This study separates the long-run from a short-run dimension in the analysis of leverage and related liability ratios. If banks exhibit constant liability ratios, decomposed sets of liabilities form cointegrating relationships. Hence, cointegration analysis absorbs the long-run patterns and can test whether banks target certain liability ratios. My analysis demonstrates that liability sets are only cointegrating when taking structural breaks into account. I consider two possible structural break that might shape long-run ratios. The Lehman collapse and the subsequent freeze of the interbank market in September 2008 serve as one structural break. In the case of public sector banks, I incorporate the abolition of state guarantees in July 2005 as a second structural break. For the long run, this procedure allows me to trace the channels that banks invoke to adjust their long-run liability structure when facing key ruptures in their funding conditions. For the short run, my results point at those liabilities that adjust for past deviations from the long-run ratios as induced by changes in financial market risks. A tailored version of a banking model by Baltensperger and Milde (1987) allows me to form hypotheses about the optimal adjustment patterns to ruptures in banks’ funding conditions or risks in financial markets. My long-run approach finds that the Lehman failure has led to major reallocations in the liability structure and hence leverage of all banking groups. Large commercial banks cut their leverage after the Lehman collapse with the effect mainly operating through a decline in foreign, bank and bond finance. Small commercial banks provide weak evidence of a slight increase in leverage operating through foreign and domestic debt. Public sector banks increase their leverage after the termination of guarantees, but reduce it in the wake of the Lehman collapse operating through foreign, bank and bond debt. Cooperative banks take a neutral stance on leverage in view of changes in the funding conditions in international banking markets.
4.4. DISCUSSION AND CONCLUSION 123
My short-run approach finds that considerable heterogeneity governs the adjustment patterns of banking groups given changes in financial market risks. Large commercial banks expand their balance sheets and raise equity which does not yield any clear-cut implications for their leverage ratio. Small commercial banks replace bonds for bank debt and thus take a neutral stance on leverage. Solely cooperative banks act broadly in line with the Baltensperger model, by reducing their leverage. As public sector banks experience two structural breaks, the first one as early as July 2005, the reduced estimation sample does not leave enough observations to conduct a short-run analysis. A more general consideration of the short-run suggests that VECMs reflect short-run variation in the liability structure quite well. Large and small commercial banks differ substantially from cooperative banks with respect to the balance-sheet items that restore the long-run equilibrium ratios. In case of commercial banks, the total balance sheet, equity and debt, in particular foreign and bank debt, correct for past deviations. In case of cooperative banks, bonds restore the long-run equilibrium ratios.
To conclude, a proper analysis of banks’ liability structures requires to distinguish between a short- and a long-run dimension. Heterogeneity governs the adjustment of different banking groups when facing key ruptures in their funding conditions or changes in financial market risks.
These results yield valuable insights for policymakers. In the wake of the Lehman crisis some German banks enjoyed direct government support measures, others benefited from concerted actions (see Buch et al., 2011a). Recently, the ECB has provided huge amounts of liquidity by means of two long-run refinancing operations in December 2011 and February 2012. The aim was to keep banks afloat and secure the well functioning of the interbank market. Even if not all German banks are immediately affected, these initiatives have repercussions throughout the whole banking sector. For this reason it is of key importance to bear in mind that changes in the funding conditions have different impacts on different banking groups.
Appendix C
Risky Adjustments or Adjustments
to Risks
C.1
Log-Linearization
To derive the cointegration term in logs, I draw on set I of Table C.1 as an example which features the total balance sheet tbst, non-securitized liabilities debtt, securitized liabilities bondt, other liabilities lother and equity equityt. This procedure borrows from Lettau and Ludvigson (2001); Hoffmann (2006) who found their argument on the inter- temporal budget-constraint of households instead of the balance-sheet identity used in this paper. As a starting point, I express these balance-sheet items in absolute terms as evidenced by capital letters. The balance-sheet identity states that non-securitized liabilities DEBTt, securitized liabilities BON Dt, other liabilities LOT HERt and equity EQU IT Yt sum up to equal total liabilities and thus the total balance sheet. Hence T BSt= DEBTt+ BON Dt+ LOT HERt+ EQU IT Yt. To simplify the derivation, I will reduce the focus on equity and external finance, with external finance capturing all the remaining liability items EF INt = DEBTt+ BON Dt+ LOT HERt.
This identity can also be rewritten as shares of total assets 1 = EF INt
T BSt + EQU IT Yt T BSt or 1 − EQU IT Yt T BSt = EF INt
T BSt . An equivalent transformation of exponentiating and taking logs
yields 1 − elnEQU IT YtT BSt = elnEF INtT BSt and substituting log expressions by small letters gives
1 − eequityt−tbst
= eef int−tbst
126 APPENDIX C. RISKY ADJUSTMENTS OR ADJUSTMENTS TO RISKS
sides of Equation C.1 separately:
ln 1 − eequityt−tbst
= ln eef int−tbst
(C.1)
The left-hand side of expression C.1 is a non-linear function of the log equity to balance sheet total ratio equityt−tbst= xt. By analogy to the approach of Campbell and Mankiw (1989), I apply a first-order Taylor expansion of the function ln (1 − ext) around x
t= ¯x. Put differently, I assume that banks target a fixed long-run equity ratio. The aim is to get an approximation of the long-run ratios of particular liability types to the total balance sheet based on the permanently valid balance-sheet identity. According to the Taylor approximation yt⋍ g(x) + g′(x)(xt− x), I obtain the following expression for the left-hand side of C.1:
LHSt= ln
1 − eequity−tbs+ e
equity−tbs
1 − eequity−tbs equityt− tbst− equity − tbs
Rearranging terms and subsuming time-invariant expressions by constants c1 = ln
1 − eequity−tbs further c 2 =
eequity−tbs(equity−tbs)
1−eequity−tbs and c3 = c1− c2results in:
LHSt= c3+
eequity−tbs
1 − eequity−tbs (equityt− tbst) .
The fraction 1−eeequity−tbsequity−tbs can equivalently be expressed as
EQU IT Y T BS 1−EQU IT YT BS = EQU IT Y T BS−EQU IT Y to obtain: LHSt = c3+ EQU IT Y T BS − EQU IT Y (equityt− tbst) (C.2) Now, I turn to the right-hand side of Equation C.1, namely ln eef int−tbst. Again,
I apply a first-order Taylor expansion, this time of the function ln (ext) around x
t = ¯x. Now ¯x denotes a constant debt to total balance sheet ratio .
RHSt= ln eef in−tbs+e ef in−tbs eef in−tbs ef int− tbst− ef in − tbs
The first term cancels with ef in − tbs in the second part such that I obtain: