diff --git a/paper/figures/formulation_a_optima.png b/paper/figures/formulation_a_optima.png
index 6c6bbf2..ec90c92 100644
Binary files a/paper/figures/formulation_a_optima.png and b/paper/figures/formulation_a_optima.png differ
diff --git a/paper/slides/presentation/.gitignore b/paper/slides/presentation/.gitignore
new file mode 100644
index 0000000..1fd4917
--- /dev/null
+++ b/paper/slides/presentation/.gitignore
@@ -0,0 +1,28 @@
+# dependencies
+/node_modules
+
+# next.js
+/.next/
+/out/
+
+# production
+/build
+
+# misc
+.DS_Store
+*.pem
+
+# debug
+npm-debug.log*
+yarn-debug.log*
+yarn-error.log*
+
+# local env files
+.env*.local
+
+# typescript
+*.tsbuildinfo
+next-env.d.ts
+
+# generated deck PDF
+/slides.pdf
diff --git a/paper/slides/presentation/README.md b/paper/slides/presentation/README.md
new file mode 100644
index 0000000..2852011
--- /dev/null
+++ b/paper/slides/presentation/README.md
@@ -0,0 +1,39 @@
+# VAT microsimulation presentation
+
+Conference slide app for the IMA World Congress 2026 talk on
+*A Firm-Level Microsimulation for VAT Policy Analysis*.
+
+Built on the PolicyEngine slideshow template (Next.js 16 / React 19 / Tailwind v4,
+KaTeX for math). Slides are React components; a client-side viewer swaps between
+them via keyboard (`→`/`←`/`Space`, `Home`/`End`, `f` for fullscreen) or click.
+
+## Commands
+
+Install dependencies from this directory:
+
+```bash
+npm install
+```
+
+Run the local deck:
+
+```bash
+npm run dev
+```
+
+Check the app:
+
+```bash
+npm run typecheck
+npm run lint
+npm run build
+```
+
+Export the deck to PDF (screenshots each slide via Playwright):
+
+```bash
+npm run export:pdf # one-time: npm i -D playwright pdf-lib && npx playwright install chromium
+```
+
+The deck is defined in `slides/config.ts` (order + metadata) and
+`slides/vat-ima-2026.tsx` (the slides). Figures live in `public/figures/`.
diff --git a/paper/slides/presentation/app/globals.css b/paper/slides/presentation/app/globals.css
new file mode 100644
index 0000000..0932a54
--- /dev/null
+++ b/paper/slides/presentation/app/globals.css
@@ -0,0 +1,112 @@
+@import url("https://fonts.googleapis.com/css2?family=Inter:wght@300;400;500;600;700;800;900&family=JetBrains+Mono:wght@400;500;700&display=swap");
+
+@import "tailwindcss";
+@import "@policyengine/ui-kit/theme.css";
+@import "katex/dist/katex.min.css";
+
+@source "../app";
+@source "../components";
+@source "../lib";
+@source "../slides";
+
+@theme {
+ --font-display: var(--font-sans);
+ --spacing: 0.25rem;
+
+ --text-5xl: 3rem;
+ --text-5xl--line-height: 1;
+ --text-6xl: 3.75rem;
+ --text-6xl--line-height: 1;
+ --text-7xl: 4.5rem;
+ --text-7xl--line-height: 1;
+
+ --color-pe-teal: #319795;
+ --color-pe-dark: #234e52;
+ --color-pe-darker: #0d2f33;
+ --color-pe-light: #e6fffa;
+ --color-pe-amber: #e8913a;
+}
+
+:root {
+ --slide-bg: #ffffff;
+ --slide-ink: #101828;
+ --slide-muted: #64748b;
+ --pe-teal: #319795;
+ --pe-teal-dark: #2c7a7b;
+ --pe-dark: #234e52;
+ --pe-darker: #0d2f33;
+ --pe-light: #e6fffa;
+ --pe-amber: #e8913a;
+ --border-light: #e2e8f0;
+}
+
+* {
+ box-sizing: border-box;
+}
+
+html,
+body {
+ margin: 0;
+ min-height: 100%;
+ background: var(--slide-bg);
+ color: var(--slide-ink);
+ font-family: "Inter", -apple-system, BlinkMacSystemFont, sans-serif;
+ -webkit-font-smoothing: antialiased;
+ -moz-osx-font-smoothing: grayscale;
+}
+
+button {
+ font: inherit;
+}
+
+@utility gradient-bg {
+ background:
+ linear-gradient(135deg, var(--pe-teal) 0%, var(--pe-teal-dark) 38%, var(--pe-dark) 72%, var(--pe-darker) 100%);
+ overflow: hidden;
+ position: relative;
+}
+
+.gradient-bg::before {
+ background:
+ radial-gradient(ellipse 80% 50% at 18% 118%, rgba(255, 255, 255, 0.12) 0%, transparent 50%),
+ radial-gradient(ellipse 60% 40% at 96% 10%, rgba(232, 145, 58, 0.10) 0%, transparent 42%);
+ content: "";
+ inset: 0;
+ pointer-events: none;
+ position: absolute;
+}
+
+@utility gradient-footer {
+ background: var(--pe-dark);
+ position: relative;
+}
+
+.gradient-footer::before {
+ background: linear-gradient(90deg, var(--pe-teal) 0%, var(--pe-amber) 100%);
+ content: "";
+ height: 2px;
+ left: 0;
+ position: absolute;
+ right: 0;
+ top: 0;
+}
+
+.slide-active {
+ opacity: 1;
+ transition: opacity 150ms ease-in-out;
+}
+
+.slide-exit {
+ opacity: 0;
+}
+
+.math-text {
+ font-family: "JetBrains Mono", ui-monospace, SFMono-Regular, Menlo, monospace;
+}
+
+.figure-grid {
+ background-image:
+ linear-gradient(rgba(49, 151, 149, 0.08) 1px, transparent 1px),
+ linear-gradient(90deg, rgba(49, 151, 149, 0.08) 1px, transparent 1px);
+ background-size: 32px 32px;
+}
diff --git a/paper/slides/presentation/app/layout.tsx b/paper/slides/presentation/app/layout.tsx
new file mode 100644
index 0000000..32fa506
--- /dev/null
+++ b/paper/slides/presentation/app/layout.tsx
@@ -0,0 +1,20 @@
+import type { Metadata } from "next";
+import "./globals.css";
+
+export const metadata: Metadata = {
+ title: "A Firm-Level Microsimulation for VAT Policy Analysis",
+ description:
+ "PolicyEngine conference deck for the IMA World Congress 2026 — costing UK VAT registration-threshold reforms on synthetic firm data.",
+};
+
+export default function RootLayout({
+ children,
+}: Readonly<{
+ children: React.ReactNode;
+}>) {
+ return (
+
+
{children}
+
+ );
+}
diff --git a/paper/slides/presentation/app/page.tsx b/paper/slides/presentation/app/page.tsx
new file mode 100644
index 0000000..5db862e
--- /dev/null
+++ b/paper/slides/presentation/app/page.tsx
@@ -0,0 +1,8 @@
+"use client";
+
+import SlideshowViewer from "@/components/core/SlideshowViewer";
+import { vatIma2026Config } from "@/slides/config";
+
+export default function Home() {
+ return ;
+}
diff --git a/paper/slides/presentation/components/content/AutoFitMath.tsx b/paper/slides/presentation/components/content/AutoFitMath.tsx
new file mode 100644
index 0000000..322de69
--- /dev/null
+++ b/paper/slides/presentation/components/content/AutoFitMath.tsx
@@ -0,0 +1,56 @@
+"use client";
+
+import { ReactNode, useLayoutEffect, useRef, useState } from "react";
+
+/**
+ * Scales its child down (never up) so wide content fits the available width.
+ * Used for KaTeX equations on slides, where horizontal scrolling is not an
+ * option during a live talk. Measurement uses offsetWidth, which is the
+ * untransformed layout width, so applying the transform never feeds back.
+ */
+export default function AutoFitMath({
+ children,
+ className = "",
+}: {
+ children: ReactNode;
+ className?: string;
+}) {
+ const outerRef = useRef(null);
+ const innerRef = useRef(null);
+ const [scale, setScale] = useState(1);
+
+ useLayoutEffect(() => {
+ const outer = outerRef.current;
+ const inner = innerRef.current;
+ if (!outer || !inner) return;
+
+ const fit = () => {
+ const available = outer.clientWidth;
+ const natural = inner.offsetWidth;
+ if (natural > 0 && available > 0) {
+ setScale(natural > available ? available / natural : 1);
+ }
+ };
+
+ fit();
+ const ro = new ResizeObserver(fit);
+ ro.observe(outer);
+ // KaTeX fonts can change the measured width once they load.
