Optimal monetary policy with capital and a financial accelerator

https://doi.org/10.1016/j.jedc.2018.04.006Get rights and content

Abstract

Whether there is a trade-off between price and financial stability is an open question. This paper characterises optimal monetary policy analytically in a New Keynesian economy with capital and a financial accelerator. In addition to stabilising inflation, there is an incentive to smooth volatility in the net worth of borrowers and this presents a trade-off for monetary policy. This trade-off can be eliminated if policymakers can additionally choose an optimal transfer to borrowers. Enriching the model with fire sales and countercyclical bankruptcy costs, there is also an incentive to smooth volatility in default and the capital stock. An optimal transfer to borrowers is not sufficient to eliminate the trade-off in that case. With fewer instruments than targets, optimal transfers are state contingent and countercyclical, while monetary policy stabilises inflation.

Introduction

How should monetary policy be shaped in the presence of capital and financial frictions? Prior to the 2007–08 Crisis, the consensus was that monetary policy should provide a nominal anchor and stabilise domestic prices. By mitigating volatility in domestic inflation, price dispersion is reduced and inefficient production is minimised (Clarida, Gali, Gertler, 1999, Galí, Monacelli, 2005, Woodford, 2003). The gains in departing from an inflation target, for example responding to volatility in asset prices, were considered small or negative (Bernanke, Gertler, 2001, Faia, Monacelli, 2007, Gilchrist, Leahy, 2002, Nutahara, 2014, Nutahara, 2015).

Notwithstanding, the effects of the Crisis have been severe. In the eighteen months from December 2007, the labour market deteriorated sharply: total non-farm employment fell by almost 8 million and the unemployment rate almost doubled from 5% to 9.5%. The subsequent recovery in jobs growth has been slow. There is debate as to whether an alternative monetary policy would have improved outcomes. Had central banks chosen tighter monetary policy earlier, would this have reduced leverage prior to the Crisis and its severity?

More generally, whether an inflation target is sufficient for managing financial shocks in the presence of a financial accelerator remains contested (Cecchetti, Genberg, Lipsky, Wadhwani, Dupor, 2005, Gambacorta, Signoretti, 2014, Nisticó, 2016). It has been argued that inflation targeting itself could contribute to a higher likelihood of financial instability (Borio, Lowe, 2002, Borio, White, 2004) and that it may be sub-optimal for a central bank to ignore the distribution of financial tail risks (Woodford, 2012). In short, it may be optimal for a central bank to accept greater inflation volatility if it means reduced financial volatility.1 By contrast, the ‘modified’ Jackson-hole consensus argues that monetary should mitigate volatility in inflation only (Smets, 2014, Svensson, 17 September, 2010).2

An important factor in this debate is to establish precisely what the objectives of monetary policy are when both capital and financial frictions matter. Under what assumptions does it hold that a central bank can focus solely on stabilising inflation, and under what alternatives will it be optimal to take financial volatility into consideration as well?

The central bank’s objective has been derived in a New Keynesian (NK) economy with capital, but without a financial accelerator (Edge, 2003, Takamura, Watanabe, Kudo); and with a financial accelerator applied to the payment of labour, but where capital is assumed fixed (Carlstrom, Fuerst, Paustian, 2010, De Fiore, Tristani, 2012). The implications of a financial accelerator together with investment volatility, as is common in quantitative business cycle models, have not been considered.3 This is the contribution of this paper.

There are reasons to think that capital with a financial accelerator could be important. The collapse in investment during the Crisis is a key channel through which financial volatility propagated to the real economy. Financial frictions and investment volatility are also relevant for the business cycle more generally (Gertler, Kiyotaki, 2010, Gilchrist, Zakrajšek, 2012, Jermann, Quadrini, 2012). By characterising optimal monetary policy in this environment, one can consider the optimal response to financial shocks, whether is there a trade-off between price stability and financial stability, and whether additional instruments can help resolve any trade-off faced.

