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Journal of Monetary Economics

Journal of Monetary Economics 58 (2011) 35–38

0304-39

doi:10.1

E-m1 Ko

Other re

et al. (2

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Discussion

Discussion of Gertler and Karadi: A model of unconventionalmonetary policy

Harold Cole

University of Pennsylvania, Department of Economics, Bunche Hall, 19104 Philadelphia, PA, United States

a r t i c l e i n f o

Article history:

Received 22 October 2010

Accepted 25 October 2010Available online 28 October 2010

Gertler and Karadi have developed a very interesting quantitative model of unconventional monetary policy. Their modelshows us some of the ingredients that can lead to unconventional monetary policy having an important quantitative role. Inaddition, the model provides a clear rationale for the policies that we have ended up adopting. In doing both of these things,they are helping to fill an important hole in the literature on monetary policy.1 The fact that the authors have done so in a fairlyelegant model which builds nicely on some pre-existing work (Mark’s in particular), and is computationally fairly tractable isto be commended. However, since I see my role here as poking around under the hood of their model, in what follows, Idiscuss what I see as the questionable aspects of the ingredients they use to get all of this.

The model of Gertler and Karadi has three key features which operate to make financial variables, and the net worth of theintermediaries in particular, an important constraint on the economy’s level of production. First, each period the intermediategoods firms in effect refinance themselves from scratch in order to acquire the capital they need to produce. They do thisdespite the fact that the implicit return to funds within the firm will generally be higher than the interest rate. Second, thefinancial intermediaries which supply the funds to intermediate goods producers are constrained to start out small and die offrandomly at a fast enough rate to ensure that the overall financial sector never gets large enough to relax the constraint (atleast in the steady state). And third, financial intermediaries never seek to hedge their risks, across states of the world andhence shocks to their net worth go directly into their ability to intermediate. In what follows, I discuss these variousassumptions in turn.

I start this discussion with the goods producers and their role in the Gertler and Karadi model. The intermediate goodsproducers issue claims in period t which enable them to acquire capital to be used in period in the following period. Then, inperiod t+1 they hire workers on a spot labor market and choose the utilization level of capital which in turn determines theextent to which it depreciates. Their left over capital is subject to a quality shock, which is really a form of stochasticdepreciation. This leads to the return to capital equation (25) which determines Rkt + 1. To the extent that Rktþ14Rtþ1, thegross real interest rate the intermediary pays for its funds, then the fact that the firm cannot use retained earning to financeinvestment is increasing the costs of the firm and lowering its expected profits. However, this device has the effect of makingthe behavior of the firm more sensitive to movements in this wedge. If instead some fraction of the firms were able to pile up

32/$ - see front matter & 2010 Elsevier B.V. All rights reserved.

016/j.jmoneco.2010.10.008

ail address: colehl@sas.upenn.edu

cherlakota (2009) develops a nonquantitative model of the housing bubble, in which a collapse in the price of land leads to shortage of collateral.

cent quantitative models that emphasize the role of quantitative easing in monetary policy include Curdia and Woodford (this issue) and Del Negro

010).

H. Cole / Journal of Monetary Economics 58 (2011) 35–3836

enough internal resources so that they could self-finance their investments, then the relevant cost of funds would be theeconomy wide interest rate Rt + 1 since this is the rate at which the future payout of capital would be discounted.

If Gertler and Karadi’s model of firm financing was correct, then firm balance sheets should show large amounts offinancial liabilities being offset by net worth and the value of their capital. However, this is not exactly what we see. The recentflow of funds accounts put the financial assets of the nonfarm nonfinancial corporate business sector at 13.5 trillion whiletheir tangible assets were 13.9 trillion in 2008. Since the net worth of these corporations was 14 trillion, this implies that theirfinancial assets were essentially equal to the value of their financial liabilities. These numbers are aggregates, and do notimply that no firms are financially constrained, however they strongly suggest that many firms are not. Chari and Kehoe(2009) and Ohanian (2010) utilize Compustat data to examine the extent of cash reserves relative to investment at the firmlevel. They estimate that on average firms self-finance 80% of their investment. Moreover, Bates et al. (2007) document thatthere has a been a large secular increase in firm cash holdings since 1980, and that once these cash holdings are taken accountof, net debt-to-equity measures have fallen sharply.

