Defence spending and conflict: diagnosing a thesis before the viva
A doctoral candidate regresses the annual number of armed-conflict fatalities on military expenditure as a share of GDP for five South Asian states over 25 years - 125 observations. Controls are GDP per capita and a regime-type index; a lagged dependent variable is included. R-squared is 0.78 and the military-expenditure coefficient is positive and significant at the 1 per cent level. Three problems surface at the viva. The dependent variable is a count with 38 zero-fatality state-years. An augmented Dickey–Fuller test cannot reject a unit root in the expenditure series. The examiner observes that in two of the five states, conflict in a given year is followed by a documented expenditure increase in the following budget. The candidate's defence is that 'the sample is the population, so inference does not matter' and that 'the R-squared is high'. The thesis argues that higher defence burden causes more conflict.
1. Rank the three most serious threats to the thesis's causal claim and explain why each matters more than the reported R-squared.
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Ranking by damage to the claim.
- Simultaneity (endogeneity). The examiner's observation that conflict precedes budget increases establishes reverse causation. If spending responds to conflict, the coefficient conflates the effect of conflict on spending with the effect of spending on conflict, and its sign is uninterpretable. This is fatal to a causal claim, not merely a caveat.
- Non-stationarity. A unit root in the expenditure series means the regression is a candidate for spurious correlation: two trending series will produce high R-squared and 'significant' coefficients with no relationship. The R-squared of 0.78 is therefore not evidence - it is precisely the symptom the ADF test warns about.
- Wrong estimator for a count outcome. Thirty-eight zero-fatality state-years plus a skewed count variable violate the linear-model assumptions; OLS can predict negative fatalities and gives undue weight to high-fatality years.
Why the candidate's defences fail.
- 'The sample is the population' confuses description with causation. Even a census of five states cannot license a causal claim from an endogenous, non-stationary regression.
- 'R-squared is high' is the weakest possible defence, since spurious regression is characterised by high R-squared.
A fourth, lesser problem is the lagged dependent variable combined with short panels, which biases fixed-effects estimates.
2. Propose a defensible re-specification. Be specific about estimator, identification strategy, and what each change buys.
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Outcome model. Treat fatalities as a count: negative binomial (or Poisson with robust standard errors, tested for overdispersion) with state and year fixed effects. This corrects the zeros problem and stops the model predicting negative events.
Dynamics and non-stationarity. Move to an autoregressive distributed lag or panel error-correction framework, testing for cointegration. If the series are cointegrated, estimate the long-run relationship with a valid error-correction term; if not, estimate in first differences. Either route removes the spurious-regression risk and buys a distinction between short-run and long-run effects.
Identification. The current design cannot separate the two directions. Options, in descending order of credibility:
- A natural experiment: a discrete, externally driven expenditure shock - a pay-commission award, a large single procurement, or a terms-of-trade windfall - used as a source of variation not caused by contemporaneous conflict.
- Instrumental variables with an instrument that shifts spending but not conflict directly, with the exclusion restriction argued explicitly, not assumed.
- System GMM for the dynamic panel, using internal instruments, provided the instrument count is kept well below the number of states and the Hansen test is reported and interpreted honestly.
What to drop. The lagged dependent variable within a short fixed-effects panel, unless the dynamic panel estimator is used properly.
What this buys. A coefficient that can be interpreted, a standard error that means something, and a thesis that can survive the reverse-causation objection rather than ignoring it.
3. How should the candidate handle the measurement of 'defence burden', and what difference would the choice make to the conclusion?
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The measurement problem is not cosmetic. Military expenditure as a share of GDP can be built from the national budget or from a standardised external series, and the two diverge substantially for South Asian states.
Sources of divergence.
- Off-budget items: pensions, paramilitary and border forces, strategic programmes, and subsidies to defence production are included or excluded depending on definition.
- Exchange rates: market rates versus purchasing power parity change both the numerator and cross-country comparability; PPP raises India's relative size sharply.
- Timing: budgeted versus actual expenditure, and fiscal versus calendar years.
- Capital versus revenue: a single large aircraft purchase spikes the ratio in one year and distorts the series.
Why it matters for the conclusion. If the candidate uses a narrow budget series that excludes paramilitary spending, the measure systematically understates the burden in states where internal conflict is the main driver - which is exactly the variation the thesis claims to explain. The result may be an artefact of definition rather than a finding about conflict.
Recommendation. Report the main results on a standardised series, replicate on the national budget series as a robustness check, and disclose the definitional choices in an appendix. Also justify the conflict measure itself: fatality thresholds, one-sided violence, and missing years all affect the count.
Judgement. A thesis that is robust across two defensible measures is making a claim about the world; one that survives on a single measure is making a claim about a spreadsheet.