I study the objectives of monetary policy in three NK economies. The first is a simple NK economy with capital and exogenous investment efficiency shocks.4 The second additionally includes a financial accelerator with costly state verification (CSV). Developed by Carlstrom and Fuerst (1997), and similar to the model proposed by Bernanke et al. (1999), I focus on this model because it is sufficiently rich to have both capital and a non-trivial financial accelerator, while still remaining analytically tractable when studying optimal policy. The implied debt contract in this economy is also optimal (Gale and Hellwig, 1985).5 The third model I consider is a second-generation financial accelerator model that also includes asset fire sales and countercyclical bankruptcy costs (Choi and Cook, 2012).6

In the standard NK model with fixed capital, no financing frictions and absent household heterogeneity, it is well known that disturbances to demand (for example, shocks to utility from consumption) or productivity (labour augmenting technical change) do not create a trade-off for monetary policy. There is no distinction between stabilising volatility in real quantities and inflation, and so the “divine coincidence” holds with zero inflation optimally chosen in all periods (Clarida et al., 1999).7

I examine whether the same result holds with capital and a financial accelerator. In addition to demand and productivity shocks, I also consider shocks to the marginal efficiency of investment (in the model with capital), to net worth and bankruptcy costs (in the model with CSV) and to volatility in investment returns (in the model with fire sales). These shocks have been emphasised in previous quantitative analysis.8

To understand the central bank’s objectives, I use the Linear–Quadratic (LQ) approach and study the full commitment solution, otherwise known as optimal policy from a ‘timeless perspective’ (Benigno and Woodford, 2012). Deriving an explicit welfare-theoretic loss provides maximum transparency on policy objectives and solving the LQ problem provides analytical insight into any trade-offs faced. In particular, the frictions in the economy that a central bank should be concerned with, and how these might affect any policy trade-off.

Focusing on a central bank with access to a single instrument, the nominal interest rate, I find:

  • (i)

    Introducing capital in an otherwise standard NK economy does not affect the divine coincidence. In response to all shocks – demand, productivity and the marginal efficiency of investment – the flexible-price equilibrium remains optimal and there is no trade-off between stabilising real variables and inflation.

  • (ii)

    Introducing a second friction, CSV, breaks the divine coincidence. Volatility in the net worth of borrowers becomes an additional objective for monetary policy and there is a non-trivial trade-off between stabilising volatility in it and inflation.

  • (iii)

    In the model with CSV, net worth is a sufficient statistic for capturing the extent to which monetary policy deviates from a flexible-price equilibrium. Volatility in credit spreads and asset prices only matter to the extent they affect net worth and are not sufficient statistics in their own right.

  • (iv)

    Allowing for fire sales and countercyclical bankruptcy increases the set of variables relevant to the central bank’s objective and again the divine coincidence does not hold. Volatility in default, the capital stock and net worth are all relevant to optimal monetary policy and there is a trade-off between price and financial stability.

Changes in investment efficiency are consistent with financial frictions that are important at business cycle frequencies (Justiniano, Primiceri, Tambalotti, 2010, Justiniano, Primiceri, Tambalotti, 2011). Result (i) implies that when these changes are exogenous, the conventional wisdom holds – monetary policy need only consider financial volatility to the extent that it influences forecasts of inflation and real variables. Nevertheless, the second result makes clear that when changes in investment efficiency are micro-founded and sensitive to changes in interest rates, inflation, investment, asset prices and default, then financial variables become relevant to the optimal policy calculus.9 In particular, with CSV the primitive of interest is net worth. With fire sales, volatility in default and the capital stock also become relevant.

Results (ii)–(iv) highlight that a financial accelerator constrains investment allocations relative to a frictionless equilibrium. On the supply side, costly default raises the cost of supplying new capital, which affects marginal costs. On the demand side, costly default reduces the expected return from investment to entrepreneurs and thus the resources available for them to consume. The latter affects the demand for goods and changes the distribution of consumption between entrepreneurs and households.10 Both effects imply a trade-off for monetary policy that can either stabilise inflation to reduce price dispersion, or allow for some non-zero inflation to help mitigate the effects of socially costly default. The divine coincidence does not hold either in the CSV model or with fire sales.

