Correct the paper's corporation-tax finding, and state three limits it omits (main.pdf needs rebuilding)

papers/obr-macro/sections/experiments.tex

@@ -39,7 +39,7 @@ \section{Further experiments: the direct macro levers}
 
 \paragraph{C. Corporation tax $+$2pp, and why the bridge refuses it.} By design, the bridge declines corporation-tax reforms: in the microsimulation, corporation tax has no household-resolution incidence---attributing it to households would smuggle in an incidence assumption (shareholders? workers? consumers?) that PolicyEngine's UK model deliberately does not make---so translating a corporation-tax costing into an $HHDI$ shock would be a category error, and the correct route is the model's own lever. Raising $TCPRO$ by two percentage points with the investment closure active works the user-cost channel $TCPRO \to TAF \to COC \to KSTAR \to KGAP \to IBUSX$: a higher tax rate raises the post-tax cost of capital, lowers desired capital, opens a capital-stock gap, and depresses business investment through the error-correction term of equation~\eqref{eq:ibus}. The response is small and slow---$-$\pounds 0.03bn per quarter in year one, building to $-$\pounds 0.9bn per quarter ($-$0.13 per cent of GDP) by 2027---consistent in sign and magnitude class with the OBR's treatment of corporation-tax measures as chiefly a receipts effect with modest medium-term investment drag.
 
-\emph{But the response does not converge, and the twelve-quarter horizon is what makes it look bounded.} Extending the same experiment to twenty-five quarters with a sustained $+$5pp rise, $|\Delta IF|$ runs \pounds 97m at quarter~3, \pounds 2{,}876m at quarter~12 and \pounds 43{,}387m at quarter~25 --- roughly a third of quarterly investment --- growing by a factor of 1.21--1.27 every quarter for the whole horizon with no sign of settling. The cause is the stabiliser itself: the $MSGVA$ freeze that tames the \emph{level} instability (Appendix~\ref{app:solver}) also removes the feedback that would close the capital gap, so the closure's held add-factors anchor the level but not the base-versus-shock deviation. Truncating the shock from twelve quarters to eight barely changes the quarter-11 and quarter-12 response, which means the published number is carried by accumulated drift rather than by the tax rate. Twelve quarters is not where this converges; it is where the magnitude still looks plausible. The model repository now warns on every investment-closure run. Read the sign and the direction of the corporation-tax result, not its magnitude, and do not extrapolate the path. For comparison, the \emph{direct} Exchequer yield of $+$2pp on the main rate is about \pounds 7.2bn in 2026--27 rising to \pounds 8.0bn in 2028--29 on HMRC's ready reckoner \citep{hmrc2025reckoner}; the emulator's contribution is the second-round path, not the static number. The response is hard-gated in CI for sign and boundedness (Table~\ref{tab:anchored}), and Section~\ref{sec:limitations} flags the stabilised closure it depends on as a stop-gap.
+\emph{The response converges, but slowly, and twelve quarters is well short of it.} Earlier versions of this paper reported that the deviation did not converge at all: with the closure's add-factors held as \emph{level} anchors, $|\Delta IF|$ for a sustained $+$5pp rise compounded by a factor of 1.21--1.27 every quarter, reaching \pounds 2{,}876m at quarter~12 and \pounds 43{,}387m at quarter~25 with no sign of settling. That was a bug in the anchoring, not a property of the published equation. Holding the anchors in log space instead --- the EViews convention for a \texttt{dlog} equation --- lets the published equation's own error-correction term, $-0.0418\,(\log IBUSX_{t-1} - \log KSTAR_{t-2})$, give the deviation a steady state at $\mathrm{dlog}(KSTAR) = -0.4\,\mathrm{dlog}(TAF)$. Measured on the corrected closure for the same sustained $+$5pp rise, $|\Delta IF|$ runs \pounds 0.24bn at quarter~8, \pounds 0.38bn at quarter~12 and \pounds 0.68bn at quarter~25, approaching a plateau of about \pounds 0.95bn per quarter. The error-correction root is slow ($\approx 0.958$ per quarter), so the twelve-quarter horizon every published result here uses captures only about \textbf{40 per cent} of the full effect; each run now reports its \texttt{investment\_closure\_plateau\_fraction} so a partial response is not read as the whole one. Read the sign and the direction of the corporation-tax result, and treat a twelve-quarter magnitude as a lower bound rather than the settled one. For comparison, the \emph{direct} Exchequer yield of $+$2pp on the main rate is about \pounds 7.2bn in 2026--27 rising to \pounds 8.0bn in 2028--29 on HMRC's ready reckoner \citep{hmrc2025reckoner}; the emulator's contribution is the second-round path, not the static number. The response is hard-gated in CI for sign and boundedness (Table~\ref{tab:anchored}), and Section~\ref{sec:limitations} flags the stabilised closure it depends on as a stop-gap.
 
