metadata: authors: 0: author: Eden,Maya
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docna: 0: docna: Should Wall-Street be occupied ? an
            overlooked price externality of financial intermediation
docty: Policy Research Working Paper
subtopic: Consumption,Economic Theory & Research,Fiscal & Monetary Policy,Industrial Economics,Disability,Services & Transfers to Poor,International Trade and Trade Rules,Economic Assistance,Economic Growth,Access of Poor to Social Services
teratopic: Macroeconomics and Economic Growth,Finance and Financial Sector Development
abstracts: cdata!: Does an unregulated financial system
            absorb too many productive inputs? This paper studies this
            question in the context of a dynamic model with
            heterogeneous producers. In the absence of a financial
            system, the only way to purchase inputs is using internal
            funds. Producers are subject to idiosyncratic productivity
            shocks, and will decide to produce only if their
            productivity is high enough. Otherwise, they will hold
            money. A financial intermediation technology allows
            producers to purchase inputs in excess of their internal
            funds, by borrowing from unproductive agents. However,
            intermediation requires the use of costly monitoring
            services. In equilibrium, intermediation increases the money
            in circulation and raises nominal prices, thereby reducing
            the value of internal funds and making producers
            increasingly reliant on costly monitoring services. For this
            reason, society is better off when intermediation is restricted.
repnme: repnme: Should Wall-Street be occupied ? an
            overlooked price externality of financial intermediation
display_title: Should Wall-Street be occupied an
            overlooked price externality of financial intermediation
listing_relative_url: /research/2012/05/16844872/wall-street-occupied-overlooked-price-externality-financial-intermediation
topicv3: Economic Growth m1326241 471,Trade m1326924 698,Social Assistance m1327201 1466,Macroeconomic and Structural Policies
            m1327380 439
publishtoextweb_dt: 2012-05-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Finance and Financial Sector Development
no_of_pages: 42
author_keys: 0: author_key: 1172765
model_extractions: WPS6059 Policy Research Working Paper 6059

# Should Wall-Street be Occupied?

An Overlooked Price Externality of Financial Intermediation _Maya Eden_ The World Bank Development Research Group Macroeconomics and Growth Team May 2012
Policy Research Working Paper 6059

# **Abstract**

Does an unregulated financial system absorb too many productive inputs? This paper studies this question in the context of a dynamic model with heterogeneous producers. In the absence of a financial system, the only way to purchase inputs is using internal funds. Producers are subject to idiosyncratic productivity shocks, and will decide to produce only if their productivity is high enough. Otherwise, they will hold money. A financial intermediation technology allows producers to purchase inputs in excess of their internal funds, by borrowing from unproductive agents. However, intermediation requires the use of costly monitoring services. In equilibrium, intermediation increases the money in circulation and raises nominal prices, thereby reducing the value of internal funds and making producers increasingly reliant on costly monitoring services. For this reason, society is better off when intermediation is restricted.

This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at meden@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Should Wall-Street be Occupied? An Overlooked Price Externality of Financial Intermediation

Maya Eden<sup>_∗_</sup> World Bank October 3, 2012

**Abstract**

This paper highlights a price externality that causes excessive resources to be spent on financing. Intermediated funds increase the demand for capital inputs, which raises their price (in both real and nominal terms). This implies that producers can buy less inputs with their internal funds, and must rely more heavily on financial intermediation. As intermediation is costly, this feedback is inefficient. I illustrate this mechanism in a simplified real model, and extend it to a dynamic model with money.

## **JEL Classification:** E44, G20

**Keywords:** Costs of the financial sector, financial intermediation

> _∗_ Please send comments to meden@worldbank.org. Earlier versions of this paper circulated under the titles “The Inefficiency of Financial Intermediation in General Equilibrium”, “The Wasteful ‘Money Creation’ Aspect of Financial Intermediation” and “Excessive Financial Intermediation in a Model with Endogenous Liquidity”. This work is based on a chapter of my thesis at MIT. I thank Fernando Broner, Ricardo Caballero, Ben Eden, Anton Korinek, Guido Lorenzoni, Luis Serven and Ivan Werning for helpful comments. I also benefited from comments made by various seminar and conference participants. This paper does not necessarily reflect the views of the World Bank, its Executive Board or the countries it represents. All errors are mine.

<mark>1</mark>
“Has the contribution of the modern world of finance to economic growth become so critical as to support remuneration to its participants beyond any earlier experience and expectations? Does the past profitability of and the value added by the financial industry really now justify profits amounting to as much as 35 to 40 percent of all profits by all US corporations? Can the truly enormous rise in the use of derivatives, complicated options, and highly structured financial instruments really have made a parallel contribution to economic efficiency?”

-Paul Volcker, ‘The Time We Have Is Growing Short’, _The New York Review of Books_ , June 24th 2010.

# **1 Introduction**

The recent financial crisis resurfaced the concern that too many production inputs are being absorbed by the financial sector.<sup>1</sup> At the same time, standard theoretical arguments suggest that financial intermediation improves the allocation of inputs across producers, and that this efficiency gain is enough to offset the costs of intermediation.<sup>2</sup> In this paper I argue that, while financial services are sometimes socially valuable, the idea that they are unambiguously so may be a partial equilibrium view: while financial intermediation may appear vital when input prices are fixed, in general equilibrium, when input prices are adjustable, even the most basic form of financial intermediation may be a wasteful use of productive resources. Bluntly, it is theoretically ambiguous whether or not the existence of a financial sector

> 1See Benjamin Friedman, “Overmighty Finance Levies a Tithe on Growth”, _The Financial Times_ , August 26th, 2009, and Paul Volcker, ‘The Time We Have Is Growing Short’, _The New York Review of Books_ , June 24th 2010, for op-eds on this topic.

> 2See Gorton and Winton [2003] for a survey of the literature on financial intermediation, as well as Levine [2005] and McKinnon [1973] on the role of the financial sector in promoting growth and an efficient allocation of resources.

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creates social surplus. Regardless, there is a price externality that implies that an unrestricted financial system absorbs too many inputs.

To develop intuition, consider a benchmark economy with identical producers. Land is the only input of production and is supplied inelastically. Producers are liquidity constrained in the sense that they cannot fully pledge post-production output for the purpose of buying land. The constraint is binding: given the equilibrium price of land, producers would like to buy more of it, but are unable to pledge the resources to do so. However, since the aggregate supply of land is fixed, prices adjust so that all land is used in equilibrium, and output is at its first best level. The price of land is determined by the aggregate constraint: the amount of pledgeable output determines the aggregate payment to land.

In this setup, consider the consequences of introducing an intermediation technology that allows each producer to increase the amount of output that he can pledge by employing “monitoring” services. Since liquidity constraints are binding, it is privately optimal to make use of this technology, in hope to buy more land at its depressed price. However, in general equilibrium, since the supply of land is fixed, the increase in pledgeable output merely bids up the price of land, in a way that does not allow producers to expand their production. The costs of intermediation are purely wasted.

From the producers’ perspective, there is a coordination failure: faced with constrained aggregate demand and low input prices, each individual producer tries to “beat the system” by spending resources in order to circumvent the constraint. However, in general equilibrium, when everyone tries to “circumvent the constraint”, the aggregate constraint becomes less binding and, consequently, land prices appreciate. This un-internalized price externality leaves all producers worse off as they face higher land prices and must pay intermediation costs.

In this stylized framework, the stark conclusion that intermediation is purely wasteful relies on two stark assumptions: (a) that production inputs 3
are supplied inelastically; and (b) that producers are homogeneous. When these assumptions are relaxed, there are some benefits associated with the appreciation of input prices. When there is some input supply elasticity, higher input prices increase input supply. When producers are heterogeneous, higher input prices deter less-productive producers from hiring inputs, which may improve the efficiency of input allocation. The robust conclusion is therefore less extreme: financial intermediation is not always _purely_ wasteful. However, the price externality implies that in the unregulated equilibrium, the social expenditure on financial intermediation is inefficiently large.

The price externality is exacerbated by its monetary implications. I embed this mechanism in a monetary model, in which money is used both as a store of value and as a medium of exchange. The price externality operates through an additional nominal channel: when producers borrow money from idle money holders (savers), they are increasing the money in circulation. This leads to an inflation in nominal prices and a decline in real balances. Interestingly, a steep increase in _nominal_ input prices need not coincide with a large _real_ increase in input prices. In this case, the conclusion that financial intermediation is purely wasteful generalizes to settings with elastic input supply and heterogeneous producers, as the “positive” effects of the (real) price appreciation are no longer relevant. In this case, intermediation is similar to a counterfeit money printing machine: it increases the money in circulation at some real cost, but, in general equilibrium, this merely translates into higher nominal prices, leaving real prices unchanged (and wasting resources on intermediation services, which, in the counterfeit money analogy, are analogous to resources spent on counterfeit money printing machines).

The implications of the monetary model are broadly consistent with recent trends in the US economy. The increase in the size of the financial system in the US (as documented by Philippon [2008]) has been accompanied by a decline in the amount of real balances: the average value of M1 as a fraction of nominal output ( _PY_<sup>_<u>M</u>_</sup><sup><u>1</u>instandardnotation)droppedfromaround</sup> 4
0.18 between the years 1960-1989 to around 0.12 between the years 19902007.<sup>3</sup> This is consistent with the view that, at the aggregate level, financing reduces the equilibrium amount of real balances.<sup>4</sup>

# **2 Related literature**

In most models of financial intermediation, the price of inputs is essentially fixed, and pledgeability directly determines the quantity of inputs that can be employed. For example, in Holmstrom and Tirole [1997], external funds are direct inputs in investment - implicitly, the price of investment goods in terms of funds is fixed at 1. Under similar assumptions, Philippon [2008] considers a model of costly financial intermediation, and shows that (despite its costs) financial intermediation is efficient. The key difference in this paper is the endogenous determination of the relative price of inputs, that may reverse this conclusion.<sup>5</sup> This paper is related to other papers that study the welfare implications of financial intermediation. Arcand et al. [2011] show empirically that, beyond a certain threshold, there is a negative relationship between the size of the financial sector and economic growth. They present a model that attributes excessive financing to an implicit subsidy in the form of bailouts. This paper emphasizes a different mechanism through which the financial system may become overblown: in the spirit of Tobin [1984], the model highlights the dif-

> 3The corresponding numbers for M2 are 0.59 and 0.51 respectively. These figures are calculated based on data from the Federal Reserve Bank of St. Luis (FRED) database.

> 4In this paper, banks increase the amount of nominal bills in circulation - this will increase M1, but lead to a decline in real balances. There are other (more positive) ways to think about the role of banks in money creation. Stein [2012] presents a model in which real riskless claims provide money-like services. The ability of banks to diversify risk allows them to create riskless claims, which is equivalent to the creation of real balances.

> 5Similar to Philippon [2008] and other standard models, in this model, the final good can be used both for consumption and investment. However, physical capital is different from the final good; the emphasis is on the relative price of physical capital in terms of the final good. In this model, agents are not constrained in investment, but rather in the amount of production inputs that they can employ.

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ference between the private return to finance and the social return, that leads to too many productive inputs being employed on financial intermediation. The main critique in Tobin [1984] is that only a fraction of the financial system’s activities are consistent with its social objectives, such as transferring funds from surplus firms to firms that need financing, or diversifying risk. In related work, Simsek [2012] illustrates that financial innovation may be driven by speculative trading motives, rather than by traditional risk sharing motives. Here, I argue that even the traditional roles of finance may lead to general equilibrium inefficiency.

The literature on the interaction between the price of capital and borrowing has largely focused on the collateral channel emphasized in Kiyotaki and Moore [1997]. When capital is used as collateral, a higher price of capital enables constrained producers (who are also capital owners) to borrow more. Through this channel, the appreciation of capital prices may improve the allocation of inputs. In this paper, I abstract from this well-known channel by assuming that capital has no collateral role.<sup>6</sup> However, the spirit of the results are incorporated into this model, as less-productive users of capital find it less profitable to employ capital at higher capital prices, implying a favorable reallocation of inputs to more productive agents.

The mechanism in this paper is conceptually related to the Friedman Rule (Friedman [1969]). In a monetary economy with constant money supply, binding liquidity constraints cause consumers to waste resources on trips to the bank. The mechanism here is similar in spirit: binding liquidity constraints (on the producer’s side) cause agents to spend resources inefficiently

> 6In this model, introducing a collateral role for capital may create “increasing returns” in the intermediation technology: the use of financial intermediation increases the price of capital. Through the collateral channel, this price increase may make monitoring “cheaper”; thus, as the amount of intermediation increases, the marginal cost of intermediation declines. While this channel is potentially important, there are standard considerations to do with operation scale that would suggest a decreasing returns intermediation technology. In this model I assume that there is a fixed cost to intermediation (section 3) or a constant return to scale intermediation technology (section 4), and reserve this important discussion for future work.

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on financial intermediation. The common theme is that when agents are against a constraint, actions taken to relax the constraint may be socially Other papers with related mechanisms include Bolton et al. [2012] and Glode et al. [2012]. In these papers, intermediaries inefficiently compete to extract rents from agents faced with binding constraints. These papers focus on the micro structure of the problem, and endogenize the costs of intermediation. Here, I take the costs of financial intermediation basically as exogenous, and focus on the general equilibrium price externality.