These results apply when the central bank uses a single instrument, the nominal interest rate. Two additional instruments are also considered: a transfer to entrepreneurs financed by a lump-sum tax on households (in the CSV and fire-sales models); and a subsidy on liquidation services (in the fire-sales model only). These instruments are considered because they align with the underlying financial distortions associated with each model. One can think of a central bank choosing them, or alternatively a separate fiscal authority or prudential regulator choosing them and who shares the same welfare-theoretic loss.11

The first instrument is equivalent to a time-varying subsidy (or tax) on borrowing and is therefore similar to a policy of choosing optimal liquidity requirements. The second, also referred to as ‘heterodox policy’ (Choi and Cook, 2012), captures how a time-varying subsidy (or tax) can be used to help stabilise impaired asset prices. With access to these additional instruments:

  • (v)

    In the CSV model, a transfer to entrepreneurs restores the divine coincidence and the flexible-price equilibrium is optimal in this case.

  • (vi)

    In the model with fire sales, access to transfers and liquidation subsidies are not sufficient to restore the divine coincidence.

  • (vii)

    With fewer instruments than targets in the model with fire sales, it is optimal to increase transfers and liquidation subsidies in response to increased volatility in investment returns or declines in net worth. It is optimal to reduce transfers and liquidation subsidies in response to higher demand or productivity. The optimal choice of nominal interest rate offsets the effects of these policies and the underlying shocks on inflation. However, the divine coincidence does not hold.

Result (v) highlights that access to transfers can fully restore the optimality of a central bank’s focus on inflation in the CSV model (the modified Jackson-hole consensus holds). Result (vi) makes clear that further instruments are required with fire sales. Indeed, allowing for transfers to entrepreneurs and liquidation subsidies is not sufficient for restoring the divine coincidence as there are four objectives (volatility in default, the capital stock, net worth and inflation), but only three instruments. Result (vii) makes clear that with fewer instruments than targets, optimal transfers and liquidation subsidies are countercyclical. However, it is also optimal for the nominal interest rate to offset the effects of those policies on inflation. That is, optimal ‘prudential’ and monetary policy offset one another.

While earlier literature has emphasised the role of credit spreads with financial frictions when capital is fixed (Carlstrom, Fuerst, Paustian, 2010, Cúrdia, Woodford, 2010), that emphasis is not as strong in the models with time-varying capital considered here. Credit spreads, default rates and investment all matter, either through their effects on net worth in the CSV model, or as separate objectives in their own right when fire sales are included. Credit spreads alone are not sufficient for capturing the optimal deviation from a flexible-price equilibrium. Asset prices, a focus of previous literature on interest rate rules (Bernanke, Gertler, 2001, Faia, Monacelli, 2007, Gilchrist, Leahy, 2002, Nutahara, 2014, Nutahara, 2015), also do not capture all relevant information when optimally deviating from the flexible-price equilibrium.

These results connect to a broader literature on how monetary policy should be conducted optimally in the presence of financial frictions. Cúrdia and Woodford (2016) and Nisticó (2016) study optimal monetary policy with incomplete financial markets and consumer heterogeneity (again with fixed capital), and find that consumption dispersion becomes an additional objective for monetary policy.12 Collard et al. (2017) study optimal Ramsey policy, jointly monetary and prudential policy, in a model with capital and socially inefficient lending. By setting capital requirements sufficiently high, all inefficient lending is removed and welfare is maximised. Faia and Monacelli (2007) study optimal interest rate rules numerically in a first generation financial accelerator model, similar to that proposed by Carlstrom and Fuerst (1997), and find that constrained efficient interest rate rules that respond to asset price volatility are sub-optimal.

With capital and financial frictions, and using an LQ approximation of optimal policy, I find that neither credit spreads, asset prices, or consumption dispersion are sufficient for capturing the underlying trade-off for monetary policy. In a model with capital and CSV, it is the net worth of borrowers that is most relevant for capturing this trade-off. With fire sales additionally included, volatility in default and capital also become relevant. These results do not require lending to be socially inefficient, or that prudential policy need also be optimal.13

The next section describes the three economies in which optimal monetary policy is studied analytically. Section 3 discusses the main findings and compares them with existing literature. The final section concludes.

