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The Economics of War: Militarization and Growth in an AK Economy

This paper utilizes an endogenous growth model to demonstrate that while moderate military spending can temporarily stimulate economic growth through demand and innovation, excessive militarization ultimately hinders long-term development by crowding out civilian investment and creating structural rigidities.

Original authors: Arpan Chakraborty

Published 2026-03-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Arpan Chakraborty

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the economy of a country as a giant, complex garden. The goal of the garden is to grow bigger and produce more fruit every year (economic growth). To do this, the garden needs two main things:

Seeds and Water: Money invested in planting new crops and building better tools (Capital Investment).
Soil Quality: The technology and know-how that make every seed grow faster (Productivity/Innovation).

This paper asks a difficult question: What happens to the garden if the gardener spends a lot of money building a giant wall and buying weapons to protect it?

Here is the breakdown of the paper's findings using simple analogies:

1. The Short-Term Boost: The "Party" Effect

In the short run, spending money on the military is like throwing a big party in the garden.

The Analogy: You hire people to build the wall, buy materials, and pay soldiers. Everyone gets paid, they go to the local shops, and the garden feels very busy and lively.
The Result: For a little while, the garden looks like it's doing great. This is the Keynesian view: spending money creates jobs and keeps the economy moving, even if that money is going to a wall instead of a new orchard.

2. The Long-Term Trap: The "Opportunity Cost"

But a garden has a limited amount of water and seeds. If you use a huge bucket of water to fill a moat around the wall, you have less water for the fruit trees.

The Analogy: Every dollar spent on a tank is a dollar not spent on a new tractor or a better irrigation system.
The Result: Over time, if you keep pouring money into the wall, you stop planting new seeds. The garden stops growing as fast as it could have. This is the Crowding Out effect.

3. The Twist: The "Spillover" Effect

However, the paper admits it's not all bad. Sometimes, building a wall forces you to invent better locks, stronger steel, or better radar.

The Analogy: While building the wall, the gardener accidentally invents a super-efficient watering hose that works for the fruit trees, too.
The Result: A little bit of military spending can actually help the garden grow faster because of these accidental inventions (innovation).

4. The "Hump-Shaped" Curve: The Sweet Spot

The paper combines these ideas into a single curve that looks like a hill (a hump).

The Left Side (Too Little): If you spend nothing on defense, you miss out on the cool inventions that come from military research. The garden grows, but slowly.
The Peak (The Sweet Spot): There is a "Goldilocks" zone. You spend just enough on defense to get those cool inventions, but not so much that you run out of seeds for the fruit trees. This is where the garden grows the fastest.
The Right Side (Too Much): If you spend too much on the wall, you starve the fruit trees. The inventions aren't enough to make up for the lack of seeds. The garden starts to shrink.

5. The Two Gardeners: The Rich vs. The Struggling

The paper compares two different types of gardeners to see how they handle a war:

Gardener A (The Advanced Economy - like the US):
- The Setup: This gardener has a massive warehouse of seeds, a team of brilliant scientists, and very strong tools.
- The War: When a war starts, they spend more on the wall and lose a few tools.
- The Outcome: Because they are so rich and efficient, they can still grow fruit, just a little slower than before. They survive the war, but they miss out on the potential growth they could have had in peace.
Gardener B (The Sanctioned Economy - like Iran):
- The Setup: This gardener has a small pile of seeds, older tools, and the soil is already a bit dry (due to sanctions).
- The War: When a war starts, they are forced to spend almost all their remaining seeds on the wall. Their tools get broken (destruction).
- The Outcome: They have no seeds left for the fruit trees. The garden doesn't just grow slower; it dies. The economy shrinks rapidly, leading to a collapse in living standards.

The Big Takeaway

The paper concludes that militarization is a double-edged sword.

A little bit of sword-fighting can sharpen your skills (innovation).
But if you spend your whole life sharpening swords, you forget how to farm.

The danger is when a country gets stuck in a "Permanent War Economy." This happens when political forces keep the spending on the "Right Side" of the hill (too high), locking the country into a cycle where they spend so much on defense that they can never reach their full potential for growth.

In short: War might make a rich country grow a bit slower, but for a poorer or weaker country, it can be the difference between a thriving garden and a barren wasteland.

1. Problem Statement

The paper addresses the long-standing debate regarding the macroeconomic impact of military spending. While military expenditure is often justified by national security needs, economists question whether it promotes sustainable growth or diverts resources from productive sectors (education, health, infrastructure). The central problem is to determine the non-linear relationship between the "military burden" (military spending as a share of GDP) and long-run economic growth. Specifically, the paper seeks to resolve the tension between:

Short-term demand stimulation: Military spending acting as a Keynesian aggregate demand component.
Long-term structural costs: The "crowding out" of civilian investment and the potential distortion of technological trajectories.

2. Methodology

The paper employs a hybrid methodological approach combining formal theoretical modeling with calibrated numerical simulations.