The nominal price externality highlighted in this model is similar in spirit to Bewley [1987], who considers a model in which agents with idiosyncratic income shocks hold money. In equilibrium, agents behave as if their marginal utility of holding money is constant, and use money reserves to smooth consumption. The mechanism here is similar: in the absence of financial intermediation, agents can respond to productivity shocks by using money reserves. The nominal price level is low (and real balances are high) because not all agents decide to use all of their money all of the time. In other words, “idle” money is important; the inefficiency of financial intermediation in this model stems, in part, from the reduction in “idle” money, that compromises its ability to buffer shocks.<sup>7</sup>

# **3 A simplified single period model**

**Setup.** Consider a single period economy with a unit measure of _producers_ , indexed _i ∈_ [0 _,_ 1], and a unit measure of _capital suppliers_ . Capital is the only input of production. Each producer is endowed with an _AK_ production technology, and no capital. Note that all producers share a common technology, and a common productivity parameter ( _A_ ). Each capital supplier is endowed

> 7This paper illustrates that money can buffer idiosyncratic shocks. Allen et al. [2012] illustrate that, with flexible prices, money may help buffer aggregate liquidity shocks and even mitigate financial crisis.

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with _K_ units of capital, but no production technology.

In order to produce, producers must purchase capital from capital suppliers. For this purpose, producers issue promises on post-production output. The price of capital (in terms of promises) is denoted _R_ . Capital suppliers always sell their capital at the market price.<sup>8</sup> The timing of the model is summarized in figure 1.

The amount of capital employed by producer _i_ is denoted _ki_ . Producers maximize profits, which are given by production revenues minus capital costs ( _Aki − Rki_ ).

**The liquidity constraint.** Producers are _liquidity constrained_ , in the sense that they are unable to fully commit post-production output.<sup>9</sup> For simplicity, I assume that the maximum amount of output that a producer can promise to repay is some constant _l_ (for “liquidity”).<sup>10</sup> I assume that _l < AK_ , which will guarantee that the liquidity constraint binds in equilibrium.

**Equilibrium without financial intermediation.** Consider the producer’s optimization problem:

To see that the liquidity constraint is binding, note that _l_ is the maximum aggregate payment to capital. It follows that _R < A_ :

> 8The consumption value of capital is assumed 0.

> 9This friction can be seen as a reduced form formulation of a moral hazard problem as in Holmstrom and Tirole [1997].

> 10Similar results can be obtained in more elaborate frameworks, in which the intermediation technology is arbitrary and the amount of output that producers can pledge is an increasing function of post-production output.

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Figure 1: The timeline of the model

|•Producers born|Market:|Production,|
|---|---|---|
|with AK technology|capital is sold|repayment|
|<br>•Capital suppliers|<br>for promises on||
|born with capital|<br>post-production output||

As _R < A_ , profits are increasing in _ki_ ; absent the liquidity constraint, the producers would choose _ki_ = _∞_ . As the capital supply is finite, the liquidity constraint must bind.

The aggregate liquidity constraint pins down the equilibrium price of capital, _R_ . To see this, note that each producer’s demand for capital is pinned down by his liquidity constraint: 1 Capital market clearing requires that �0<sup>_kidi_=</sup><sup>_K_.Thus,giventheex-</sup> pression above we can conclude that _K_ = _Rl_<sup>,andthereforetheequilibrium</sup> _<u>l</u>_ price of capital is given by _R_ = _K_<sup>.</sup> Note that the price of capital is constrained by the aggregate supply of liquidity, and is increasing in _l_ . Despite the fact that the liquidity constraints are binding, output is at its “first best” level, as all capital is employed in equilibrium at its most productive use: The reason that output is unaffected by the binding liquidity constraints is that capital is supplied inelastically. The binding liquidity constraints merely affect the price of capital ( _R_ ).

**Financial intermediation.** In the economy described above, assume a financial intermediation technology that allows producers to be “monitored”,

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thereby increasing the amount of post-production output that they can pledge from _l_ to _l_<sup>_′_</sup> _> l_ . However, monitoring is costly.<sup>11</sup> For simplicity, I assume that there is a fixed cost of monitoring: a monitored producer must forgo _ι_ units of output, which are lost on intermediation activities (in section 4, the costs of intermediation will depend the value of intermediated funds; similar results can be obtained if the costs of intermediation are specified in terms of capital inputs rather than output). To summarize, the financial intermediation technology (when used) modifies the producer’s problem as follows: I will continue to assume that _l_<sup>_′_</sup> _< AK_ , so that the aggregate liquidity constraint continues to bind.

**Equilibrium with financial intermediation.** For _ι_ sufficiently small, I conjecture an equilibrium in which all producers use financial intermediation. Intuitively, liquidity-constrained producers are willing to pay a real cost in order to relax their constraints.

To prove this conjecture, recall that the assumption _l_<sup>_′_</sup> _< AK_ implies that in equilibrium, it must be the case that _R < A_ . Thus, the liquidity constraint is binding for every producer.

It is left to show that given _R_ , producers find it optimal to use the financial intermediation technology. When a producer uses the intermediation technology, he increases the amount of capital that he can employ (given _R_ ). If intermediation were free ( _ι_ = 0), this would be a strict gain, as _A > R_ , so profits are strictly increasing in capital. Continuity implies that producers

> 11Intermediation costs are modeled as the cost of monitoring (as in, for example, Diamond [1984]). However, the setup is sufficiently general to allow for a richer interpretation of intermediation costs, such as search costs as in Duffie and Strulovici [2011], or information acquisition costs such as in Farhi and Tirole [2012].

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Figure 2: The economy’s equilibria with and without intermediation <!-- Start of picture text --> K K d =l/R K d =l′/R<br>K S e e′<br>R=A R<br><!-- End of picture text --> Capital supply is constant at _K_<sup>_s_</sup> . The solid declining curve is the constrained demand for capital without intermediation. The intersection (point _e_ ) is the equilibrium in the no-intermediation economy. The use of a financial intermediation technology causes an outward shift of the constrained demand curve, which is illustrated with the dotted line. The equilibrium with financial intermediation is the point _e_<sup>_′_</sup> .

opt for intermediation even when _ι >_ 0 but sufficiently small.

It follows that for _ι >_ 0 sufficiently small, all producers use financial intermediation in equilibrium. Despite the fact that producers privately find intermediation profitable, aggregate output is lower compared to the nointermediation economy, as the costs of intermediation are socially wasted: The intuition is straightforward: privately, each producer would like to increase his liquidity in order to buy more capital. However, as the entire capital stock is already employed, intermediation works only towards increasing the price of capital without expanding production. Figure 2 illustrates graphically the equilibrium of this economy with and without financial intermediation.

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**The partial equilibrium view.** The result that financial intermediation reduces equilibrium output may seem counter-intuitive. It is therefore useful to illustrate how the standard intuition can be recovered from partial equilibrium analysis of this model, that ignores the endogenous determination of the price of capital ( _R_ ).

Consider an economy that uses financial intermediation. The equilibrium capital bill is given by _RK_ = _l_<sup>_′_</sup> . Holding _R_ fixed, one would erroneously conclude that financial intermediation increases the employment of capital: absent financial intermediation, the capital bill would be bounded by _l < l_<sup>_′_</sup> , leaving part of the capital stock unemployed. More broadly, ignoring the endogenous determination of the costs of inputs leads to an overestimate of the extent to which financial intermediation increases efficiency, as, absent financial intermediation, input prices would be lower and producers would be able to employ more inputs with their internal funds.

**Financial crises.** While the partial equilibrium analysis leads to misleading conclusions regarding the social value of financial intermediation, it may be useful for thinking about “partial equilibrium” situations, such as financial crises. Consider a simple model of financial crises, in which the intermediation technology ceases to “work”, while the price of inputs remains fixed in the short run. In other words, liquidity drops from _l_<sup>_′_</sup> to _l < l_<sup>_′_</sup> , but _R_ remains at its pervious level.

This type of financial shock would lead to a drop in employment and output, as the available liquidity is insufficient to employ all inputs at the price _R_ . This suggests that while there is an argument for reducing the “steady-state” size of the financial system, there is still a case for bailing out the financial system during financial crises.

**The non-monotone implications of financial development.** It is interesting to note that this model predicts a _non-monotone relationship_ between output and financial development. When financial intermediation is

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prohibitively costly ( _ι_ is sufficiently large), producers refrain from using it and output is at its first best level. For smaller values of _ι_ , financial intermediation is used in equilibrium, and output is lower.

However, conditional on _ι_ low enough such that intermediation is used, the resources spent on intermediation are increasing in _ι_ (equation 6).<sup>12</sup> Thus, a smaller value of _ι_ , which can be interpreted as a more efficient financial technology, implies a smaller output loss. The picture that emerges is therefore a non-monotone one: output is maximized either when _ι_ = 0, or when _ι_ is in the range that financial intermediation is not used at all. In the interim, there are resources wasted on financial intermediation, but the resource cost is smaller when the cost of intermediation ( _ι_ ) is smaller.<sup>13</sup>

# **3.1 A generalized real model**

Before presenting the dynamic monetary model, it may be useful to take an interim step and generalize the model’s conclusion on two important dimensions while still abstracting from monetary concerns.

Consider the following two extensions: first, assume that capital supply is increasing in the price of capital, _R_ . There is an increasing cost of supplying capital; thus, as the demand for capital increases, there is an equilibrium increase both in the supply of capital and in its price.

Second, assume that there are heterogeneous producers. The productivity of producer _i_ is denoted by _Ai_ .

It is easy to cook up examples where, given these extensions, introducing a financial intermediation technology increases output. For example, consider an economy where _R_ is fixed. In this case, the producer’s decision to use

> 12The expression in equation 6 is true only for _ι >_ 0 sufficiently small; in the interim, there is a region in which intermediation is used but not by all agents.

> 13More generally, in this model, the output implications of financial development (or technological progress in the financial industry) depend on the elasticity of the use of financial services. If financial development makes agents spend more resources on financial services, it reduces output. Alternatively, if it makes agents reduce their expenditure on financial intermediation, it increases output.

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financial intermediation is efficient: he is right to take the price as given, and tradeoff the cost of intermediation with the benefits of increased pledgeability (at the given price). There is no price externality.

Alternatively, maintaining the assumption that the capital supply is fixed, financial intermediation may improve the allocation of capital in the presence of heterogeneous producers. Notice that producers find it optimal to hire capital only when _Ai > R_ . Financial intermediation leads to an increase in pledgeability and hence an increase in the demand for capital, that translates into an increase in _R_ . This increase in _R_ discourages producers with low productivity from hiring capital, freeing up capital for more productive users. Depending on the the distribution of productivities and the cost of financial intermediation, intermediation may increase or decrease output.

Given these extensions, the price externality discussed in the previous section may not be strong enough to deem financial intermediation entirely un-useful. However, regardless, it creates an inefficiency, and there are gains from restricting the amount of intermediation.

**Proposition 1** _In the above environment, consider a planner who can set a tax on financial intermediation (the cost of intermediation that producers face is_ (1 + _τ_ ) _ι). The planner’s objective is to maximize output net of intermediation costs. Whenever the supply of capital is not entirely elastic, the planner chooses some τ >_ 0 _._

The proof of this proposition, together with other omitted proofs, is in the appendix. The proposition implies that there is excessive financial intermediation in an “unregulated” equilibrium, in which producers face the undistorted price of financial services. This result is due to the price externality discussed in detail in the previous section: producers fail to internalize that, when they use financial services, they cause an increase in the price of capital, that makes it more costly for everyone to produce. They are therefore “too quick” to spend resources on financial services.

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# **4 A dynamic monetary model**

In the model in the previous section, liquidity was determined only by pledgeability constraints. There was no notion of producers dynamically accumulating _liquid reserves_ , in anticipation of binding liquidity constraints. How does the incentive to accumulate liquid reserves alter the conclusions, if at all?

In this section, I allow producers to accumulate money that can be used for the purchase of inputs. While the accumulation of money and the accumulation of capital are privately substitutes, from a social perspective, they are not: holding large amounts of liquid reserves is socially desirable.<sup>14</sup> The analysis of the dynamic monetary model highlights that, in addition to a “real” price externality, financial intermediation is associated with a _nominal_ price externality. The decision to borrow money from idle money holders increases the money in circulation, and hikes up the _nominal_ demand for capital. This causes the nominal price of capital to increase, and leads to a decline in equilibrium real balances. When intermediation is costly, the increase in the price of capital may be entirely nominal; thus, the benefits of a real price appreciation in terms of allocative efficiency and capital supply disappear, and we are left again with a purely wasteful financial system.

Compared to the model in section 3, the model in this section allows for richer welfare analysis, that incorporates distributional concerns. It is fairly straightforward to show that in the simplified framework in the previous section, intermediation may be wasteful in terms of output but is not necessarily Pareto inefficient, as capital suppliers benefit from a higher price of capital. In the dynamic version of the model, this is no longer the case: intermediation may reduce both equilibrium output and equilibrium consumption for

> 14This result is in the spirit of Friedman [1969]. Recently, there has been some research focused on the idea that “liquidity hoarding” is socially harmful. Most of this literature focuses on crisis situations, in which the price level is effectively fixed in the short run. A notable exception is Malherbe [2012], who illustrates that low real balances may be socially desirable as they mitigate adverse selection.

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every agent.

