Do regulators need to use the macroprudential policy tools to control financial risks?

Economic Modelling 42 (2014) 77–93

Contents lists available at ScienceDirect

Economic Modelling

journal homepage: www.elsevier.com/locate/ecmod

Macro effects of capital requirements and macroprudential policy

Q. Farooq Akram ⁎ Research Department, Norges Bank, Bankplassen 2, P.O. Box 1179 Sentrum, 0107 Oslo, Norway

⁎ Tel.: +47 22316692. E-mail address: [email protected].

http://dx.doi.org/10.1016/j.econmod.2014.05.033 0264-9993/© 2014 Elsevier B.V. All rights reserved.

a b s t r a c t

Article history: Accepted 23 May 2014 Available online 2 July 2014

JEL classification: C52 C53 E52 G38

Keywords: Basel III Capital requirements Macroprudential policy

I investigate macro effects of higher bank capital requirements on the Norwegian economy and their use as a macroprudential policy instrument under Basel III. To this end, I develop a macroeconometric model where the capital adequacy ratio, lending rates, asset prices and credit interact with each other and with the real econ- omy. The empirical results suggest that changes in capital requirements are primarily transmitted via lending rates to the other variables in the model. The proposed increases in capital requirements under Basel III are found to have significant effects especially on house prices and credit. I also derive optimal paths for the counter- cyclical capital buffer in response to various shocks. The buffer is found to equal its imposed ceiling of 2.5% in response to most of the shocks considered while its duration varies in the range of 1–12 quarters depending on the shock and its persistence.

© 2014 Elsevier B.V. All rights reserved.

1 Basel III also entails more stringent requirements for the level and the quality of a bank's

1. Introduction

I investigate macroeconomic effects of higher capital requirements on the Norwegian economy and their use as a macroprudential policy instrument. Macroprudential policy aims at promoting financial stabili- ty partly by e.g. managing growth in asset prices and credit. Excess growth in these variables over extended periods may be seen as a necessary condition for financial instability (e.g. Borio and Lowe, 2002; Reinhart and Rogoff, 2009; Schularick and Taylor, 2012). A number of studies have argued for time-varying capital require- ments to avoid destabilizing credit growth (e.g. Bank of England, 2009; Brunnermeier et al., 2011). I investigate in particular possible effects of the capital requirements recently proposed by the Basel Committee on Banking Supervision (BCBS), which are referred to as Basel III (BCBS, 2010a). The new regulatory framework proposes a permanent increase in the common equity ratio of 2.5 percentage points (conservation buffer) and a systemic-risk dependent variation in the common equity ratio in the range of 0–2.5 percentage points

(countercyclical buffer).1 Furthermore, I shed light on the implementa- tion of the countercyclical capital buffer in response to various shocks with different persistence.

I employ a quarterly macroeconometric model of the Norwegian (mainland) economy to conduct the analyses. The model includes em- pirical relationships between several real and financial variables, includ- ing those between house prices and credit to households, and between banks' capital adequacy ratio and lending rates. The latter relationship is among the novel features of this model, as an explicit account of capital requirements in macroeconometric models is rare (see Angelini et al., 2011; BCBS, 2010b and the references therein). To my knowledge, this is the first such model based on Norwegian data. The model employed is essentially a smaller version of a model that has been maintained by

core capital. It also proposes restrictions on the maturity structure of banks' assets and liabilities to ensure sufficient liquidity and hedge against particularly large withdrawals of liabilities. These restrictions are formulated as two quantitative liquidity requirements: a liquidity coverage ratio (LCR) and a net stable funding ratio (NSFR). The liquidity coverage ra- tio concerns the required level of liquid assets a bank must have in order to be able to with- stand periods of stress in the markets for funding while the net stable funding ratio concerns the composition of sources of funding or the stability of the funding. These restrictions may have additional effects on banks' funding costs and thereby lending rates which are not accounted for in the following analyses. Basel III is expected to be phased in gradually over the period 2013–2019, see www.bis.org/bcbs/basel3.htm for more details.

78 Q.F. Akram / Economic Modelling 42 (2014) 77–93

Norges Bank. However, it has been further developed, updated and adapted to conduct the analyses of interest to this paper.2

The literature on the design and effectiveness of macroprudential policy tools as well as the development of appropriate models for their investigation is still in its infancy. In general, there is a lack of theo- retically well founded models for policy analyses that account for key relationships between the financial economy and the real economy in a satisfactory way (see e.g. Galati and Moessner, 2013; Tovar, 2008 and the references therein). Obtaining precise estimates of how the economy would have performed or how it will perform under alternative capital requirements is inherently difficult. It is not possible to say whether and to what extent the model's param- eters will shift with new policy changes. However, I proceed under the assumption that the macroeconomic effects of changes in capital requirements will be comparable to those observed historically.

In the analysis of the countercyclical capital buffer as a macro prudential policy tool, the policymaker is assumed to minimize excessive fluctuations in aggregate credit growth while taking into account the effects of policy decisions on economic activity (cf. Haldane, 2012). I use aggregate credit growth as an indicator of systemic risk, for the sake of simplicity and because growth rates of credit and GDP are relatively more robust to data revisions than their levels (e.g. Edge and Meisenzahl, 2011; Orphanides and Norden, 2002). In response to a given shock, the policymaker is as- sumed to minimize the loss function by deciding on a future path for the countercyclical capital buffer. The path is defined by the size and duration of the countercyclical capital buffer. I derive such paths in response to various shocks for different degrees of persis- tence. I also investigate the sensitivity of such paths to the strength of the policymaker's concern for fluctuations in economic activity, and alternatively for fluctuations in the inflation rate.

The paper is organized as follows. Section 2 presents the empir- ical framework, while Section 3 employs the model to investigate the effects of increases in capital requirements on the Norwegian economy. In Section 4, capital requirements are used as a macro- prudential policy tool within the Basel III framework in response to various shocks. Section 5 contains the main conclusions. Finally, the appendices contain data definitions, model documentation and sensitivity analyses.

2. The empirical framework

I first develop a system of dynamic econometric equations for the capital adequacy ratio, lending rates, house prices, credit to households and credit to (non-financial) firms to characterize their interaction with one another.3 This equation system is then integrated into a macroeconometric model briefly presented in Section 2.4. This model contains dynamic equations for a number of other financial and real economic variables including short-term interest rates, equity returns, the nominal effective exchange rate, inflation and output. It was not fea- sible to develop a closed system of dynamic equations for a relatively large number of variables of interest to investigate how changes in capital requirements may be transmitted to the economy. The macro econometric model is therefore composed of a few small equation systems as well as single equation models, while conditioning on variables such as oil prices, foreign interest rates and foreign GDP (see e.g. Bårdsen et al., 2005, ch. 2, for a discussion of blockwise composition of macroeconometric models). Efficient inference about the parameters of interest in a partial model requires, however, that the conditioning

2 The model used at Norges Bank is documented in Hammersland and Træe (2014) and is mainly based on Bårdsen et al. (2003, 2005).

3 Capital adequacy ratio is defined as the sum of common equity, hybrid equity and ad- ditional equity (Tier 2), divided by risk-weighted assets. I also made an attempt to develop econometric models of the main subcomponents of the capital adequacy ratio but without much success.

variables are weakly exogenous with respect to the parameters of inter- est (Engle et al., 1983). Appendix B presents evidence of this with re- spect to key parameters in the (partial) system of dynamic equations for the capital adequacy ratio, lending rates, house prices, credit to households and credit to firms.

2.1. Capital ratio, lending rates, house prices and credit

The system of dynamic econometric equations for the capital ade- quacy ratio, lending rates, house prices, credit to households and credit to firms has been developed in two steps using quarterly data over the period 1992 q4–2010 q4. First, long-run relationships between a given set of variables in levels were established by testing for cointegration between the variables. The variables in levels were found to be unit- root non-stationary. Upon finding evidence of cointegrating relation- ships between the variables, a Vector Equilibrium Correction Model (VECM) was formulated, estimated by FIML, tested and, if required, respecified to satisfy a number of statistical model diagnostic tests and economic intuition (cf. Hendry, 1995).

In the following, I first present the estimated long-run relation- ships and then the VECM in Table 1. Unless stated otherwise, variable names in small letters denote the natural log of the corresponding variables, while Greek letters without subscript t represent parame- ter values. Δ and Δ4 denote first- and fourth-difference operators, respectively.

2.2. Long-run relationships

The equilibrium value of the capital adequacy ratio (CAR) may be decomposed into the minimum common equity ratio required by Basel regulations and the equilibrium value of other capital components including hybrid capital, Tier 2 capital and additional capital held by banks beyond that required by capital adequacy rules. Banks may choose to hold capital in addition to that required by regulations as a hedge against credit and liquidity risk (Booth et al., 2001; Flannery and Rangan, 2006; Peura and Keppo, 2006).

The actual ratio of capital adequacy may temporarily deviate from its equilibrium value owing to prevailing regulatory and market con- ditions as well as banks' response to them. Such a characterization of the capital adequacy ratio is consistent with its quarterly time series suggesting that CAR fluctuates around a fairly stable value over the sample period 1992 q4–2010 q4. The null hypothesis of a unit root in CAR is rejected by an augmented Dickey Fuller test at the 5% level of significance. The long-run relationship for capital adequacy ratio may be described as:

CARt ¼ κ þ ε1;t; ð1Þ

where κ represents the equilibrium value of CAR while ε1,t represents a zero mean stationary process. Accordingly, CARt deviates tempo- rarily from κ. I estimate κ by taking the sample average of CARt, which equals 12.5% (see Eq. (1)).

When modeling lending rates (iL), I assume that they reflect banks' funding costs in the long run, which depend on (short-term) money market rates (i) and costs of equity. The latter costs are assumed to de- pend on banks' return on equity and other possible costs of equity asso- ciated with e.g. issuing equity, monitoring and asymmetric information (e.g. Bolton and Freixas, 2006; Holmstrom and Tirole, 1997; Jensen, 1986; Kashyap et al., 2008; Repullo and Suarez, 2000). The following long-run relationship for lending rates may be specified:

i L t ¼ 1−CARtð Þit þ CARt Δ4betð Þ þ γCARt þ α þ ε2;t: ð2Þ

This equation expresses that lending rates (per annum) reflect a weighted average of money market rates (i) and return on bank equity (Δ4be). The weights depend on the capital adequacy ratio, which is also

79Q.F. Akram / Economic Modelling 42 (2014) 77–93

used to represent other possible costs of equity. α and ε2,t denote an intercept term and a stochastic error term, respectively.

However, access to quarterly data on return on bank equity is lim- ited in Norway, as only a few Norwegian banks are listed on the stock exchange. I therefore assume that excess return on bank equity (Δ4be − i) is proportional to excess return on the overall Oslo Stock Exchange (Δ4ose − i), consistent with the capital asset pricing model (CAPM). Accordingly, the long-run relationship for lending rates can be expressed as a function of the excess return on the overall Oslo Stock Exchange (Δ4ose − i):

i L t ¼ 1−CARtð Þit þ CARt it þ β Δ4oset−itð Þð Þ þ γCARt þ α þ ε3;t;

¼ it þ βCARt Δ4oset−itð Þ þ γCARt þ α þ ε3;t: ð3Þ

β can be interpreted as a measure of risk associated with bank equity and determines required return on bank equity in excess of the risk free rate together with excess return on the market portfolio. Argu- ably, the value of β declines with banks' capital ratio: the safer banks become, the less will equity holders demand in terms of required return on bank equity. The Modigliani–Miller theorem im- plies that required return on equity is invariant to firms' funding structure, i.e. the share of equity versus debt. Accordingly, an increase in the capital adequacy ratio will be fully outweighed by a decline in β leaving equity return unchanged. The evidence of such a negative relationship is inconclusive, in general. A few recent stud- ies suggesting a negative relationship include Hanson et al. (2011) and Miles et al. (2013).

For the sake of simplicity, however, I assume β to be invariant to changes in the capital adequacy ratio. I estimate the value of β to be 0.10 and that of γ to be 0.14 with asymptotic t-values equal to 3.93 and 11.10, respectively (see Table 1).4 The estimated value of β implies a pass-through of short-term money markets to lending rates equal to 0.90, which is comparable with estimates of short-term interest rate pass-through based on Norwegian micro data on banks' lending to households and firms (e.g. Raknerud and Vatne, 2011). Recursive estimates of β suggest that it has been stable over the sample period.

The empirical analysis suggests that credit to firms in real terms (crf–p) depends on real GDP (y) and real lending rates (iL − Δ4p) in the long run:

dcrf−p ¼ 2:16y−4:67 iL−Δ4p� �−12:67: ð4Þ Here, the income elasticity of real credit to firms is greater than one

and suggests that the ratio between real credit to firms and income (crf–p–y) increases with real GDP and falls with real interest rates. The long-run relationship may be interpreted as a combination of two sta- tionary terms. The relationship between the non-stationary variables real credit to firms and GDP is assumed to be stationary through cointegration, while real lending rates are assumed to be stationary by themselves. The long-run effect of real GDP on real credit to firms is close to the long-run effect of real GDP on aggregate real credit in Bårdsen et al., 2005, p. 212, 2, estimated on quarterly data over the period 1972 q4–2001 q1.