+ if (typeof document !== "undefined" && document.fonts?.ready) {
+ document.fonts.ready.then(fit).catch(() => {});
+ }
+ return () => ro.disconnect();
+ }, [children]);
+
+ return (
+
+ );
+}
diff --git a/paper/slides/presentation/components/content/BulletList.tsx b/paper/slides/presentation/components/content/BulletList.tsx
new file mode 100644
index 0000000..0d485a5
--- /dev/null
+++ b/paper/slides/presentation/components/content/BulletList.tsx
@@ -0,0 +1,20 @@
+import { ReactNode } from "react";
+
+interface BulletListProps {
+ /** Each item may be plain text or rich JSX (e.g. inline ). */
+ items: ReactNode[];
+ className?: string;
+}
+
+export default function BulletList({ items, className = "" }: BulletListProps) {
+ return (
+
+ {items.map((item, index) => (
+
+
+ {item}
+
+ ))}
+
+ );
+}
diff --git a/paper/slides/presentation/components/content/ContentCard.tsx b/paper/slides/presentation/components/content/ContentCard.tsx
new file mode 100644
index 0000000..fd2f3b1
--- /dev/null
+++ b/paper/slides/presentation/components/content/ContentCard.tsx
@@ -0,0 +1,31 @@
+import { ReactNode } from "react";
+
+interface ContentCardProps {
+ title?: string;
+ children: ReactNode;
+ accent?: "teal" | "amber" | "slate";
+ className?: string;
+}
+
+export default function ContentCard({
+ title,
+ children,
+ accent = "teal",
+ className = "",
+}: ContentCardProps) {
+ const accentClass =
+ accent === "amber"
+ ? "border-t-pe-amber"
+ : accent === "slate"
+ ? "border-t-slate-400"
+ : "border-t-pe-teal";
+
+ return (
+
+ {title &&
{title} }
+ {children}
+
+ );
+}
diff --git a/paper/slides/presentation/components/content/EquationCard.tsx b/paper/slides/presentation/components/content/EquationCard.tsx
new file mode 100644
index 0000000..5b4854c
--- /dev/null
+++ b/paper/slides/presentation/components/content/EquationCard.tsx
@@ -0,0 +1,23 @@
+import AutoFitMath from "@/components/content/AutoFitMath";
+import Math from "@/components/content/Math";
+
+interface EquationCardProps {
+ title: string;
+ /** LaTeX source rendered as display math via KaTeX, auto-fit to the card width. */
+ equation: string;
+ note: string;
+}
+
+export default function EquationCard({ title, equation, note }: EquationCardProps) {
+ return (
+
+ );
+}
diff --git a/paper/slides/presentation/components/content/Figure.tsx b/paper/slides/presentation/components/content/Figure.tsx
new file mode 100644
index 0000000..fa7cc2d
--- /dev/null
+++ b/paper/slides/presentation/components/content/Figure.tsx
@@ -0,0 +1,23 @@
+import Image from "@/components/core/BasePathImage";
+
+interface FigureProps {
+ src: string;
+ alt: string;
+ width: number;
+ height: number;
+}
+
+export default function Figure({ src, alt, width, height }: FigureProps) {
+ return (
+
+
+
+ );
+}
diff --git a/paper/slides/presentation/components/content/FigurePlaceholder.tsx b/paper/slides/presentation/components/content/FigurePlaceholder.tsx
new file mode 100644
index 0000000..851917f
--- /dev/null
+++ b/paper/slides/presentation/components/content/FigurePlaceholder.tsx
@@ -0,0 +1,44 @@
+interface FigurePlaceholderProps {
+ title: string;
+ subtitle: string;
+ kind?: "frontier" | "bars" | "tradeoff";
+}
+
+export default function FigurePlaceholder({
+ title,
+ subtitle,
+ kind = "frontier",
+}: FigurePlaceholderProps) {
+ const lines =
+ kind === "bars"
+ ? "items-end"
+ : kind === "tradeoff"
+ ? "items-center"
+ : "items-end";
+
+ return (
+
+
+
+ {[38, 56, 74, 64, 86].map((height, index) => (
+
+ ))}
+
+
+ Figure pending final sweep outputs
+
+
+ );
+}
diff --git a/paper/slides/presentation/components/content/Math.tsx b/paper/slides/presentation/components/content/Math.tsx
new file mode 100644
index 0000000..9fde438
--- /dev/null
+++ b/paper/slides/presentation/components/content/Math.tsx
@@ -0,0 +1,35 @@
+import katex from "katex";
+
+interface MathProps {
+ tex: string;
+ display?: boolean;
+ className?: string;
+}
+
+// Server-rendered KaTeX. renderToString is pure JS, so this stays a server
+// component and the typeset markup ships in the initial HTML (no hydration flash).
+export default function Math({ tex, display = false, className = "" }: MathProps) {
+ const html = katex.renderToString(tex, {
+ displayMode: display,
+ throwOnError: false,
+ strict: false,
+ trust: false,
+ });
+
+ if (display) {
+ return (
+
+ );
+ }
+
+ return (
+
+ );
+}
diff --git a/paper/slides/presentation/components/content/StatNumber.tsx b/paper/slides/presentation/components/content/StatNumber.tsx
new file mode 100644
index 0000000..7686231
--- /dev/null
+++ b/paper/slides/presentation/components/content/StatNumber.tsx
@@ -0,0 +1,20 @@
+interface StatNumberProps {
+ value: string;
+ label: string;
+ sublabel?: string;
+ compact?: boolean;
+}
+
+export default function StatNumber({ value, label, sublabel, compact = false }: StatNumberProps) {
+ return (
+
+
+ {value}
+
+
+ {label}
+
+ {sublabel &&
{sublabel}
}
+
+ );
+}
diff --git a/paper/slides/presentation/components/core/BasePathImage.tsx b/paper/slides/presentation/components/core/BasePathImage.tsx
new file mode 100644
index 0000000..5ff5f45
--- /dev/null
+++ b/paper/slides/presentation/components/core/BasePathImage.tsx
@@ -0,0 +1,9 @@
+import Image, { ImageProps } from "next/image";
+import { resolveImageSrc } from "@/lib/base-path-image";
+
+const BASE_PATH = process.env.NEXT_PUBLIC_BASE_PATH || "";
+
+export default function BasePathImage({ alt, src, ...props }: ImageProps) {
+ const resolvedSrc = typeof src === "string" ? resolveImageSrc(src, BASE_PATH) : src;
+ return ;
+}
diff --git a/paper/slides/presentation/components/core/Slide.tsx b/paper/slides/presentation/components/core/Slide.tsx
new file mode 100644
index 0000000..c59291f
--- /dev/null
+++ b/paper/slides/presentation/components/core/Slide.tsx
@@ -0,0 +1,65 @@
+"use client";
+
+import { ReactNode } from "react";
+import Image from "@/components/core/BasePathImage";
+import { useSlideshowContextSafe } from "@/components/core/SlideshowContext";
+
+interface SlideProps {
+ children: ReactNode;
+ className?: string;
+ isCover?: boolean;
+ isEnd?: boolean;
+ showFooter?: boolean;
+ fullBleed?: boolean;
+}
+
+export default function Slide({
+ children,
+ className = "",
+ isCover = false,
+ isEnd = false,
+ showFooter = true,
+ fullBleed = false,
+}: SlideProps) {
+ const context = useSlideshowContextSafe();
+ const footerText = context?.footerText ?? "";
+
+ return (
+
+ {fullBleed ? (
+ {children}
+ ) : (
+
+ )}
+
+ {showFooter && !isCover && !isEnd && (
+
+ )}
+
+ );
+}
diff --git a/paper/slides/presentation/components/core/SlideshowContext.tsx b/paper/slides/presentation/components/core/SlideshowContext.tsx
new file mode 100644
index 0000000..6d3babb
--- /dev/null
+++ b/paper/slides/presentation/components/core/SlideshowContext.tsx
@@ -0,0 +1,35 @@
+"use client";
+
+import { createContext, ReactNode, useContext } from "react";
+
+export interface SlideshowContextValue {
+ id: string;
+ title: string;
+ date: string;
+ location?: string;
+ footerText: string;
+ currentSlide: number;
+ totalSlides: number;
+ /** Jump to a slide by zero-based index (used by in-deck appendix links). */
+ goToSlide: (index: number) => void;
+}
+
+const SlideshowContext = createContext(null);
+
+export function SlideshowProvider({
+ children,
+ value,
+}: {
+ children: ReactNode;
+ value: SlideshowContextValue;
+}) {
+ return (
+
+ {children}
+
+ );
+}
+
+export function useSlideshowContextSafe() {
+ return useContext(SlideshowContext);
+}
diff --git a/paper/slides/presentation/components/core/SlideshowViewer.tsx b/paper/slides/presentation/components/core/SlideshowViewer.tsx
new file mode 100644
index 0000000..db4cdb7
--- /dev/null
+++ b/paper/slides/presentation/components/core/SlideshowViewer.tsx
