Petrostates & Conflict Initiation

// the argument

Petrostates behave more aggressively abroad than other states. My theory locates the cause not in oil wealth alone, but in the strategic position of vulnerable leaders. When a leader faces a credible internal threat — a high coup risk — oil revenue gives them the means to start interstate conflicts that coup-proof the regime: co-opting the military with budgets and missions, rallying the public around nationalism, and buying time to repress opposition. Conflict initiation, on this account, is a tool of domestic survival.

// data & measurement

The unit is the country-year, 1960–2010, restricted to non-democracies (Polity < 7). The outcome is the count of militarized interstate disputes a state initiates in a year (Correlates of War / UCDP via the peacesciencer package). Coup risk follows Belkin & Schofer / Sudduth (2017); oil dependence is fuel income as a share of GDP from Haber & Menaldo's fiscal-reliance data (petrostate = fuel ≥ 10% of GDP); controls cover fuel exports, military spending, GDP per capita, and ongoing civil war. The pipeline ships a calibrated simulation so it runs offline; flip USE_REAL_DATA to load the merged panel.

def poisson_irls(X, y):
    """log E[y] = Xβ via iteratively reweighted least squares (= Newton for a GLM)."""
    beta = np.zeros(X.shape[1]); beta[0] = np.log(y.mean())
    for _ in range(100):
        mu = np.exp(np.clip(X @ beta, -30, 30))   # mean = variance (Poisson)
        z  = (X @ beta) + (y - mu) / mu           # working response
        W  = mu                                    # IRLS weights
        beta = np.linalg.solve((X*W[:,None]).T @ X, (X*W[:,None]).T @ z)
    return beta

// why count models

MID initiation is a count: a non-negative integer, mostly zero, occasionally several. Ordinary regression would predict negative and fractional conflicts and mis-state the uncertainty. The Poisson model fixes the support by modelling the log rate, but it assumes the mean equals the variance — and conflict data are far more dispersed than that, with a glut of zeros and a long right tail.

Figure 1 · Observed MID counts vs. a Poisson fit at the mean. The excess of zeros and the heavy tail signal overdispersion.

A Pearson dispersion of 1.30 (> 1) confirms it, so I also fit a negative binomial, which adds a parameter α so the variance can exceed the mean (Var = μ + αμ²). It fits substantially better on AIC — the inference below uses it.

// interactive · simulate a regime

The widget runs the fitted negative-binomial model in your browser. Set a country's oil dependence and controls, then watch how its predicted conflict rate rises with coup risk — and how the petrostate and non-petrostate curves diverge. The dot marks the coup-risk level you select.

// results · the models

Both estimators agree on the story. Higher coup risk and petrostate status each raise the rate of conflict initiation, and the interaction is positive: the marginal effect of coup risk is larger for petrostates. Coefficients are reported as incidence-rate ratios (e^β) — the multiplicative change in the expected MID count.

# Negative binomial: Var = μ + αμ²  (α>0 absorbs the overdispersion)
def loglik(theta):
    beta, alpha = theta[:-1], np.exp(theta[-1]); r = 1/alpha
    mu = np.exp(np.clip(X @ beta, -30, 30))
    return np.sum(gammaln(y+r) - gammaln(r) - gammaln(y+1)
                  + r*np.log(r/(r+mu)) + y*np.log(mu/(r+mu)))
# maximized by Newton-Raphson + line search -> α = 1.49, beats Poisson on AIC

Figure 2 · Negative-binomial incidence-rate ratios. Petrostate status, coup risk, and their interaction all push conflict up.

// the central finding · the interaction

The interaction is the heart of the argument. For a non-petrostate, rising coup risk nudges conflict up modestly. For a petrostate, the same rise in coup risk produces a far steeper climb — oil revenue converts domestic vulnerability into the capacity for diversionary war. This is the pattern behind cases like Iraq under Saddam Hussein and revolutionary Iran.

Figure 3 · Predicted MID initiations vs. coup risk, petrostates vs. non-petrostates — the central interaction, and the engine of the dashboard above.

Figure 4 · Model-predicted vs. observed initiation rate across the coup-risk distribution.

// what this demonstrates

• Count-data modelling — Poisson by IRLS and a negative binomial by maximum likelihood, both coded from scratch, with the log-Gamma evaluated via a Lanczos approximation (no SciPy).
• Diagnosing the right model — detecting overdispersion and excess zeros, and choosing the estimator the data actually require.
• Interactions & quantities of interest — translating an interaction coefficient into incidence-rate ratios and predicted counts a reader can feel.
• From paper to product — turning my own published research design into a reproducible pipeline and a dependency-free interactive visualization.