Appendix 2A Literature on Transient and Dynamic Stochastic General Equilibrium (DSGE) Estimates

Transient Estimates

In 2010 the Macroeconomic Assessment Group (MAG 2010) of the Basel Committee on Banking Supervision estimated the prospective effects of the transition to higher capital requirements under Basel III.

IMF estimates indicate that additional adverse spillover effects from simultaneous increases in capital requirements across countries would boost the maximum loss by an additional 0.02 percent by the 35th quarter. Among about 70 models based primarily on credit spread impacts, about halfexcluded induced monetary policy changes and found larger maximum losses (0.18 percent); the half that included endogenous monetary policy found smaller maximum losses (0.11 percent). By implication monetary policy was capable of offsetting about one-third of the transient impact.

Simulations indicate that if the full adjustment were compressed to a much shorter period of only two years, the maximum output loss per percentage point increase in capital ratio would be 0.22 percent from base­line before partial recovery rather than 0.17 percent (0.15 percent plus the 0.02 percent spillover; p.

The estimates also imply a surprisingly small increase of only 1.3 percent in the capital ratio to get from actual practice in 2009 to the Basel III targets. Thus the study places the common equity tier 1 capital ratio of large internationally active banks at 5.7 percent of risk-weighted assets in December 2009. It estimates that reaching the new Basel III target of 7 percent (4.5 percent plus 2.5 percent capital conservation) would cause an increase of only 1.3 percentage points in the capital ratio from the “starting point” for large internationally active banks (p. 7).

A 2011 study by researchers at the OECD (Slovik and Cournede 2011) estimates the medium-term decline in growth associated with the increases in capital requirements under Basel III of 0.05 to 0.15 percentage points a year. They estimate that by 2019, banks in the United States, the euro area, and Japan would need to raise common equity relative to risk-weighted assets by an average of 3.7 percentage points (p. 6)-even though the result would be to boost the ratio in the United States (for example) from 10.5 percent in 2009 to 13.6 percent, far above the Basel III minimum of 9.5 percent even for G-SIBs. The authors assume that banks would maintain relatively high voluntary buffers above the minimum requirements. They estimate that a 1 percentage point increase in the capital ratio would raise bank lending spreads by 15 basis points. They use the OECD's New Global Model to place the semi-elasticity of long-term GDP with respect to bank lending rates at -1.45 percent of GDP per 100 basis points (p. 9). With full phase-in of Basel III boosting bank lending rates by 52 basis points, they calculate that the long-term impact on GDP (five years after implementa­tion) would be a decline of 0.75 percent. They thus place the reduction in annual growth in the medium term at 0.05 to 0.15 percent, reflecting interim (2015) and full (2019) effects.

The parameters from the OECD study provide a useful comparison with those used in chapter 4. In Slovik and Cournede (2011), a 1 percentage point increase in the ratio of capital to risk-weighted assets has a long-term negative effect on GDP of 0.22 percent (15.2 basis points on the lending spread and 1.45 percent of GDP for 100 basis points on the bank lending rate (0.152 ? 1.45 = 0.22)). Considering the relationship of total assets to risk-weighted assets (set at 1.78 in chapter 4), the corresponding param­eter would be a reduction of 0.39 percent in GDP for a 1 percentage point increase in the ratio of capital to total assets. This parameter is more than twice as large as that estimated in chapter 4 (0.15). However, much of this difference is explained by the fact that Slovik and Cournede make no allow­ance for an M&M offset, whereas I set the offset at 45 percent of the direct impact of increased capital requirements on lending spreads.

A key study by the leading global association of financial institutions, the Institute of International Finance (IIF 2011), examines the prospective impact of the set of regulatory reforms in Basel III, including especially the increased capital requirements for banks.^[44] It estimates that the reforms would cause an average increase in bank lending rates to the private sector in the United States, the euro area, the United Kingdom, Switzerland, and Japan of 364 basis points in 2011-15 and 281 basis points in 2011-20 (p.