@@ -0,0 +1,130 @@
+"use client";
+
+import { Suspense, createElement, useEffect, useMemo, useState } from "react";
+import { useSearchParams } from "next/navigation";
+import { SlideshowProvider } from "@/components/core/SlideshowContext";
+import { buildSlideUrl } from "@/lib/slide-url";
+import { getSlideComponent, SlideshowConfig } from "@/lib/types";
+
+interface SlideshowViewerProps {
+ config: SlideshowConfig;
+}
+
+function SlideshowViewerClient({ config }: SlideshowViewerProps) {
+ const searchParams = useSearchParams();
+ const slides = useMemo(() => config.slides, [config.slides]);
+ const isExport = searchParams.get("export") === "1";
+ const [currentSlide, setCurrentSlide] = useState(() => {
+ const initialSlide = Number.parseInt(searchParams.get("slide") || "0", 10);
+ return Math.max(0, Math.min(initialSlide, slides.length - 1));
+ });
+ const [isFullscreen, setIsFullscreen] = useState(false);
+
+ useEffect(() => {
+ const handleFullscreenChange = () => {
+ setIsFullscreen(!!document.fullscreenElement);
+ };
+
+ document.addEventListener("fullscreenchange", handleFullscreenChange);
+ return () => document.removeEventListener("fullscreenchange", handleFullscreenChange);
+ }, []);
+
+ useEffect(() => {
+ const url = buildSlideUrl(window.location.href, currentSlide);
+ window.history.replaceState(null, "", url);
+ }, [currentSlide]);
+
+ useEffect(() => {
+ const handleKeyDown = (event: KeyboardEvent) => {
+ if (event.key === "ArrowRight" || event.key === " ") {
+ event.preventDefault();
+ setCurrentSlide((previous) => Math.min(previous + 1, slides.length - 1));
+ } else if (event.key === "ArrowLeft") {
+ event.preventDefault();
+ setCurrentSlide((previous) => Math.max(previous - 1, 0));
+ } else if (event.key === "Home") {
+ event.preventDefault();
+ setCurrentSlide(0);
+ } else if (event.key === "End") {
+ event.preventDefault();
+ setCurrentSlide(slides.length - 1);
+ } else if (event.key === "f" || event.key === "F11") {
+ event.preventDefault();
+ if (document.fullscreenElement) {
+ void document.exitFullscreen();
+ } else {
+ void document.documentElement.requestFullscreen();
+ }
+ }
+ };
+
+ window.addEventListener("keydown", handleKeyDown);
+ return () => window.removeEventListener("keydown", handleKeyDown);
+ }, [slides.length]);
+
+ const currentSlideElement = createElement(getSlideComponent(slides[currentSlide]));
+ const footerText = config.footerText ?? `${config.id.replace(/-/g, " ")} - ${config.date}`;
+
+ return (
+
+ setCurrentSlide(Math.max(0, Math.min(index, slides.length - 1))),
+ }}
+ >
+ setCurrentSlide((previous) => Math.min(previous + 1, slides.length - 1))}
+ >
+ {currentSlideElement}
+
+ {!isFullscreen && !isExport && (
+
+ {
+ event.stopPropagation();
+ setCurrentSlide((previous) => Math.max(previous - 1, 0));
+ }}
+ type="button"
+ >
+ {"<"}
+
+
+ {currentSlide < (config.mainSlideCount ?? slides.length)
+ ? `${currentSlide + 1} / ${config.mainSlideCount ?? slides.length}`
+ : "Appendix"}
+
+ {
+ event.stopPropagation();
+ setCurrentSlide((previous) => Math.min(previous + 1, slides.length - 1));
+ }}
+ type="button"
+ >
+ {">"}
+
+
+ )}
+
+
+ );
+}
+
+export default function SlideshowViewer(props: SlideshowViewerProps) {
+ return (
+ }>
+
+
+ );
+}
diff --git a/paper/slides/presentation/components/layout/CoverSlide.tsx b/paper/slides/presentation/components/layout/CoverSlide.tsx
new file mode 100644
index 0000000..7d04e98
--- /dev/null
+++ b/paper/slides/presentation/components/layout/CoverSlide.tsx
@@ -0,0 +1,79 @@
+import Slide from "@/components/core/Slide";
+import Image from "@/components/core/BasePathImage";
+import { formatDate, SpeakerInfo } from "@/lib/types";
+
+interface CoverSlideProps {
+ title: string;
+ subtitle?: string;
+ event: string;
+ date: string;
+ speakers: SpeakerInfo[];
+}
+
+export default function CoverSlide({
+ title,
+ subtitle,
+ event,
+ date,
+ speakers,
+}: CoverSlideProps) {
+ return (
+
+
+
+
+
+
+
+ {title}
+
+
+ {subtitle && (
+
+ {subtitle}
+
+ )}
+
+
+ {speakers.map((speaker) => (
+
+ {speaker.headshot ? (
+
+ ) : (
+
+ {speaker.name
+ .split(" ")
+ .map((part) => part[0])
+ .join("")}
+
+ )}
+
+
{speaker.name}
+
{speaker.title}
+
+
+ ))}
+
+
+
+
{event}
+
{formatDate(date)}
+
+
+
+ );
+}
diff --git a/paper/slides/presentation/components/layout/SectionSlide.tsx b/paper/slides/presentation/components/layout/SectionSlide.tsx
new file mode 100644
index 0000000..e7c9946
--- /dev/null
+++ b/paper/slides/presentation/components/layout/SectionSlide.tsx
@@ -0,0 +1,27 @@
+import Slide from "@/components/core/Slide";
+
+interface SectionSlideProps {
+ section: string;
+ title: string;
+ subtitle: string;
+}
+
+export default function SectionSlide({ section, title, subtitle }: SectionSlideProps) {
+ return (
+
+
+
+
+ {section}
+
+
+ {title}
+
+
+ {subtitle}
+
+
+
+
+ );
+}
diff --git a/paper/slides/presentation/components/layout/SlideTitle.tsx b/paper/slides/presentation/components/layout/SlideTitle.tsx
new file mode 100644
index 0000000..9a92ccc
--- /dev/null
+++ b/paper/slides/presentation/components/layout/SlideTitle.tsx
@@ -0,0 +1,22 @@
+import { ReactNode } from "react";
+
+interface SlideTitleProps {
+ children: ReactNode;
+ kicker?: string;
+ className?: string;
+}
+
+export default function SlideTitle({ children, kicker, className = "" }: SlideTitleProps) {
+ return (
+
+ {kicker && (
+
+ {kicker}
+
+ )}
+
+ {children}
+
+
+ );
+}
diff --git a/paper/slides/presentation/eslint.config.mjs b/paper/slides/presentation/eslint.config.mjs
new file mode 100644
index 0000000..60c4535
--- /dev/null
+++ b/paper/slides/presentation/eslint.config.mjs
@@ -0,0 +1,11 @@
+import { globalIgnores } from "eslint/config";
+import nextVitals from "eslint-config-next/core-web-vitals";
+import nextTypescript from "eslint-config-next/typescript";
+
+const eslintConfig = [
+ ...nextVitals,
+ ...nextTypescript,
+ globalIgnores([".next/**", "node_modules/**", "out/**"]),
+];
+
+export default eslintConfig;
diff --git a/paper/slides/presentation/lib/base-path-image.ts b/paper/slides/presentation/lib/base-path-image.ts
new file mode 100644
index 0000000..aede35b
--- /dev/null
+++ b/paper/slides/presentation/lib/base-path-image.ts
@@ -0,0 +1,7 @@
+export function resolveImageSrc(src: string, basePath: string): string {
+ if (!basePath) return src;
+ if (src.startsWith("/") && !src.startsWith(`${basePath}/`)) {
+ return `${basePath}${src}`;
+ }
+ return src;
+}
diff --git a/paper/slides/presentation/lib/slide-url.ts b/paper/slides/presentation/lib/slide-url.ts
new file mode 100644
index 0000000..2bfc596
--- /dev/null
+++ b/paper/slides/presentation/lib/slide-url.ts
@@ -0,0 +1,5 @@
+export function buildSlideUrl(currentUrl: string, slide: number): string {
+ const url = new URL(currentUrl);
+ url.searchParams.set("slide", String(slide));
+ return `${url.pathname}${url.search}${url.hash}`;
+}
diff --git a/paper/slides/presentation/lib/types.ts b/paper/slides/presentation/lib/types.ts
new file mode 100644
index 0000000..740bc77
--- /dev/null
+++ b/paper/slides/presentation/lib/types.ts
@@ -0,0 +1,57 @@
+import { ComponentType } from "react";
+
+export interface SpeakerInfo {
+ name: string;
+ title: string;
+ /** Optional headshot image path (under /public); falls back to initials. */
+ headshot?: string;
+}
+
+export interface SlideEntry {
+ component: ComponentType;
+}
+
+export type SlideConfig = ComponentType | SlideEntry;
+
+export interface SlideshowConfig {
+ id: string;
+ title: string;
+ description: string;
+ date: string;
+ location?: string;
+ footerText?: string;
+ speakers?: SpeakerInfo[];
+ slides: SlideConfig[];
+ /**
+ * Number of leading "main" slides. Slides at or beyond this index are
+ * appendix slides and are excluded from the page counter.