# **4.1 Setup**

Consider an economy with a unit measure of infinitely lived agents, indexed _i ∈_ [0 _,_ 1]. Unlike the model in section 3, the decision whether to become a “producer” or a “capital supplier” will be determined endogenously in every period. Time is discrete and indexed _t ∈{_ 0 _,_ 1 _, ..}_ . In every period, each agent receives an i.i.d productivity shock, _Ai,t_ , which allows him to operate an _Ai,tK_ production technology. Denote by _F_ ( _·_ ) the cumulative density of _Ai,t_ , and denote by _f_ ( _·_ ) the probability density function of _Ai,t_ , where _f_ ( _·_ ) takes positive values on [0 _, A_<sup> ̄</sup> ].

Each agent ( _i_ ) has some initial endowment of capital, _ki,_ 0, and some initial endowment of _money_ , _mi,_ 0. The within-period timing of the model (without financial intermediation) is summarized in figure 3. Denote by _ki,t_ and _mi,t_ the amounts of capital and money with which agent _i_ enters period _t_ . As agents’ productivity shocks are i.i.d, the distributions of _ki,t_ and _mi,t_ are independent from _Ai,t_ ; thus, there is a mismatch between the owners of capital and its most productive users. To reduce this mismatch, a market opens in which agents can trade capital for money, before production takes place. In other words, productive agents can use their money to buy additional capital for production; unproductive agents can sell their capital in exchange for money. In this market, there is essentially a cash in advance constraint on the purchase of existing capital.<sup>15</sup> The _nominal_ price of capital in this market (at time _t_ ) is _Rt_ . The net amount of capital purchased by agent _i_ at time _t_ is denoted _k_<sup> ̃</sup> _i,t_ . A negative _k_<sup> ̃</sup> _i,t_ indicates that the agent is a net seller of capital. The nominal value of capital that an agent can buy is bounded by his money, _mi,t_ . The amount of capital that an agent can sell is

> 15See Abel [1985] or Stockman [1981] for models of cash in advance constraints on the purchase of inputs. However, money can be interpreted here more broadly as transferable claims on output.

16
bounded by his capital ( _ki,t_ ): This setup departs slightly from the setup in section 3, in that absent financial intermediation, no post-production output can be pledged: the only way that producers can purchase additional capital is by using their liquid reserves. The results trivially extend to more similar settings in which producers can pledge some post-production output even without financial intermediation.

After production takes place, a second market opens in which agents can buy and sell the final good at the nominal price _pt_ . This means that producing agents can sell the final good in exchange for money, and unproductive agents can use their money holdings to buy goods.

At the end of the period, agents decide how much to consume, and how much to save towards the next period. Agents can save in two ways: they can carry over money to the next period ( _mi,t_ +1), or use current output to install physical capital to be used or sold in the next period ( _ki,t_ +1).

Denote the consumption of agent _i_ at time _t_ by _ci,t_ . The agents’ utility function is given by _Ui_ ( _{ci,t}_<sup>_∞_</sup> _t_ =0<sup>) =</sup><sup>_E_(�</sup><sup>_∞_</sup> _t_ =0<sup>_βt_ln(</sup><sup>_ci,t_)).</sup> Social welfare is the average of expected utilities, where all agents are 1 weighted equally (�0<sup>_E_(</sup><sup>_Ui_(</sup><sup>_{ci,t}_</sup> _t_<sup>_∞_</sup> =0<sup>))</sup><sup>_di_).</sup> Let _M_ denote the aggregate money supply, and let _Kt_ denote the aggregate supply of capital at time _t_ . The money supply is assumed to be constant across time. Capital fully depreciates after one period.<sup>16</sup>

> 16The analysis can be generalized to allow for a depreciation rate 1 _≤ δ <_ 1, as long as 1 _− δ <_ 1 _−ββ_<sup>_E_(</sup><sup>_A_)(thisconditionisnecessaryforasolutioninwhichthereisacapital</sup> market in equilibrium with _R < ∞_ ). In this case, the analysis carries through with a modified productivity distribution, _A_<sup>ˆ</sup> = _A_ + 1 _− δ_ . An agent that employes _k_ units of capital can sell _A_ + 1 _− δ_ units of output at the end of the period.

17
Figure 3: The within-period timeline of the no-intermediation economy

|Agents enter|Ai,t|1<sup>st </sup>market:|Production|2<sup>nd</sup>market:|Consumption|
|---|---|---|---|---|---|
|the period|revealed|capital sold||output sold|(ci,t) and|
|with mi,t, ki,t||for money (R)||for money (p)|saving (mi,t+1, ki,t+1)|

# **4.2 The no-intermediation economy**

I restrict attention to recursive equilibria. A recursive equilibrium is defined as follows. There are three vectors of state variables, _{Ai}i∈_ [0 _,_ 1], _{ki}i∈_ [0 _,_ 1] and _{mi}i∈_ [0 _,_ 1]. To save on notation, I will denote the set of state variables by _S_ = _{_ ( _Ai, ki, mi_ ) _}i∈_ [0 _,_ 1]. A recursive equilibrium of the no-intermediation economy is defined as a price function _p_ ( _S_ ), a capital price function _R_ ( _S_ ), a set of consumption plans _{ci_ ( _S_ ) _}i∈_ [0 _,_ 1], capital accumulation plans _{ki_<sup>_′_(</sup><sup>_S_)</sup><sup>_}i∈_[0</sup><sup>_,_1],</sup> money accumulation plans _{m_<sup>_′_</sup> _i_<sup>(</sup><sup>_S_)</sup><sup>_}i∈_[0</sup><sup>_,_1]andcapitalpurchases</sup><sup>_{k_ ̃</sup><sup>_i_(</sup><sup>_S_)</sup><sup>_}i∈_[0</sup><sup>_,_1]</sup> that jointly solve the following:

1. Agent _i_ ’s optimization problem:

s.t. the inequalities in equation 7; _m_<sup>_′_</sup> _i_<sup>_≥_0;</sup><sup>_k_</sup> _i_<sup>_′≥_0;andthebudget</sup> constraint:

- 1

- 2. Capital market clearing: �0<sup>_k_ ̃</sup><sup>_idi_= 0</sup>

- 1

- 3. Money aggregation: �0<sup>_m_</sup> _i_<sup>_′di_=</sup><sup>_M_</sup>

It is fairly straightforward to show that any equilibrium is characterized by a cutoff _<u>A</u>_ such that all agents with productivities _Ai >_ _<u>A</u>_ produce as 18
much as they can (given their capital and money supplies), and all agents with productivities _Ai <_ _<u>A</u>_ do not produce. To see this, note that an agent finds it optimal to produce only if the following condition holds: The left hand side is the nominal return from employing one unit of capital. The right hand side is the nominal price of capital. If this condition holds, the agent can generate more revenue from employing his own capital than from selling it to another producer. The same condition also implies that the agent finds it optimal to use his money to buy capital: with one unit of money, the agent can buy _R_<sup><u>1</u>units of capital, that generate a nominal</sup> revenue of<sup>_<u>pAi</u>_Thealternativestrategyofholdingmoneyyieldsawithin-</sup> _R_<sup>.</sup> period return of 1. Dividing both sides of the above inequality by _R_ yields the equivalent condition,<sup>_<u>p</u>_</sup> _R_<sup>_Ai>_1.</sup> The following lemma characterizes the unique<sup>17</sup> recursive equilibrium of the no-intermediation economy:

**Lemma 1** _There is a unique recursive equilibrium in the no-intermediation economy, in which:_

_1. The real price of capital,_<sup>_<u>R</u>_</sup> _p_<sup>_,andtheproduction_</sup> _β_ <u>�</u> _<u>AA</u>_ ̄ _Af_ ( _A_ ) _dA_<sup>_threshold,_</sup><sup>_<u>A</u>_</sup> _<u>,</u> are time invariant and jointly satisfy:_ _<u>A</u>_ =<sup>_<u>R</u>_</sup> _p_<sup>=</sup> 1 _−βF_ ( _<u>A</u>_ <u>)</u> _._

- <u>))</u> _M_

- _2. The nominal price of capital R is given by: R_ =<sup><u>(1</u></sup><sup>_−_</sup> _F_<sup>_F_</sup> ( _<u>A</u>_<sup><u>(</u></sup><sup>_<u>A</u>_</sup> <u>)</u> _K ._

_3. The consumption of an agent with Ai ≥_ _<u>A,</u> ki and mi is: ci_ = (1 _− β_ ) _Ai_ ( _ki_ +<sup>_<u>m</u>_</sup> _R_<sup>_<u>i</u>_)</sup><sup>_.TheconsumptionofanagentwithAi<_</sup><sup>_<u>A</u>_</sup> _, ki and mi is: ci_ = (1 _− β_ <u>)</u> _<u>A</u>_ <u>(</u> _ki_ +<sup>_<u>m</u>_</sup> _R_<sup>_<u>i</u>_)</sup><sup>_._</sup>

> 17Typically in models of fiat money, there are at least two equilibria: one in which money is valued and one in which the value of money is 0. Here, the equilibrium in which money is not valued is ruled out mechanically by the assumption that the nominal prices of capital and goods _p_ ( _S_ ) and _R_ ( _S_ ) are real-valued (if money were not valued, these nominal prices would be _∞_ ).

19
_5. Capital accumulation follows K_<sup>_′_</sup> =<sup>_<u>R</u>_</sup> _p_<sup>_K._</sup> In equilibrium, there is a time-invariant cutoff, _<u>A</u>_ <u>.</u> Log utility implies that all agents consume a fraction 1 _− β_ of their wealth, and save the rest in money and capital (in equilibrium, agents are indifferent between these two saving facilities).

Agents with _Ai ≥_ _<u>A</u>_ produce as much as they can: they employ their own capital ( _ki_ ) and use their money holdings to purchase additional capital ( _k_<sup> ̃</sup> _i_ =<sup>_<u>m</u>_</sup> _R_<sup>_<u>i</u>_).Theirwealthistheirproductionrevenue.</sup> Agents with _Ai <_ _<u>A</u>_ do not produce. They sell their physical capital to productive agents ( _k_<sup> ̃</sup> _i_ = _−ki_ ). Their real wealth is the sum of the revenue from their capital sales (<sup>_<u>Rk</u>_</sup> _p_<sup>_<u>i</u>_)andthevalueoftheirmoneyholdings(</sup><sup>_<u>m</u>_</sup> _p_<sup>_<u>i</u>_).</sup> Capital accumulation is a function of the real price of capital. In other words, a low nominal price of capital does not lead to less capital accumulation, provided that the nominal price of the final good is proportionately lower as well. This is why, from a social perspective, real balances (measured as<sup>_<u>m</u>_</sup> _R_<sup>or</sup><sup>_<u>m</u>_</sup> _p_<sup>)donotnecessarilycrowdoutphysicalcapital.</sup> Unlike the simplified model in section 3, output is not at its “first best” level (defined as the level of output that would be produced in an economy with no liquidity constraints<sup>18</sup> ). Capital is misallocated, since it is employed at an entire range of productivities <u>[</u> _<u>A,</u> A_<sup> ̄</sup> ]<sup>19</sup> ; output would increase if capital were reallocated from relatively unproductive producing agents to more productive ones. Traditionally, financial intermediation is thought of as a remedy to this type of misallocation. However, it turns out that misallocation may be just as bad in the presence of an unregulated financial sector;

> 18In this framework, the “first best” allocates the entire capital stock to the agent with the highest productivity - here, output would be _AK_<sup> ̄</sup> .

> 19The misallocation of capital as an equilibrium outcome of liquidity constraints is in the spirit of Kiyotaki and Moore [1997].

20
Figure 4: The within-period timeline with financial intermediation

|Agents enter<br>the period<br>with mi,t, ki,t|Ai,t<br>revealed|1<sup>st </sup>market:<br>•capital sold<br>for money (R)<br>•**borrowing**<br>**and lending**<br>**of money**|Production|**Loans**<br>**are**<br>**repaid**|2<sup>nd</sup>market:<br>output sold<br>for money (p)|Consumption<br>(ci,t) and<br>saving (mi,t+1, ki,t+1)|
|---|---|---|---|---|---|---|

in fact, if we take into account the fact that capital is employed inefficiently on financial intermediation, the allocation of capital may be even worse.

# **4.3 The intermediation economy**

Consider an economy identical to the one described above, in which there is a technology that allows for financial intermediation. Agents can use a monitoring technology that allows them to pledge post-production sales. Monitored producers can borrow money from non-producing agents to finance the purchase of additional capital.

Formally, the timing of the model is modified as follows (see figure 4). During the first market, in which agents exchange money for capital, agents can also exchange money for promises on post production output (where enforcing such promises requires capital inputs). After production takes place, borrowers repay lenders at the agreed upon rate.

Similar to the model in section 3, operating the intermediation technology is costly in real terms. Denote by _ki,t_<sup>_I_theamountofcapitalthatagent</sup><sup>_i_</sup> purchases with borrowed (“intermediated”) funds. With a slight departure from the model in section 3, I assume that the cost of intermediation is proportional to _ki,t_<sup>_I_.Formally, I assume that a fraction</sup><sup>_θ_of each unit of capital</sup> employed through intermediation is absorbed on intermediation activities. To illustrate, consider an agent with productivity _Ai_ that uses intermediation to finance the purchase of _ki_<sup>_I_unitsofcapital.Afraction</sup><sup>_θ_ofeachunitof</sup> capital is lost, so his net production is _Ai_ (1 _− θ_ ) _ki_<sup>_I_.</sup> 21
Unproductive agents can lend both their money reserves ( _mi_ ) and their nominal revenues from capital sales ( _−Rk_<sup> ̃</sup> _i_ ). A way to think about this is that there are several “rounds” (within each period) in which agents can trade capital for money, and lend the revenues from capital sales: at the beginning of the first round, agents can lend _mi_ and put up their capital for sale. Some of the capital will be sold in the first round; the nominal revenues from sold capital can be lent. A second round opens, in which productive agents use intermediated funds to buy more capital. Revenues from secondround capital sales are lent to productive agents, who use it to buy more capital, and so on and so forth, until the market clears. The bottom line is that an unproductive agent’s loanable funds are _mi_ + _Rki_ (assuming that all of his capital is sold, so _ki_ = _−k_<sup> ̃</sup> _i_ ).