Credit to households in real terms (crh–p) has been found to depend on real GDP and real house prices (ph–p) in the long run (see Eq. (5)). I did not find evidence of a direct effect of real lending rates on credit to

4 Given that CAR, CAR(Δ4ose − i) and (iL − i) are assumed to be stationary variables, OLS estimators are no longer superconsistent. Hence, a possible neglect of short-run effects can lead to omitted variable bias if one employs OLS on Eq. (3). I therefore formulated an autoregressive distributive lag (ADL) model of iL using the variables entering Eq. (3) in ad- dition to three impulse dummies and derived the estimated model's static long-run solu- tion to obtain estimates of β and γ. Their asymptotic t-values are based on the algorithm by Bårdsen (1989) implemented in PcGive. The dynamic model of iL in Table 1 is a refor- mulation of the ADL model.

households in the long run, only an indirect effect through real house prices (see Eq. (6)).

dcrh−p ¼ 1:00y þ 1:00 ph−pð Þ þ 2:0: ð5Þ The long-run relationship for credit to households suggests that the

ratio between real credit to households and income (crh–p–y) depends on real house prices. Another interpretation of this relationship is that the (real) household-credit-to-value ratio (crh–ph) depends on real in- come. The long-run relationship is interpreted as a cointegrating rela- tionship between non-stationary real credit to households, GDP and house prices. The long-run effect of real house prices on real credit to households is equal to that in Jacobsen and Naug (2004) but somewhat different from that in Hammersland and Træe (2014) and Anundsen and Jansen (2013), where it is 0.9 and 0.76, respectively. The long-run relationships for credit to households in these studies are otherwise more elaborate than Eq. (5).

Finally, I find evidence of a long-run relationship between real house prices, real GDP and real lending rates:

dph−p ¼ 1:8y−3:8 iL−Δ4p� �−23:7: ð6Þ This long-run relationship may also be interpreted as a linear combi-

nation of two stationary terms: real house prices and real GDP through cointegration and real lending rates, which are assumed to be stationary (cf. Eq. (4)).5

2.3. Dynamic relationships

Table 1 presents a system of dynamic equations for the capital ade- quacy ratio, lending rate, house prices, credit to households and credit to (non-financial) firms. This system, formulated as a VECM, is based on the long-run relationships presented above. Initially, a rather general VECM was formulated by including several lagged difference terms and/ or levels of the variables included in the long-run relationships and other potentially relevant variables. I then simplified the general VECM by excluding most of the statistically insignificant variables from the model as well as those with counterintuitive signs and obtain- ed the VECM presented. Statistically insignificant variables that have been retained represent short-term effects of variables usually expected to be relevant. They have been retained to avoid a possible erroneous neglect of their effects. Diagnostic tests documenting the statistical adequacy of the general VECM and its final version presented in Table 1 are reported in Appendix B.

The (econometric) equation for the capital adequacy ratio suggests that it fluctuates around a fairly constant value over the sample period, which is estimated to be 12.5%. The capital adequacy ratio increases fol- lowing a decline in the actual capital adequacy ratio below its average value and decreases when it has been above the average value. One sim- plifying assumption is that a change in the long-run average value of the capital adequacy ratio would have the same effect on capital ratio ad- justment irrespective of whether it is due to a regulatory change or due to a change in banks' internal target affecting κ. Some evidence in the relevant literature suggests the speed of adjustment may be rela- tively lower in the former case (e.g. Ediz et al., 1998). Another simplify- ing assumption is that the speed of adjustment is symmetric around the average value and not dependent on the state of the economy. Arguably,

5 Previous econometric models of Norwegian real house prices include Jacobsen and Naug (2005) who find a long-run relationship between real house prices, real interest rates after tax, wage income, unemployment and housing stock on quarterly data for the period 1990 q2–2004 q1. Their estimates of the long-run effects of wage income and (af- ter-tax) real interest rates are 2.26 and −4.19, respectively. Anundsen and Jansen (2013) also include housing stock in the long-run relationship but find a long-run effect of house- holds' disposable income equal to 1.69. The sample period in the latter study is 1986 q2–2008 q4.

7 However, the observed relationship could be partly due to e.g. recessions contributing

Table 1 A VECM of the capital adeq. ratio, lending rate, house prices and credit.

ΔCARt ¼ − 0:19 −4:46ð Þ

CARt−1−κ½ � þ 0:01 4:07ð Þ

Δut−3− 0:04 −4:67ð Þ

Δyt−2

− 0:02 −2:16ð Þ

Δyt−3 þ 0:01 2:55ð Þ

Δ ose−pð Þt−3 þ 0:19 3:13ð Þ

ΔCARt−4

þ 0:02 6:13ð Þ

id93q4 þ 0:01 4:17ð Þ

id10q4 þ ε̂CAR;t; σ̂CAR ¼ 0:28%

ΔiLt ¼ − 0:36−12:10ð Þ i L−i−0:10CAR � Δ4ose−ið Þ

n o t−1

þ 0:42 18:30ð Þ

Δit

þ 0:05 9:94ð Þ

CARt−1 þ 0:02 14:60ð Þ

id98q3− 0:01 −3:84ð Þ

id03q3

− 0:01 −4:20ð Þ

id09q1 þ ε̂iL ;t; σ̂ iL ¼ 0:16%

Δ ph−pð Þt ¼ − 0:10−4:47ð Þ ph−pð Þ−1:8y þ 3:8 i L−Δ4p

� �n o t−1

− 1:20 −6:19ð Þ

ΔiLt

þ 0:06 3:26ð Þ

Δ ose−pð Þt þ 0:43 4:62ð Þ

Δ ph−pð Þt−1

þ 0:27 1:87ð Þ

Δ crh−pð Þt−2 þ 0:16 2:35ð Þ

Δ crf −pð Þt−2 þ 0:36 6:16ð Þ

q1− 2:37 −4:47ð Þ

þε̂ph;t; σ̂ph ¼ 2:3%

Δ crh−pð Þt ¼ − 0:01−2:69ð Þ crh−pð Þ− ph−pð Þ−yf gt−1 þ 0:072:15ð Þ Δ ph−pð Þt−1

− 0:25 −3:47ð Þ

Δ iL−Δ4p � �

t−2 − 0:31

−4:58ð Þ Δ iL−Δ4p � �

t−3

þ 0:52 6:97ð Þ

Δ crh−pð Þt−4 þ 0:06 10:20ð Þ

id94q2− 0:03 −4:18ð Þ

id95q2 þ 0:02 3:21ð Þ

þε̂crh;t; σ̂crh ¼ 0:88%

Δ crf −pð Þt ¼ − 0:08−4:84ð Þ crf−pð Þ−2:16y½ �t−1− 0:34−1:51ð Þ Δ i L−Δ4p

� � t−1

− 0:42 −4:46ð Þ

iL−Δ4p � �

t−4 þ 0:41

� 4:33Δ e þ pf −p

� � t þ 0:16

3:08ð Þ Δyt−2

þ 0:14 1:84ð Þ

Δ crf−pð Þt−4 þ 0:09 4:17ð Þ

id92q4 þ 0:11 6:35ð Þ

id00q3− 1:14 −4:70ð Þ

þε̂crf ;t; σ̂crf ¼ 1:77% Note: sample period: 1992 q4–2010 q4. Estimation method: FIML. Parentheses below the coefficient estimates include t-values. Estimates of sigma associated with each of the equa- tions are the standard errors of the corresponding residuals. See Appendix B for diagnostic tests.

80 Q.F. Akram / Economic Modelling 42 (2014) 77–93

it could be more demanding to raise equity in recessions than in expansions.

Business cycle fluctuations represented by lagged GDP growth rate (Δy) and unemployment rate (u) contribute to a higher capital adequa- cy ratio in downturns and a lower one in upturns.6 This is consistent with banks increasing their capital buffers to weather potential losses on e.g. loans to firms and households in (macroeconomic) downturns. Such a countercyclical response of the capital adequacy ratio may con- tribute, however, to reducing credit growth during economic recessions and increasing credit growth during expansions and thereby to an amplification of business cycles. Such procyclical implications of the re- lationship between the capital adequacy ratio and business cycle indica- tors are consistent with much previous evidence (e.g. Drumond, 2009). In this model, the procyclical implications are due to the positive rela- tionship between the capital adequacy ratio and lending rates (shown next) and the negative relationship between lending rates and economic activity. One of the main motivations for introducing a countercyclical capital buffer is to moderate the procyclicality of capital requirements

6 The presence of both (mainland) GDP and unemployment as indicators of economic activity in the CAR equation is consistent with the argument that mainland GDP may be an insufficient indicator of economic activity in Norway as petroleum production and in- ternational shipping are left out. Banks' capital adequacy ratios may however also be af- fected by changes in these sectors. The presence of unemployment together with output does not seem to be due to the omission of variables such as interest rates. For example, the null hypotheses that CAR does not respond to changes in lending interest rates (ΔiL) up to three lags have not been rejected at the standard levels of significance individually or jointly. In the latter case, the p-value was 0.65.

(BCBS, 2010a).7 The capital adequacy ratio reacts to changes in the real economy and stock returns with some lags. This may reflect that it takes time to adjust the capital adequacy ratio, especially increases through e.g. retained earnings and changes in banks' portfolios.

The equation for lending rates suggests that lending rates mainly follow money market rates in both the short run and the long run. Costs of capital requirements are found to affect lending rates in addition to money market interest rates.

The equation for house prices implies that they mainly follow vari- ables representing income, lending rates and credit to both households and firms. House prices and credit to households affect each other in the short run as well as in the long run. In the short run, they are also affect- ed by stock market returns (Δose), and changes in lending rates (ΔiL). Stock market returns as well as growth in credit to firms may reflect up- turns in business activity and hence higher demand for commercial property, which tends to be highly correlated with house prices. The effects of stock market returns could also reflect their wealth effects on house prices through higher demand for housing.

The equation for credit to households implies a short-run and long- run interaction between credit to households and house prices. House prices may have collateral effects on (real) credit to households. Credit also depends on income (represented by GDP) and changes in real lending rates (Δ(iL − Δ4p)). I did not find evidence of direct effects of changes in the capital adequacy ratio on credit to households. Hence, these effects seem to be transmitted through lending rates only.

To test explicitly for possible direct effects of changes in the capital adequacy ratio on credit to households, I included up to 4 lags of ΔCAR in the equation for credit to households jointly and individually and tested for their statistical significance. In all cases, I found statistically in- significant effects of changes in the capital adequacy ratio on credit to households using standard levels of significance. For example, in the test of the null hypothesis of no effects of the contemporaneous and lagged effects (up to 4) of ΔCAR in the credit to households equation, the Wald test gave a chi-square statistic (χ(5)) equal to 6.37 with a p-value of 0.27.8

As shown above, credit to (non-financial) firms reflects movements in GDP and real lending rates in the long run. In the short run, GDP growth and changes in the real lending rate and the real exchange rate (Δ(e + pf − p)) also affect credit growth to firms. The real lending rate has a relatively strong negative effect on credit to firms. As in the case of credit to households, changes in the capital adequacy ratio do not appear in the equation for credit to firms due to their statistically in- significant effects. For example, the null hypothesis of no contempora- neous and lagged effects (up to 4) of ΔCAR in the equation for credit to firms was not rejected at standard levels of significance. The outcome of the Wald test was a chi-square statistic equal to 5.65 with a p-value of 0.34.

There could be several explanations why a direct negative empirical relationship between capital adequacy ratio and credit to households and firms may not be observed even when such a relationship exists. First, higher capital requirements do not necessarily imply a reduction in lending as they can be met by retained earnings and shifts in banks'

to lower credit growth, which can reduce the volume of (risk-weighted) assets, and there- by lead to an increase in the equity ratio by lowering the denominator in the capital-to- risk-weighted-assets ratio (CAR). The latter explanation could be somewhat less relevant after the introduction of Basel II, as risk weights tend to increase during recessions, counteracting some of the effects of a reduction in assets owing to a fall in credit growth. Moreover, banks' equity also tends to decline in downturns due to reduced cash flows and higher loan defaults.

8 Another hypothesis of interest is that of a possible negative relationship between changes in the capital adequacy ratio and credit growth during downturns only. Accord- ingly, higher capital requirements can make banks lower their loan supply and thereby their assets to meet the regulatory capital ratio if it proves difficult to raise equity during downturns. There does not seem to be sufficient information in the data set used to firmly test this hypothesis, however.

Policy rate i

Lending rate iL

GDP Y

House prices PH

Exchange rate E

Unemployment U

Import price PM

Productivity Z

Equity prices OSE

Credit to households CRH

Credit to firms CRF

Wages (W) and

Prices (P)

Capital/RWA CAR

Fig. 1. Main linkages between the endogenous variables in the macroeconometric model. Two-way arrows between variables indicate direct interactions between them.

81Q.F. Akram / Economic Modelling 42 (2014) 77–93

portfolios toward less risky forms of exposures. Authorities usually provide banks sufficient time to enable them to meet regulatory re- quirements at least partly through retained earnings or portfolio shifts. Second, a possible reduction in credit supply in response to higher cap- ital requirements may also be difficult to identify at the aggregate level as a reduction in credit supply by some banks can be outweighed by their more well-capitalized competitors. And third, the data set used could also lack sufficient information for detecting a possible negative relationship between credit to households and firms and capital re- quirements. The sample period (1992 q4–2010 q4) mainly covers a gradual shift from Basel I to Basel II from 2007 onwards. Basel I was adopted by Norway in early 1991 during the Norwegian banking crisis (1989–1992). Extending the sample backward to include the shift to Basel I is unlikely to be helpful in this regard as Basel I is not believed to have had any noticeable effect on banks' capital ratios and lending as they were already fulfilling the formal capital requirements (Kredittilsynet, 1993).

