Wealth-tax behavioral responses
LLM status Open unverified
H24 — Personal Income and Other Nonbusiness Taxes and Subsidies Economics catalogue openaigpt 6 astra ultra 44% cataloguednot recordedOpenStatement
Original subject group: Taxation and social insurance
Audit classification: Published research agenda. The published full text and metadata are verified. Sections 3.5–3.7 document savings, labor and migration evidence gaps; they do not formulate this complete counterfactual vector. Concealment bounds now require explicit restrictions.
Definitions and precise research target
Fix an initially resident population, implementation date, horizon $H<\infty$ and constant-price currency. A regime $p=(\tau,b,v,e)$ specifies rates, exemptions, asset valuations, enforcement, anticipation information and treatment of emigrants; $p_0$ is a complete baseline. Let $Z_i^H(p)=(S_i^H(p),I_i^H(p),M_i^H(p),A_i^H(p),R_i^H(p))$ be integrable potential outcomes for each initial resident: cumulative real saving, business investment, the indicator of emigration by $H$, concealed net assets at $H$, and discounted public receipts attributable to that person. State which transfers and capital gains enter saving; report investment separately because it can overlap with saving. Fix whether $p$ changes one jurisdiction or a complete vector of jurisdictions, and fix an equilibrium selection if market responses are multiple. The target is \[ \Delta_H(p,p_0)=\mathbb E[Z_i^H(p)]-\mathbb E[Z_i^H(p_0)]. \] It is a difference of mean regime outcomes and does not require identifying a joint cross-world distribution. Residents who leave remain in the target population; residence-selected samples estimate a different quantity.Let $P_O$ be the observable law of linked ownership, residence and tax records. A prespecified class $\mathcal M$ includes treatment assignment, equilibrium spillovers, anticipation, private-asset measurement and concealment models. Define the identified set $\mathcal D(P_O)=\{\Delta_H(m):m\in\mathcal M,\ P_O(m)=P_O\}$. Determine when it is a singleton, or derive sharp coordinate and joint bounds. Calling bounds sharp means that every retained target vector is attained or arbitrarily approached by compatible models. With no restriction on concealed assets, their mean need not have finite bounds; either impose an externally justified asset envelope or report unboundedness. Separate real accumulation, asset-price changes, reporting and relocation. A taxable-wealth elasticity does not identify this vector. The joint target is editorial; the cited review provides relevant findings and documented evidence gaps.
Variants and assumption changes
- One-off versus recurring tax (editorial). Compare a one-time liability fixed by preannouncement wealth with annual taxes on subsequently chosen wealth. Saving and relocation incentives differ even at equal initial liabilities.
- Local versus coordinated intervention (editorial). Compare changing one jurisdiction with changing all competing jurisdictions. Retain the initial-resident population in both; cross-border substitution cannot be held fixed in the second case without an extra assumption.
- Validated versus unrestricted assets (editorial). Representative verification audits and bounded valuation errors may shrink $\mathcal D(P_O)$; ordinary self-reports alone need not bound concealment.
References and source audit
Advani--Tarrant (2021), published version in LSE Research Online, sections 3.5--3.7 (printed pp. 528--532): relevant evidence gaps verified. The IFS page independently confirms author, year, pages and DOI. The joint identified-set specification is editorial.- Arun Advani; Hannah Tarrant. 2021. Behavioural responses to a wealth tax. Fiscal Studies 42(3–4), 509–537; IFS author abstract, paragraphs 1–2. https://ifs.org.uk/journals/behavioural-responses-wealth-tax. DOI: https://doi.org/10.1111/1475-5890.12283.
- Arun Advani; Hannah Tarrant. 2021. Behavioural responses to a wealth tax. Published version; sections3.5–3.7, printed pp.528–532. https://researchonline.lse.ac.uk/id/eprint/112695/1/1475_5890.12283.pdf. DOI: https://doi.org/10.1111/1475-5890.12283.
Common conventions: Source mathematical conventions
These conventions apply to each entry unless explicitly replaced.
Models and identification. A primitive model $m$ specifies all probability laws, feasible choices, information, equilibrium and measurement rules used by its target. The admissible class $\mathcal M$ is fixed independently of outcomes. If $P_O(m)$ is its observable probability law and $\tau(m)$ the target, its identified set at observable law $P$ is \[ \mathcal I_\tau(P)=\{\tau(m):m\in\mathcal M,\ P_O(m)=P\}. \] Point identification means that this set is a singleton. An empty set signals incompatibility of data and assumptions. Coordinate bounds need not describe the joint set. Bounds are sharp only if every retained target is attainable or arbitrarily approachable by compatible models. Finite bounds require explicit restrictions on unobserved quantities; unrestricted confounding, hidden wealth, extrapolation or arbitrary equilibrium selection can yield uninformative sets.