+ */
+ mainSlideCount?: number;
+}
+
+export function formatDate(iso: string): string {
+ const [year, month, day] = iso.split("-").map(Number);
+ const monthNames = [
+ "January",
+ "February",
+ "March",
+ "April",
+ "May",
+ "June",
+ "July",
+ "August",
+ "September",
+ "October",
+ "November",
+ "December",
+ ];
+ const monthName = monthNames[month - 1] ?? "";
+ return day === 1 ? `${monthName} ${year}` : `${monthName} ${day}, ${year}`;
+}
+
+export function getSlideComponent(slide: SlideConfig): ComponentType {
+ if (typeof slide === "object" && "component" in slide) {
+ return slide.component;
+ }
+ return slide;
+}
diff --git a/paper/slides/presentation/next.config.ts b/paper/slides/presentation/next.config.ts
new file mode 100644
index 0000000..8334880
--- /dev/null
+++ b/paper/slides/presentation/next.config.ts
@@ -0,0 +1,12 @@
+import type { NextConfig } from "next";
+
+const nextConfig: NextConfig = {
+ images: {
+ unoptimized: true,
+ },
+ turbopack: {
+ root: process.cwd(),
+ },
+};
+
+export default nextConfig;
diff --git a/paper/slides/presentation/package-lock.json b/paper/slides/presentation/package-lock.json
new file mode 100644
index 0000000..35265fa
--- /dev/null
+++ b/paper/slides/presentation/package-lock.json
@@ -0,0 +1,9165 @@
+{
+ "name": "vat-microsim-presentation",
+ "version": "0.1.0",
+ "lockfileVersion": 3,
+ "requires": true,
+ "packages": {
+ "": {
+ "name": "vat-microsim-presentation",
+ "version": "0.1.0",
+ "dependencies": {
+ "@policyengine/ui-kit": "^0.9.0",
+ "@tabler/icons-react": "^3.36.0",
+ "katex": "^0.16.47",
+ "next": "^16.2.6",
+ "react": "^19.2.0",
+ "react-dom": "^19.2.0"
+ },
+ "devDependencies": {
+ "@eslint/eslintrc": "^3.3.5",
+ "@eslint/js": "^9.39.1",
+ "@tailwindcss/postcss": "^4.2.4",
+ "@types/katex": "^0.16.8",
+ "@types/node": "^24.10.1",
+ "@types/react": "^19.2.5",
+ "@types/react-dom": "^19.2.3",
+ "eslint": "^9.39.1",
+ "eslint-config-next": "^16.2.6",
+ "eslint-plugin-react-hooks": "^7.0.1",
+ "globals": "^16.5.0",
+ "pdf-lib": "^1.17.1",
+ "playwright": "^1.61.1",
+ "postcss": "^8.5.6",
+ "tailwindcss": "^4.2.4",
+ "typescript": "~5.9.3",
+ "typescript-eslint": "^8.46.4"
+ }
+ },
+ "node_modules/@alloc/quick-lru": {
+ "version": "5.2.0",
+ "resolved": "https://registry.npmjs.org/@alloc/quick-lru/-/quick-lru-5.2.0.tgz",
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+ "dev": true,
+ "license": "MIT",
+ "engines": {
+ "node": ">=10"
+ },
+ "funding": {
+ "url": "https://github.com/sponsors/sindresorhus"
+ }
+ },
+ "node_modules/@babel/code-frame": {
+ "version": "7.29.7",
+ "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.29.7.tgz",
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diff --git a/paper/slides/presentation/package.json b/paper/slides/presentation/package.json
new file mode 100644
index 0000000..6d2f432
--- /dev/null
+++ b/paper/slides/presentation/package.json
@@ -0,0 +1,40 @@
+{
+ "name": "vat-microsim-presentation",
+ "version": "0.1.0",
+ "private": true,
+ "scripts": {
+ "dev": "next dev",
+ "build": "next build",
+ "start": "next start",
+ "lint": "eslint .",
+ "typecheck": "tsc --noEmit",
+ "export:pdf": "node scripts/export-pdf.mjs"
+ },
+ "dependencies": {
+ "@policyengine/ui-kit": "^0.9.0",
+ "@tabler/icons-react": "^3.36.0",
+ "katex": "^0.16.47",
+ "next": "^16.2.6",
+ "react": "^19.2.0",
+ "react-dom": "^19.2.0"
+ },
+ "devDependencies": {
+ "@eslint/eslintrc": "^3.3.5",
+ "@eslint/js": "^9.39.1",
+ "@tailwindcss/postcss": "^4.2.4",
+ "@types/katex": "^0.16.8",
+ "@types/node": "^24.10.1",
+ "@types/react": "^19.2.5",
+ "@types/react-dom": "^19.2.3",
+ "eslint": "^9.39.1",
+ "eslint-config-next": "^16.2.6",
+ "eslint-plugin-react-hooks": "^7.0.1",
+ "globals": "^16.5.0",
+ "pdf-lib": "^1.17.1",
+ "playwright": "^1.61.1",
+ "postcss": "^8.5.6",
+ "tailwindcss": "^4.2.4",
+ "typescript": "~5.9.3",
+ "typescript-eslint": "^8.46.4"
+ }
+}
diff --git a/paper/slides/presentation/postcss.config.mjs b/paper/slides/presentation/postcss.config.mjs
new file mode 100644
index 0000000..61e3684
--- /dev/null
+++ b/paper/slides/presentation/postcss.config.mjs
@@ -0,0 +1,7 @@
+const config = {
+ plugins: {
+ "@tailwindcss/postcss": {},
+ },
+};
+
+export default config;
diff --git a/paper/slides/presentation/public/figures/bunching_analysis_85k.png b/paper/slides/presentation/public/figures/bunching_analysis_85k.png
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diff --git a/paper/slides/presentation/public/figures/dynamic_cost_vs_elasticity.png b/paper/slides/presentation/public/figures/dynamic_cost_vs_elasticity.png
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diff --git a/paper/slides/presentation/public/figures/dynamic_notch_fit_e017.png b/paper/slides/presentation/public/figures/dynamic_notch_fit_e017.png
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diff --git a/paper/slides/presentation/public/figures/firms_by_turnover_band_85k.png b/paper/slides/presentation/public/figures/firms_by_turnover_band_85k.png
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diff --git a/paper/slides/presentation/public/figures/firms_impact_2025_26.png b/paper/slides/presentation/public/figures/firms_impact_2025_26.png
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diff --git a/paper/slides/presentation/public/figures/formulation_a_optima.png b/paper/slides/presentation/public/figures/formulation_a_optima.png
new file mode 100644
index 0000000..ec90c92
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diff --git a/paper/slides/presentation/public/figures/obr_vat_bunching_85k.png b/paper/slides/presentation/public/figures/obr_vat_bunching_85k.png
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diff --git a/paper/slides/presentation/public/figures/revenue_impact_2025_26.png b/paper/slides/presentation/public/figures/revenue_impact_2025_26.png
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@@ -0,0 +1,18 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
\ No newline at end of file
diff --git a/paper/slides/presentation/public/qr-paper.png b/paper/slides/presentation/public/qr-paper.png
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diff --git a/paper/slides/presentation/scripts/export-pdf.mjs b/paper/slides/presentation/scripts/export-pdf.mjs
new file mode 100644
index 0000000..3601a5b
--- /dev/null
+++ b/paper/slides/presentation/scripts/export-pdf.mjs
@@ -0,0 +1,116 @@
+// Export the slide deck to a single PDF — one page per slide.