2.4. The macroeconometric model: an overview

To investigate the macroeconomic effects of changes in capital re- quirements, I include the VECM presented above in a macroeconometric model.9 In addition to the five-equation VECM, the macroeconometric model contains systems as well as single-equation dynamic models for ten financial and real variables (see Appendix C). These variables are returns on the Oslo Stock Exchange, the nominal effective exchange rate, import prices, aggregate demand, unemployment, productivity, wages, domestic consumer prices, core consumer price inflation and the short-term money market rate. The key monetary policy rate is rep- resented by the short-term money market rate, which is therefore modeled in accordance with a Taylor-type interest rate rule. Specifically,

9 This model builds on a macroeconometric model for the Norwegian economy that has been developed and applied in e.g. Bårdsen et al. (2003), Bårdsen et al. (2005) and Akram and Eitrheim (2008). The main difference with the models used in these studies is that the model used here characterizes the capital adequacy ratio and takes into account its effects on banks' lending rates and thereby on the rest of the economy. In addition, the current model has been somewhat respecified and reestimated on recent and revised data.

the short-term interest rate adjusts in response to deviations from the (core) inflation target, a measure of the unemployment gap and lagged short-term interest rate.10 Norway adopted a flexible inflation targeting regime in March 2001, under which explicit weight is attached to out- put stabilization while targeting inflation. Foreign GDP, a world stock price index (MSCI-World), foreign consumer prices and interest rates, crude oil prices, domestic government expenditures and electricity prices are all treated as exogenous variables.

The macroeconometric model characterizes a linear stable (economic) system where the effects of nominal shocks eventually die out. This applies to monetary policy as well as macroprudential policy shocks. Moreover, even permanent changes in banks' capital require- ments tend to have persistent but not permanent effects in the model. This is consistent with evidence based on long time series e.g. from the UK, where no clear relationship has been found between banks' equity ratios and economic growth (Miles et al., 2013).

A linear stable model may be considered more appropriate for ana- lyzing policy decisions aimed at promoting monetary policy and finan- cial stability in the normal course of policymaking than in situations of crisis or near-crisis. Non-linear models are required to model the latter situations.

Fig. 1 presents an overview of the macroeconometric model, sketching the main linkages between different endogenous variables in the model.

The different system and single-equation models constituting the macroeconometric model are largely econometrically well specified. Specifically, for most of the equations the null hypotheses of no autocor- relation, normally distributed residuals and no heteroscedasticity are not rejected at the standard levels of significance (see Appendix C for details).

The estimated parameters in most of the equations have been found to be stable in response to various policy and structural changes over the sample period (see Appendix D). Notably, only some parameter estimates in equations that have been directly affected by changes in policy have been found to vary over time. Other model equations appear

10 The use of the unemployment gap is motivated by relatively large uncertainty in real time measures of GDP gaps (cf. Orphanides and Norden, 2002).

0.2

0.4

0.6

0.8

1.0

1.2

01 02 03 04 05 06 07 08

Common equity ratio

0.0

0.2

0.4

0.6

0.8

1.0

1.2

01 02 03 04 05 06 07 08

Capital Adequacy Ratio

.00

.04

.08

.12

.16

01 02 03 04 05 06 07 08

Lending rate

-.4

-.3

-.2

-.1

.0

.1

.2

01 02 03 04 05 06 07 08

House prices; ann. growth

-.8

-.6

-.4

-.2

.0

01 02 03 04 05 06 07 08

Credit to households

-1.2

-0.8

-0.4

0.0

0.4

01 02 03 04 05 06 07 08

Credit to firms

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

01 02 03 04 05 06 07 08

Credit, Aggregate

-.20

-.15

-.10

-.05

.00

.05

01 02 03 04 05 06 07 08

Mainland GDP

-.004

.000

.004

.008

.012

01 02 03 04 05 06 07 08

Unemployment rate

-.025

-.020

-.015

-.010

-.005

.000

.005

01 02 03 04 05 06 07 08

Wage inflation (annum)

-.020

-.015

-.010

-.005

.000

.005

01 02 03 04 05 06 07 08

CPI inflation (annum)

-.05

-.04

-.03

-.02

-.01

.00

.01

01 02 03 04 05 06 07 08

Policy rate

-.03

-.02

-.01

.00

.01

01 02 03 04 05 06 07 08

Nominal depreciation (annum)

-.01

.00

.01

.02

.03

.04

.05

01 02 03 04 05 06 07 08

Real exchange rate

-.020

-.016

-.012

-.008

-.004

.000

.004

.008

01 02 03 04 05 06 07 08

Import prices; ann. growth

-.03

-.02

-.01

.00

.01

.02

.03

01 02 03 04 05 06 07 08

Equity prices; ann. growth

Deviation

Fig. 2. Responses (+/− SE) to a one percentage point permanent increase in the common equity ratio when monetary policy follows a Taylor-type rule. The implementation period is four quarters and the simulation period is of 32 quarters. The vertical axes denote values in percentage points for the common equity ratio, capital adequacy ratio, lending rate, key policy rate and unemployment rate. For the other variables, the vertical axes denote values in percent.

82 Q.F. Akram / Economic Modelling 42 (2014) 77–93

to be quite robust to these changes. Such a lack of evidence of significant parameter instability in the face of shifts in policy is in line with most empirical investigations on the importance of the Lucas critique (Ericsson and Iron, 1995; Leeper and Zha, 2003; Rudebusch, 2005).11

In particular, I have not found significant effects on the model's pa- rameters of changes in the regulatory regime in Norway. The regulatory changes could be associated with the move from Basel I to Basel II in 2007 and with the expectations of the gradual implementation of Basel III over the period 2013–2019. For example, Fig. 4 in Appendix D shows the relative stability of the estimates of key parameters in the equations for the capital adequacy ratio.

Although the parameter estimates of the model have been found to be invariant to actual and expected changes in the regulatory regime in- sample, changes in the parameters cannot be ruled out when Basel III is implemented. Therefore, more uncertainty may be associated with the effects of the policy analyses than indicated by the standard confidence intervals.

11 To what extent parameters of a reduced form econometric model vary with changes in policy mainly depends on three factors: (a) the importance of forward-looking expecta- tions, (b) the size of the policy shift, and (c) the responsiveness of the economy to the pol- icy shift (e.g. Rudebusch, 2005). In particular, up to a moderate degree of forward-looking expectations combined with relatively weak response of the economy to policy shifts may lead to negligible changes in reduced form parameters.

3. Macro effects of higher capital requirements

Regulatory proposals following the recent financial crisis have main- ly focused on the common equity to risk-weighted assets ratio. I con- duct response analyses by varying the minimum common equity ratio, which contributes to the steady state level of total capital, κ. A variation in any of the other components in the total capital held by banks would have identical effects in the model used, however, as constituents of κ enter the model symmetrically (see Table 1). This is a simplification as possible differences between the effects of various constituents of κ cannot be distinguished empirically here. While investigating the effects of a higher equity ratio, I assume that monetary policy will respond in line with the estimated Taylor-type rule (see Table 13 in Appendix C).

Fig. 2 plots responses of the modeled variables to a one percentage point permanent increase in the minimum common equity ratio imple- mented linearly over four quarters. The overall impression is that the in- crease in the common equity ratio affects the capital adequacy ratio and thereby the lending rate, which directly affects house prices, credit to households, credit to firms and aggregate demand. The initial negative responses of these variables are then amplified by their mutual interac- tions. There are no first-round effects on the other variables of the increase in the equity ratio, as they do not directly respond to lending rates. In particular, both the nominal exchange rate and equity returns

Table 2 Comparing the effects of higher equity with the MAG study.

1 pp over 8 qtrs After 18 qtrs After 32 qtrs

I. This study: Norwegian evidence Lending rate 14 {12, 16} 12 {10, 13} Credit −23 {−31, −16} −71 {−97, −45} GDP −7 {−11, −2} −10 {−20, −2}

II. MAG study: International evidence Lending rate 17 [5, 25] 15 [5, 26] Credit −140 [−360, −6] −190 [−360, −80] GDP −12 [−96, 39] −10 [−314, 3] GDP; std −12 [−96, 39] −10 [−314, 3] GDP; dsge −11 [−41, −1] −7 [−25, −2] GDP; rf −30 [−87, 18] −24 [−88, 2]

Note: the effects are measured in basis points. Panel I presents the means and the 68% con- fidence intervals (in curly brackets) of the effects of a 1 percentage point increase in the equity ratio on selected Norwegian variables 18 and 32 quarters after the start of implementing the equity increase. Panel II presents median estimates from the MAG study and the ranges of estimated effects across models defined by minimum and maxi- mum effects in hard brackets. The results reported come from Graph 1 and Tables 1 and 2 in BCBS (2010b). std denotes the standard approach where implications for lending rates are derived using an accounting approach and the implications for GDP are obtained by implementing the change in the lending rate in the national models; dsge denotes an integrated approach where a group of DSGE models with banks are used. Finally, rf refers to an integrated approach where a group of reduced-form models is used.

83Q.F. Akram / Economic Modelling 42 (2014) 77–93

do not respond directly to the lending rate but to the short-term money market rate, which responds to changes in the inflation and unemploy- ment gaps. The second-round effects on the other variables may also be considered negligible because of relatively small direct effects on aggre- gate output and thereby on unemployment, productivity, wages, con- sumer prices and the nominal exchange rate. All of the variables respond as expected to the increase in the lending rate following a higher equity ratio.

In detail, the increase in the common equity ratio is for the most part transmitted (84%) to the capital adequacy ratio within a year after its full increase. The lending rate rises by at most 14 basis points, within 4.5 years since the start of the increase in the common equity ratio. House price growth per annum falls by about 25 basis points while cred- it to households and firms declines, by around 25 and 35 basis points, respectively, within 4.5 years. As a result, aggregate credit falls by around 28 basis points over the same time span. The effects on aggre- gate credit after eight years and beyond are at most −65 basis points. GDP falls at most by 9 basis points over the simulation horizon and by only 7 basis points after eight years. The unemployment rate increases by only a negligible amount. By simulating the model for a sufficiently long period, it can be shown that the real economic effects are reversed in the very long run.

The effects on the other macro variables are for the most part quite small. Notably, inflation and wage growth fall at most by 1 basis point, while the short-term money market rate, which represents the key pol- icy rate, falls by 2 basis points. The nominal exchange rate depreciates slightly due to the fall in the interest rate, but thereafter tends to appre- ciate because of the fall in the inflation rate. Equity returns increase somewhat due to the fall in the short-term interest rate.

The monetary policy rule serves to dampen the effects of higher cap- ital requirements in the model. If short-term interest rates had not fallen as prescribed by the estimated Taylor-type rule, the effects of changes in the common equity ratio on key macroeconomic variables such as real and nominal lending rates, credit to households, credit to firms and GDP would have been a few basis points greater (in absolute terms). The effects would also have been somewhat greater if capital require- ments had also been increased in Norway's trading partners, contribut- ing to a fall in foreign GDP and thereby in domestic GDP and other macroeconomic variables.

I have found the macroeconometric model and the main results to be generally invariant to changes in the sample period, which covers changes in the structure of the economy, the introduction of inflation targeting in 2001, the introduction of the Basel II framework in Norway in 2007 as well as the recent financial crisis and the accompany- ing changes in monetary policy and actual and/or expected changes in financial regulation (see Appendix D for details). In particular, re- sponses to higher capital requirements based on the macroeconometric model when estimated partly on data until the end of 2006 q4 are comparable to those based on the full sample estimation of the macroeconometric model (see Appendix D).

3.1. Comparison with international evidence

The regulatory response to the recent financial crisis has motivated a number of empirical studies on the possible effects of higher capital re- quirements on banks' funding costs, lending rates, credit and economic activity (e.g. Angelini et al., 2011; BCBS, 2010b; Elliott et al., 2012; Hanson et al., 2011; Miles et al., 2013; Slovik and Cournede, 2011). Their findings, however, are generally quite dependent on their approach and underlying assumptions. For the sake of brevity, I will only compare some of the results with those from the study by the Macroeconomic Assessment Group (MAG): BCBS (2010b). This study reports evidence based on 89 models for 15 advanced economies. The relatively large range of variation in estimated effects across these models, which is reported in Table 2, are likely to cover even estimated effects based on models not utilized by the MAG study.

To ease comparison with the MAG study, I implement a one percent- age point increase in capital requirements while letting the policy rate remain unresponsive to changes in inflation and economic activity. I also implement higher capital requirements gradually over eight quar- ters and study their effects after 18 and 32 quarters from the start of im- plementation; the 32nd quarter was the end point of the simulation period in the MAG study. As in the MAG study, I focus on the estimated response of lending rates, (aggregate) credit and GDP. Allowing for an implementation period of 16 quarters did not substantially affect the conclusion from the comparative analysis reported below. In some of the models employed in the MAG study, the length of the implementa- tion period seems to matter to a relatively larger extent.

Panel I of Table 2 presents estimated responses of the key variables, measured as deviations from the baseline paths in basis points together with their 68% confidence intervals (see Akram (2012) for more de- tails). Panel II of the table reports median estimates for the responses of key variables from the MAG study together with ranges of variation across models used. For GDP, I report median estimates and ranges based on all 89 models, and with models divided into three subgroups. The relatively wide ranges of estimated effects on the three key vari- ables reveal relatively large differences in the estimated effects across the models. I therefore compare the estimated effects of this study with the MAG's median effects on the three variables at selected periods.

