16  Interactive: PPP exchange rate

Set the basket prices in two countries. Get the PPP exchange rate. Then sliders for inflation rates project the ER over time.

viewof PUS = Inputs.range([100, 2000], {value: 400, step: 10, label: "US basket price ($)"})
viewof PUK = Inputs.range([100, 2000], {value: 200, step: 10, label: "UK basket price (£)"})

E_now = PUS / PUK

md`**PPP exchange rate today:** \`E = $${PUS} / £${PUK} = $${E_now.toFixed(3)} per £\``

16.1 How does the ER move if relative inflation differs?

viewof piUS = Inputs.range([0, 0.20], {value: 0.05, step: 0.005, label: "US annual inflation"})
viewof piUK = Inputs.range([0, 0.20], {value: 0.02, step: 0.005, label: "UK annual inflation"})
viewof horizon = Inputs.range([1, 20], {value: 10, step: 1, label: "Years to project"})

years = d3.range(0, horizon + 1)
ePath = years.map(t => ({
  year: t,
  PUS_t: PUS * Math.pow(1 + piUS, t),
  PUK_t: PUK * Math.pow(1 + piUK, t),
  E_t: (PUS * Math.pow(1 + piUS, t)) / (PUK * Math.pow(1 + piUK, t))
}))

Plot.plot({
  width: 600,
  height: 320,
  marginLeft: 70,
  marginBottom: 50,
  x: {label: "Years from now"},
  y: {label: "PPP exchange rate ($/£)"},
  marks: [
    Plot.line(ePath, {x: "year", y: "E_t", stroke: "#0e7c7b", strokeWidth: 2.2}),
    Plot.dot(ePath, {x: "year", y: "E_t", fill: "#0e7c7b", r: 3}),
    Plot.ruleY([E_now], {stroke: "#888", strokeDasharray: "4 3"}),
    Plot.text([{year: 0, E_t: E_now, l: `Today: $${E_now.toFixed(2)}/£`}], {x: "year", y: "E_t", text: "l", dx: 80, dy: -10, fill: "#888", fontSize: 11})
  ]
})

md`**ER in year ${horizon}:** \`$${ePath[horizon].E_t.toFixed(3)}/£\` (vs. today: \`$${E_now.toFixed(3)}/£\`)

The dollar ${ePath[horizon].E_t > E_now ? "**depreciates**" : "**appreciates**"} over the projection horizon.`

16.2 What to play with

• US inflation 5%, UK 2%. Dollar depreciates roughly proportionally — about 3% per year against the pound.
• Set both to the same rate. ER stays flat. PPP says the currency only moves when relative inflation differs.
• Reverse them. UK at 5%, US at 2%. Now the dollar appreciates. The country with lower inflation sees its currency strengthen.

16.3 Where PPP fails

• Short-run (months to a year). Sticky prices and trade frictions break the law of one price.
• For non-traded goods (haircuts, restaurant meals). They never face arbitrage and can stay out of line indefinitely.
• During financial crises, when capital flows dominate trade flows.

For long horizons (5+ years) and traded goods, PPP gives a useful first-order benchmark. The Big Mac Index is the famous popular version.