Theoretical Framework:
- Short-Run: A standard Keynesian income-expenditure model is used to establish the multiplier effect of military spending ( $G_m$ ) on output ( $Y$ ).
- Long-Run: The core analysis utilizes a one-sector AK endogenous growth model. In this framework, output is linear in capital ( $Y_t = A_t K_t$ ), implying constant returns to scale and no diminishing returns to capital accumulation.
- Mechanism: The model introduces a military burden variable ( $m$ $m$ ) that affects growth through two opposing channels:
  1. Crowding-out: Reduces the share of output available for civilian investment ( $1-m$ ).
  2. Productivity/Innovation: Military spending influences the productivity parameter $A(m)$ , modeled as a quadratic function to capture diminishing returns and eventual negative effects of excessive militarization.
Calibration and Simulation:
- Parameters (savings rate $s$ , depreciation $\delta$ , innovation coefficients $\phi$ and $\chi$ ) are calibrated using values from standard macroeconomic literature (e.g., Barro, 1990) and empirical studies on military spending (e.g., Dunne et al., 2005).
- Two-Country Extension: The model is extended to a two-country scenario comparing an advanced economy (modeled after the US) and a sanctioned middle-income economy (modeled after Iran). This allows for the analysis of asymmetric growth costs during conflict, incorporating war-induced capital destruction ( $d$ ).

3. Key Contributions

Formalization of the "Hump-Shaped" Relationship: The paper provides a theoretical derivation showing that the relationship between military burden and growth is non-linear (inverted U-shape). It demonstrates that moderate militarization can boost growth via defense-induced innovation, while excessive militarization leads to stagnation due to investment crowding-out and resource misallocation.
Integration of Demand and Supply Channels: Unlike reduced-form regressions, the model explicitly traces the transmission mechanisms: how military spending affects aggregate demand in the short run and capital accumulation/productivity in the long run.
Asymmetric War Costs: The two-country extension highlights that the macroeconomic costs of war are not uniform. It demonstrates that structurally weaker economies (lower savings, lower baseline productivity, higher vulnerability to destruction) suffer disproportionately higher growth losses compared to advanced economies under similar conflict conditions.
Concept of "Permanent War Economy": The paper interprets institutionalized high military spending as a political equilibrium that may lock an economy onto the downward-sloping segment of the growth curve, resulting in suboptimal long-run development.

4. Results

Single-Economy Simulation:

The calibrated growth function, $g(m) = -\delta + s(1-m)A_0[1 + \phi m - \chi m^2]$ , yields a hump-shaped curve.
Low $m$ : Growth is positive but suboptimal; potential innovation benefits are underutilized.
Intermediate $m$ : An interior maximum exists where the positive innovation effect ( $\phi m$ ) outweighs the crowding-out effect ( $1-m$ ).
High $m$ : Growth declines sharply as the negative curvature ( $\chi m^2$ ) and reduced investment share dominate, leading to secular stagnation.

Two-Country War Simulation (US vs. Iran):

United States (Advanced Economy):
- Peacetime: ~3.5% growth.
- Wartime: Growth drops to ~2.4%.
- Analysis: High baseline productivity ( $A_0$ ), strong savings ( $s$ ), and efficient innovation channels allow the US to absorb the shock of war and capital destruction, maintaining positive growth despite the opportunity cost.
Iran (Sanctioned Middle-Income Economy):
- Peacetime: ~-1.4% growth (structural stagnation).
- Wartime: Growth collapses to ~-6.2%.
- Analysis: Lower savings, lower productivity, and higher vulnerability to capital destruction ( $d$ ) mean that increased military burden pushes the economy onto the steep, negative slope of the growth curve. War transforms a stagnating economy into one of rapid cumulative contraction.

5. Significance

Policy Implications: The results suggest that while moderate defense spending can be growth-enhancing, there is a critical threshold beyond which militarization becomes self-defeating. Policymakers must balance security needs against the risk of locking the economy into a "permanent war economy" with suppressed long-term growth.
Theoretical Clarity: By using the AK model, the paper isolates the composition of demand as a primary driver of long-run growth rates, offering a transparent alternative to complex transitional dynamics found in Solow-type models.
Geopolitical Insight: The asymmetric results provide a theoretical basis for understanding why conflicts between unequal economies impose devastating, potentially existential economic costs on the weaker party, while the stronger party may experience only a temporary slowdown.
Future Research: The paper identifies the need for endogenizing the military burden (via political economy mechanisms) and incorporating heterogeneous sectors to better understand the distributional impacts of militarization.

Conclusion: The paper concludes that the economic impact of war is not merely a function of the level of spending but of the structural characteristics of the economy (savings, productivity, and resilience). While a "permanent war economy" may sustain short-term demand, it often leads to long-term developmental stagnation, particularly for economies with weaker structural foundations.