EC956 Macroeconomics
EC956 Macroeconomics
For students taking EC956 Macroeconomics at Warwick. The models below follow the lectures and their notation, and each lists its assumptions under the controls.
For students taking EC956 Macroeconomics at Warwick. The models below follow the lectures and their notation, and each lists its assumptions under the controls.
Choose a shock or a model and move the sliders; each chart redraws, and the text under it explains what changed.
A household lives for two periods and chooses how much to consume today and tomorrow. Change the interest rate, income today or income tomorrow, and the chart splits the move from the old choice A to the new one B. The substitution effect slides along the old indifference curve to the new slope (A to H); the income effect is the parallel move to the new budget line (H to B).
When the rate rises, a borrower’s debt costs more, so both effects cut consumption today. For a saver the income effect works the other way, and consumption today can rise or fall; with log utility it still falls whenever the household has income tomorrow, because a higher rate lowers the value of that income. A change in income moves the budget line without changing its slope, so there is only an income effect.
Try the Income falling preset, a saver, and raise the rate from 10% to 50%: substitution cuts consumption today by 14.0 and the income effect raises it by 6.5, so it falls by 7.5. Set σ to 0.25, less willingness to shift consumption over time, and it rises by 2.8 instead.
These are the six panels from the lectures: IS–LM, the labour market, AD–AS, the production function and the 45-degree line that carries output across. Pick a model and a shock, and every panel redraws from the same equilibrium. Black is the starting point, blue the shock, green the shift in LM when the price level moves, yellow the flexible-price benchmark (red once a supply shock moves it) and grey the medium run.
With flexible prices, output is set by the labour market and technology, so demand shocks move only prices, interest rates and the mix of spending. With simple sticky prices the AS curve is flat and output takes the whole shift in demand; with partial sticky prices AS slopes up, P = P̄ + γ(Y − Yᶠ), and the shock is split between output and prices. In the medium run firms adjust P̄ until output equals Yᶠ, the neoclassical outcome.
Press Step through to follow the transmission one link at a time, and use All three to compare the models: demand shocks move output most with simple sticky prices, real supply shocks most in the neoclassical model. Try a rise in productivity with simple sticky prices: output does not move at first and employment falls, because the same output now needs fewer workers. Add the medium run to see output reach its new flexible-price level.
The expectations-augmented Phillips curve says inflation equals expected inflation plus γ times the output gap. Inflation can fall faster than people expect only if output drops below potential, so the cost of bringing inflation down depends on how expectations are formed.
With backward-looking expectations, every point of disinflation costs 1/γ points of a year’s output, however fast or slowly it is done; with γ = 0.5 the sacrifice ratio is 2, about what the Volcker disinflation cost. If the path is credible and people expect it, inflation falls with no output cost.
Try one year instead of three: the recession is deeper but shorter, and the total loss is the same. Then switch to Credible.
When the nominal interest rate is at zero, the real rate cannot fall below −πᵉ. The economy starts in a liquidity trap: the LM curve is flat at r = −πᵉ up to a kink, so money no longer moves the interest rate and the AD curve is vertical. Yellow, red and green show a comparison economy with the same starting point whose rate can fall below zero.
At the bound a fall in demand is not cushioned by a lower rate, so output falls by the full shift of IS; printing money has no effect; and a fall in expected inflation raises the real rate. Fiscal policy is the exception: while the economy stays in the trap nothing is crowded out, and output rises one for one with government spending. In the medium run falling prices do not close the gap, because AD is vertical.
Try a fall in demand: output falls by 10.0 at the bound against 3.2 without it. Then pick G rises and double the size of the shock: the rise now lifts the rate off zero, and some crowding out returns.
In an open economy net exports depend on the real exchange rate, and the domestic interest rate is tied to the foreign one. A higher interest rate strengthens the currency and cuts net exports, so the IS and AD curves are flatter than in a closed economy. The first view compares the open economy with a closed one; the second compares a flexible exchange rate with a peg.