However, actual experience in 2011-15 was not kind to this projection. Average bank lending rates in the United States, France, and Germany fell rather than rose in this period (see figure 3C.1 in appendix 3C in chapter 3), and any increases in spreads above risk-free rates were far smaller than the IIF projected.

The report acknowledges the M&M theorem but states: “Most industry practitioners question the validity and applicability of the M&M theorem. This...[is] likely to reflect the outcome of experience.... in the short run, as ownership dilution concerns dominate...heavy required (and/or feared) equity issuance could depress bank equity prices, thus raising the short­run cost of equity finance” (p. 45). It describes official sector studies as “too sanguine about funding implications” (p. 16).

In its equation for the “return on equity,” the study calculates the “shadow” cost of equity as equal to the target return on equity plus a coeffi­cient of 0.5 multiplied by the excess in the growth of core tier 1 equity over the growth rate of nominal GDP. It allows an M&M offset of 0.25 times the excess of the core tier 1 capital ratio over 7 percent.^[45] This formulation generates an increase in lending rates of 364 basis points over five years.

The overall thrust of the study is that the rising equity costs associated with dilution effects in the face of the relatively rapid phase-in of higher capital requirements would far outweigh M&M effects, so that the average cost of capital would rise not only as a result of the increase in the fraction of financing coming from equity but also because of an increase in the cost of equity capital itself. The report does not provide specifics on these funding shares or the pre- and postreform levels of equity capital costs.

If this view is combined with the apparent outcome that effects in the near term have not been as severe as expected by the IIF, the broad implica­tion would seem to be that the tradeoff was not as adverse as the IIF feared in 2011.

In contrast, this study focuses on the persistent rather than the short­term costs of higher equity requirements. It examines much larger capital increases than those agreed to in Basel III.

Roger and Vlcek (2011) use a dynamic stochastic general equilibrium (DSGE) model to examine the transient costs of phasing in higher capital requirements. To the typical model structure of impatient and patient households, entrepreneurs, producers, government, and monetary author­ity, they add a banking sector that lends to households and the produc­tion sector. Banks face a quadratic penalty function for revenues when their capital ratio differs from the regulatory requirement. Increasing the capital requirement by 2 percentage points of risk-weighted assets over two years causes cumulative output losses over five years equivalent to 1 percent of one year's GDP if banks adjust mainly by cutting dividends and accepting lower return on equity, 2 percent if they mainly raise lending margins, and up to 4 percent if they adjust by cutting the volume of assets (these figures are averages for euro area and US banks). These costs are little affected by the speed of the phase-in.^{[46] [47] The costs are about one-fourth higher if normal monetary policy response (the Taylor rule) is unavailable (e.g., because in­terest rates are already at a zero bound). Although the model focuses on a five-year horizon, its steady state finds that in the scenario with bank adjust­ment through increased lending spreads, the 2 percentage point increase in the risk-weighted capital-to-assets ratio boosts lending spreads by 15 to 20 basis points and leads to “slightly lower” steady-state output (p.}

Roger and Vlcek do not calculate the effects of equity issuance as the mode of bank response, because “the dynamic effects are essentially nonex­istent with this model” (p. 11), a sharply different modeling approach from that of the IIF (2011). Even with adjustment limited to lending spreads, a longer (four-year) phase-in period, and allowance of monetary authority response, the costs are not trivial: The 2 percentage point increase in the capital ratio causes a cumulative loss of 2 percent of one year's output. This estimate serves as a caveat to the argument that active monetary policy could easily offset costs of higher capital requirements.

