Fiscal Event Geometry: Mapping Institutions as State Spaces

Fiscal Event Geometry: Mapping Institutions as State Spaces Author (Jim) Yongzhi Huang, CPA, TEP, LL.M (Tax Law), MBA Doctoral Researcher, Social Justice Education, University of Toronto 1. Purpose of This Note This brief white paper outlines the conceptual architecture of Fiscal Event Geometry—a coordinate-based framework for representing how tax, migration, education, and intergenerational wealth systems jointly generate observable events. The goal is to provide a scientific overview of the framework as a data-generating process (DGP) and to direct interested readers to the full working paper hosted on SSRN. 2. From Fiscal Systems to Event Geometry Most empirical work on inequality, education, or migration proceeds by modeling outcomes (income, test scores, mobility indices) as functions of covariates. Tax and administrative systems typically appear only as “background institutions” or dummy variables. Fiscal Event Geometry starts from a different premise: • Tax, migration, trust, and education rules continuously generate discrete events(tax filings, residence changes, school-boundary checks, inheritance triggers, trust distributions, etc.). • Each of these rule-triggered events can be treated as a point in a two-dimensional fiscal coordinate space. The framework therefore shifts attention from single policy shocks to the collective geometry of many rule-driven events at the population level. 3. The X–Y Fiscal Coordinate Space Fiscal Event Geometry builds on a previously developed Two-Axis Fiscal Framework, in which: • X-axis represents a unit’s cross-jurisdictional fiscal position(tax residence, treaty network position, school-district rules, access to public capital). • Y-axis represents its intergenerational carrying capacity after tax(the ability to sustain and transfer private capital through inheritance, gifts, trusts, and related structures). Each fiscal event is defined as a rule-triggered, recordable change in a unit’s (X, Y) position. When many such events are plotted, they form clusters, densities, and trajectories in the X–Y plane. The resulting geometry visualizes how public capital and private capital actually meet in everyday administrative practice. 4. Fiscal Event Geometry as a Data-Genera�ng Process (DGP) Conceptually, the framework can be viewed as a DGP: • A rule set R (tax, migration, education, trust rules), • A population N, and • An initial distribution F_0 over the X–Y space jointly generate a sequence of events—written in compact mathematical notation as \{E_{it}\}, where the subscript i stands for a specific household or unit and t stands for time. In simple terms, this just means “all the fiscal events that happen to everyone over the years.” Each event updates the unit’s coordinates to the new position (X_{it}, Y_{it}). When we plot every single one of these updated positions for the whole population, we get a cloud of points. The shape, density, and patterns in that cloud are not random—they are directly determined by the tax laws, migration rules, trust regulations, and other institutional features of the country or countries involved. Rather than focusing on a single treatment or policy shock, Fiscal Event Geometry treats: • Clusters as zones where certain rule–capital interactions are repeated, • Density gradients as indicators of institutional bottlenecks or funnels, and • Trajectories as the paths households or institutions trace as they move across jurisdictions and generations. These collective properties provide the basis for later index construction (e.g., institutional tension measures), while the formal estimator and weighting schemes remain proprietary and are not disclosed here. 5. Econometric State Space and Applica�ons In this framework, the X–Y plane becomes an econometric state space: • Each event-point is an observation in state space, • Models can be formulated in terms of paths, clusters, and boundaries rather than only “Y = βX + ε.” Conceptually, Fiscal Event Geometry can complement: • Difference-in-differences and event-study designs, • Panel regressions, and • Synthetic control methods by providing a structured geometric view of how institutions generate events before any causal design is imposed. Potential applications include: • Comparative studies of tax and education systems, • Analyses of migration corridors and residence-based taxation, • Mapping family-office and trust strategies as trajectories in the X–Y space. 6. Full Working Paper and Cita�on A full exposition of Fiscal Event Geometry—including a more detailed discussion of the X–Y framework, formal DGP specification, and its relation to the author’s Institutional Tension Index (ITI)—is available as a working paper on SSRN: Huang, Y. (2025). Fiscal Event Geometry: An X-Axis / Y-Axis Coordinate Framework for CrossJurisdiction and Intergenerational Analysis. SSRN Working Paper No. 5763186. Available at SSRN: https://ssrn.com/abstract=5763186 Suggested citation for this Zenodo note: Huang, Y. (2025). Fiscal Event Geometry: Conceptual Overview and Data-Generating Process. Zenodo Concept Paper. https://doi.org/10.5281/zenodo.17641519