The point estimates of this study are lower than the (MAG's) median estimates in Panel II at both the 18-quarters and 32-quarters horizons. The differences in the estimated effects are smaller in the long run than in the short run. That is, in the present study lending rates increase by 3 basis points less than the median estimates, irrespective of the ho- rizon. The effects on credit, however, are substantially smaller than the corresponding median estimates. For example, credit falls by 23 basis points 18 quarters after the start of implementation in the present model, while the median estimate is −140 basis points. After 32 quarters, credit falls by 71 basis points in this model, while the median estimate is −190 basis points. In the case of effects on GDP, it declines by 7 basis points at the horizon of 18 quarters, which is 5 basis points less than the median estimate at this horizon. At the horizon of 32 quarters, however, GDP declines by 10 basis points, which is equal to the median estimate of −10 basis points.

Note also that the responses of GDP estimated by this study are clos- er to the (MAG's) median estimates based on the standard approach

84 Q.F. Akram / Economic Modelling 42 (2014) 77–93

and DSGE models and differ substantially from those based on many of the reduced form models used in the MAG study. The latter models sug- gest substantially greater effects on GDP. The group of reduced form models includes a relatively large number of VAR models. Results com- parable to those based on VAR models have also been reported using a VAR model with identified shocks on Norwegian data (Jacobsen et al., 2011).

Statistically, however, in all but one case, estimates of this study are not significantly different from the median estimates at the standard levels of significance. Even the 68% confidence intervals presented in curly brackets (nearly) include the corresponding median estimates from the MAG study. One exception is the case of the estimated effect on aggregate credit after 18 quarters where neither the reported 68% confidence interval nor a 95% confidence interval would include the median estimates in Panel II. Another such exception is the case of the median of estimated effects on GDP implied by the reduced form models used by the MAG study.

3.2. Macro effects of Basel III

The Basel III framework entails a permanent 2.5 percentage point in- crease in the minimum common equity ratio (conservation buffer) and a systemic risk-dependent variation in the common equity ratio in the

2.4

2.8

3.2

3.6

4.0

4.4

4.8

5.2

00 01 02 03 04 05 06 07 08 09

Common equity ratio

0

1

2

3

4

5

6

00 01 02 03 04 05 06 07 08 09

Capital Adequacy Ratio

-.8

-.4

.0

.4

00 01 02 03 04 05 06 07 08 09

Credit to households; ann. growth

-1.5

-1.0

-0.5

0.0

0.5

1.0

00 01 02 03 04 05 06 07 08 09

Credit to firms; ann. growth

-.04

-.02

.00

.02

.04

.06

00 01 02 03 04 05 06 07 08 09

Unemployment rate

-.10

-.05

.00

.05

00 01 02 03 04 05 06 07 08 09

Wage inflation (annum)

-.15

-.10

-.05

.00

.05

00 01 02 03 04 05 06 07 08 09

Nominal depreciation (annum)

-.2

-.1

.0

.1

.2

.3

00 01 02 03 04 05 06 07 08 09

Real exchange rate

Devia

Fig. 3. The effects of the countercyclical and conservation buffers under Basel III. Responses ( percentage points, when the conservation buffer has been raised immediately by 2.5 percenta simulation period is 36 quarters. The vertical axes denote values in percentage points for the com rate. For the other variables, the vertical axes denote values in percent.

range of 0–2.5 percentage points (countercyclical buffer). In the follow- ing, I investigate the effects of such general increases in the minimum common equity ratio. I assume an implementation period of eight quar- ters. Because the model is linear, the effects of a 2.5 percentage point higher equity ratio would be a multiple of those presented above for the case of a 1 percentage point increase in the equity ratio for the same implementation period.

Specifically, the introduction of the conservation buffer contributes to raising the nominal lending rate by about 35 basis points at most and to a fall in GDP by 24 basis points. House prices fall by 70 basis points, while credit to households and firms declines by 123 and 200 basis points at most, respectively, implying a fall in aggregate credit of 157 basis points. The effects of the higher equity requirement are mod- erated somewhat by a reduction in the key policy rate of up to 5 basis points in response to lower inflation and lower economic activity (higher unemployment gap).

Fig. 3 shows the effects in a scenario where the conservation buffer has been fully implemented and the countercyclical buffer is increased by its maximum value (2.5 percentage points) for two years. Thus, for two years the common equity ratio is 5 percentage points higher than it would have been in the absence of Basel III. I assume a symmetric im- plementation period for both the increase to the maximum value and the decrease to the minimum value (zero) for the countercyclical buffer.

.0

.2

.4

.6

.8

00 01 02 03 04 05 06 07 08 09

Lending rate

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

00 01 02 03 04 05 06 07 08 09

House prices; ann. growth

-1.0

-0.5

0.0

0.5

00 01 02 03 04 05 06 07 08 09

Credit Growth, Aggregate

-.8

-.6

-.4

-.2

.0

.2

00 01 02 03 04 05 06 07 08 09

Mainland GDP

-.08

-.06

-.04

-.02

.00

.02

.04

00 01 02 03 04 05 06 07 08 09

CPI inflation (annum)

-.20

-.15

-.10

-.05

.00

.05

00 01 02 03 04 05 06 07 08 09

Policy rate

-.08

-.04

.00

.04

.08

00 01 02 03 04 05 06 07 08 09

Import prices; ann. growth

-.3

-.2

-.1

.0

.1

.2

00 01 02 03 04 05 06 07 08 09

Equity prices; ann. growth

tion

+/−SE) to a gradual change over eight quarters of the common equity ratio of up to 2.5 ge points to a permanently higher level. Monetary policy follows a Taylor-type rule. The mon equity ratio, capital adequacy ratio, lending rate, key policy rate and unemployment

Table 3 Optimal δ and q in response to various shocks with different persistence.

v: ph crh crf ose y i

ϕ δ q δ q δ q δ q δ q δ q

0 2.5 2 2.5 4 0.5 1 0.5 1 2.5 2 2.5 5 0.1 2.5 2 2.5 4 0.5 1 1.0 1 2.5 3 2.5 5 0.2 2.5 2 2.5 5 0.5 1 1.0 1 2.5 3 2.5 5 0.3 2.5 2 2.5 5 0.5 1 1.0 1 2.5 3 2.5 5 0.4 2.5 2 2.5 5 1.5 1 1.5 1 2.5 3 2.5 5 0.5 2.5 3 2.5 6 2.0 1 2.0 1 2.5 4 2.5 6 0.6 2.5 3 2.5 6 2.0 1 2.5 1 2.5 5 2.5 6 0.7 2.5 4 2.5 7 2.5 1 2.5 1 2.5 6 2.5 7 0.8 2.5 6 2.5 9 2.5 3 2.5 2 2.5 7 2.5 9 0.9 2.5 8 2.5 12 2.5 5 2.5 3 2.5 10 2.5 9

Note: the top row indicates the shocked variables while the first column contains the

85Q.F. Akram / Economic Modelling 42 (2014) 77–93

It is seen that lending rates increase by around 67 basis points while GDP falls by 44 basis points, at most. House price inflation falls by 113 basis points, while credit to households and firms falls by 210 and 360 basis points, at most, respectively. Hence, aggregate credit falls at most by about 280 basis points. As above, the effects of the relatively high capital requirements are moderated by the reduction in the key policy rate, which falls by up to 10 basis points in response to lower inflation and economic activity.

The effects of the temporary increase in the countercyclical capital buffer diminish over time, and the effects on the macroeconomic vari- ables converge toward those in the case of the higher conservation buff- er. Ultimately, however, even the effects of the higher conservation buffer die out due to the equilibrium correction properties of the model's equations and the monetary policy rule.

4. Implementing the countercyclical capital buffer

In the following, I investigate how much and for how long equity re- quirements should be changed in response to different shocks of a tran- sitory or persistent nature. I assume that a forward-looking macro prudential policymaker facing a certain shock will minimize the follow- ing loss function by choosing a path for the countercyclical capital buffer:

Lt ¼ Var CRgrð Þ þ λVar Ygrð Þ: ð7Þ

The loss function depends on the variance of growth in aggregate credit and output, Var(CRgr) and Var(Ygr). It is a reformulation of a quadratic loss function assuming that the discount factor is close to one (e.g. Svensson, 2000; Walsh, 2003). Subscript t indicates that the fluctuations in credit and output growth will depend on the properties of the given shock at time t, in addition to the model and the policy re- sponse.12 λ indicates the degree of concern for fluctuations in output growth relative to that for fluctuations in credit growth.

The policymaker aims to reduce systemic risk by stabilizing aggregate credit around its presumably sustainable value, while avoiding to some extent possible excess volatility in output growth (cf. Haldane, 2012). The objective function has been formulated in terms of annual rates of aggregate credit growth and (mainland) GDP growth instead of the aggregate credit-to-GDP ratio gap, which is implied by e.g. BCBS (2010a). The choice of growth rates over levels is due to substantially smaller data revisions to GDP growth relative to revisions of the level of GDP, in particular (e.g. Edge and Meisenzahl, 2011; Orphanides and Norden, 2002). Changes in the cap- ital buffer stabilize aggregate credit growth and other macro variables by reducing the procyclicality of the capital adequacy ratio and thereby of lending rates. I assume that the key policy rate follows the Taylor- type rule presented in Table 13, while macroprudential policy is con- ducted as outlined below.

I assume that in response to a given shock, the policymaker chooses a path for the countercyclical capital buffer by deciding simultaneously on the change in the capital requirement within a given range of 0–2.5% and on its duration. For simplicity, it is also assumed that the capital requirement is changed only when the shock appears in period t and remains effective for q quarters. That is, the capital requirement relative to a given fixed level (κt + 1 − κ) is changed by δ a[0,2.5] for q quarters:

κtþi−κ ¼ δ ; i ¼ 0; 1; 2; …q−1; ð8Þ

12 Such an analysis is, of course, a considerable simplification of the actual conduct of pol- icy as the economy is continuously buffeted by combinations of shocks that vary in mag- nitude and degree of persistence. However, the procedure can be easily adapted to a more realistic case by providing multiple new shocks to the model economy while taking into account the effects of the previous shocks.

¼ 0 ; i ¼ q; q þ 1; q þ 2; :::: ð9Þ

A given shock (εv) may follow an AR(1) process with the degree of persistence denoted by ϕ:

εv;tþi ¼ ϕεv;tþi−1 þ ηv;t; ð10Þ

where ϕ ∈ [0, 0.9]. Precisely, εv denotes the residual in the econometric equation of a variable v while ηv,t is an impulse shock implying a percentage point change in v.

To derive optimal paths for the buffer in response to different shocks, I expose the model to a specific shock with persistence ϕ and then min- imize the loss function (7) with respect to δ and q. When deriving values of the loss function, the value of λ has been set equal to 0.4. The optimal values of δ and q have been obtained by undertaking a grid search within the ranges 0–2.5, with step size 0.50 percentage point, and 1–16 quarters, with step size 1 quarter, respectively. In every case, the model has been simulated over a sufficiently long period for convergence to the steady state; in many cases, a period of 32 quarters was found to be more than sufficient.

Table 3 presents optimal additions in capital requirements, δ, and their duration, q, in response to different shocks with persistence values of 0–0.9 degrees. The following variables have been shocked in turn to (temporarily) increase their value by one percentage point: house prices, credit to households, credit to firms, return on equity and aggre- gate demand. In contrast, short-term money market rates have been shocked to obtain a reduction of one percentage point.

Table 3 suggests that optimal changes in capital requirements and their duration tend to increase with the degree of persistence of the shocks. This is especially the case for the duration of higher capital requirements. The optimal change in capital requirements is 2.5 percent- age points for most shocks, irrespective of their degrees of persistence. The exceptions to this pattern are shocks to credit to firms and return on equity. In these cases, the capital requirement increases gradually to 2.5 percentage points with increases in the degree of persistence.

Given that the upper boundary (2.5 percentage points) for changes in capital requirements has been selected (through simulations) for most of the shocks, only the duration of higher capital requirements in- creases when the persistence of shocks increases. Shocks to firm credit and return on equity reveal that the optimal change in capital require- ments increases with the degree of persistence without an accompany- ing change in its duration as long as the change is lower than the upper boundary. When in response to a shock, changes in capital

degree of persistence (ϕ) in the corresponding shocks (see Eq. (10)). The shocked variables increase initially by one percentage point, except the short term money market rate, which declines. Values of δ (in percentage points) and q (in quarters) minimize the loss function (7) for a given shock with a specified degree of persistence. The weight on the variance of the GDP growth gap in the loss function, i.e. λ, has been set equal to 0.4. The optimal values of δ and q have been obtained by simulating the macroeconometric model over 32 quarters.