 \paragraph{D. The fourth lever: government investment is dead.} Section~\ref{sec:results} lists nominal government investment $CGIPS$ among the direct levers. It does not work, and the failure is silent rather than loud. Shocking $CGIPS$ by \pounds 3bn per quarter for twelve quarters leaves $\Delta IF$ at \emph{exactly} 0.0 in all twelve: $IF$ has no live equation in the published listing, so the $CGIPS \to GGIPS \to GGI \to IF$ chain never reaches the expenditure identity. What does reach GDP is deflator residue of indeterminate sign, and here it comes out \emph{negative} --- $-$0.005 to $-$0.021 per cent of GDP after a positive impact quarter --- against a published capital multiplier of 1.0 \citep{obr2010multipliers}. A user reading only the GDP column would conclude that public investment contracts the economy. The model repository now raises a warning on every $CGIPS$ shock stating that the result is not a public-investment multiplier; this paper reports no $CGIPS$ experiment because there is no response to report.
 

papers/obr-macro/sections/limitations.tex

@@ -8,7 +8,13 @@ \section{Limitations}
 
 \item \textbf{The free-running model is weak, and says so.} 6 of 11 computed headline variables land within band; 10 of 21 are passthroughs held at the OBR value (Table~\ref{tab:rawscore}). The suite's documentation describes the free-running fit as ``deliberately report-only, and weak,'' and this paper endorses that description. That count improved from 4 of 11 in earlier versions of this paper only because the published figures had gone stale, not because anything was re-tuned.
 
-\item \textbf{Only one of the four fiscal levers contains behaviour.} Government consumption is a pure accounting identity (multiplier exactly 1.0000 on impact at any shock size, flat thereafter), government investment is dead and its GDP residue is wrong-signed, and the corporation-tax response does not converge on any horizon longer than the twelve quarters every published result here uses. Only the household-tax channel produces a behavioural response. Section~\ref{sec:experiments} documents each in full; a user should treat the first three as arithmetic or as directional at best, not as policy multipliers.
+\item \textbf{Only one of the four fiscal levers contains behaviour.} Government consumption is a pure accounting identity (multiplier exactly 1.0000 on impact at any shock size, flat thereafter), government investment is dead and its GDP residue is wrong-signed, and the corporation-tax response converges only slowly, so the twelve quarters every published result here uses reach roughly 40 per cent of its plateau. Only the household-tax channel produces a behavioural response. Section~\ref{sec:experiments} documents each in full; a user should treat the first three as arithmetic or as directional at best, not as policy multipliers.
+
+\item \textbf{No quarter of a reform solve reaches tolerance.} Appendix~\ref{app:solver} describes the stall-break mechanism; what it does not say is how often it fires. On a scored reform it fires everywhere: all twenty quarters of both the baseline and the shocked solve exit \texttt{stall}, none on \texttt{tol}. A reported delta is therefore the difference of two non-converged solves, and the residuals do not cancel --- under a costing path that is \emph{flat} across the first four quarters the GDP response can still change sign within them. Read the direction and the scale of a reform result; do not read an individual quarter.
+
+\item \textbf{The reform path is configuration-dependent.} The twelve-quarter 2025Q1--2027Q4 experiment reported here is smooth and monotone, but the same reform scored over the adapter's default twenty-quarter 2026Q1--2030Q4 window is neither, and reaches $-$0.085 per cent by 2027Q4 against the $-$0.057 per cent of Figure~\ref{fig:reform}. Both are the same equations on the same vintage; they differ only in solve window. That spread is a consequence of the previous point and bounds how precisely any single quarterly figure here should be taken.
+
+\item \textbf{Whole blocks do not respond to policy at all.} Distinct from the passthrough labelling of Section~\ref{sec:rawscore}, which concerns baseline \emph{fit}: under every lever tested --- government consumption, the household-tax bridge, corporation tax, Bank Rate and the exchange rate --- the unemployment rate, employment, retail prices, exports and imports move by \emph{exactly} zero. There is no Okun channel, no Phillips channel and no trade channel; a six per cent sterling appreciation moves exports and imports not at all. The second round is consumption, or under the investment closure business investment, and nothing else.
 