Estimates by the European Commission (2011) are close to those of the MAG (2010) and far from those of the IIF (2011). Using its QUEST model (a DSGE model incorporating a financial sector), it estimates that a 1 percentage point increase in the capital requirement would reduce output by 0.1 percent from baseline by year 4, 0.15 percent by year 8, and 0.36 percent in the long term. This estimate is far more optimistic than that of the IIF, which the European Commission interpreted as indicating a decline in output from baseline by 2.1 percent in year 4. Although its estimate for year 8 is virtually the same as the median-model estimate by the MAG (2010), its “long-term” estimate is much larger than implied by the MAG results (which show output returning partially to baseline after a maximum decline by the 35th quarter). In an attempt to consider the IIF argument regarding higher rather than lower required return on equity in the face of higher capital requirements, the European Commission calcu­lated that an increase of 50 basis points in return on equity would boost the potential long-term loss from a 1 percent additional capital require­ment from 0.36 to 0.58 percent (still considerably smaller than the IIF esti­mate).

Cohen (2013) provides an early review of the experience of banks in adjusting to the new capital requirements of Basel III. For 82 large global banks over the period 2009-12, he finds that retained earnings accounted for the bulk of the increase in risk-weighted capital ratios; reduction in risk weights played a smaller role. Lower dividend payouts and wider lending spreads contributed to retained earnings. Lending continued to expand, as banks from advanced economies increased their assets by 8 percent (European banks by less) and banks from emerging-market economies increased their assets by 47 percent. Banks that emerged from the crisis with relatively low levels of capital tended to have slower asset growth.^[48] For the large global banks, the weighted average of capital ratios (common equity) rose from 5.7 percent of risk-weighted assets at the end of 2009 to 9 percent at the end of 2012.^[49] Their common equity capital rose 34 percent. The denominator of the capital ratio (risk-weighted assets) rose 5 percent (an increase of 14 percent in total assets moderated by an 8 percent decline in the ratio of risk-weighted to total assets). Three-fourths of the increase in risk-weighted capital ratios came from higher capital.

Cohen finds that higher capital requirements did indeed lead to higher spreads, amounting to 11 basis points per percentage point increase in the capital ratio, but notes that this increase is smaller than the 15- to 17-basis- point increase estimated by the MAG (2010) and much smaller than the 30- to 80-basis-point increase estimated by the IIF (2011). He also finds that the ratio of net income to book equity fell sharply, from almost 21 to 8 percent, driven by a decline for advanced economy banks. Price-to- book ratios also fell below unity after the crisis for many banks. In Europe lending growth lagged far behind asset growth, as banks shifted toward cash and government securities. The broad thrust of Cohen's findings is that the transition was going more smoothly than many had feared and that there had not been sharp cutbacks in assets that would have been contractionary (although there was “a pronounced shortfall in lending growth [emphasis added] among European banks” [p. 39]).

In late 2015 the Financial Stability Board released its first annual report to the G-20 on the implementation and effects of financial regula­tory reform (FSB 2015b). It finds that “all large internationally active banks already meet the fully phased-in risk-based minimum capital require­ments” (p. 7) of Basel III, three years ahead of the January 1, 2019 deadline. In addition, 80 percent of these banks met the fully phased-in targets for liquidity.^[50] However, the report finds variations in banks' risk-weighting of assets based on internal models and indicates that the Basel Committee was working on improving the consistency of risk weighting. The report also notes that the Financial Stability Board had agreed to an international standard for TLAC for G-SIBs and that assessments indicated that “the benefits [of TLAC] exceed costs by a good margin” (p. 9).^[51]

Cecchetti (2014) reviews the experience of initial implementation of Basel III capital requirements. He notes the wide gap between the early predictions of the IIF (2011) and the MAG (2010) regarding economic consequences and observes that most analysts outside the banking and regulatory communities considered that the drag on output would be rela­tively small and closer to the MAG end of the spectrum. Noting that most large internationally active banks already met the 2019 requirements, he argues that “the jury is in.... The optimists were not optimistic enough. Capital requirements have gone up dramatically, and bank capital levels have gone up with them. In the meantime, lending spreads have barely moved, bank interest margins are down, and loan volumes are up” (p. 1). Cecchetti cites the Basel Committee's periodic quantitative impact studies showing an increase in common equity tier 1 from 5.7 percent of risk-weighted assets at end-2009 to 10.2 percent at end-2013 for 102 large global banks, noting that the increase is large (4.5 percentage points) and the 2019 target had already been reached.