My skepticism about extent to which nonfinancial firms are cash constrained is further strengthened by observations fromthe great depression. The most important of which concerns the behavior of firms and in particular the extent to which theypaid out dividends even during this extreme downturn. Cole and Ohanian (2000) developed this line of argument. Back then,the situation was reversed, and Mark was our discussant, and he expressed his reservations about our argument in hisdiscussion (see Gertler, 2000).

When we compare our standard business cycle models to the data, one of the consistent findings is that our models havetrouble properly accounting for the variations in labor (taking productivity as given), but do relatively well in accounting forinvestment. Several researchers have considered adding tax-style wedges to enable the standard real business cycle model tofit the U.S. business cycle data. They have consistently found a large role for the labor wedge and a small role for the capitalwedge (see Mulligan, 2002; Chari et al., 2007). Surprisingly Ohanian (2010) shows that even during the current GreatRecession, the role of the capital wedge remains small and while role of the labor wedge is even larger than normal. Thisfinding by Ohanian is consistent with a slew of newspaper reports of firms piling up cash, or borrowing cheap in order toexpand their cash holdings. Some of these articles are quite recent, but others date back to 2008.2

The Gertler and Karadi model does have a labor wedge coming through its sticky price assumption, but the impact of thefinancial friction they introduce is to generate a capital wedge in their model relative to its perfect capital markets version.These wedge results, while not uncontroversial, do raise questions about the true extent of the role played by financialfrictions. However, their model also implies that a very large nonconventional intervention by Fed would reduce the wedge,so one might interpret the recent findings in a more positive light.

Additionally, Gertler and Karadi might want to consider adding in an assumption that firms must borrow in order tofinance some fraction of their labor as well as their capital. If the firm had to finance the fraction t of their labor bill. In thiscase, the first-order condition for labor choice by the intermediate goods producers (24) would become

Pmtð1�aÞYt

Lt¼Wtð½1þtðRkt�RtÞ�:

Now increases in the financial friction will generate a labor wedge too through increases in the return gap Rkt–Rt.I turn next in my discussion to the financial sector. Financial intermediaries in the model have a simple life. A household

member at some t gets chosen to be an intermediary and is given some start-up funding which is a fixed fraction of the fundscoming from the closing of other financial intermediaries owned by the household. Assuming that the incentive constraint (9)binds in every period, then the internal rate of return exceeds the external cost of funds and the intermediary optimallychooses to borrow up to the constraint and pile up as much net worth as possible before the random termination date.

At each point in time, the value of the intermediary, Vjt, is determined by the level of net worth. Gertler and Karadi showthat the linearity of their problem implies equation (10), or

Vjt ¼ utQtSjtþZtNjt ,

where ut and Zt are time-varying factors, Qt is the price of a claim to capital, Sjt is the quantity of claims to capital held byintermediary j, and Njt is its net worth. The intermediary can steal a fraction of these claims and this leads to the incentiveconstraint (13) which I will assume binds and leads to

QsSjt ¼ftNjt ,

where ft is the private leverage ratio. Taken together, these expressions imply that

Vjt ¼ ½utftþZt�Njt : ðAÞ

If we make use of (13) in the transition equation for net worth (7),we get

Njtþ1 ¼ ðRktþ1�Rtþ1ÞftNjtþRtþ1Njt : ðBÞ

2 For example:

‘‘Unlike consumers, companies are piling up cash,’’ New York Times, March 4, 2008.

‘‘Cheap debt for corporations fails to spur economy,’’ New York Times, October 3, 2010.