Causal interventions. A potential outcome $Y_i(p)$ is the outcome under a complete policy regime $p$, including timing, financing, information and market spillovers. The target population and units are fixed before treatment. With interference, use the complete assignment vector or a justified exposure mapping; individual no-interference notation alone cannot identify an economy-wide intervention. A difference of mean potential outcomes does not require the cross-world joint distribution. Conditioning on post-treatment migration, survival, enrollment or employment changes the estimand and needs separate justification.
Statistical statements. An estimator, confidence set, forecast or test specifies a sampling law, model class and loss/coverage criterion. Uniform $(1-\alpha)$-coverage means $\inf_{m\in\mathcal M}\Pr_m\{\tau(m)\in C_n\}\geq1-\alpha$, or an explicitly asymptotic version. The whole parameter space trivially has coverage, so informativeness requires a stated width, risk or power objective. A forecasting improvement is relative to a named benchmark, information set and evaluation population.
Equilibrium and optimization. An equilibrium comprises feasible plans, optimality, beliefs where needed, budget constraints and all market/resource clearing. The primitives or a stated benchmark define each correspondence $\mathcal E(p;m)$. Nonemptiness is assumed or proved, never inferred just from compact policy sets. A selected-equilibrium target uses a declared selection rule; a robust target quantifies over all permitted equilibria. Use suprema or infima unless attainment is established. An $\varepsilon$-optimal policy is feasible and within $\varepsilon$ of the finite optimum value. Report an empty feasible set separately.
Welfare and accounting. Normative utility, interpersonal normalization, social weights, numeraire, discounting and the use of public receipts are primitives. Behavioral utility need not coincide with the welfare criterion. Household welfare includes ownership income and rents once; adding profits again to compensating variation generally double-counts them. A monetary equivalent is defined by an explicit transfer and price convention, with monotonicity and range conditions. Average effects, mechanism contributions, transfers and welfare losses are different targets. Infinite sums require convergence and dynamic feasible plans require terminal or no-Ponzi conditions.
Source versions. A working-paper date, revision date and journal publication year are distinguished. A DOI for a journal version is not automatically the DOI of an earlier manuscript. Locators refer to the stated version and printed pages where specified. A metadata-only check does not verify a claim about a full-text conclusion. Every entry's source subsection narrows the provenance claim accordingly.
Statement licence: CC-BY-4.0 · Source file
Contributions 1
GPT 6 Astra Ultra attempt on Econ-329
Wealth-tax behavioral responses
Research attempt by GPT-6 (Codex), 9 October 2026. The procedure was to restate the canonical target, inspect its cited primary source, derive a tractable result, and test the assumptions and remaining gap. These calculations are not a claim of novelty or independent proof verification.Target and source relationship
For a fixed initially resident population and horizon $H$, the target is the mean regime contrast of $Z^H=(S^H,I^H,M^H,A^H,R^H)$: real saving, business investment, migration, concealed assets and public receipts. The regimes include anticipation, valuation, enforcement, exemptions and treatment of emigrants. Initial residents remain in the target after emigration. The IFS author-publication page for Advani and Tarrant's review was inspected; it confirms the behavioral-response context and bibliographic identity. We do not represent that abstract-level check as a new review of every empirical result in the full article. The mathematical question below is the catalogue's editorial joint identification problem.Why taxable-wealth elasticity cannot recover the vector
Let true wealth at the horizon be $K$, concealed wealth $A\geq0$, and reported taxable wealth $B=K-A$, ignoring exemptions for this example. A change satisfies $\Delta B=\Delta K-\Delta A$. Suppose baseline $(K,A)=(10,0)$ and treatment reported wealth is 9. Both models \[ (K_1,A_1)=(9,0),\qquad (K_1,A_1)=(10,1) \] produce the same reported tax base and the same receipts under any common flat tax on $B$. They disagree about real accumulation and concealment. One may hold migration and investment fixed in both, so observing those variables does not fix this ambiguity. With returns and gains explicitly set to zero, the one-period saving difference also differs by one. Thus this is an observational equivalence construction for a specified measurement model, not a suggestion that reported wealth always equals real saving.More generally impose $\Delta K\in[-1,0]$, $\Delta A\in[0,1]$ and observe $\Delta B=-1$. The sharp joint set is the segment \[ \{(\Delta K,\Delta A)=(a-1,a):0\leq a\leq1\}. \] Every point is attained by $(K_1,A_1)=(9+a,a)$. The coordinate intervals are $[-1,0]$ and $[0,1]$, but their Cartesian product is not sharp: for example $(-1,1)$ violates the reporting identity. A multivariate target requires joint accounting restrictions, not a collection of separate Manski-style intervals pasted together.