Like Cohen (2013), Cecchetti emphasizes that most of the increase in the capital ratio came from the buildup of capital from retained earnings, not a collapse in assets. Presenting data indicating falling bank profit­ability from the average in 2000-07 to 2013, he infers that the costs of increased capital were borne by shareholders and emphasizes that net interest margins did not balloon.

Other data show that with the exception of Europe, lending spreads fell and lending standards eased—but these trends stem mainly from a contrast between the high-risk crisis period (2008-09) and the postcrisis (2010-13) period. Cecchetti acknowledges that weak demand could explain falling spreads and easing standards but cites rising ratios of total credit to GDP as inconsistent with a weak-demand explanation. Most of the big increases in the credit to GDP ratio were in emerging-market economies, however; the ratios were lower in 2013 than in 2006 for the United States, Germany, the United Kingdom, Belgium, Norway, and Ireland (p. 5).

Cecchetti's broad conclusion is that the social costs of raising capital seem to have been small so far and that policymakers should consider further increases—while being wary of a shift in intermediation to shadow banks. An alternative interpretation would be that the extraordinary condi­tions of this period, including zero interest rates and quantitative easing, mean that the observed trends may provide a less reliable guide to long­term impacts than do calibrated estimates based on more normal condi­tions.

DSGE Model Estimates

Angelini et al. (2011) provide what may be seen as a mainstream synthesis of DSGE model results for the long-term impact of higher capital require­ments on economic output. Their study conducts simulations of 13 models, primarily for the United States and the euro area. All of the models allow for an influence of the capital requirement on steady-state output; they exclude models with strict M&M irrelevance of capital structure.

A second criterion for inclusion was that the model's steady state should be straightforward to compute, a criterion that tended to rule out most of the large-scale semistructural models used in BCBS (2010a). In the models considered, higher capital requirements “affect economic activity via an increase in the cost of bank intermediation... [as] banks increase lending spreads to compensate for the higher cost of funding..................................................................................................... This

leads to lower investment, which then affects employment and output” (pp. 2-3). This framework is the same as that applied in chapter 4. The framework does not hinge on the notion that banks take excessive risks as a consequence of the implicit subsidy of deposit insurance, a premise that underlies some other DSGE analyses of bank capital.

Based on the median results of the model simulations, Angelini et al. (2011) arrive at a central estimate of a 0.09 percent reduction in steady­state output (and consumption) as a consequence of a 1 percentage point increase in capital requirements against risk-weighted assets. This estimate is close to the estimate of 0.10 percent reduction in BCBS (2010a). It is also close to the parameter estimated in chapter 4 (in the base-case specification of parameters): an increase in capital requirements of 1 percent of total assets causes a loss in long-term output of 0.15 percent. Given that the ratio of total assets to risk-weighted assets averages 1.78 for US and euro area banks (BCBS 2010b), 1 percent of risk-weighted assets amounts to only 0.56 percent of total assets. The Angelini et al. result of 0.09 percent output impact thus translates into a 0.16 percent loss of output.

Angelini et al. also investigate the long-term impact on output of higher liquidity requirements and of higher capital requirements on output volatility.^[52] However, they do not attempt to model the benefits of increased capital requirements stemming from the reduced probability of financial crises.

In Clerc et al. (2015), eight authors from six central banks and one think tank analyze optimal capital requirements using a DSGE model. Their model involves several “dynasties” that maximize welfare over an infinite horizon: households (a patient dynasty of net lenders and an impatient one of net borrowers), bankers, and entrepreneurs. Output is a function of labor and capital, and capital formation is lower when borrowing rates are higher. Because of limited liability and subsidized deposit insurance, banks have an incentive to undertake excessively risky projects. The dominant influence of an initial amount of required equity capital is thus to curb socially ineffi­cient investments and defaults, increasing welfare. However, equity is more expensive than debt not only because it is not subsidized but also because “bankers' wealth is limited and in equilibrium appropriates some scarcity rents” (p. 34). (The paper does not mention the M&M offset.)