+//
+// The deck is a Next.js/React slideshow (not reveal.js), so there is no built-in
+// export. This drives a headless Chromium over each `?slide=N` view, screenshots
+// it at 1080p (2x for crisp text), and assembles the shots into one PDF at the
+// standard 16:9 slide size. Screenshots (rather than print-to-PDF) guarantee the
+// output matches the on-screen render exactly — KaTeX, gradients, custom layout.
+//
+// One-time setup:
+// npm i -D playwright pdf-lib && npx playwright install chromium
+//
+// Run:
+// npm run export:pdf # build, serve, export -> slides.pdf
+// SKIP_BUILD=1 npm run export:pdf # reuse an existing .next build
+// SLIDE_COUNT=28 OUT=deck.pdf npm run export:pdf
+//
+import { spawn } from "node:child_process";
+import { setTimeout as sleep } from "node:timers/promises";
+import { readFileSync, writeFileSync } from "node:fs";
+import { dirname, resolve } from "node:path";
+import { fileURLToPath } from "node:url";
+import { chromium } from "playwright";
+import { PDFDocument } from "pdf-lib";
+
+const root = resolve(dirname(fileURLToPath(import.meta.url)), "..");
+const PORT = Number(process.env.PORT || 3210);
+const BASE = `http://localhost:${PORT}`;
+const VIEW_W = Number(process.env.SLIDE_WIDTH || 1920);
+const VIEW_H = Number(process.env.SLIDE_HEIGHT || 1080);
+const PAGE_W = 960; // PDF points: standard 16:9 slide (13.3in)
+const PAGE_H = 540;
+const OUT = resolve(root, process.env.OUT || "slides.pdf");
+
+// Number of slides: the `slides: [ ... ]` array in slides/config.ts, or SLIDE_COUNT.
+function slideCount() {
+ if (process.env.SLIDE_COUNT) return Number(process.env.SLIDE_COUNT);
+ const cfg = readFileSync(resolve(root, "slides/config.ts"), "utf8");
+ const m = cfg.match(/slides:\s*\[([\s\S]*?)\]/);
+ if (!m) throw new Error("Could not find slides array in slides/config.ts; set SLIDE_COUNT.");
+ const names = m[1]
+ .split(",")
+ .map((s) => s.replace(/\/\/.*$/gm, "").trim())
+ .filter((s) => /^[A-Za-z]/.test(s));
+ return names.length;
+}
+
+function run(cmd, args) {
+ return new Promise((res, rej) => {
+ const p = spawn(cmd, args, { cwd: root, stdio: "inherit" });
+ p.on("exit", (c) => (c === 0 ? res() : rej(new Error(`${cmd} ${args.join(" ")} -> exit ${c}`))));
+ });
+}
+
+async function waitForServer(url, timeoutMs = 90000) {
+ const start = Date.now();
+ while (Date.now() - start < timeoutMs) {
+ try {
+ if ((await fetch(url)).ok) return;
+ } catch {
+ // server not up yet
+ }
+ await sleep(500);
+ }
+ throw new Error(`Server not ready at ${url} after ${timeoutMs}ms`);
+}
+
+async function main() {
+ const count = slideCount();
+ console.log(`Exporting ${count} slides -> ${OUT}`);
+
+ if (!process.env.SKIP_BUILD) {
+ console.log("Building (next build)…");
+ await run("npm", ["run", "build"]);
+ }
+
+ console.log(`Starting server on :${PORT}…`);
+ const server = spawn("npx", ["next", "start", "-p", String(PORT)], {
+ cwd: root,
+ stdio: "inherit",
+ });
+
+ try {
+ await waitForServer(BASE);
+ const browser = await chromium.launch();
+ const page = await browser.newPage({
+ viewport: { width: VIEW_W, height: VIEW_H },
+ deviceScaleFactor: 2,
+ });
+
+ const pdf = await PDFDocument.create();
+ for (let i = 0; i < count; i++) {
+ await page.goto(`${BASE}/?slide=${i}&export=1`, { waitUntil: "networkidle" });
+ await page.evaluate(() => document.fonts.ready);
+ await page.waitForTimeout(400); // settle KaTeX / transitions
+ const shot = await page.screenshot({
+ type: "png",
+ clip: { x: 0, y: 0, width: VIEW_W, height: VIEW_H },
+ });
+ const png = await pdf.embedPng(shot);
+ const pg = pdf.addPage([PAGE_W, PAGE_H]);
+ pg.drawImage(png, { x: 0, y: 0, width: PAGE_W, height: PAGE_H });
+ console.log(` slide ${i + 1}/${count}`);
+ }
+
+ await browser.close();
+ writeFileSync(OUT, await pdf.save());
+ console.log(`Wrote ${OUT}`);
+ } finally {
+ server.kill("SIGTERM");
+ }
+}
+
+main().catch((err) => {
+ console.error(err);
+ process.exit(1);
+});
diff --git a/paper/slides/presentation/slides/config.ts b/paper/slides/presentation/slides/config.ts
new file mode 100644
index 0000000..0f23de4
--- /dev/null
+++ b/paper/slides/presentation/slides/config.ts
@@ -0,0 +1,84 @@
+import { SlideshowConfig } from "@/lib/types";
+import {
+ AppendixBehavSlide,
+ AppendixGenSlide,
+ AppendixNotchSlide,
+ AppendixSecondarySlide,
+ BehaviouralLayerSlide,
+ BunchingMechanicalSlide,
+ ConclusionSlide,
+ DataSlide,
+ DominatedRegionSlide,
+ FirmProblemSlide,
+ FirmsClusterSlide,
+ LiteratureSlide,
+ QuestionSlide,
+ ReformMenuSlide,
+ SectionBehavioural,
+ SectionConclusion,
+ SectionData,
+ SectionDistortion,
+ SectionMotivation,
+ SectionStatic,
+ StaticCostingSlide,
+ StaticSweepSlide,
+ ThankYouSlide,
+ ThisPaperSlide,
+ TitleSlide,
+ TurnoverDistSlide,
+ ValidationSlide,
+ WhichReformsSlide,
+ WhyThresholdSlide,
+} from "@/slides/vat-ima-2026";
+
+export const vatIma2026Config: SlideshowConfig = {
+ id: "vat-ima-2026",
+ title: "A Firm-Level Microsimulation for VAT Policy Analysis",
+ description:
+ "PolicyEngine conference deck for the IMA World Congress 2026 — costing UK VAT registration-threshold reforms on synthetic firm data.",
+ date: "2026-07-01",
+ location: "IMA World Congress 2026, Brussels",
+ footerText: "IMA World Congress 2026 · firm microsimulation",
+ speakers: [{ name: "Vahid Ahmadi", title: "PolicyEngine" }],
+ // Slides 0–24 are the main deck; 25+ are appendix (excluded from the counter).
+ mainSlideCount: 25,
+ slides: [
+ // 0 · Open
+ TitleSlide,
+ // 1 · Motivation
+ SectionMotivation,
+ QuestionSlide,
+ WhyThresholdSlide,
+ FirmsClusterSlide,
+ ThisPaperSlide,
+ LiteratureSlide,
+ // 2 · Data and calibration
+ SectionData,
+ DataSlide,
+ TurnoverDistSlide,
+ // 3 · Static costing
+ SectionStatic,
+ StaticCostingSlide,
+ ValidationSlide,
+ StaticSweepSlide,
+ ReformMenuSlide,
+ // 4 · The notch's distortion
+ SectionDistortion,
+ BunchingMechanicalSlide,
+ DominatedRegionSlide,
+ WhichReformsSlide,
+ // 5 · Behavioural layer
+ SectionBehavioural,
+ FirmProblemSlide,
+ BehaviouralLayerSlide,
+ // 6 · Conclusion
+ SectionConclusion,
+ ConclusionSlide,
+ ThankYouSlide,
+ // Appendix (linear, after the main deck — excluded from the page counter)
+ AppendixNotchSlide,
+ AppendixGenSlide,
+ AppendixBehavSlide,
+ AppendixSecondarySlide,
+ ],
+};
diff --git a/paper/slides/presentation/slides/vat-ima-2026.tsx b/paper/slides/presentation/slides/vat-ima-2026.tsx
new file mode 100644
index 0000000..bac346d
--- /dev/null
+++ b/paper/slides/presentation/slides/vat-ima-2026.tsx
@@ -0,0 +1,1177 @@
+"use client";
+
+import { ReactNode } from "react";
+
+import AutoFitMath from "@/components/content/AutoFitMath";
+import Figure from "@/components/content/Figure";
+import Math from "@/components/content/Math";
+import Image from "@/components/core/BasePathImage";
+import Slide from "@/components/core/Slide";
+import { useSlideshowContextSafe } from "@/components/core/SlideshowContext";
+import CoverSlide from "@/components/layout/CoverSlide";
+import SectionSlide from "@/components/layout/SectionSlide";
+import SlideTitle from "@/components/layout/SlideTitle";
+
+/**
+ * Zero-based slide indices, kept in sync with the order in `slides/config.ts`.