Compared to the no-intermediation economy, agents have an additional choice variable which is how much money to borrow or lend. Denote the demand for borrowing by _m_ ̃ _i_ (a negative value implies that the agent is a lender). It is assumed that agents (who are, in this model, doubling as financial firms) are subject to a reserve requirement: only a fraction 1 _− γ_ (where 0 _< γ <_ 1) of their loanable funds can be lent, while the rest must be held in liquid reserves. Thus, the maximum amount that agent _i_ can lend is: The return to intermediated funds is denoted _Rm_ (in nominal terms; the real return in terms of output is<sup>_<u>R</u>_</sup> _p_<sup>_<u>m</u>_).</sup> Borrowers bear the costs of intermediation. An agent with productivity _A_ will want to borrow as long as the returns to intermediated funds exceed their costs: The left hand side is the nominal revenue generated by one unit of borrowed money: one unit of borrowed money can finance the purchase of _R_ <u>1</u> 22
units of capital. A fraction _θ_ of each unit is lost on intermediation, so the “net” production is<sup><u>(1</u></sup><sup>_−_</sup> _R_<sup>_θ_</sup><sup><u>)</u></sup><sup>_A_</sup> units of output, that are sold at the nominal price _p_ . The right hand side is the cost of one unit of borrowed money, _Rm_ .

Note that as long as the inequality above is strict, the agent will want to borrow an infinite amount. Thus, competition among constrained producers would necessitate an equality for _A_ = _A_<sup> ̄</sup> . Only agents with _A_ = _A_<sup> ̄</sup> will borrow in equilibrium, and they will be indifferent between borrowing and not borrowing. The equilibrium return to intermediation is therefore given by: For unproductive agents to be willing to lend, it must be the case that the nominal return to intermediated funds is greater than the within-period nominal return on holding money, which is 1. Thus, for intermediation to take place in equilibrium it must be the case that: This condition restricts the values of _θ_ under which the intermediation technology will be used in equilibrium. For high values of _θ_ , the equilibrium without financial intermediation is a stable one: for example, if _θ_ = 1, no unproductive agent will be willing to lend, as the nominal return to intermediation is 0, which is lower than the return to holding money. The exact condition under which intermediation will be used in equilibrium is as follows. Denote with superscript _NI_ equilibrium values of the no-intermediation economy. A sufficient condition for intermediation to be used in equilibrium is: Denote by _θ_<sup>0</sup> the value of _θ_ for which the above condition holds with 23
_A_ equality (<sup>_<u>pNI</u>_</sup><sup><u>(</u></sup> _R_<sup>1</sup><sup>_NI−θ_0) ̄</sup> = 1). If _θ_ = _θ_<sup>0</sup> , agents are indifferent between using intermediation or not; if _θ < θ_<sup>0</sup> , the equilibrium without financial intermediation is not stable, as at no-intermediation equilibrium prices, unproductive agents strictly prefer lending. I will therefore focus on the parameter range _θ < θ_<sup>0</sup> .

A recursive equilibrium of the intermediation economy is defined as a price function _p_ ( _S_ ), a capital price function _R_ ( _S_ ), a price function for intermediated funds _Rm_ ( _S_ ), a set of consumption plans _{ci_ ( _S_ ) _}i∈_ [0 _,_ 1], a set of capital accumulation plans _{ki_<sup>_′_(</sup><sup>_S_)</sup><sup>_}i∈_[0</sup><sup>_,_1],moneyaccumulationplans</sup><sup>_{m′_</sup> _i_<sup>(</sup><sup>_S_)</sup><sup>_}i∈_[0</sup><sup>_,_1],</sup> capital purchase plans _{k_<sup> ̃</sup> _i_ ( _S_ ) _}i∈_ [0 _,_ 1], intermediated money plans _{_ ̃ _mi_ ( _S_ ) _}i∈_ [0 _,_ 1] and plans for capital purchased with intermediation _{ki_<sup>_I_(</sup><sup>_S_)</sup><sup>_}i∈_[0</sup><sup>_,_1]that jointly</sup> solve the following:

1. Agent _i_ ’s optimization problem:

_V_ ( _Ai, ki, mi, R, p, Rm_ ) = max ln( _ci_ )+ _βEA_<sup>_′_</sup> _i_<sup>(</sup><sup>_V_(</sup><sup>_A_</sup> _i_<sup>_′, k_</sup> _i_<sup>_′, m′_</sup> _i_<sup>_, R′, p′, R_</sup> _m_<sup>_′_))</sup> _ki_<sup>_′,m′_</sup> _i_<sup>_,k_ ̃</sup><sup>_i,_ ̃</sup><sup>_mi,k_</sup> _i_<sup>_I,ci_</sup> s.t. the inequalities in equation 7; the inequality in equation 11; _m_<sup>_′_</sup> _i_<sup>_≥_0;</sup> _ki_<sup>_′≥_0;</sup><sup>_m_ ̃</sup><sup>_i−Rk_</sup> _i_<sup>_I≥_0;andthebudgetconstraint:</sup> _pci_ + _pki_<sup>_′_+</sup><sup>_m′_</sup> _i_<sup>=</sup><sup>_mi_+</sup><sup>_m_ ̃</sup><sup>_i_(1</sup><sup>_−Rm_)</sup><sup>_−R_( ̃</sup><sup>_ki_+</sup><sup>_k_</sup> _i_<sup>_I_)+</sup><sup>_pAi_(</sup><sup>_ki_+ ̃</sup><sup>_ki_+(1</sup><sup>_−θ_)</sup><sup>_k_</sup> _i_<sup>_I_)</sup>

- 1

- 2. Capital market clearing: �0<sup>( ̃</sup><sup>_ki_+</sup><sup>_k_</sup> _i_<sup>_I_)</sup><sup>_di_= 0</sup> 1

- 3. Money aggregation: �0<sup>_m_</sup> _i_<sup>_′di_=</sup><sup>_M_</sup>

The following proposition characterizes the properties of the recursive equilibrium:

