Estimating Safe to Spend with a Bayesian Household Spending Prior: Evidence from the BLS Consumer Expenditure Survey

This paper estimates a day-one Safe to Spend (STS) prior for the Goji budgeting engine using the U.S. Bureau of Labor Statistics Consumer Expenditure Survey (CE Survey) Public Use Microdata (PUMD), Interview Survey component. We fit category-level ordinary least squares (OLS) regressions on a cohort of 1,774 renter consumer units aged 22–40 with annual pre-tax income between 40,000 and 160,000 (median income $77,010), producing log-linear Engel curve spending priors for ten categories: housing, food at home, food away from home, transport, healthcare, entertainment, apparel, utilities, education, and personal care. A literature-informed prior is used for gifts and social spending where BLS coverage is absent. The resulting coefficients initialize the STS engine before a user has sufficient transaction history for personalized estimates. At runtime, a conjugate Normal-Normal Bayesian update incrementally shifts weight from the population prior to the user's observed spending as transactions accumulate, at a rate governed by each category's empirical measurement uncertainty. Living situation modifiers (alone, roommates, family) provide the first layer of personalization before any transactions are logged. The model is intentionally simple, transparent, and fast to update. Validation on a 20% holdout (n = 355) confirms directionally correct priors across all ten categories; high MAPE values in sparse categories are expected and by design — they drive faster prior abandonment. The paper documents the complete data pipeline, variable selection decisions, income signal diagnostics, age cohort sensitivity analysis, and the full runtime STS formula including the buffer rate, commitment prior, and confidence labeling system.