“Costly state verification” means that banks play a key role in credit allocation; when their leverage is excessively constrained, so is credit cre­ation. As a consequence, “the negative effects on economic activity coming from the reduction in the supply of credit to the economy dominate when capital requirements are high enough” (p. 43). Welfare thus follows an in- verted-U curve in relation to the capital requirements. The authors' base parameter values generate maximum welfare at an optimal capital require­ment of 10.5 percent for business loans (risk weight 1.0) and 5.25 percent for mortgages (risk weight 0.5). Applying the ratio of total assets to risk- weighted assets identified by BCBS (2010a) for US and European banks, the corresponding optimal ratio of capital to total assets would be 5.9 percent (10.5/1.78).

It is unclear whether the model adequately captures the benefit of banking crisis avoidance. There is no explicit mapping from capital require­ments to the probability of a banking crisis or any explicit calibration of the expected welfare loss from the occurrence of a banking crisis. The model does incorporate an influence of aggregate shocks that supplement idiosyncratic shocks in determining defaults, but the relationship of these shocks to past international experience in banking crises is opaque. No entry in the authors' table of parameter values corresponds to an estimate of welfare (or output) loss in the event of a banking crisis (p. 41). In addi­tion, the study applies a loss given default ratio of only 30 percent (p. 40), far below the range of 50 to 75 percent suggested by Dagher et al. (2016).

Mendicino et al. (2015) apply the Clerc et al. (2015) model as calibrated to euro area banks for the period 2001-13. Bank lending is high, with mort­gages set at 143 percent of GDP and loans to nonfinancial corporations representing an additional 182 percent of GDP (p. 19). Idiosyncratic risk gives a log-normal distribution of return shocks. Below a given threshold in the lower tail, the borrower defaults, with loss given default of 30 percent. The model calibration yields annual bank default rates of 1.68 percent (p. 21), which the authors note is for a period including bank crises. The op­timization results depend on the weight assigned to borrower versus saver households.

A key finding is that “it is always optimal to impose an average capital requirement and a mortgage risk weight high enough to keep bank defaults low and to reduce the strength of bank-related amplification channels” (p. 3). Beyond a certain level, still higher capital requirements benefit savers (56 percent of households) by avoiding the tax costs of deposit insur­ance losses, but they reduce the welfare of borrowers (44 percent, p. 21) by reducing the supply of bank loans.^[53]

At the authors' preferred benchmark weights of 0.3 to savers and 0.7 to borrowers, the two groups of households share the welfare gains from optimal capital requirements equally. The optimal capital ratio is 13.5 percent of risk-weighted assets—3 percentage points higher than the cali­brated base-period actual capital ratio of 10.5 percent. The optimal ratio is also 3 percent above the Basel III ratio of 10.5 percent, including the capital conservation buffer (p. 26).^[54] Of the welfare gains from a move to the optimal capital ratio, the gains from the influence of “aggregate uncer- tainty”—the model's apparent incorporation of systemwide banking crisis effects—accounts for almost the entirety for borrower households, but only about one-third of the gains for saver households (p. 30). The simulations show relatively little gain from altering the risk-weighting on mortgages from the base rate of 50 percent and relatively little gain from reducing volatility through larger variation in countercyclical capital levies. Overall, the optimal ratio for capital against risk-weighted assets is approximately the same as that identified in chapter 4, even though the methodology is completely different. Even so, considerable inherent opacity remains in the model and its results in comparison with the simpler but more transparent formulation suggested in chapter 4 and applied in such studies as BCBS (2010a) and Miles, Yang, and Marcheggiano (2012).