Table 4 Alternative loss function: optimal δ and q when shocks of different persistence.

v: ph crh crf ose y i

ϕ δ q δ q δ q δ q δ q δ q

0 2.5 2 2.5 4 0.5 1 0.5 1 2.5 2 2.5 5 0.1 2.5 2 2.5 4 0.5 1 1.0 1 2.5 3 2.5 5 0.2 2.5 2 2.5 5 0.5 1 1.5 1 2.5 3 2.5 5 0.3 2.5 2 2.5 5 0.5 1 1.5 1 2.5 3 2.5 5 0.4 2.5 3 2.5 6 1.0 1 1.5 1 2.5 4 2.5 5 0.5 2.5 3 2.5 6 1.0 1 2.0 1 2.5 4 2.5 6 0.6 2.5 4 2.5 7 2.5 1 2.0 1 2.5 5 2.5 6 0.7 2.5 5 2.5 8 2.5 1 2.5 1 2.5 6 2.5 7 0.8 2.5 6 2.5 9 2.5 3 2.5 2 2.5 8 2.5 8 0.9 2.5 8 2.5 11 2.5 5 2.5 3 2.5 11 2.5 10

Note: optimal paths for countercyclical capital buffers under a loss function which is defined by the sum of the variances of the aggregate credit growth gap and the inflation gap. The top row indicates the shocked variables while the first column contains the degree of persistence (ϕ) in the corresponding shocks (see Eq. (10)). The shocked variables increase initially by one percentage point, except the short term money market rate which declines. Values of δ (in percentage points) and q (in quarters) minimize the loss function for a given shock with a specified degree of persistence.

86 Q.F. Akram / Economic Modelling 42 (2014) 77–93

requirements have reached the ceiling, duration increases with the de- gree of persistence.

There appears to be a non-linear relationship between the degree of persistence of shocks and the duration of higher capital requirements. The duration tends to increase gradually, if at all, with persistence in the range of 0–0.7, but rises with bigger steps to higher levels when the degree of persistence increases from 0.7. The duration is one to five quarters for various kinds of strictly transitory shocks (with ϕ =0), and still in the range of one to six quarters for degrees of persistence up to 0.5. In contrast, when the degree of persistence is 0.9, the duration varies in the relatively high range of eight to twelve quarters for shocks to house prices, credit to households, aggregate de- mand and short-term interest rates. The duration for shocks to return on equity and credit to firms increases to two and four quarters, respectively.

The next subsection indicates that the optimal paths of the counter- cyclical capital buffer in response to different shocks are quite robust to the parameter representing the policymaker's concern for output fluctuations, and even inflation volatility. This result owes mainly to the relatively strong correlation between the variances of credit growth, output growth and inflation under the set of shocks considered.

4.1. Optimal capital buffer paths and the loss function

Optimal choices of δ and q in response to different shocks and their properties presented in Table 3 are based on the assumption of λ = 0.4, where λ indicates the policymaker's concern for output stabilization while pursuing credit growth stabilization. To investigate how sensitive the optimal values of δ and q are to changes in the value of λ in the loss function, I have redone the analysis above with λ values equal to 0, 0.2, 0.6, 0.8 and 1. For λ = 0, minimizing the loss function amounts to min- imizing the variance of aggregate credit growth, while for λ = 1, mini- mizing the loss function equals the minimization of the sum of the variances of aggregate credit growth and GDP growth.

In brief, the variation of λ within the range of 0–1 does not gener- ally affect the optimal choices of δ and q in response to the different shocks considered.13 This is because of the relatively high correlation between the variance of aggregate credit growth and the variance of GDP growth in the cases of the shocks considered.14 Besides that, changes in capital requirements represented by δ and q have rela- tively small effects on the variance of GDP growth relative to the var- iance of aggregate credit growth (cf. Fig. 2). Therefore, changes in the variance of aggregate credit growth in response to different values of δ and q dominate the influence of changes in the variance of GDP growth on the loss function, even when the weight of the latter is 1.

In cases where an increase in the value of λ from 0 to 1 matters, δ and q change by only 0.5 percentage point and/or 1 quarter, respectively. Such exceptions to the general pattern are found in the cases of shocks to credit to firms, return on equity and GDP. In the latter case, λ = 1 entails a different δ-value than λb 1.15

If I instead assume that the decision maker is concerned about the variance of the inflation gap rather than that of the GDP growth gap while pursuing stabilization of the credit growth gap, the optimal values of the δ and q are also unaffected in most cases (see e.g. Table 4). In cases where they are affected, the values do not differ by more than one per- centage point and/or one quarter relative to the values presented in Table 3, where the loss function includes concern for fluctuations in

13 More details about the analysis in this section are presented in Akram (2012). 14 See also Olsen et al. (2003) for evidence on the strong relationship between output and credit in Norwegian data. 15 In the case of shocks to credit to firms, for degrees of persistence equal to 0.2 and 0.9, δ increases by 0.5 percentage point while duration increases by 1 quarter relative to values in Table 3. In the case of shocks to return on equity, q remains invariant but δ increases by 0.5 percentage point, when λ is reduced. That is, δ = 0.5 for λ ≥ 0.4, while δ = 1 for λ ≤ 0.2.

GDP growth. As above, the changes in the optimal values of δ and q occur mostly for shocks to credit to firms and return on equity. For other shocks, optimal values of δ do not change while the optimal values of duration may differ by one quarter from those presented in Tables 3.16

The relatively minor differences between the outcomes presented in Tables 3 and 4 are mainly due to the relatively strong correlation be- tween the variances of the aggregate credit growth gap and inflation gap for the shocks considered.

5. Conclusions

I have investigated the effects of higher bank capital requirements on key Norwegian macroeconomic variables and their implications for macroprudential policy under Basel III. To this end, I have further developed and updated a quarterly macroeconometric model of the Norwegian (mainland) economy. To shed light on the countercyclical capital buffer as a macroprudential policy instrument, it is assumed that the policymaker stabilizes aggregate credit growth while taking into account possible destabilizing effects on output growth. The policymaker is also assumed to respond to a given shock by choosing a path for the countercyclical capital buffer characterized by the size and duration of the countercyclical capital buffer. The following results may be highlighted:

First, higher capital requirements affect credit growth, house prices and other macroeconomic variables through their effects on lending rates. I do not find statistically significant direct effects of changes in capital requirements on credit to households and firms.

Second, the effects on credit growth and house prices are found to be of considerable size, especially when capital requirements are in- creased by as much as 2.5 percentage points or more. The effects on the other variables such as GDP and inflation are relatively modest. The macroeconomic effects could have been somewhat larger than those presented if one had taken into account possible

16 The optimal values in Table 4 are based on the assumption that the decision maker minimizes the variance of the aggregate credit growth gap while placing equal weight on the variance of the inflation gap. It can be shown that it is the replacement of the var- iance of the GDP growth gap with the variance of the inflation gap rather than the change in λ from 0.4 to 1 that accounts for the differences between Tables 3 and 4. Results based on a loss function defined by the sum of the variances of the credit growth gap, inflation gap and output growth gap were close to those in Table 3 or Table 4 and occasionally somewhere in-between those presented in these tables.

87Q.F. Akram / Economic Modelling 42 (2014) 77–93

recessionary effects of a simultaneous imposition of capital require- ments in Norway's trading partners.

Third, the analysis of the countercyclical capital buffer in response to various shocks suggests that the buffer increases by 2.5 percentage points in response to most of the shocks considered, while its duration varies in the range of 1–12 quarters depending on the persistence of the shock.

And fourth, the size and duration of the countercyclical capital buffer in response to different shocks do not vary notably with the parameter representing the policymaker's concern for output stabilization while sta- bilizing aggregate credit growth. Accordingly, the countercyclical capital buffer that minimizes the variance of credit growth also minimizes a combination of the variances of credit growth and output growth. More- over, comparable results are obtained even when the variance of output growth in the loss function is replaced by the variance of the inflation gap. This outcome is primarily due to the relatively strong correlation be- tween credit growth, output growth and inflation in the model for the shocks considered, and the relatively stronger effects of changes in the capital buffer on credit growth compared to effects on output growth and inflation. It follows that stabilization of aggregate credit growth in re- sponse to selected shocks may not conflict with output stabilization or in- flation stabilization. It remains to be investigated, however, whether this outcome is supported by other models.

Finally, I would like to stress that the analyses presented in this paper are based on a number of heroic assumptions, particularly about the out-of-sample relevance of the model and results under a different regulatory framework. They should therefore be treated more cautious- ly than suggested by the confidence intervals and significance values presented in the paper.

Acknowledgment

The views expressed in this paper are those of the author and should not be interpreted as reflecting those of Norges Bank (Central Bank of Norway). I am grateful to two anonymous referees for their insightful comments and suggestions. I have also received useful comments from seminar participants at Norges Bank and University of Oslo, espe- cially Sigbjørn Atle Berg, Jin Cao, Bjørn Naug, Vegard Mokleiv Nygård, Ragnar Nymoen and Kasper Kragh-Sørensen.

Appendix A. Data

The primary source of most of the series is Statistics Norway. Unless another source is given, the time series have been extracted from the database HISTDATA maintained by Norges Bank. Variables as named in the database are noted in hard brackets [.] below. Where relevant, the base year is 1991 and the unit of measurement is millions of NOK. The mainland economy is defined as the total Norwegian economy ex- cluding oil and gas production and international shipping. In the text, except for interest rates, variable names in small letters are natural logs of the corresponding variables listed below. Impulse dummies are denoted as iyyqx, where e.g. i80q2 is 1 in 1980 q2 and 0 otherwise.

CG Public consumption in NOK million; [CO]. CRH Domestic credit to households. Stock in millions of NOK;

[KFC2H]. CRF Credit to non-financial firms, mainland Norway. Stock in mil-

lions of NOK; [KFC3EMN]. CR Aggregate credit: CRH + CRF. qj Seasonal dummy variable (centered) for the jth quarter. E Import-weighted nominal exchange rate relative to Norway's

44 main trading partners; [SI44]. CAR Capital adequacy ratio, i.e. capital to risk-weighted assets.

Capital consists of both Tier 1 and Tier 2 capital, where Tier 1 capital is composed of common equity and hybrid equity

while Tier 2 capital is additional capital; [Netto ansvarlig kapital]. Source: ORBOF database.

i The 3-month effective nominal money market rate. NIBOR (ask); [RN3M].

idyyqx Impulse dummy for year yy and quarter (q) x. For example variable id80q2 is 1 in 1980 q2 and 0 otherwise.

if The 3 month effective nominal money market rate, euro area. EURIBOR; [RN3M_EURO].

iL Nominal lending rate; average of floating interest rates for bank loans (total); [RNBL].

IT A step dummy that is 0 before 2001 q1 and 1 afterwards. MSCIW MSCI-World share index; Source: Datastream. OILP Brent Blend crude oil prices in USD per barrel; [POILUSD]. OSE Oslo Stock Exchange All Share Index; [OSEAX]. P Consumer price index; [PCPI]. PC Consumer price index adjusted for tax changes and excluding

energy products; [PCPIJAE]. PEL Electricity prices, subcomponent of CPI; [PCPIEL]. Pf Consumer price index for Norway's main trading partners (25

countries); [PCPI_F25]. PH House prices: in thousands of NOK per square meter; [PHN]. PM Deflator of total imports; [PB]. PX Producer price index for Norway's trading partners in foreign

currency, a proxy for deflator of export prices in foreign cur- rency; [PPIKONK].

PD1 Composite dummy for introduction and removal of direct price controls. 1 in 1971 q1, 1971 q2, 1976 q4, 1979 q1; −1 in 1975 q1, 1980 q1, 1981 q1, 1982 q1; and zero otherwise.

U Unemployment rate (registered); [URR]. W Wage income per hour, mainland Norway; [WILMN]. WD1 Composite dummy for wage freeze: 1 in 1979 q1, 1979 q2,

1988 q2 and 1988 q3. Y Real GDP for mainland Norway, measured in millions of NOK

at fixed market prices; [YMN]. Yf Gross domestic product index for Norway's 26 main trading

partners; [Y_F26]. Z Productivity: value added per man hour at factor costs for

mainland economy; [ZYF].

Appendix B. Diagnostic tests for the VECMs

Table 5 presents diagnostic tests for the unrestricted VECM and its final version in Table 1. Tests of their statistical properties suggest that they have been adequately specified. There is no violation of the standard assumptions regarding residuals of these equations, especially when I control for some outliers by using impulse dummies. In particu- lar, the null hypotheses of no autocorrelation and normally distributed errors are not rejected at the standard levels of significance. Statistically, however, the final VECM with 39 parameters is rejected as a valid simplification of the unrestricted VECM with 190 parameters; the chi-square test (chi2(151)) of overidentifying restriction was rejected at the 1% level of significance. The reason is that I have left out some var- iables from the individual equations that were statistically significant but had counterintuitive signs and hence were difficult to interpret.

It is quite difficult, if not infeasible, to derive a closed econometric model of some size with interpretable long-run and short-run proper- ties from a data congruent VAR model. It is common to build up such a model piecewise and develop partial systems by conditioning on some of the variables and developing separate single equations or systems of equations for the conditioning variables (see e.g. Bårdsen et al., 2005, ch. 2 and Juselius, 2006, ch. 19). This way one can also model different parts of the large model on available subsamples. Sample sizes available for modeling different variables may not be the same for all variables that one would like to model jointly. One may also wish to develop models of some of the variables on specific sample periods covering the period of a relevant policy regime rather than on all

Table 6 Testing weak exogeneity.