 \item \textbf{Unpublished inputs impose hard floors.} The OBR does not publish its full databank: the $OSHH$ base constant (behind the 63.3 per cent company-profits error), the $I7$/$PR$ index history (behind decaying RPI inflation), and the overseas rate-of-return normalisers (behind the 3.60 per cent-of-GDP current-account error) are unrecoverable from public sources. These errors are gated against regression, not chased to zero, because closing them would mean fitting to the answer.
 

papers/obr-macro/sections/results.tex

@@ -36,4 +36,4 @@ \section{Results: a worked reform}
 
 \paragraph{Comparison with HMRC's ready reckoner.} HMRC's \emph{Direct effects of illustrative tax changes} bulletin---the official ready reckoner, produced on the OBR-certified costing basis---puts a 1p change in the basic rate at \pounds 6.9 billion in 2026--27, rising to about \pounds 8.2 billion a year in 2027--28 and 2028--29 \citep{hmrc2025reckoner}, and published vintages over recent years span roughly \pounds 6--8 billion per 1p. The PolicyEngine static costing of \pounds 6.46--7.38 billion sits within that range, toward its lower end; differences of this size are expected across costings that differ in data vintage (survey microdata versus HMRC administrative Survey of Personal Incomes), baseline policy assumptions (threshold-freeze paths), and behavioural adjustments (HMRC's figures embed taxable-income elasticities for higher incomes). Under the OBR's policy-costing conventions \citep{obr2014costings}, the ready-reckoner figure corresponds to the post-behavioural \emph{direct} effect, while the economy-wide feedback is applied at the forecast level---exactly the decomposition the bridge reproduces: the microsimulation supplies the direct effect, the macro model the indirect one.
 
-\paragraph{Direct macro levers.} Reforms outside the household tax--benefit space use the exogenous levers directly---government consumption $CGG$, nominal government investment $CGIPS$, the corporation-tax rate $TCPRO$, and (because the CPI is exogenous in this configuration) the consumer price level. Section~\ref{sec:experiments} works three such experiments in full, and reports that only one of the four levers contains a behavioural response: $CGG$ is a pure accounting identity, $CGIPS$ is dead with a wrong-signed GDP residue, and the $TCPRO$ response does not converge past twelve quarters. The household channel worked above is the exception.
+\paragraph{Direct macro levers.} Reforms outside the household tax--benefit space use the exogenous levers directly---government consumption $CGG$, nominal government investment $CGIPS$, the corporation-tax rate $TCPRO$, and (because the CPI is exogenous in this configuration) the consumer price level. Section~\ref{sec:experiments} works three such experiments in full, and reports that only one of the four levers contains a behavioural response: $CGG$ is a pure accounting identity, $CGIPS$ is dead with a wrong-signed GDP residue, and the $TCPRO$ response converges only slowly, twelve quarters reaching roughly 40 per cent of its plateau. The household channel worked above is the exception.