H. Cole / Journal of Monetary Economics 58 (2011) 35–38 37

Gertler and Karadi assume that financial intermediaries are initially established at a suboptimally small size and cannotacquire new funds other than by borrowing. They also assumed that the financial intermediary could abscond with thefraction l of their funds and turn them over to their own household. Hence, other households face the same incentive issue aslenders if they sought to buy an equity stake in the financial intermediary. However, the family of the financial intermediarycould invest in the firm without facing this incentive issue. For the family of the intermediary, the opportunity cost of thesefunds would be Rt +1, however the state-contingent return would be Rkt +1, and to the extent that the financial constraintbound, the expected net payoff would be positive, or

EtbLt,tþ1ðRktþ1�RtÞ40:

The fact that this margin is positive implies that financial intermediaries are strictly on their incentive constraint and henceare investing all available funds.

One way to investigate the reliance of these assumptions to the real world is to try and examine the extent to which theyseem consistent with the data during the recent financial crisis. On the one hand, if we look at risk spreads and the volume oflending in certain markets, we do see a picture that appears to be consistent with the Gertler and Karadi model. Risk spreadsopened up sharply in many bond markets, and the volume dropped, particularly in the asset-backed commercial papermarket.

On the other hand, in the traditional intermediation sector, the banks, did not appear to have been constrained in theirlending or investing activities. First, on the household side, the crisis did not lead household depositors to withdraw theirfunds from the banking system. Total deposits at U.S. banks actually grew by 5% in 2008 relative to 2007. One potentialexplanation for this is that we have deposit insurance in the real world and hence the increase in the risk associated with thebond market led people to invest in bank deposits. Second, the Federal Reserve’s statistics show that not only were excessreserves positive during 2008, the main year of the crisis, but these excess reserves were extremely large after Fed’sintervention. In September of 2008, the total seasonally adjusted reserves of the banking system shot up from 46 billion in theprior month to over 103 billion. They then rose to 315 billion in October, to 609 billion in November, and finally to 820 billionin December; a level that they stayed around or above throughout the next year. At same time required reserves only rosevery slightly during this period. They went from 44 billion in August to 53 billion in December of 2008.

Overall, one is struck by the extent to which some sort of financial market segmentation must be an important part of thestory that Gertler and Karadi want to tell. However, a segmentation based story raises the question of how long thesegmentation would last in the face of large interest rate differentials. If this segmentation broke down quickly, then onewould expect only a fairly temporary impact from a fall in the net worth of the affected portion of the intermediation sector.While this segmentation seems to have lasted for a while during the current crisis, it may well be the case that the next timearound it is more porous as financial agents learn how to overcome this segmentation in response to large profitopportunities.

Another critical assumption by Gertler and Karadi is that financial intermediaries do not efficiently hedge their risk.3 Tounderstand the role of this assumption, consider allowing intermediaries to enter into state-contingent contracts whichallow them to transfer net worth across states of the world tomorrow. For now, assume that these contracts are enforceablebut cannot serve as a source of new loans. Let otþ1 denote the quantity of these state-contingent claims (where we havefollowed Gertler and Karadi’s notation and repressed the representation of the state variable. We will require that these state-contingent contracts break-even in a present-value sense to ensure that they do not result in the injection of additional fundsinto the intermediary:

EtbfLt,tþ1otþ1g ¼ 0: ðCÞ

Then, note that we can combine Eqs. (A) and (B) to form the expected value of an intermediary today as

EtbfLt,tþ1½utþ1ftþ1þZtþ1�½ðRktþ1�Rtþ1ÞftNjtþRtþ1Njtþotþ1�g: ðDÞ

The intermediaries problem with respect to the optimal choice ofotþ1 is to maximize (D) subject to (C). One can trivially seethat this will involve positive transfers in states in which the return to net worth, ½utþ1ftþ1þZtþ1�, is high, and the reversewhen low. Note also that the fact that the intermediaries are risk neutral will mean that their optimal allocation of net worthwill be bang–bang; i.e. put all of it at the highest payout state.

The addition of these contracts to their model would change the distribution of net worth across states and prevent theability of shocks to create states with a relative shortage of net worth. My conjecture is that this could severely dampen theimpact of shocks in their model and bring the impact closer to the perfect capital markets model. I suspect this would be trueeven though there could be an overall shortage of net worth, since much of the impact of a negative shock probably comesfrom creating relative shortages of net worth.