Parameters in: ecm_CARt − 1 ecm_it − 1 L ecm_pht − 1 ecm_crht − 1 ecm_cret − 1

Weak exog of: F(1, 67) χ2(1) χ2(1) F(1, 58) F(1, 68)

Δoset 0.58 [0.45] 0.19 [0.66] 0.15 [0.70] 0.16 [0.69] 0.15 [0.70] Δet 0.92 [0.34] 2.46 [0.12] 0.55 [0.46] 2.74 [0.10] 0.77 [0.38] Δpt 2.97 [0.09] 0.00 [0.96] 0.04 [0.84] 0.00 [0.98] 0.06 [0.81] Δyt 0.64 [0.43] 0.04 [0.83] 0.12 [0.73] 1.67 [0.20] 0.47 [0.50] Δut 0.92 [0.34] 4.81 [0.03]⁎ 0.20 [0.66] 1.73 [0.19] 2.08 [0.15]

Note: test whether the equilibrium correction terms in the different equations of the final VECM enter the equations of variables listed in the first column. Test statistics of F and chi-square tests with p-values are presented in square brackets. The asterisk denotes significance at the 5% level.

Table 7 Return on the Oslo Stock Exchange.

Δose−ið Þt ¼ 0:47 0:086ð Þ

Δmsciw−ið Þt þ 0:42 0:083ð Þ

Δmsciw−ið Þt−1 þ 0:43

0:057ð Þ Δoilpt− 2:74

0:905ð Þ Δit þ ε̂ose;t

σ̂ose ¼ 0:070 Summary statistics

AR 1–5 F(5, 63) = 0.993 [0.429] ARCH 1–4: F(4, 64) = 0.117 [0.976] Hetero F(8, 63) = 4.681 [0.000]⁎⁎

Normality ϰ2 = 2.323 [0.313] RESET23 F(2, 66) = 6.577 [0.003]⁎⁎

Sample period 1992 q4–2010 q3 Estimation method OLS

Note: see Table 5 for information about the tests.

Table 5 Diagnostics for the unrestricted and restricted VECMs.

Single equation diagnostics ΔCARt Δit L Δ(ph − p)t Δ(crh − p)t Δ(crf − p)t I. Diagnostic tests for the unrestricted VECM AR 1–5: F(5, 32) 1.49 [0.22] 0.21 [0.95] 1.01 [0.43] 0.54 [0.75] 0.60 [0.70] ARCH 1–4: F(4, 65) 0.92 [0.46] 0.54 [0.71] 0.25 [0.91] 1.19 [0.33] 2.52 [0.05] Normality: χ2(10) 2.12 [0.35] 2.26 [0.32] 2.60 [0.27] 0.74 [0.69] 1.22 [0.54] Hetero: F(50,13) 0.66 [0.85] 1.03 [0.51] 0.68 [0.84] 0.80 [0.73] 0.41 [0.99] System diagnostics:

Vector AR 1–5: F(125, 34) 0.86 [0.73] Vector Normality: χ2(2) 7.31 [0.70] Vector RESET23: F(50, 99) 1.28 [0.15]

II. Diagnostic tests for the final VECM in Table 1 AR 1–5: F(5, 62) 0.70 [0.63] 1.00 [0.43] 10.21 [.00]⁎⁎ 2.37 [0.05] 1.43 [0.23] ARCH 1–4: F(4, 65) 0.84 [0.50] 1.69 [0.16] 1.99 [0.11] 0.48 [0.75] 0.52 [0.72] Normality: χ2(2) 0.15 [0.94] 4.44 [0.11] 4.88 [0.09] 2.92 [0.23] 0.58 [0.75] Hetero: F(6, 66) 0.93 [0.53] 2.41 [0.04]⁎ 0.88 [0.63] 1.039 [0.42] 0.67 [0.78] System diagnostics:

Vector AR 1–5: F(125,187) 0.90 [0.73] Vector Normality: χ2(10) 7.60 [0.67]

Note: AR 1–5 denotes an LM test of the null hypothesis of no autocorrelation up to order 5 in the errors (Harvey, 1990). ARCH 1–4 is an LM test for the null hypothesis of unconditional homoscedasticity of errors against the alternative hypothesis of autoregressive conditional heteroscedasticity up to order 4 of errors (Engle, 1982). Hetero tests the null of unconditional homoscedasticity of errors against the alternative hypothesis of heteroscedasticity, as proposed by White (1980). Normality tests the null hypothesis of normally distributed errors as sug- gested by Doornik and Hansen (1994). RESET23, a general regression specification test based on Ramsey (1969), tests the null of correct specification of the specified model by testing the significance of the second and third power of the fitted value of the left-hand-side variable. Vector AR 1–5, is a vector error autocorrelation test of the null hypothesis of no autocorrelation up to order 5 of errors. Vector Normality and Vector RESET23 tests are the multivariate equivalent tests of the single equation normality test and regression specification test, respectively. p- values are presented in square brackets. An asterisk (⁎) indicates rejection of the null hypothesis at the 5% level, while two asterisks denote rejection at the 1% level. The estimation and tests of the VECMs and of the other models presented have been undertaken using the PcGive module of OxMetrics 6.20 (see www.doornik.com).

88 Q.F. Akram / Economic Modelling 42 (2014) 77–93

available data. However, the conditioning variables need to be weakly exogenous with respect to parameters of interest in the partial models for efficient estimation (Johansen, 1992).

Weak exogeneity of the conditioning variables for the parameters of the VECM would imply that these parameters can vary freely with respect to the parameters of the models for conditioning variables. Table 6 shows the results of testing weak exogeneity of equity prices (ose), nominal effective exchange rate (e), consumer prices (p), mainland GDP (y) and unemployment rate (u) with respect to the parameters defining the long-run relationships for capital adequacy ratio, lending interest rates, house prices, credit to households and credit to firms. One simultaneously tests for the weak exogeneity of the conditioning variables with respect to the coefficients determin- ing adjustment to deviations from the long-run relationships. Weak exogeneity of the conditioning variables with respect to the param- eters defining the long-run relationships and adjustment coefficients requires that the equilibrium-correction terms in the VECM do not enter the models of the conditioning variables (Johansen, 1992).

The corresponding null hypotheses of weak exogeneity are not rejected at the 5% level of significance in all but one case. The weak exogeneity of unemployment with respect to the parameters in the long-run relationship for lending rates is rejected at the 5% level; the p-value is 3%. The rejection of the weak exogeneity assumption is interpreted as suggesting loss of efficiency in modeling lending rates separately from the unemployment rate.

Appendix C. The macroeconometric model

In addition to the VECM for the capital adequacy ratio, lending rates, house prices, credit to households and credit to firms, the macroecono- metric model contains single equations and systems of econometric equations for a number of other variables. These are nominal equity returns, wages, consumer prices, labor productivity, nominal effective exchange rate, aggregate import prices, aggregate demand and unem- ployment rate. I also specify an econometric equation for core inflation

Table 8 A system of the nominal effective exchange rate and import prices.

Δet ¼ − 0:29 0:066ð Þ

� e− p−pf � ��

t−1 þ 0:51 0:207ð Þ

Δ4pt−1− 0:33 0:138ð Þ

i−if � �

t

− 2:17 0:714ð Þ

Δ i−if � �

t � IT− 0:009 0:002ð Þ

oilpt � IT þ 0:09

0:016ð Þ id08q4t þ 1:32þ

0:298ð Þ ε̂e;t

σ̂e ¼ 0:0150

Δpmt− 0:06 0:033ð Þ

pm− e þ pxð Þ � �

t−1 þ 0:56 0:135ð Þ

Δpxt þ 0:48 0:136ð Þ

Δpxt−1

þ 0:43 0:076ð Þ

Δet þ 0:30 0:074ð Þ

Δ w−pð Þ−z � �

t−1 þ 0:46 0:0817ð Þ

Δyt−1

− 0:03 0:006ð Þ

q1− 0:27 0:152ð Þ

þε̂pm;t σ̂pm ¼ 0:0111

Summary statistics

Vector AR 1–5 F(20, 98) = 0.74 [0.783] Vector Normality test Chi2(4) = 4.08 [0.395] Vector Hetero test F(63, 129) = 1.23 [0.166] Sample period 1994q2–2010q4 Estimation method FIML

Note: see Table 5 for information about the tests.

Table 9 A system of wages, consumer prices and labor productivity.

Δwt ¼ − 0:13 0:028ð Þ

− 0:59 0:054ð Þ

Δwt−1− 0:36 0:068ð Þ

Δwt−2− 0:15 0:064ð Þ

Δwt−3

− 0:13 0:038ð Þ

Δwt−4 þ 0:58 0:19ð Þ

Δpt−1 þ 0:46 0:115ð Þ

Δzt− 0:21 0:035ð Þ

w−p−z½ �t−1 − 0:026

0:005ð Þ ut−1 þ 0:066

0:011ð Þ q2 þ 0:13

0:020ð Þ q3 þ 0:044

0:016ð Þ WD1t

− 0:018 0:003ð Þ

WD2t

σ̂w ¼ 0:019

Δpt ¼ − 0:19 0:013ð Þ

Δ3pt−2 þ 0:098 0:013ð Þ

Δyt−1 þ 0:15 0:011ð Þ

Δ2 w−zð Þt− 0:07 0:015ð Þ

Δzt−3

þ 0:028 0:012ð Þ

Δpmt− 0:029 0:010ð Þ

p−0:78 w−zð Þ−0:22pm−0:72½ �t−1 þ 0:051

0:004ð Þ Δpelt− 0:020

0:002ð Þ q3 þ 0:012

0:004ð Þ id80q1− 0:017

0:004ð Þ PD1t

σ̂p ¼ 0:0046

Δzt ¼ 0:39 0:047ð Þ

Δzt−4 þ 0:26 0:035ð Þ

Δyt−4 þ 0:34 0:020ð Þ

Δ w−pð Þt − 0:22

0:048ð Þ z− 0:49 w−pð Þ þ 0:04u þ 0:0021t þ 3:171 � � �

t−1

þ 0:013 0:003ð Þ

q1 þ 0:02 0:004ð Þ

q3− 0:041 0:010ð Þ

id06q1

σ̂z ¼ 0:010

Summary statistics

Vector AR 1–5 F(45, 297) = 1.619 [0.011] Vector Normality test: Chi2(6) = 9.954 [0.127] Vector Hetero test: F(372, 361) = 1.657 [0.000]⁎⁎

Sample period: 1979 q2–2010 q4 Estimation method: FIML

Note: a system of three equations estimated by FIML using time series data over the period 1992q4–2010q4. See Table 5 for information about the tests.

Table 10 Core CPI inflation.

Δ4pct ¼ 0:9 0:176ð Þ

Δ4pt− 0:028 0:012ð Þ

Δpelt− 0:031 0:012ð Þ

Δpelt−1− 0:035 0:010ð Þ

Δpelt−2

− 0:038 0:012ð Þ

Δpelt−3− 0:019 0:012ð Þ

Δoilpt− 0:025 0:009ð Þ

Δoilpt−1

− 0:035 0:01ð Þ

Δoilpt−2− 0:033 0:011ð Þ

Δoilpt−3 þ 0:0043 0:003ð Þ

þε̂pc;t σ̂pc ¼ 0:0046

Summary statistics

AR 1–5 F(5, 12) = 4.562 [0.015]⁎

ARCH 1–4: F(5, 19) = 0.327 [0.856]

89Q.F. Akram / Economic Modelling 42 (2014) 77–93

defined as consumer price inflation adjusted for energy prices, i.e. electricity and oil prices. Finally, the model includes an estimated Taylor-type interest rate equation representing monetary policy re- sponse. The various equations are briefly described in the following and presented in Tables 7–13.

Nominal equity returns based on the all share index of the Oslo Stock Exchange are modeled in the light of the capital asset pricing model (CAPM) by treating the Norwegian stock market portfolio as a single asset and the international stock market portfolio as the market portfo- lio. The model in Table 7 suggests that excess returns on the Norwegian stock market portfolio (Δose − i) move closely in line with excess returns on the international market portfolio. There is a strong negative relationship between changes in short-term interest rates and excess returns on the domestic stock market. In addition, an increase in oil prices has a positive effect on equity prices, and thereby on e.g. aggre- gate demand, credit growth and 'house prices (see Tables 1 and 11).

I model the nominal effective exchange rate (e) and aggregate import prices (pm) as a simultaneous equation system in order to take into account possible contemporaneous interdependence between them (see Table 8). The nominal effective exchange rate reflects the difference between domestic and foreign prices, a possible difference be- tween domestic and foreign interest rates and oil prices in the long run; a lower value of the exchange rate indicates appreciation. Accordingly, do- mestic prices become fully reflected in the nominal exchange rate in the long run. The nominal exchange rate reacts to correct deviations from the purchasing power parity relationship and thereby contributes to sta- bilizing the real exchange rate. In the short run, the nominal exchange rate appreciates when the interest rate and/or the interest rate differen- tial increases, ceteris paribus. Also, higher oil prices tend to appreciate the nominal exchange rate in the short run as well as in the long run. This is as expected given the relatively large volume of Norwegian petro- leum exports, which constitute more than half of Norwegian exports.

However, there is mixed evidence on a possible relationship be- tween oil prices and the Norwegian exchange rate when we use data from the stable exchange rate regime preceding the inflation targeting regime from 2001 q1 onwards (e.g. Akram, 2004; Hammersland and Træe, 2014). I have therefore let the log of oil prices enter the model from 2001q1 and onwards to better represent their effect on the nomi- nal exchange rate under the current regime.17

17 Log of oil prices (oilp) obtained a t-value of −2.41 when included in the exchange rate equation over the whole sample period, but a t-value of −4.26 when included from 2001 q1 onwards. In the former case, oil prices, which are integrated of order one, are not sta- tistically significant at the 5% level if one uses appropriate critical values from e.g. MacKinnon (1991).