Section snippets

The NK economy with capital

The environment with capital, but no credit friction, reflects a standard NK economy with a flexible rental market for capital. As this economy is well known, I discuss it only briefly. There is a continuum of ex ante identical households on the unit interval. Each infinitesmal household supplies labour to one infinitesimal firm, consumes and can invest in capital and government bonds. Household utility is additively separable in consumption, Ci,t, and labour effort, Hi,t, and there is perfect

Optimal monetary policy

I now consider optimal monetary policy in these three economies. I focus on the LQ problem and the optimal commitment solution from a timeless perspective (Benigno, Woodford, 2012, Woodford, 2003).23 An important assumption that facilitates

Conclusion

This paper provides an analytic characterisation of optimal monetary policy in New Keynesian economies where both capital and a financial accelerator matter. Previous literature has considered capital, but abstracted from a financial accelerator, or considered financial accelerator effects on the demand for labour but held capital fixed. The objectives of monetary policy in economies where there is a credit friction on the supply of new capital, which captures salient features of the 2007–08

Acknowledgments

This paper is a substantial revision of the first chapter of my PhD thesis for which I received financial support from the Reserve Bank of Australia (RBA). I am also very grateful to Klaus Adam, Kosuke Aoki, Gianluca Benigno, Tommaso Monacelli, Bruce Preston, Kevin Sheedy and to two anonymous referees for all of their helpful suggestions, and to seminar participants at the London School of Economics, Workshop on Macroeconomic Dynamics, RBA and Quantitative Economics workshops. The views

References (40)

  • M. Gertler et al.

    Financial intermediation and credit policy in business cycle analysis

  • S. Gilchrist et al.

    Credit spreads and business cycle fluctuations

    Am. Econ. Rev.

    (2012)
  • A. Justiniano et al.

    Investment shocks and the relative price of investment

    Rev. Econ. Dyn.

    (2011)
  • S. Nisticó

    Optimal monetary policy and financial stability in a non-ricardian economy

    J. Eur. Econ. Assoc.

    (2016)
  • F. Smets

    Financial stability and monetary policy: how closely interlinked?

    Int. J. Central Bank.

    (2014)
  • B. Bernanke et al.

    Should central banks respond to movements in asset prices

    Am. Econ. Rev.

    (2001)
  • N. Bloom

    The impact of uncertainty shocks

    Econometrica

    (2009)
  • C. Borio et al.

    Asset prices, financial and monetary stability: exploring the nexus

    Working Paper 114

    (2002)
  • C. Borio et al.

    Whither monetary and financial stability? The implications of evolving policy regimes

    Working Paper 147

    (2004)
  • C.T. Carlstrom et al.

    Agency costs, net worth, and business fluctuations: a computable general equilibrium analysis

    Am. Econ. Rev.

    (1997)
  • Cited by (12)

    • Should macroprudential policy be countercyclical?

      2024, Journal of Economic Dynamics and Control
    • Should monetary policy target financial stability?

      2023, Review of Economic Dynamics
      Citation Excerpt :

      These results together show monetary policy can mitigate aggregate demand and aggregate supply issues caused by financial frictions. Hansen (2018) characterizes LQ-optimal monetary policy near an efficient deterministic steady state in a New Keynesian economy with a Bernanke and Gertler (1989) financial accelerator. Equilibrium in our model is inefficient with a stochastic steady state.

    • Optimal simple objectives for monetary policy when banks matter

      2021, European Economic Review
      Citation Excerpt :

      In such cases, inflation volatility remains the principal source of welfare losses, as in standard textbook models, and strict inflation targeting remains (almost) optimal (Woodford, 2003). That quantitative result turns out to carry over to the case of models that include capital accumulation (Hansen, 2018).7 The analysis in this paper differs from the existing literature in two regards.

    View all citing articles on Scopus
    View full text