+ * Used to wire the in-deck appendix jump links (forward) and back links.
+ */
+const SLIDE = {
+ whyThreshold: 3,
+ data: 8,
+ reformMenu: 14,
+ dominated: 17,
+ conclusion: 23,
+ appNotch: 25,
+ appGen: 26,
+ appBehav: 27,
+ appSecondary: 28,
+} as const;
+
+/* ------------------------------------------------------------------ */
+/* Shared helpers */
+/* ------------------------------------------------------------------ */
+
+const speakers = [
+ { name: "Vahid Ahmadi", title: "PolicyEngine", headshot: "/headshots/vahid-ahmadi.png" },
+];
+
+/** Teal-dot bullet list; items may be plain text or rich JSX (inline Math). */
+function BList({
+ items,
+ className = "",
+ size = "text-xl",
+}: {
+ items: ReactNode[];
+ className?: string;
+ size?: string;
+}) {
+ return (
+
+ {items.map((item, i) => (
+
+
+ {item}
+
+ ))}
+
+ );
+}
+
+/** Indented, muted sub-bullets under a BList item. */
+function SubList({ items }: { items: ReactNode[] }) {
+ return (
+
+ {items.map((item, i) => (
+
+
+ {item}
+
+ ))}
+
+ );
+}
+
+function Caption({ children, className = "" }: { children: ReactNode; className?: string }) {
+ return {children}
;
+}
+
+/** Auto-fitting centred display equation. */
+function DisplayEq({ tex, className = "" }: { tex: string; className?: string }) {
+ return (
+
+
+
+ );
+}
+
+/** Clickable pointer that jumps to a matching appendix slide. */
+function SeeAppendix({ to, children }: { to: number; children: ReactNode }) {
+ const ctx = useSlideshowContextSafe();
+ return (
+ {
+ event.stopPropagation();
+ ctx?.goToSlide(to);
+ }}
+ className="pointer-events-auto mt-6 text-sm font-medium uppercase tracking-[0.14em] text-pe-teal/80 transition hover:text-pe-teal hover:underline"
+ >
+ → {children}
+
+ );
+}
+
+/** Clickable "back" link on an appendix slide that returns to its source slide. */
+function BackTo({ to, children }: { to: number; children: ReactNode }) {
+ const ctx = useSlideshowContextSafe();
+ return (
+ {
+ event.stopPropagation();
+ ctx?.goToSlide(to);
+ }}
+ className="pointer-events-auto mt-8 text-sm font-medium uppercase tracking-[0.14em] text-pe-teal/80 transition hover:text-pe-teal hover:underline"
+ >
+ ← {children}
+
+ );
+}
+
+const teal = (children: ReactNode) => (
+ {children}
+);
+
+/* ================================================================== */
+/* 0 · Open */
+/* ================================================================== */
+
+export function TitleSlide() {
+ return (
+
+ );
+}
+
+/* ================================================================== */
+/* 1 · Motivation */
+/* ================================================================== */
+
+export function SectionMotivation() {
+ return (
+
+ );
+}
+
+export function QuestionSlide() {
+ return (
+
+
+
+ The question
+
+
+ How should the UK {teal("cost reforms")} to its VAT registration threshold — changes to
+ its {teal("level")}, {teal("shape")}, or {teal("rate")} — on a{" "}
+ {teal("single, common, reproducible basis")},
+
+
+ when the firm-level data needed are {teal("not openly available")}?
+
+
+
+ );
+}
+
+export function WhyThresholdSlide() {
+ return (
+
+
+ Why the VAT threshold matters
+
+ The UK VAT threshold is a {teal("notch, not a kink")}: cross it and 20% falls due on
+ the firm’s entire turnover — not just the slice above.
+ >,
+ <>
+ A discrete liability jump of (
+ ) at the threshold.
+ >,
+ <>
+ Threshold was {teal("£85,000")} (2023–24), raised to {teal("£90,000")} on 1 April 2024
+ — after a seven-year nominal freeze, the longest in the tax’s history.
+ >,
+ <>
+ Among the highest thresholds in the OECD, and it sits in a dense part of the
+ firm-size distribution.
+ >,
+ <>
+ Firms respond by {teal("bunching just below")} it; the cliff-edge keeps the threshold
+ under recurrent pressure for reform.
+ >,
+ ]}
+ />
+ notch vs. kink — appendix
+
+
+ );
+}
+
+export function FirmsClusterSlide() {
+ const figs = [
+ {
+ src: "/figures/firms_by_turnover_band_85k.png",
+ w: 2636,
+ h: 1784,
+ cap: "All UK firms by turnover band (ONS)",
+ },
+ {
+ src: "/figures/vat_firms_by_turnover_band_85k.png",
+ w: 2636,
+ h: 1784,
+ cap: "VAT-registered firms by band (HMRC)",
+ },
+ {
+ src: "/figures/obr_vat_bunching_85k.png",
+ w: 2969,
+ h: 1762,
+ cap: "Bunching below £85k (OBR, 2023)",
+ },
+ ];
+ return (
+
+
+
Firms cluster just below the threshold
+
+ Cross {teal("£85,000")} and 20% VAT falls due on the firm’s entire turnover, so
+ firms cluster {teal("right below it")}.
+
+
+ {figs.map((f) => (
+
+ ))}
+
+
+
+ );
+}
+
+export function ThisPaperSlide() {
+ return (
+
+
+ This project
+
+ An {teal("open, reproducible firm-level microsimulation")} that costs UK VAT threshold
+ reforms on a common static basis.
+ >,
+ <>
+ Built on {teal("synthetic firm microdata")} calibrated to published HMRC + ONS
+ aggregates — released openly and regenerable under any counterfactual schedule.
+ >,
+ <>
+ Prices three reform families — {teal("level")} (move the threshold), {teal("shape")} (a
+ graduated taper), {teal("rate")} (a reduced-rate band) — {teal("three ways")}:
+ statically (mechanical reclassification);>,
+ <>
+ by the elasticity-free {teal("dominated-region")} distortion each removes;
+ >,
+ <>
+ behaviourally, conditional on an assumed turnover elasticity .
+ >,
+ ]}
+ />
+ >,
+ <>
+ Headline: only the graduated taper
+ removes the notch’s distortion; raising the threshold is the dearest, least efficient
+ option.
+ >,
+ ]}
+ />
+
+
+ );
+}
+
+export function LiteratureSlide() {
+ const rows: [ReactNode, string][] = [
+ [
+ <>Bunching / notch methodology — source of the “dominated region”>,
+ "Saez (2010); Kleven and Waseem (2013); Kleven (2016)",
+ ],
+ [
+ <>VAT registration threshold (empirical)>,
+ "Liu et al. (2021) (UK notch, ~43% voluntary registration); Liu, Lockwood and Tam (2024); Onji (2009); Asatryan and Peichl (2017); Waseem (2024)",
+ ],
+ [
+ <>Does bunching identify a structural elasticity?>,
+ "Blomquist et al. (2021); Bertanha et al. (2023) — not non-parametrically identified",
+ ],
+ [
+ <>Structural models of size-based thresholds>,
+ "Garicano et al. (2016); Gourio and Roys (2014)",
+ ],
+ ];
+ return (
+
+
+
Related literature
+
(
+ <>
+ {head}
+ {cites}
+ >
+ ))}
+ />
+
+
+ );
+}
+
+/* ================================================================== */
+/* 2 · Data and calibration */
+/* ================================================================== */
+
+export function SectionData() {
+ return (
+
+ );
+}
+
+export function DataSlide() {
+ return (
+
+
+
+
+ Synthetic firms calibrated to public aggregates
+
+
+ {teal("No open firm-level VAT microdata exist")} build a
+ synthetic population calibrated to published aggregates (data year 2023–24).
