed the real world manifestations of power in international relations, then it will be challenging to demonstrate the soundness of that interpretation until the historical time series for that data is more fully developed. In the meantime, our models will have to rely upon proxy data and reasonable methods of estimation, seeking approximations rather than exact quantities. The approach in each case will depend upon what data is available for the time period at issue: for example, modeling the Peloponnesian War will require different sources and techniques than, say, World War I.

## Methods of Approximation

How can we make back-of-the-envelope approximations of national wealth, military expenditure, bilateral trade, and foreign assistance, using general data suggestive of national power?

### Estimating national wealth from GDP

Since GDP data is plentiful for the postwar era, we can estimate national wealth from it using world average wealth-income ratios from Piketty (2014) and Bauluz (2019), Fig. 3. For example, to estimate the national wealth of Argentina in 1970, we would multiply its GDP of 31.6B (1970 USD) by 3.5, the average capital-income ratio at the time, to get 110.6B (1970 USD). This is obviously a very rough approximation, almost certainly subject to future revision, but it should enable us to tinker with various historical scenarios.

### Other

• Baselining military expenditure as percentage of national wealth
• Baselining trade volume and foreign assistance as percentage of national wealth

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