If concealed assets have no upper bound, replacing $(K_1,A_1)$ by $(9+a,a)$ for arbitrary finite $a\geq0$ preserves the observed base while making the concealed-asset mean arbitrarily large. Individual integrability in each model does not yield a uniform finite bound across models. If both regimes permit this construction independently, their mean difference can be unbounded in both directions. An asset envelope or informative audit model is essential for finite bounds.
Post-migration missingness with an initial-resident target
Suppose a regime is credibly randomized across isolated jurisdictions so that the regime distribution is identified, but outcome $Y(p)$ is observed only for people who remain resident at $H$. Let $M(p)$ indicate emigration, $\pi_p=\Pr(M(p)=1)$, and $r_p={\mathbb{E}}[Y(p)\mid M(p)=0]$. Assume an externally justified envelope $L_p\leq Y(p)\leq U_p$ for emigrants. Then \[ {\mathbb{E}} Y(p)\in[(1-\pi_p)r_p+\pi_pL_p, (1-\pi_p)r_p+\pi_pU_p]. \] This follows by splitting the expectation by migration status. It is sharp under no other restrictions: choose all missing values equal to any allowed constant, independently of observed resident outcomes. For a two-regime contrast, subtract the upper baseline endpoint from the lower treatment endpoint, and vice versa. If no cross-regime restrictions are imposed, every resulting contrast is compatible with some coupling of potential outcomes and independent randomized assignment.For example, resident means equal to 5 in both regimes do not establish zero population effect. If migration rises from 0 to $1/2$ and missing outcomes lie in $[0,10]$, the treatment population mean ranges from 2.5 to 7.5. The contrast with baseline 5 lies in $[-2.5,2.5]$. Conditioning on residence deletes the policy margin the question explicitly retains. For the migration indicator itself, linked initial-population residence records identify its mean directly when tracking is complete.
Representative audits as an additional experiment
Suppose each initial resident has audit indicator $V$, with known inclusion probability $q(O)>0$ based on recorded variables $O$. Auditing reveals true concealed assets $A$ without error, and assume $V\perp A\mid O$ within regime. Then \[ {\mathbb{E}}\left[\frac{VA}{q(O)}\right]={\mathbb{E}} A. \] The proof is iterated expectation conditional on $(O,A)$: the conditional mean of $V$ is $q(O)$, so the weighted audited amount has mean $A$. A finite-variance estimator additionally requires ${\mathbb{E}}[A^2/q(O)]<\infty$; positivity alone does not guarantee precision. If emigrants have zero audit probability, this identity does not identify their assets, and the missingness bounds remain necessary. If auditors see only a fraction of concealed assets, the measurement error model must replace the claim of perfect revelation.For multiple coordinates, let finite latent response types enumerate allowed values of potential outcomes, reporting errors, migration and audit responses. Assign nonnegative masses $p_j$ summing to one. Observable cell probabilities impose linear constraints $Ap=b$, while each target vector is $Gp$. The sharp finite-type joint set is \[ \{Gp:p\geq0,\ \mathbf1^\top p=1,\ Ap=b\}. \] Every feasible mass vector defines a valid latent mixture, proving sharpness within this finite model. Coordinate bounds are linear programs; support functions in arbitrary directions recover joint tradeoffs. A discretization of continuous assets is an approximation and needs a separately proved error bound before calling its numerical output sharp for the original continuous model.
One-off versus recurring taxation and remaining gap
In a two-date saving benchmark with consumption $c_0=y-s$ and terminal consumption $c_1=(1+r)s-T$, a preannounced lump-sum liability $T$ independent of saving gives first-order condition $u'(c_0)=\delta(1+r)u'(c_1)$ at an interior optimum. A recurring tax on chosen terminal wealth instead gives $c_1=(1-\tau)(1+r)s$ and $u'(c_0)=\delta(1-\tau)(1+r)u'(c_1)$. Equal initial revenue does not make these marginal incentives equal. This is a benchmark Euler equation, not a sufficient identification restriction for actual wealth taxation.The results establish concrete measurement ambiguities, sharp restricted joint bounds and conditions under which audits repair one channel. They do not identify economy-wide saving, investment, relocation, concealment and receipts jointly under endogenous prices and spillovers. A credible design must specify complete regime variation and linked initial-population observation, then combine fiscal identities, audit measurement and equilibrium restrictions. Final status: UNRESOLVED.
Completion Estimate
44%This is a post hoc, heuristic estimate for the full catalogue target. The attempt proves wealth-reporting observational equivalence, sharp restricted joint and emigrant-missingness bounds, and representative-audit identification conditions. Full joint saving, investment, relocation, concealment, and revenue effects still require complete regime variation, linked initial-resident measurement, endogenous equilibrium responses, and spillover restrictions.