With a flexible rate, monetary policy is stronger in the open economy: a lower rate also weakens the currency and raises net exports. Shocks to IS are partly offset, because the currency moves against them. Under a peg it is the other way round: the central bank must set the money supply to hold the exchange rate, so it gives up monetary policy, and IS shocks such as higher government spending are amplified.
Try higher government spending in the flexible-versus-fixed view: to stop the currency from appreciating the central bank prints 10% more money, and output rises by 10.0 against 4.0 with a flexible rate. Then set the net-export sensitivity to 0 and the open economy behaves like the closed one.
Firms borrow at the real interest rate plus a credit spread, r + f. The tool compares an exogenous spread with one that narrows when output rises, f = f̄ − aY: the financial accelerator. With the accelerator the expenditure line is steeper, so the IS and AD curves are flatter and shift by more; the Keynesian cross view shows why.
With sticky prices, demand shocks are amplified: a wider spread lowers output, and lower output widens the spread further. Supply shocks are amplified only when prices are partly sticky. With flexible prices output is set by supply, so the spread cannot feed back on it, and with simple sticky prices a supply shock does not move output in the short run.
Try the default: with partly sticky prices a rise in the spread of 1.5 points lowers output by 3.6 with the accelerator against 3.0 without. Raise a to 0.12 and the fall grows to 4.0.
The saving rate changes in year 10. The first view shows the old and new steady states, where investment just covers depreciation and the growth of population and technology. The second follows output and consumption per worker over time, on a log scale.
Saving more raises the level of income per worker but not its long-run growth, which returns to the rate of technical progress. Consumption drops when saving rises and recovers as capital builds up. In the long run it is highest when the saving rate equals the capital share, 1/3 here: the golden rule.
Try a saving rate of 0.5 after year 10. In the long run output per worker ends up 58% above its old path, while consumption ends up about 1% below its own.
The same event hits four models from the lectures: the Solow model, the AK model, a poverty trap with a productivity threshold, and the OLG model, where a period is a generation. The first view tracks output per worker against each model’s own path without the event; the second shows one model’s investment and break-even lines.
In Solow and OLG diminishing returns pull the economy back, so losses and gifts of capital fade and a higher saving rate has only a level effect. The AK model has no such pull: a temporary shock has a permanent effect, and saving changes the growth rate. In the poverty trap history matters: a large enough loss sends a rich economy into the trap, and a large enough push lets a poor one escape. The threshold itself is not a steady state, because the investment curve jumps across the break-even line there.
Try destroying half the capital stock: Solow is back within a few decades, AK stays 50% poorer for good, and the trap economy ends 54% poorer. Then try a big push of 60%: the gain fades in Solow and OLG, lasts in AK, and in the trap output more than doubles.
Each month a share s of workers lose their jobs and a share f of the unemployed find one. Unemployment settles where the two flows balance, at u* = s/(s + f). The defaults follow the lecture: separations of 1.7% a month, and a job-finding rate that falls from 30% to 19% a month, much as it did in the Great Recession.
The flows are large next to the number of people unemployed, so the rate moves to its new steady state within months rather than years.
Try leaving job finding at 30% and raising separations to 2.5% instead. Unemployment rises to 7.7%, and it gets there faster, because the unemployed still find jobs quickly.
Firms post vacancies until the expected profit from one, the chance of filling it times z − w, just covers its cost k, and the wage splits the surplus of a match through Nash bargaining. Together these fix labour-market tightness j, vacancies per searcher, and with it the share of searchers who find no job (u) and the share of vacancies left unfilled (v).
Benefits b, productivity z and bargaining power a change tightness, so they move the economy along the Beveridge curve: higher z brings more vacancies and less unemployment. A fall in matching efficiency e shifts the curve out instead. Unemployment rises while the vacancy rate stays put, because free entry fixes the chance of filling a vacancy.
Try lowering matching efficiency from 0.80 to 0.70: unemployment rises from 20% to about 39%, and the vacancy rate stays at 20%. In this one-period version u and v are shares left unmatched within a period, so their levels are high.