Industry: Government and Public Sector Product: ModelRisk Application: Social program analysis
A national housing-assistance program runs on a fixed annual appropriation: $3,600M, set by the budget committee and not easily reopened mid-year. The program office had built its request on point estimates — a 46% take-up rate, about 470,000 households served, an average case cost near $7,400 — which multiplied out to roughly $3.5B and looked comfortably inside the line. The committee approved it. What nobody had quantified was the chance the program would run out of money and need a supplemental appropriation.
That probability is the whole game in program budgeting, and it cannot be read off a point estimate. ModelRisk was used to forecast the distribution of total program cost and caseload, and to put a number on the over-run risk.
A deterministic budget multiplies best-guess values together and reports one cost. But caseload is a count of people who show up, and how many show up depends on a take-up rate that varies, an eligible population that swells in a downturn, and a per-case cost that is right-skewed and itself climbs when the economy weakens. Multiply three central guesses and you get a single number that sits, by construction, near the middle of the real distribution — telling the committee nothing about the upside tail that triggers a supplemental.
The simulation, run over 100,000 trials, puts annual program cost at a mean of $3,688M, a P50 of $3,369M, a P90 of $5,832M, and a P95 of $6,799M. Against the $3,600M appropriation, the probability of an over-run is 43.8%. The point-estimate budget that looked safely inside the line is in fact a near coin-flip, with a P90 that exceeds the appropriation by more than 60%.
Total program cost is caseload multiplied by per-case cost, and each side is modelled from its own uncertain components — with one shared macroeconomic factor running through both.
The decisive modelling choice is the shared macro factor. A recession does not politely raise eligibility while leaving costs alone — it raises both at once. Modelling caseload and per-case cost as independent would have let their swings partially cancel and produced a deceptively tight cost distribution. The common factor instead couples them, and that coupling is what fattens the upper tail where the supplemental-appropriation risk lives.
Plotting caseload against total cost shows the program's budget does not live on a single axis — it lives in a plane, and the two axes move together.
The correlation between caseload and total cost is 0.63 — driven by the shared macro factor, not assumed away. The practical consequence is in the joint tail. The probability of landing in the danger quadrant — caseload above its 75th-percentile mark of 538,657 households and cost above the $3,600M appropriation — is 20.0%. If caseload and cost were treated as independent, that joint probability would be only 10.9%. Ignoring the coupling would understate the worst-case scenario — a surge in enrolment colliding with a surge in per-case cost — by nearly half. That is the exact scenario in which a program runs out of money and households are turned away mid-year.
A rank-correlation tornado ranks the contributors to the spread in total program cost around its $3,369M median.
Per-case cost is the single largest lever — its long LogNormal tail does most of the damage — but eligible population, the shared macro factor, and take-up are all close behind. There is no one dominant driver to manage; the over-run risk is broad-based, which argues for a contingency reserve rather than a single targeted control.
The three core program uncertainties — a bounded take-up rate, a skewed per-case cost, and a macro-driven eligibility multiplier — are exactly the quantities a point-estimate budget replaces with single numbers.
The take-up Beta keeps participation inside [0, 1]; the per-case-cost LogNormal carries the right skew that a Normal would miss; the eligibility multiplier captures the macro swing that links the two. Collapsing any of them to its mean is what produced the comfortable-looking $3.5B that the simulation reveals to be a 44%-over-run gamble.
The program office had been ready to manage to a budget it believed was safe. The simulation reframed the appropriation as a risk position. It put the over-run probability at 43.8% — close enough to even odds that planning for a supplemental, rather than hoping to avoid one, became the responsible posture. It quantified the headroom needed for real safety: covering the P90 of $5,832M would require about $2.2B more than the appropriation, letting the committee decide explicitly how much over-run risk to fund versus accept. And by exposing the 0.63 coupling between caseload and cost, it showed that the dangerous case — a downturn driving enrolment and per-case cost up together, at 20% probability versus 11% under naive independence — is far more likely than an independence assumption would suggest.
For a benefits program, Monte Carlo turns the budget from "it costs about $3.5B" into "there is a 44% chance it overruns $3.6B, and the worst case is a downturn driving caseload and cost up together" — the difference between funding a program and funding the risk of running it.