There is a complete pass-through of the nominal exchange rate and foreign export prices (px) to aggregate import prices in the long run (see Table 8). The complete long-run exchange rate pass-through is consis- tent with Bache (2002) for import prices in Norwegian manufacturing. However, she finds a long-run elasticity of import prices with respect to foreign export prices equal to 1.35 and a negative long-run effect of the unemployment rate on import prices in line with Naug and Nymoen (1996). In contrast with these studies, cost-push variables such as higher growth in real wages relative to growth in labor produc- tivity (Δ(w − p − z)) and domestic economic activity (Δy) contribute to higher import prices in the short-run only. Such effects could be reflecting a procyclical mark-up on import costs, possibly owing to pricing-to-market behavior by exporters.

Wages (w), consumer prices (p) and labor productivity (z) are also modeled as a simultaneous equation system (see Table 9). Their short- and long-run relationships are comparable to those in e.g. Bårdsen et al. (2003). The wage equation suggests a partial pass-through of con- sumer price inflation to nominal wage growth in the short run. In each period, nominal wages also adjust toward their long-run relationship where there is a full pass-through of consumer prices and productivity.

Hetero test F(18, 8) = 0.744 [0.715] Normality ϰ2(2) = 0.603 [0.740] RESET23 F(2, 15) = 0.616 [0.553] Sample period 2001 q2–2007 q4 Estimation method OLS

Note: a technical equation for determining core inflation. See Table 5 for information about the tests.

Table 13 Interest rate rule for short-term money market rates.

it ¼ 1−0:69ð Þ 0:06 0:005ð Þ

þ 2:15 ð0:266Þ

Δ4pc−0:025ð Þt− 0:04 0:012ð Þ

log Ut 3:5

� ! þ 0:69

0:059ð Þ it−1 þ ε̂i;t

σ̂i ¼ 0:0029

Summary statistics

AR 1–3 F(3, 20) = 4.117 [0.020]⁎

ARCH 1–3: F(3, 21) = 0.484 [0.697] Hetero F(6, 20) = 1.182 [0.355] Normality ϰ2(2) = 2.999 [0.223] Sample period 2001 q2–2007 q4 Estimation method NLS

Note: see Table 5 for information about the tests.

Table 11 A single equation model of Norwegian (mainland) GDP.

Δyt ¼ − 0:52 0:088ð Þ

Δyt−1− 0:13 0:054ð Þ

y−yf � �

t−1 þ 0:18 0:062ð Þ

Δ e þ pf −p � �

t

− 0:04 0:096ð Þ

ðiL−Δ4pÞt−1 þ 0:58 0:058ð Þ

Δcgt þ 0:29 0:080ð Þ

Δcgt−1

þ 0:03 0:014ð Þ

Δ ose−pð Þt þ 0:041 0:013ð Þ

Δ ose−pð Þt−1 þ 0:13 0:049ð Þ

Δ ph−pð Þt−3 þ 0:29

0:102ð Þ Δ crh−pð Þt−3 þ 0:02

0:05ð Þ Δ crf−pð Þt−5

− 0:048 0:006ð Þ

q1− 0:052 0:007ð Þ

q2− 0:034 0:006ð Þ

q3 þ 1:03 0:45ð Þ

þε̂y;t σ̂y ¼ 0:0109

Summary statistics

AR 1–5 F(5, 56) = 2.464 [0.044] ARCH 1–4: F(4, 68) = 0.906 [0.466] Hetero F(25, 50) = 1.133 [0.345] Normality ϰ2(2) = 2.561 [0.278] RESET23 F(2, 59) = 1.405 [0.253] Sample period: 1991 q1–2009 q4 Estimation method: OLS

Note: see Table 5 for information about the tests.

90 Q.F. Akram / Economic Modelling 42 (2014) 77–93

However, the mark-up of real wages on productivity falls with the unemployment rate.

In the short run, consumer price inflation varies with changes in aggregate demand and to some extent nominal wage growth (see Table 9). In addition, it adjusts to correct deviations from the long-run relationship for consumer prices. In the long run, consumer prices re- flect a weighted average of domestic and imported costs, represented by unit labor costs and import prices.

The equation for labor productivity is rather rudimentary, as it is in- herently difficult to explain productivity growth. One interpretation of the equation derived is that the productivity level follows a determinis- tic trend as well as real wages in the long run, which also have positive short-run effects on productivity (cf. Bårdsen et al., 2003). A positive relationship between real wages and productivity is consistent with ef- ficiency wage models. The latter models can also explain positive effects of the unemployment rate. I also find that labor productivity tends to be procyclical in the short run as it tends to increase in booms and fall in recessions. This could be a reflection of labor hoarding in firms, which implies that output falls more than labor in downturns and increases more than employment in upturns.

The model of core inflation (Δpc) in Table 10 reflects its definition, which is CPI inflation adjusted for energy prices (i.e. electricity and oil prices) and indirect taxes.

Aggregate demand in the relatively open Norwegian economy fol- lows foreign GDP (yf), real exchange rate movements and real lending rates (see Table 11). Moreover, real equity returns and house prices, in particular, have effects on aggregate demand which may be interpreted as wealth effects. I also find effects on aggregate demand of credit to households and firms. There are also positive short-run effects on

Table 12 A single equation model of the registered unemployment rate.

Δut ¼ 0:31 0:064ð Þ

Δut−1 þ 0:42 0:070ð Þ

Δut−4− 0:039 0:015ð Þ

ut−1 þ 0:061 0:015ð Þ

� 0:64 0:232ð Þ

Δ2yt−1− 0:13 0:024ð Þ

Δ3 ose−pð Þt− 0:40 0:193ð Þ

Δcgt

þ 0:23 0:031ð Þ

q1 þ 0:14 0:024ð Þ

q3 þ ε̂u;t σ̂u ¼ 0:051

Summary statistics

AR 1–5 F(5, 95) = 1.028 [0.406] ARCH 1–4: F(4, 101) = 0.549 [0.700] Hetero F(14, 94) = 1.468 [0.139] Normality ϰ2(2) = 4.130 [0.127] RESET23 F(2, 98) = 3.384 [0.038]⁎

Sample period 1983 q4–2010 q4 Estimation method OLS

Note: see Table 5 for information about the tests.

aggregate demand of growth in government expenditures.18 The ag- gregate demand equation is largely comparable with that in Bårdsen et al. (2003). The main difference is in the role of government con- sumption, which here does not have a long-run effect on aggregate demand.

The (registered) unemployment rate follows output growth in the short run, as in the Okun's law relationship (see Table 12). In addition, it reverts slowly toward a constant rate (cf. Bårdsen et al., 2003). The unemployment rate also falls with higher real equity returns, which could be interpreted as an effect of current and/or expected higher earn- ings in financial and non-financial firms. An increase in government consumption also contributes to reducing the unemployment rate in the short run.

Finally, I let the short-term money market interest rate represent the key policy rate and model it as a Taylor-type interest rate rule with interest rate smoothing (see Table 13). The short-run rates respond to deviations between core inflation and the inflation target of 2.5%, and deviations from the natural unemployment rate, assumed to 3.5%. I use the unemployment gap instead of the output gap, which may be more prone to measurement errors than the unemployment rate. I in- clude one lag of the interest rate to take into account interest rate smoothing. When estimating the coefficient estimates, I also limited the sample period to the period of 2001 q2–2007 q4, as inflation targeting in Norway was formally introduced in March 2001 and to avoid influencing coefficient estimates with the turbulence in the money market rate during the recent financial crisis and the associated monetary policy actions.

Appendix D. Robustness to changes in the sample period?

I have tested the stability of each of the equations in the macro econometric model by estimating them recursively on increasingly larger data samples and examining estimates of their (main) parame- ters for changes. I have also conducted a number of break point tests (cf. Chow, 1960). In the latter tests, one looks for unusually large one- step or several-step ahead prediction errors after estimating the model each time. Such prediction errors can reflect shifts in parameter estimates.

Overall, I find parameter estimates in equations of variables that have not been directly affected by policy changes to be fairly stable over time. In particular, there is no evidence of changes in parameter estimates coinciding with the introduction of inflation targeting in 2001 and the introduction of the Basel II framework in 2007. Parameter

18 I have not found any significant direct effect of oil prices on aggregate demand (in the mainland economy). However, oil prices indirectly affect aggregate demand through their positive effects on equity prices and the nominal exchange rate. One reason for the ab- sence of direct oil price effects could be that the effects of oil prices are already taken into account by the government consumption variable. Norwegian oil revenues are invested abroad, while the return on the petroleum assets abroad is spent by the central govern- ment in accordance with a fiscal policy rule.

Δ CAR t −4 × +/-2SE

1997 2001 2005 2009

0.2

0.4 Δ CAR t −4 × +/-2SE ECM t −1 × +/-2SE

1997 2001 2005 2009

-0.2

-0.1

0.0 ECM t −1 × +/-2SE Δ ut −3 × +/-2SE

1997 2001 2005 2009

0.01

0.03 Δ ut −3 × +/-2SE

Δ y t −2 × +/-2SE

1997 2001 2005 2009

-0.075

-0.050

-0.025

0.000 Δ y

t −2 × +/-2SE Δ yt −3 × +/-2SE

1997 2001 2005 2009

0.00

0.05 Δ y

t −3 × +/-2SE Δ (ose −p )t −3 × +/-2SE

1997 2001 2005 2009

0.01

0.03 Δ (ose −p )t −3 × +/-2SE

Res 1Step +/−2 σ t

1997 2001 2005 2009

0.00

0.01 Res 1Step +/−2 σ t 1up CHOWs 5%

1997 2001 2005 2009

2

4 1up CHOWs 5% Nup CHOWs 5%

1997 2001 2005 2009

0.5

1.0 Nup CHOWs 5%

Fig. 4. Recursive OLS estimates (+/− 2SE) of main parameters in the equation for the capital adequacy ratio (see Table 1). The initial estimates are based on the sample period 1992 q4–1997 q1, which is extended by one observation at a time until the full sample 1992 q4–2010 q4 is used to obtain the final estimates. In the bottom panel: recursive one-step ahead prediction errors and recursive estimate of the standard errors of residuals, followed by plots of recursively obtained statistics of break point Chow tests scaled by their critical values at the 5% percent level. Values higher than one indicate rejection of the null hypothesis of parameter stability at the 5% level of significance.

91Q.F. Akram / Economic Modelling 42 (2014) 77–93

estimates in equations of variables that have been directly affected by regulations such as capital adequacy ratio also seem to be remarkably stable over time, even around the period of the regulatory changes.

For example, Fig. 4 shows recursive estimates for the main parame- ters in the equations for capital adequacy ratio (CAR). As shown in the

Constant × +/-2SE

2000 2005 2010

0

2

4 Constant × +/-2SE

(i −i f ) t × +/-2SE

2000 2005 2010

0.0

2.5 (i −i f )t × +/-2SE

o i l p t × I T × +/-2SE

2005 2010

-0.02

0.00

o i l p t × I T × +/-2SE

-0.

0.

0.

1up CHOWs 5%

2000 2005 2010

0.5

1.0

1.5 1up CHOWs 5%

Fig. 5. Panels 1–3 display recursive OLS estimates (+/− 2SE) of main parameters in the excha q2–1998 q1, which is extended by one observation at a time until the full sample 1994 q2–201 ahead prediction errors and recursive estimate of the standard errors of residuals. The bottom p critical values at the 5% percent level. Values higher than one indicate rejection of the null hypo fitted values of changes in the exchange rate over the sample period.

figure, the parameter estimates do not display significant changes over the sample periods; they are well within the 95% confidence bands over increasingly larger samples. The lack of evidence against the null hypothesis of parameter stability in the equation for capital ad- equacy ratio is notable given the introduction of Basel II in 2007 as well

(e −(pf −p )) t −1 × +/-2SE

2000 2005 2010

-0.5

0.0

(e −(pf −p )) t −1 × +/-2SE

Δ (i −i f ) t × I T × +/-2SE

2005 2010

0

10 Δ (i −i f )

t × I T × +/-2SE

1-step ahead residuals

2000 2005 2010

025

000

025 1-step ahead residuals

Δ e t

Fitted

1995 2000 2005 2010

0.0

0.1 Δ e

t Fitted

nge rate equation (see Table 8). The initial estimates are based on the sample period 1994 0 q4 is used to obtain the final estimates. The third panel also displays recursive one-step anel shows plots of recursively obtained statistics of break point Chow tests scaled by their thesis of parameter stability at the 5% level of significance. The final graph plots actual and

Δ i t × +/-2SE

1996 1998 2000 2002 2004 2006 2008 2010 0.3

0.4

0.5 Δ i

t × +/-2SE

C A R t −1 × +/-2SE

1996 1998 2000 2002 2004 2006 2008 2010

0.04

0.05

0.06

0.07

C A R t −1 × +/-2SE

E C M t −1 × +/-2SE

1996 1998 2000 2002 2004 2006 2008 2010

-0.4

-0.3

E C M t −1 × +/-2SE

R e s 1S t e p +/−2σ t

1996 1998 2000 2002 2004 2006 2008 2010

-0.005

0.000

0.005 R e s 1S t e p +/−2σ

t

1up CHOWs 5%

1996 1998 2000 2002 2004 2006 2008 2010

2

4 1up CHOWs 5% Nup CHOWs 5%

1996 1998 2000 2002 2004 2006 2008 2010

0.5

1.0 Nup CHOWs 5%

Fig. 6. Recursive OLS estimates (+/− 2SE) of main parameters in the lending rate equation (see Table 1). The initial estimates are based on the sample period 1992 q4–1997 q1, which is extended by one observation at a time until the full sample 1992 q4–2010 q4 is used to obtain the final estimates. The middle panel displays recursive one-step ahead prediction errors and recursive estimate of the standard errors of residuals. The bottom panel shows plots of recursively obtained statistics of break point Chow tests scaled by their critical values at the 5% percent level. Values higher than one indicate rejection of the null hypothesis of parameter stability at the 5% level of significance.