One might be concerned that these insurance contracts would lead to violations of the intermediaries incentive constraint.In this case, an alternative way to implement the efficient outcome would be to have the goods producing firms themselvestransform their payout per unit of capital from Rktþ1 to something like Rktþ1þotþ1 (where we might have to worry about the

3 This assumption of a lack of efficient risk hedging is fairly pervasive in the literature on endogenous financial frictions. It shows up, for example, in

Bernanke et al. (1999) and Carlstrom and Fuerst (1997), two of the classic papers in this literature.

H. Cole / Journal of Monetary Economics 58 (2011) 35–3838

scaling of otþ1 relative to Rktþ 1in order to replicate the efficient insurance contract). The firms could do this by changing the

state-contingency of wages Wt +1 and payouts to capital Rkt +1 to yield the desired result.One way to defend the assumptions of Gertler and Karadi would be to assume that there are very rare shocks which create

large relative shortages of net worth, and that the rarity of these shocks might lead to their not being insured against. Thecurrent financial crisis might well fit that mold. Of course one might also fear that the response of the Fed along with the TARPbailout would create a moral hazard problem going forward.

Finally, let me note that one aspect of the modeling bothered me. The friction on financial intermediaries that in this papercomes from a fear that they will steal. However, I would argue that the real concern with financial intermediaries is that theywill take on excessive risk because of the skewed nature of their compensation. Substantively, a change in the friction fromstealing to gambling may not change the results very much. But, it may make it seem less plausible that the government has areal advantage in recovery funds from defaulting intermediaries if they have gambled them away. Since this recoveryadvantage is important to generate the positive impact of nonconventional monetary policy, rethinking the friction to make itmore realistic may reduce the ability of the government to stimulate the economy.

Overall, this is a very nice contribution to an important new area in monetary policy. It sets out a clear and tractablequantitative model that makes the case that quantitative easing is important. I suspect that it will have considerable impacton our thinking going forward.

References

Bates, T., Kahle, K. Stulz, R., 2007. Why do U.S. firms hold so much more cash than they use to? Dice Center for Research in Financial Economics Workingpaper.

Bernanke, B., Gertler, M., Gilchrist, S., 1999. The financial accelerator in a quantitative business cycle framework. In: Taylor, J., Woodford, M. (Eds.), Handbookof Macroeconomics, vol. 1. Elsevier Science BV.

Chari, V.V., Kehoe, P., Slide presentation, Federal Reserve Bank of St. Louis Policy Form, 2009.Chari, V.V., Kehoe, P., McGrattan, E., 2007. Business cycle accounting. Econometrica 75 (3), 781–836.Carlstrom, C., Fuerst, T., 1997. Agency costs, net worth, and business fluctuations: a computational general equilibrium analysis. American Economic Review

87 (5), 893–910.Cole, H. Ohanian, L., 2000. Re-examining the contributions of money and banking shocks to the U.S. great depression. In: Bernanke, B., Rogoff, K. (Eds.), NBER

Macro Annual 2000, National Bureau of Economic Research, pp. 183–226.Curdia, V., Woodford, M., this issue. The central-bank balance sheet as an instrument of monetary policy, doi:10.1016/j.jmoneco.2010.09.011.Del Negro, M., Eggertsson, G., Ferrero, A., Kiyotaki, N., 2010. A quantitative evaluation of the Fed’s non-standard policies. CEPR Working paper.Gertler, M., 2000. Comment. In: Bernanke, B., Rogoff, K. (Eds.), NBER Macro Annual 2000, National Bureau of Economic Research, pp. 237–258.Kocherlakota, N., 2009. Bursting bubbles: consequences and cures. Research Memo.Mulligan, C., 2002. A century of labor-leisure. NBER Working paper 8774.Ohanian, L., 2010. The economic crisis from a neoclassical perspective. Journal of Economic Perspectives 24 (4), 1–24.