The macroeconomic impact of changes in economic bank capital buffers Prepared by Derrick Kanngiesser, Reiner Martin, Diego Moccero and Laurent Maurin

Box 1
A panel data econometric model to estimate economic bank capital buffers
It is assumed that banks adjust their capital ratios towards a pre-specified target economic capital ratio. However, owing to adjustment costs, a bank cannot adjust its actual capital ratio immediately. In particular, the change in the capital ratio in period t is assumed to depend on the gap between the target and the actual ratio in the previous period:
T1CRi,t-T1CRi,t-1=γT1CRi,t-1*-T1CRi,t-1+εi,t (1)
where T1CRi,t and T1CRi,t-1* denote the observed and the target Tier 1 capital ratio respectively, γ is the parameter driving the speed of adjustment and εi,t is a bank-specific shock. The target economic capital ratio is unobserved and assumed to be a linear combination of bank ( Bi,t) and country-specific macroeconomic variables ( Mc,t):
T1CRi,t-1*=αi+θBBi,t+θMMc,t (2)
Since the target for the Tier 1 capital ratio is unobservable, it is not possible to estimate Equation (2) directly. Instead, the conjectured functional form (2) is substituted into Equation (1), as follows:
T1CRi,t=γαi+θBBi,t-1+θMMc,t-1-T1CRi,t-1-T1CRi,t-1+εi,t (3)
Rewriting equation (3), it is possible to obtain:
T1CRi,t=β0+β1Bi,t-1+β2Mc,t-1+β3T1CRi,t-1+εi,t (4)
where β0≡γαi, β1≡γθB, β2≡γθM and β3≡1-γ. Equation (4) is then estimated with bank-level fixed effects to obtain its coefficient estimates and to recover γ^, αi^,θB^ and θM^. These estimates are then used to construct the bank’s target for its capital ratio:
T1CRi,t*^=αi^+θB^Bi,t+θM^Mc,t (5)
With the individual target estimate, T1CRi,t*^, it is possible to construct individual economic bank capital buffers:
CBi,t=TICRi,t-T1CRi,t*^ (6)
The buffers for the banks are then aggregated to obtain the aggregate economic bank capital buffer series for the euro area countries:
CBc,t=∑i=1Nωi,t-1CBi,t (7)
where ωi,t-1 denotes the share of bank i in the total assets at time t −1.
The calculation of the economic bank capital buffers is based on data from 18 systemically important euro area financial institutions. This is the largest number of financial institutions for which quarterly information on the Tier 1 capital ratio is available for a sufficiently long period of time. Stock price data are obtained from Bloomberg, while the Tier 1 ratio and total assets are obtained from Bloomberg, Bankscope, S&P CapitalIQ and SNL Financial. The source of the one-year ahead real GDP growth forecast is Consensus Economics, that of the sovereign bond yield spread is DataStream and that of the euro area aggregate corporate bond yield spread is the Federal Reserve Bank of St. Louis. The data spans the period from the first quarter of 2005 to the fourth quarter of 2018.