92 Q.F. Akram / Economic Modelling 42 (2014) 77–93

as the recent financial crisis. It is too early, however, to draw conclusions on the possible effects of the recent financial crisis on the parameter estimates of this equation. In our data set, there is just one relatively large increase in the capital adequacy ratio in 2010 q4 whose effect has been controlled for by including an impulse dummy in the equation for the capital adequacy ratio.

However, in equations of variables that have been directly affected by changes in policy, some parameter estimates display shifts in periods coinciding with the policy changes. This applies to equations for the nominal effective exchange rate, wages, consumer prices, the short- term interest rate and the lending rate. The parameter instabilities asso- ciated with policy changes have been reduced by using dummy variables for the relevant periods, or by discarding observations under previous policy regimes, to simplify the relevant equations.

In the nominal effective exchange rate equation, the effects of changes in the interest rate differential and oil prices become stronger after the formal move from exchange rate targeting to inflation targeting in 2001 q1. This has been taken into account by a multiplicative step dummy (IT), which changes its value from zero to 1 in 2001 q1. Fig. 5 presents ev- idence on the stability of the nominal exchange rate equation over the sample period, which includes the recent financial crisis.

While the parameter estimates in the equations for wages and prices do not display any shift coinciding with the change in the monetary pol- icy regime, the wages and prices seem to be affected by the introduction and the subsequent removal of several wage and price freezes during the 1970s and the 1980s. I have controlled for their effects by dummy variables. The behavior of the short-term interest rate also changes around the time of the shift in the monetary policy regime. The Taylor-type interest rate rule has therefore been estimated using obser- vations from 2001 q1 onwards.

I have also found small but statistically significant changes in the co- efficient estimate associated with the short-term interest rate in the equation for the lending rate. The shifts seem to occur quite abruptly in the autumn of 2008 (see Fig. 6). The break point tests in the lower panel of the figure also indicate possible changes in the parameter

estimate from autumn 2008 onwards. The change in the pass-through of the short-term rates to the lending rate may be associated with the possible effects of the recent financial crisis on the money market and on the accompanying changes in monetary policy and regulatory policy proposals. The Norwegian money market was affected by the Lehman default in mid-September 2008 and the defaults in late September and October 2008 of two Icelandic banks, Glitnir and Kaupthing, respective- ly, which had branches in Norway.

Finally, I have examined to what extent the impulse responses of financial and real economic variables presented in Fig. 2 are influenced by data observations from the period since early 2007. To this end, I have reestimated the VECM presented in Table 1 using data only up to 2006 q4 and implemented it in the macroeconometric model. Akram (2012) shows that the responses are comparable to those presented in Fig. 2, which is based on the full sample.

References

Akram, Q.F., 2004. Oil prices and exchange rates: Norwegian evidence. Economet J. 7, 476–504.

Akram, Q.F., 2012. Macro effects of higher capital requirements and macroprudential policy. Working Paper 21 Norges Bank.

Akram, Q.F., Eitrheim, Ø., 2008. Flexible inflation targeting and financial stability: is it enough to stabilize inflation and output? J. Bank. Financ. 32, 1242–1254.

Angelini, P., Clerc, L., Gambacorta, L., Gerali, A., Locarno, A., Motto, R., Roeger, W., Van den Heuvel, S., Vlcek, J., 2011. Basel III: long-term impact of economic performance and fluctuations. Working Paper 338 Bank for International Settlements.

Anundsen, K.A., Jansen, E.S., 2013. Self-reinforcing effects between housing prices and credit. J. Hous. Econ. 22, 192–212.

Bache, I.W., 2002. Empirical modelling of Norwegian import prices. Working Paper 2002/1 Norges Bank.

Bank of England, 2009. The role of macroprudential policy. Discussion Paper Bank of England (November).

Bårdsen, G., 1989. Estimation of long run coefficients in error correction models. Oxf. Bull. Econ. Stat. 51, 345–350.

Bårdsen, G., Jansen, E.S., Nymoen, R., 2003. Econometric inflation targeting. Economet J. 6, 429–460.

Bårdsen, G., Eitrheim, Ø., Jansen, E.S., Nymoen, R., 2005. The Econometrics of Macroeco- nomic Modelling. Oxford University Press, Oxford.

93Q.F. Akram / Economic Modelling 42 (2014) 77–93

BCBS, 2010a. Guidance for National Authorities Operating the Countercyclical Capital Buffer. Bank for International Settlements, Basel.

BCBS, 2010b. Interim Report: Assessing the Macroeconomic Impact of the Transition to Stronger Capital and Liquidity Requirements. Bank for International Settlements, Basel.

Bolton, P., Freixas, X., 2006. Corporate finance and monetary transmission mechanism. Rev. Financ. Stud. 19, 829–870.

Booth, L., Aivazian, V., Demirguc-Kunt, A., Maksmovic, V., 2001. Capital structure in developing countries. J. Financ. 56, 87–130.

Borio, C., Lowe, P., 2002. Asset prices, financial and monetary stability: exploring the nexus. Working Paper 114 Bank for International Settlements.

Brunnermeier, M., Crocket, A., Goodhart, C., Persaud, A.D., Shin, S., 2011. The fundamental principles of financial regulation. Geneva Report on the World Economy. 11. International Center for Monetary and Banking Studies, CEPR.

Chow, G.C., 1960. Tests of equality between sets of coefficients in two linear regressions. Econometrica 28, 591–605.

Doornik, J.A., Hansen, H., 1994. A practical test for univariate and multivariate normality. Discussion paper Nuffield College, University of Oxford.

Drumond, I., 2009. Bank capital requirements, business cycle fluctuations, and the Basel accords: a synthesis. J. Econ. Surv. 23, 798–830.

Edge, R.M., Meisenzahl, R.R., 2011. The unreliability of credit-to-GDP ratio gaps in real time: implications for countercyclical capital buffers. Int. J. Cent. Bank. 261–298 (December).

Ediz, T., Michael, I., Perraudin, W., 1998. The impact of capital requirements on U.K. bank behaviour. FRBNY. Econ. Policy Rev. 15–22 (October).

Elliott, D., Salloy, S., Santos, A.O., 2012. Assessing the cost of financial regulation. Working Paper WP/12/233 International Monetary Fund.

Engle, R.F., 1982. Autoregressive conditional heteroscedasticity, with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.

Engle, R.F., Hendry, D.F., Richard, J.F., 1983. Exogeneity. Econometrica 51, 277–304. Ericsson, N.R., Iron, J.S., 1995. The Lucas critique in practice: theory without measurement.

In: Hoover, K.D. (Ed.), Macroeconometrics: Developments, Tensions and Prospects. Kluwer Academic Publishers, Boston, Massachusetts, pp. 263–312.

Flannery, M., Rangan, K., 2006. Partial adjustment and target capital structures. J. Financ. Econ. 79, 469–506.

Galati, G., Moessner, R., 2013. Macroprudential policy — a literature review. J. Econ. Surv. 27, 846–878.

Haldane, A.G., 2012. We Are Not ‘Risk Nutters’ Stifling the Recovery. The Times, London, (11 July).

Hammersland, R., Træe, C.B., 2014. The financial accelerator and the real economy: a small macroeconometric model for Norway with financial frictions. Econ. Model. 36, 517–537.

Hanson, S.G., Kashyap, A.K., Stein, J.C., 2011. A macroprudential approach to financial regulation. J. Econ. Perspect. 25, 3–28.

Harvey, A.C., 1990. The Econometric Analysis of Time Series. The MIT Press, Cambridge, MA.

Hendry, D.F., 1995. Dynamic Econometrics. Oxford University Press, Oxford. Holmstrom, B., Tirole, J., 1997. Financial intermediation, loanable funds, and the real

sector. Q. J. Econ. 112, 663–691.

Jacobsen, D.H., Naug, B.E., 2004. What influences the growth of household debt? Econ. Bull. Q1, 103–111.

Jacobsen, D.H., Naug, B.E., 2005. What drives house prices? Econ. Bull. Q1, 29–41. Jacobsen, D.H., Kloster, T.B., Kvinlog, A.B., Larsen, U., 2011. Makroøkonomiske virkninger

av høyere kapitalkrav for bankene. Staff Memo, 14. Norges Bank. Jensen, M.C., 1986. Agency costs of free cash flow, corporate finance and takeovers. Am.

Econ. Rev. 77, 323–329. Johansen, S., 1992. Cointegration in partial systems and the efficiency of single-equation

analysis. J. Econ. 52, 389–402. Juselius, K., 2006. The Cointegrated VAR Model — Methodology and Applications. Oxford

University Press, Oxford. A.K.Kashyap, A.K., R.Rajan, R., J.C.Stein, J.C., 2008. Rethinking capital regulationFederal

Reserve Bank of Kansas City Symposium on Maintaining Stability in a Changing Financial System, pp. 431–471.

Kredittilsynet, 1993. Annual Report 1993 Kredittilsynet; Oslo. Leeper, E.M., Zha, T., 2003. Modest policy interventions. J. Monet. Econ. 50, 1673–1700. MacKinnon, J., 1991. Long-run economic relationships. In: Engle, R.F., Granger, C.W.J. (Eds.),

Critical Values for Cointegration Tests. Oxford University Press, Oxford, pp. 267–276. Miles, D., Yang, J., Marcheggiano, G., 2013. Optimal bank capital. Economet J. 123, 1–37. Naug, B.E., Nymoen, R., 1996. Pricing to market in a small open economy. Scand. J. Econ.

98, 329–350. Olsen, K., Qvigstad, J.F., Røisland, Ø., 2003. Monetary policy in real time: the role of simple

rules. In: BIS (Ed.), Monetary Policy in a Changing Environment. Bank for International Settlements, Basel, pp. 368–382.

Orphanides, A., Norden, S.V., 2002. The unreliability of output gap estimates in real time. Rev. Econ. Stat. 84, 569–583.

Peura, S., Keppo, J., 2006. Optimal bank capital with costly recapitalization. J. Bus. 79, 2163–2201.

Raknerud, A., Vatne, B.H., 2011. How do banks funding costs affect interest margins? Working Paper 2011/09 Norges Bank.

Ramsey, J.B., 1969. Tests for specification errors in classical linear least squares regression analysis. J. R. Stat. Soc. Ser. B 31, 350–371.

Reinhart, C.M., Rogoff, K., 2009. This Time Is Different: Eight Centuries Of Financial Folly. Princeton University Press, Princeton, NJ.

R.Repullo, R., J.Suarez, J., 2000. Entreprenurial moral hazard and bank monitoring: a model of the credit channelEur. Econ. Rev. 44, 1931–1950.

Rudebusch, G., 2005. Assesing the Lucas critique in monetary policy models. J. Money Credit Bank. 37, 245–272.

Schularick, M., Taylor, A.M., 2012. Credit booms gone bust: monetary policy, leverage cycles and financial crises, 1870–2008. Am. Econ. Rev. 102, 1029–1061.

Slovik, P., Cournede, B., 2011. Macroeconomic impact of Basel III. OECD Economics Department Working Paper 844 OECD.

Svensson, L.E.O., 2000. Open economy inflation targeting. J. Int. Econ. 50, 155–183. Tovar, C.E., 2008. DSGE models and central banks. Working Paper 258 Bank for Interna-

tional Settlements. Walsh, C., 2003. Speed limit policies: the output gap and optimal monetary policy. Am.

Econ. Rev. 93, 265–278. White, H., 1980. A heteroskedasticity-consistent covariance matrix estimator and a direct

test for heteroskedasticity. Econometrica 48, 817–838.

1-s2.0-S0304393214000725-main.pdf

• Testing macroprudential stress tests: The risk of regulatory risk weights
• Introduction
• Macroprudential stress tests
• Why do we need macroprudential stress tests?
• How capital requirements are measured in a stress test?
• US stress tests
• EU stress tests
• V-Lab stress test
• An alternative to stress tests: V-Lab
• V-Lab vs. regulatory stress tests design
• Scenarios
• Data
• Strengths and weaknesses of V-Lab and regulatory stress tests
• V-Lab vs. regulatory stress test risk measures
• Concerns about Basel I and Basel II risk-weighted assets
• V-Lab risk weight
• Assessing the outcomes of macroprudential stress tests
• Evaluating regulatory risk weights in stress tests
• Stress tests vs. V-Lab risk weight
• Forecasting risk during the European sovereign debt crisis
• Risk weights-based vs. leverage-based capital requirements
• Risk-based ratio, leverage ratio, and V-Lab ratio
• Stress tests capital shortfalls vs. SRISK: the European case
• Conclusion
• Acknowledgments
• Supplementary materials
• References