+ >,
+ <>
+ Calibration targets:
+ ONS UK Business: Activity, Size and Location — firm counts by sector × turnover band>,
+ <>HMRC VAT Annual Statistics — registered counts and net VAT liability by band / sector>,
+ ]}
+ />
+ >,
+ <>Mirrors open tax-benefit microsimulation (Ghenis et al., 2022).>,
+ ]}
+ />
+ how firms are built — appendix
+
+
+
+
+
+
+
+
+ );
+}
+
+function Stat({ value, label, sub }: { value: string; label: string; sub: string }) {
+ return (
+
+
{value}
+
{label}
+
{sub}
+
+ );
+}
+
+export function TurnoverDistSlide() {
+ return (
+
+
+
The calibrated turnover distribution
+
+
+
+
+ Density steps down at the {teal("£85,000")} registration threshold and again at the{" "}
+ {teal("£150,000")} Flat Rate Scheme ceiling. {teal("The step is inherited from coarse HMRC band targets")}{" "}
+ — quantified later by a placebo test.
+
+
+
+ );
+}
+
+/* ================================================================== */
+/* 3 · Static costing */
+/* ================================================================== */
+
+export function SectionStatic() {
+ return (
+
+ );
+}
+
+export function StaticCostingSlide() {
+ return (
+
+
+
+
Static revenue
+
+
+
+
+ Recompute under each new schedule and difference against the base.
+
+
+
+ Mechanical reclassification
+
+ Turnover held fixed revenue moves only through firms whose{" "}
+ {teal("registration status flips")} (those between the old and new cutoff).
+ >,
+ <>
+ Three reform levers, four schedules, all on one base:
+ Level — move the threshold up or down>,
+ <>Shape — graduated taper, 0% at £85k → 20% at £105k>,
+ <>Rate — reduced-rate band (10% or 15%) in £85k–£105k>,
+ ]}
+ />
+ >,
+ ]}
+ />
+
+
+
+ );
+}
+
+export function ValidationSlide() {
+ return (
+
+
+
+
+ Validation: the April-2024 anchor reform
+
+ Cost the April-2024 rise, my
+ estimate vs HMRC’s published costing.
+ >,
+ <>
+ {teal("2025–26: £175m vs £185m")} — agree within £7–21m per year across the horizon.
+ >,
+ <>Both turn to a small gain by 2028–29 as fiscal drag lifts the frozen baseline.>,
+ <>
+ Microdata are calibrated to HMRC aggregates a{" "}
+ {teal("consistency check")}, not out-of-sample validation.
+ >,
+ ]}
+ />
+
+
+
+ );
+}
+
+export function StaticSweepSlide() {
+ return (
+
+
+
+ Static sweep: cost of moving the threshold
+
+
+ Validated on the one move HMRC published, {teal("now sweep the whole schedule")} — the same
+ mechanical reclassification at every threshold.
+
+
+
+
+
+
+ From a £90k base (£203.8bn), roughly linear, {teal("≈£150–220m per £5k step")}: e.g.{" "}
+ {teal("−£374m")} to raise to £100k, {teal("+£665m")} to lower to £70k. Even a £30k rise to
+ £120k costs ~£1.2bn — under 0.6% of the base.
+
+
+
+ );
+}
+
+export function ReformMenuSlide() {
+ const rows: { reform: string; lever: string; stat: string; region: ReactNode; hi?: boolean }[] = [
+ { reform: "Raise to £100k", lever: "Level", stat: "−£508m", region: "relocated" },
+ {
+ reform: "Taper £85–105k",
+ lever: "Shape",
+ stat: "−£336m",
+ region: removed ,
+ hi: true,
+ },
+ { reform: "Reduced 10%", lever: "Rate", stat: "−£343m", region: "split in two" },
+ { reform: "Reduced 15%", lever: "Rate", stat: "−£171m", region: "split in two" },
+ ];
+ return (
+
+
+
The reform menu
+
+
+ {["Reform", "Lever", "Static", "Dominated region"].map((h, i) => (
+
+ {h}
+
+ ))}
+
+ {rows.map((r) => (
+
+
{r.reform}
+
{r.lever}
+
+ {r.stat}
+
+
{r.region}
+
+ ))}
+
+
+ Common £85,000-notch / £183.6bn 2023–24 base. {teal("The level move is the most expensive yet removes no distortion")};
+ the taper removes it entirely for less. “Split in two” = a second notch appears where the
+ reduced-rate band ends (£105k reverts to 20%), so the empty band is fragmented, not shrunk.
+
+
behavioural costs across e — appendix
+
+
+ );
+}
+
+/* ================================================================== */
+/* 4 · The notch's distortion */
+/* ================================================================== */
+
+export function SectionDistortion() {
+ return (
+
+ );
+}
+
+export function BunchingMechanicalSlide() {
+ return (
+
+
+
+
+
+
+
+
+ Excess mass over a polynomial no-bunching counterfactual :
+
+
+
+
+
+ Bunching in the synthetic data is mechanical
+
+ Reproduced density step: ratio (SE 0.005), excess mass{" "}
+ firms (SE 662).
+ >,
+ <>
+ {teal("Placebo")}: remove the step from the calibration target{" "}
+ collapses to {teal("0–99 firms")}.
+ >,
+ <>
+ So the step is {teal("inherited from coarse HMRC bands")}, not firm behaviour — the
+ generator has no location choice.
+ >,
+ <>Genuine threshold bunching remains the administrative fact of Liu et al. (2021).>,
+ ]}
+ />
+
+
+
+ );
+}
+
+export function DominatedRegionSlide() {
+ return (
+
+
+
+
+
+
+
+
The notch in the firm’s profit:
+
+
+
+
+
+ The dominated region: an elasticity-free distortion
+
+
+ At , profit jumps down by{" "}
+ — VAT on turnover already earned.
+ >,
+ <>
+ The {teal("dominated region")} is the band just above where no
+ firm locates: {teal("£21,250")}.
+ >,
+ <>Interval (£85,000, £106,250), ≈137,000 weighted firms.>,
+ <>
+ Depends on and {teal("alone")} — no
+ elasticity. An order of magnitude wider than a kink’s ~£1k.
+ >,
+ ]}
+ />
+ secondary-notch arithmetic — appendix
+
+
+
+ );
+}
+
+export function WhichReformsSlide() {
+ return (
+
+
+
Which reforms actually shrink the band?
+
+ Raise the threshold —{" "}
+ {teal("relocates")} the £21,250 band unchanged to the new cutoff.
+ >,
+ <>
+ Banded reduced rate — does{" "}
+ not shrink it. Lowers the single notch (£17,000 → £12,750 at 15%) but adds a{" "}
+ {teal("secondary notch")} where the band reverts at £105k:
+
+
+
+
+ It splits one wide empty band into two, not shrinks it.
+
+ >,
+ <>
+ Graduated taper — continuous, no
+ notch and no dominated region: {teal("removes the distortion entirely")}.
+ >,
+ ]}
+ />
+
+ Only the taper removes the distortion — and for less (£336m).
+
+
+
+ );
+}
+
+/* ================================================================== */
+/* 5 · Behavioural layer */
+/* ================================================================== */
+
+export function SectionBehavioural() {
+ return (
+
+ );
+}
+
+export function FirmProblemSlide() {
+ return (
+
+
+
+
+ The firm’s problem: VAT on value added
+
+
+ A firm of ability chooses turnover to maximise
+
+
+
+
+
+ VAT falls on {teal("value added")} , not whole turnover;{" "}
+ is the firm’s deductible-input share.
+ >,
+ <>
+ is the firm’s own-factor cost (labour, capital): inputs{" "}
+ are already netted by .
+ >,
+ <>
+ Low — labour-intensive services (consultants, hairdressers,
+ tutors): value added ≈ turnover. High — retail, wholesale,
+ construction: large deductible input purchases.
+ >,
+ <>
+ Optimum .{" "}
+ is parametric for now — ONS Supply–Use value-added shares to
+ come.
+ >,
+ ]}
+ />
+
+
+
+
+
+
+ Higher scales the curve down and pulls the registered optimum toward
+ the threshold (eventually bunching).
+
+
+
+
+ );
+}
+
+export function BehaviouralLayerSlide() {
+ return (
+
+
+
+
+
+
+
+
Each firm rescales turnover under the reform:
+
+
+
+
+
+ Conditional on an assumed elasticity
+
+
+ Iso-elastic simulator (value-added base, formulation A) re-optimises each firm;
+ flat-rate optimum , with {" "}
+ {teal("assumed")}, not identified.
+ >,
+ <>
+ Sweep . At base-broadening
+ offsets much of each static loss:
+ raise to £100k: £508m → £292m >,
+ <>10% band: £343m → £273m >,
+ <>15% band: £171m → £135m >,
+ ]}
+ />
+ >,
+ <>
+ Static cost is the limit; only has an
+ external anchor (Kleven and Waseem, 2013).
