EBA calibration, regime discipline and nominal rigidities — consumption falls and the crisis now lasts

[adambutlin]

What this adds

Nominal rigidities. Prices are now sticky in both countries, and deposits are nominal contracts. Previously the model was fully real — no inflation, no nominal side at all.

Because Greece and Germany share a currency, the terms of trade is the inflation differential, so the nominal side closes without needing an ECB policy rate: a Greek downturn shows up as Greek deflation (about 93% of the adjustment, on the ECB capital key) rather than German inflation. That matches the internal-devaluation pattern of 2010–14.

Banks now hold real assets against nominal deposits, so that deflation raises the real value of what they owe and deepens the hit to bank capital — a debt-deflation channel the real model had no way to express.

A crisis that lasts. The sovereign-risk shock's persistence was a hardcoded 0.80, implying a 14-month crisis. Our own Markov-switching estimation says otherwise: the Greek crisis state has a 50-month expected duration and the realised episode ran 2010-04 to 2017-12 (92 months), giving a quarterly persistence of 0.94. That parameter is now disciplined by the regime estimate rather than picked by hand, and the amplification dial was re-tuned alongside it so the model still hits its 150bp spread target.

Where the model now stands

Three pillars, all up for review together:

EBA-calibrated bank balance sheets	Bilateral Greek/German sovereign exposures from the 2011 stress test, so the doom-loop channel runs on measured holdings rather than a placeholder.
Markov-switching empirical discipline	A three-state model on peripheral–Bund spreads dates the ECB's stance and now pins two things: the three backstop regimes, and the persistence of the crisis itself.
Sticky prices and nominal deposits	Output responds to demand rather than being pinned by technology and capital alone, and nominal debt revaluation reaches bank balance sheets.

Where to find each: the EBA and regime work went onto main ahead of this branch, so the diff here is the nominal-rigidities and shock-persistence layer on top. The results below are the combined model.

Outcomes

Consumption now falls, and the crisis now lasts

The model previously said a sovereign crisis raised Greek consumption on impact, and that output recovered within a quarter. Both are fixed.

impact response to a 1pp default shock	before	now
Consumption	+0.22%	−0.70%
Output	−0.01%	−0.75%
Investment	−0.77%	−1.71%
Bank net worth	−3.38%	−6.27%
Cumulative output loss, 40 quarters	−0.05	−2.54

Investment is now negative in all 40 quarters and the spread stays above half its peak until quarter 11. Both columns hit the same 150bp Greece–Germany spread target, so this is like-for-like.

Two capital-adjustment frictions were tried first and both rejected — they only shuffled the impact between investment and consumption. The persistence of the shock was the binding constraint, and it was an empirical question we already had the data to answer.

Distributional incidence is progressive

The crisis costs the top income quintile 1.12% of its own consumption while the bottom quintile gains 0.64%, monotone across the distribution. The backstop's protection runs the same way — worth +5.4% to the poorest against +3.5% to the richest.

The backstop results — one of them needs a decision

backstop	spread compression	output	consumption	bank net worth	loading
passive	—	−0.75%	−0.70%	−6.27%	—
medium	25%	+0.18%	+0.74%	−2.92%	5.48×
aggressive	50%	+1.13%	+2.24%	+0.47%	5.17×

The one thing I'd most like your view on

The self-extinguishing premium claim has weakened, and I don't think I should decide alone how to write it.

The loading schedule — the ECB's compensation per unit of expected loss — still declines monotonically in the size of the backstop, and is still comfortably above 1. But its shape has changed:

	before	now
schedule across the full γ range	4.43 → 1.49	5.65 → 4.59
decline	−66%	−19%
minimum	1.49 (near fair value)	4.59

The over-compensation result is now stronger — the floor rises from 1.49 to 4.59, so it no longer depends on where on the schedule you look. But the self-extinguishing story was compelling because the loading fell toward 1: intervene hard enough and the ECB earns roughly the actuarially fair expected loss. It no longer approaches that. A longer crisis accumulates premium over more quarters than it accumulates expected loss, so the ratio stays high even under heavy intervention.

Three readings seem open, and it's your call which the paper takes:

1. Reframe as "declining but persistent over-compensation" and lean on the stronger Claim 1.
2. Argue the 19% decline still carries the mechanism.
3. Treat the tension as evidence that reading a Markov regime duration as an AR(1) persistence is too aggressive — the p³ mapping is a first pass, not an identity.

Two smaller flags

• The default-loading split moved from 3.4%/96.6% to 8.6%/91.4% fundamental versus collateral friction. The constrained-seller claim survives in direction, but "essentially all of it" should become "roughly nine tenths of it".
• Some recorded psi_lambda_B sweeps in the repo may be unreliable. A shortcut that patches the parameter onto a solved steady state misses one of the two places it enters, and was off by 10bp where it was checked. The adopted values were re-derived without it; the brackets around them were not.

All figures and results are regenerated on the current model, and the steady state is unchanged throughout, so the calibration targets you've already signed off on still hold.

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