Begenau (2015) sets forth a DSGE model that finds that “higher capital requirements leading to a reduction in the supply of bank debt can in fact result in more lending” (p. 1). She argues that bank debt provides safe and liquid assets “coveted” by households, so that when banks reduce debt in response to capital requirements inducing lower leverage, the interest on debt falls substantially. The decline in the interest rate swamps the impact of the higher funding cost from increased equity, resulting in a lower rather than a higher lending rate and more rather than less lending.

This approach seems to fail to distinguish between insured deposits (the safe liquid assets held by households) and bank debt to bondholders. The scope for interest reductions on bank deposits would seem limited. The model also includes other unusual assumptions (e.g., decreasing returns to scale in production in the production sector, which depends on bank finance). Sufficient questions and opacity characterize the study that it is unclear whether its quantitative estimate of optimal capital warrants much emphasis.^[55]

Writing before the Great Recession, Van den Heuvel (2008) examined the welfare costs of bank capital requirements in a general equilibrium model in which households derive utility from liquid assets provided in the form of bank deposits. Capital requirements reduce banks' liabilities, which include deposits relative to equity, so they curb the provision of bank deposit services. Van den Heuvel treats the benefits of capital requirements as stemming solely from their effect in limiting moral hazard arising from deposit insurance. He pays no attention to the risk of a systemic banking crisis (or other macroeconomic shock) effectively imposing a shock from outside the individual bank as opposed to a disturbance originating from incentive distortions within the bank. Indeed, he states that “if one believes that deposit insurance does not create a moral hazard problem... then capital requirements have no benefits” (p. 315).

On the basis of the revealed willingness to pay for deposit liquidity (as indicated by the spread between the interest rate on deposits and that on subordinated debt as a proxy for the return on equity), Van den Heuvel esti­mates the gross welfare costs of the existing effective bank capital require­ment of 10 percent of risk-weighted assets (including subordinated debt in capital) at 0.10 to 0.22 percent permanent reduction in annual consump­tion, a large number.^[56] On the basis of a comparison with the relatively small costs of additional supervision as a means of substituting for bank capital requirements, he estimates the marginal costs of capital require­ments as several times the marginal benefit and concludes that “capital requirements are currently too high” (p. 316). This type of general equi­librium model omits the main benefits in the calibrated optimal capital studies: the reduction in the probability of a banking crisis multiplied by the output loss in the event of a banking crisis. The study was written in late 2007, when it was still possible to refer to the “very low rate of bank failures in the United States, since the implementation of the Basel Accord” (p. 315).

De Nicold, Gamba, and Lucchetta (2014) develop a DSGE model that finds an inverted U-shaped relationship between the amount of bank lending and the stringency of capital requirements and a corresponding inverted U-shaped relationship between welfare and capital requirements (p. 2099). They do not report the optimal level of capital requirements in the simulations. They do state that as their model is calibrated, if capital requirements are initially raised to a “mild” level, lending will rise to a peak of 15 percent above the no-regulation case (p. 2100). The reason for the initial increase is that “the capital requirement lowers the return of holding cash relative to the expected return on loan investment” (p. 2115). In other words, higher capital requirements would initially raise the ratio of loans to holdings of safe bonds in the portfolio of banks.

Why higher capital requirements would even initially boost rather than reduce the amount of lending is counterintuitive, contrary to the standard modeling of the impact of higher capital requirements, and rela­tively opaque in the paper. Considering that in practice there would tend to be a zero risk weighting on safebond assets, it is even more difficult to see why higher capital requirements would (initially) boost lending.

More fundamentally, the model excludes two elements that are central to the analysis. First, it does not include a production function, making it impossible to estimate the impact of a higher price of capital (resulting from higher lending costs) on output. Second, it does not include damages from a banking crisis—the centerpiece of the more usual calibrated model calculations of optimal capital requirements. As it turns out, at least for one interpretation of the main calibrations, the study arrives at an optimal capital ratio similar to that found in chapter 4 (about 7 percent).^[57] However, questions about the underlying method suggest that great caution should be taken in weighing the study's findings.