+ >,
+ <>Taper excluded: its marginal-rate channel is not credibly identified iso-elastically.>,
+ ]}
+ />
+
+
+
+ );
+}
+
+/* ================================================================== */
+/* 6 · Conclusion */
+/* ================================================================== */
+
+export function SectionConclusion() {
+ return (
+
+ );
+}
+
+export function ConclusionSlide() {
+ return (
+
+
+
Conclusion
+
+
+
+ What we find
+
+
+ What this is: an open,
+ reproducible firm-level microsimulation of the UK VAT threshold as a turnover-tax
+ notch; prices level / shape / rate reforms {teal("three ways")}.
+ >,
+ <>
+ Static: reproduces HMRC’s anchor
+ within ~£10m; raising to £100k costs £508m, the taper £336m.
+ >,
+ <>
+ Distortion: the dominated region{" "}
+ is elasticity-free — {teal("only the taper removes it")};
+ the level move relocates it, a reduced rate splits it in two.
+ >,
+ <>
+ Behavioural offsets are
+ conditional on assumed ; the static cost and dominated region are the
+ elasticity-free anchors.
+ >,
+ ]}
+ />
+
+
+
+ Limitations & future work
+
+
+ Value added, parametric {" "}
+ — not yet measured firm by firm ({teal("ONS Supply–Use to come")});
+ the dominated region still uses the statutory-rate notch, and ~43% voluntary
+ registration (Liu et al., 2021) is abstracted from.
+ >,
+ <>
+ Partial efficiency metric —
+ dominated-region width indexes misallocation only; a full welfare / MVPF accounting
+ (Keen and Mintz, 2004) is needed.
+ >,
+ <>
+ Aggregate only — no sectoral
+ incidence (VAT liability by sector excluded from the optimiser).
+ >,
+ <>
+ Link to household microsimulation {" "}
+ — connect the firm-side VAT model to PolicyEngine’s household tax-benefit model to
+ trace incidence and distributional effects onto households.
+ >,
+ ]}
+ />
+
+
+
+
+ );
+}
+
+export function ThankYouSlide() {
+ return (
+
+
+
+
+
Thank you
+
+
policyengine.org
+
vahid@policyengine.org
+
+
+
+
+
+
+ Scan for the paper, data & code
+
+
+
+
+ );
+}
+
+/* ================================================================== */
+/* Appendix (linear, after the main deck) */
+/* ================================================================== */
+
+export function AppendixNotchSlide() {
+ return (
+
+
+ Notch vs. kink
+
+ A kink taxes only the turnover{" "}
+ above the threshold — the marginal rate jumps, but liability is continuous.
+ >,
+ <>
+ A notch taxes the firm’s{" "}
+ entire turnover once it registers — liability jumps discretely by{" "}
+ .
+ >,
+ <>
+ The UK VAT threshold is a notch a strict{" "}
+ {teal("dominated region")} exists, whereas a kink leaves only a ~£1k smoothed gap.
+ >,
+ <>This is why the distortion can be measured exactly and without any elasticity.>,
+ ]}
+ />
+ back to “Why the VAT threshold matters”
+
+
+ );
+}
+
+export function AppendixGenSlide() {
+ return (
+
+
+
How the synthetic firms are built
+
+
+ Draw firms by sector × ONS turnover band; turnover smoothed within band:
+
+
+
+ Input share ( , rescaled
+ Beta) net VAT base .
+ >,
+ <>
+ Each firm gets a positive weight ; weighted target{" "}
+ .
+ >,
+ ]}
+ />
+
+ Fit by gradient descent on a symmetric relative-error loss:
+
+
+
+ {teal("The threshold is a generator parameter")}: every counterfactual regenerates a
+ fresh, internally consistent population.
+
+
+
back to “Data”
+
+
+ );
+}
+
+export function AppendixBehavSlide() {
+ const headers = [
+ <>Reform>,
+ <> >,
+ <> >,
+ <> >,
+ <> >,
+ ];
+ const rows = [
+ ["Raise to £100k", "−£508m", "−£444m", "−£292m", "−£111m"],
+ ["Reduced 10% band", "−£343m", "−£322m", "−£273m", "−£210m"],
+ ["Reduced 15% band", "−£171m", "−£160m", "−£135m", "−£107m"],
+ ];
+ return (
+
+
+
Behavioural costs across e
+
+
+ {headers.map((h, i) => (
+
+ {h}
+
+ ))}
+
+ {rows.map((r) => (
+
+ {r.map((c, i) => (
+
+ {c}
+
+ ))}
+
+ ))}
+
+
+ A larger makes every flat reform cheaper (base-broadening). The taper is
+ omitted — its channels cannot both be netted iso-elastically. The limit
+ reproduces the static costs to within ~£1m.
+
+
back to “The reform menu”
+
+
+ );
+}
+
+export function AppendixSecondarySlide() {
+ return (
+
+
+
Secondary-notch arithmetic (reduced rate)
+
+ A reduced rate in with{" "}
+ :
+
+
+ Primary notch shrinks: jump{" "}
+ , width £15,000 (15%), £9,444
+ (10%).
+ >,
+ <>
+ Secondary notch at the band top:
+ jump (15%), width{" "}
+ £6,562 (15%), £13,125 (10%).
+ >,
+ <>
+ Total dominated width{" "}
+ (15%), (10%) — both
+ marginally above the £21,250 baseline.
+ >,
+ ]}
+ />
+
+ The reduced rate splits the empty band; it does not shrink it.
+
+ back to “The dominated region”
+
+
+ );
+}
diff --git a/paper/slides/presentation/tsconfig.json b/paper/slides/presentation/tsconfig.json
new file mode 100644
index 0000000..ac5c732
--- /dev/null
+++ b/paper/slides/presentation/tsconfig.json
@@ -0,0 +1,33 @@
+{
+ "compilerOptions": {
+ "target": "ES2017",
+ "lib": ["dom", "dom.iterable", "esnext"],
+ "allowJs": false,
+ "skipLibCheck": true,
+ "strict": true,
+ "noEmit": true,
+ "esModuleInterop": true,
+ "module": "esnext",
+ "moduleResolution": "bundler",
+ "resolveJsonModule": true,
+ "isolatedModules": true,
+ "jsx": "react-jsx",
+ "incremental": true,
+ "plugins": [
+ {
+ "name": "next"
+ }
+ ],
+ "paths": {
+ "@/*": ["./*"]
+ }
+ },
+ "include": [
+ "next-env.d.ts",
+ "**/*.ts",
+ "**/*.tsx",
+ ".next/types/**/*.ts",
+ ".next/dev/types/**/*.ts"
+ ],
+ "exclude": ["node_modules"]
+}
diff --git a/results/formulation_a_optima.png b/results/formulation_a_optima.png
index 6c6bbf2..ec90c92 100644
Binary files a/results/formulation_a_optima.png and b/results/formulation_a_optima.png differ
diff --git a/src/firm_microsim/dynamic/formulation_a_optima.py b/src/firm_microsim/dynamic/formulation_a_optima.py
index 429eb27..682e911 100644
--- a/src/firm_microsim/dynamic/formulation_a_optima.py
+++ b/src/firm_microsim/dynamic/formulation_a_optima.py
@@ -163,13 +163,20 @@ def make_figure(path, *, n=N_ABILITY, e=E_DEFAULT, deltas=DELTAS) -> Path:
_style_ax(ax)
axes[0].set_ylabel(r"Value-added profit $\pi_A$ (£k)", fontsize=LABEL_SIZE)
- axes[0].legend(frameon=False, fontsize=TICK_SIZE, loc="upper left",
- title="deductible share")
- axes[0].get_legend().get_title().set_fontsize(TICK_SIZE)
- fig.tight_layout()
+ # Reserve bottom margin, then place a single horizontal boxed legend below
+ # both panels so it never overlaps the profit curves.
+ fig.tight_layout(rect=(0.0, 0.10, 1.0, 1.0))
+ handles, labels = axes[0].get_legend_handles_labels()
+ legend = fig.legend(
+ handles, labels, title="deductible share", loc="lower center",
+ ncol=len(labels), frameon=False, fontsize=TICK_SIZE,
+ bbox_to_anchor=(0.5, 0.005),
+ )
+ legend.get_title().set_fontsize(TICK_SIZE)
+
path.parent.mkdir(parents=True, exist_ok=True)
- fig.savefig(path, dpi=300, bbox_inches="tight")
+ fig.savefig(path, dpi=300, bbox_inches="tight", bbox_extra_artists=(legend,))
plt.close(fig)
print(f" saved {path}")
return path