# **Proposition 2** _For θ < θ_<sup>0</sup> _,_

24
_1. There exists a unique recursive equilibrium. For θ sufficiently large, the equilibrium is welfare inferior to the no-intermediation economy._ _2. The return to intermediated funds (Rm) is decreasing in θ, and approaches 1 as θ → θ_ 0 _._ _3. Assume that mi and ki are equally distributed across agents. Denote by ci_ ( _θ_ ) _the equilibrium consumption of agent i given θ, and let c_<sup>_NI_</sup> _i denote the agent’s consumption in the no-intermediation economy. At the limit θ → θ_<sup>0</sup> _, the values of_<sup>_<u>R</u>_</sup> _p_<sup>_andK′convergetotheirlevelsinthe_</sup> _no-intermediation equilibrium, and:_ The welfare comparison with the no-intermediation economy depends on _θ_ . For _θ_ close to 0, the “standard” intuition holds, and financial intermediation increases output. The transfer of money to the most productive agents improves the allocation of capital within the productive sector. When this is done at a negligible real cost, equilibrium output increases. Intermediation may also imply a favorable redistribution of surplus, as unproductive agents can realize high returns to their intermediated funds.

However, these acclaimed benefits of financial intermediation are relevant only when _θ_ is small; for _θ_ close to _θ_ 0, welfare is lower than in the nointermediation economy. The intuition behind the welfare loss is as follows. For intermediation to improve the allocation of capital, it must induce inefficient producers to switch over from self-financing to lending. However, if the costs of intermediation are high, self-financing producers will continue to opt for production; the funds channeled through intermediation will originate primarily from unproductive agents, who would otherwise choose to hold idle money reserves. The capital purchased with these funds would be relatively unproductive, as a large fraction of it would be lost on intermediation.

25
In fact, as _θ → θ_ 0, the price externality of financial intermediation is purely nominal. At the limit, the real price of capital is the same as in the no-intermediation economy, and the decision whether or not to become a producer remains the same as well. The only prices that change are the nominal prices: instead of holding idle reserves, unproductive agents lend their money (at a rate of return close to 1). This inflates the nominal price of capital. In turn, the higher nominal price of capital implies that the return to carrying over money to the next period is lower: one unit of money will be able to purchase less capital. The lower return to holding money translates into a higher nominal price of the final good ( _p_ ).

At the limit _θ → θ_ 0, the financial intermediation technology is analogous to a counterfeit money printing machine. Financial intermediation increases the amount of money in circulation, which raises nominal prices. As the real price of capital remains unchanged, production decisions and capital accumulation decisions - that depend the real price of capital - are the same as in the no-intermediation economy. From a social perspective, the resources spent on financial intermediation are analogous to the operating costs of a counterfeit-money printing machine.

**How realistic is the case** _θ → θ_ 0 **?** One way to gauge at this is by looking at the return to deposits. By Proposition 2, the return to deposits approaches 1 only as _θ →− θ_ 0. As a deposit rate of 1 is close to observed levels in the US,<sup>20</sup> the choice _θ_ = _θ_ 0 does not seem unrealistic.

Under this assumption, we can use equation 16 to quantify the implied consumption gain from eliminating the financial system. To calibrate the 1 _−F_ <u>(</u> _<u>A</u>_ <u>)</u> expression in equation 16, note that, in this model, _F_ ( _<u>A</u>_ <u>)</u> is the ratio of producers to lenders. Let _L_ denote the average amount that non-producers lend. The total amount of lending is therefore _LF_ <u>(</u> _<u>A</u>_ ). This amounts to

> 20In the US, most checking accounts bear no interest. However, there are some services associated with checking accounts (such as access to ATMs) that are provided to depositors free of charge. This can be thought of as a small return to deposits.

26
_LF_ <u>(</u> _<u>A</u>_ <u>)</u> 1 _−F_ ( _<u>A</u>_ <u>)</u><sup>unitsof“loans”perproducer,whichisalsotheaveragesizeofloans.</sup> For the average loan, I use $550 _,_ 000, the average size of corporate and industrial loans in the US in 2007.<sup>21</sup> For _L_ , I use $400 _,_ 000 times (1 _− γ_ ). $400 _,_ 000 is the average size of US household wealth in 2007, excluding housing wealth.<sup>22</sup> A fraction 1 _− γ_ of this wealth can be lent. We therefore have: In other words, by equation 16, the estimated consumption gains from eliminating the financial system are 137.5%. This is obviously an unrealistically high number.

Part of the problem is that, in this model, _θ_ captures both the marginal cost of financial intermediation and its average cost. In the presence of a decreasing returns intermediation technology, the average cost of intermediation is lower than its marginal cost, implying some productivity gains from using financial intermediation and some profits associated with intermediation activities. However, adding decreasing returns to the intermediation technology is not a trivial extension.<sup>23</sup> To summarize, while this model highlights a price externality that potentially leads to quantitatively significant welfare losses, it is too soon to conclude that the financial system should be eliminated entirely. A richer quantitative investigation that takes into account decreasing returns (both in intermediation and in production) would be necessary in order to assess the optimal scope of financial intermediation.

> 21Data source: Average Loan Size for All C&I Loans, All Commercial Banks (EAANQ), Federal Reserve Bank of St. Luis (FRED database)

> 22Data source: table 1.B, Wolff [2010].

> 23When profits from intermediation are included in income, the model is no longer linear and becomes harder to solve analytically. I therefore reserve this important quantitative exercise for future work.

27
**Excessive financial intermediation in an unregulated economy.** While it is difficult to use this model to quantitatively assess the “net” welfare implications of financial intermediation, the insight of Proposition 1 extends to this richer framework: an unrestricted financial system absorbs too many inputs. The proposition below summarizes this result:<sup>24</sup>

**Proposition 3 (Generalization of Proposition 1)** _when γ →_ 0 _, there are excessive resources spent in equilibrium on financial intermediation. There exists γ_<sup>0</sup> _such that for every γ < γ_<sup>0</sup> _, the equilibrium allocation given γ is welfare inferior to the allocation given γ_<sup>0</sup> _._

# **5 Conclusion**

The prevailing sense that the financial sector is “too large” may at first seem at odds with traditional economic theory. Typically, in hyper-competitive environments such as the financial sector, income reflects the contribution to output.

This paper suggests that the financial sector is inherently different. The income generated by the financial sector does not reflect its contribution to output, because of the partial equilibrium nature of this income. Unlike other sectors, if financial intermediation were restricted, the economy’s need for it would decline as well, as producers would face lower input prices and would be better able to self-finance. As agents do not internalize this price externality, there is excessive financing in an unregulated equilibrium.

> 24Unlike Proposition 1, the proposition is framed in terms of a reserve requirement rather than a tax on intermediation services. The implications are the same: both are instruments to restrict the usage of financial services.

28