metadata: authors: 0: author: Eden,Maya
count: World
docna: 0: docna: Financial distortions and the distribution
            of global volatility
docty: Policy Research Working Paper
subtopic: Consumption,Fiscal & Monetary Policy,Trade and Services,Crime and Society
teratopic: Macroeconomics and Economic Growth,Finance and Financial Sector Development,Private Sector Development
abstracts: cdata!: Why are emerging economies excessively
            vulnerable to shocks to external funding? What was the role
            of financial flows from emerging to developed economies in
            setting the stage for the subprime crisis? This paper
            addresses these questions in a simple general equilibrium
            framework that emphasizes the aggregate implications of the
            misallocation of funds on the micro level. The analysis
            shows that the misallocation of funds amplifies volatility
            even in a closed economy. Financial integration between
            relatively distorted emerging economies and relatively
            undistorted developed economies leads to a further
            divergence in volatility, thereby providing a new and simple
            explanation for the divergent trends in output volatility up
            to the recent crisis. In the integrated environment, cheap
            funding leads to an endogenous deterioration of the
            financial system in developed economies. These predictions
            are consistent with a wide variety of microfoundations, in
            which distortions cause productive projects to be relatively
            more sensitive to aggregate shocks. The paper provides some
            empirical evidence for these microfoundations.
repnme: repnme: Financial distortions and the distribution
            of global volatility
display_title: Financial distortions and the
            distribution of global volatility
listing_relative_url: /research/2012/01/15593059/financial-distortions-distribution-global-volatility
topicv3: Trade in Services m1326928 780,Criminal Justice m1326993 1014,Macroeconomic and Structural Policies
            m1327380 439
publishtoextweb_dt: 2012-01-03T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Finance and Financial Sector Development,Private Sector Development
no_of_pages: 74
author_keys: 0: author_key: 1172765
model_extractions: WPS5929 Policy Research Working Paper 5929 Financial Distortions and the Distribution of Global Volatility _Maya Eden_ The World Bank Development Research Group Macroeconomics and Growth Team January 2012
Policy Research Working Paper 5929

# **Abstract**

Why are emerging economies excessively vulnerable to shocks to external funding? What was the role of financial flows from emerging to developed economies in setting the stage for the subprime crisis? This paper addresses these questions in a simple general equilibrium framework that emphasizes the aggregate implications of the misallocation of funds on the micro level. The analysis shows that the misallocation of funds amplifies volatility even in a closed economy. Financial integration between relatively distorted emerging economies and relatively undistorted developed economies leads to a further divergence in volatility, thereby providing a new and simple explanation for the divergent trends in output volatility up to the recent crisis. In the integrated environment, cheap funding leads to an endogenous deterioration of the financial system in developed economies. These predictions are consistent with a wide variety of microfoundations, in which distortions cause productive projects to be relatively more sensitive to aggregate shocks. The paper provides some empirical evidence for these microfoundations.

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
# Financial Distortions and the Distribution of Global Volatility

## Maya Eden<sup>_∗_</sup> The World Bank, DECMG

January 3, 2012

**Abstract**

Why are emerging economies excessively vulnerable to shocks to external funding? What was the role of financial flows from emerging to developed economies in setting the stage for the subprime crisis? This paper addresses these questions in a simple general equilibrium framework that emphasizes the aggregate implications of the misallocation of funds on the micro level. The analysis shows that the misallocation of funds amplifies volatility even in a closed economy. Financial integration between relatively distorted emerging economies and relatively undistorted developed economies leads to a further divergence in volatility, thereby providing a new and simple explanation for the divergent trends in output volatility up to the recent crisis. In the integrated environment, cheap funding leads to an endogenous deterioration of the financial system in developed economies. These predictions are consistent with a wide variety of microfoundations, in which distortions cause productive projects to be relatively more sensitive to aggregate shocks.

The paper provides some empirical evidence for these microfoundations.

**JEL Classification:** E44, F36, G01, G15 **Sector Board:** FSE

**Keywords:** financial distortions, log supermodularity, emerging market volatility, the Great Moderation, financial crises, matching

> _∗_ This article is based on the first chapter of my thesis at MIT. I am very grateful to my advisors Ricardo Caballero, Arnaud Costinot and Guido Lorenzoni for their invaluable input. I have also benefited from comments made by Daron Acemoglu, George-Marios Angeletos, Harjoat Bhamra, Dave Donaldson, Ana Fostel, Veronica Guerrieri, Bengt Holmstrom, Leora Klapper, Aart Kraay, Roberto Rigobon, Luis Serven, Jenny Simon, Ivan Werning, participants of the NBER Summer Institute 2010 (IFM) as well as participants of various other conferences and seminars. I thank the World Economy Laboratory (WEL) for financial support. All errors are mine. This paper reflects my own views and not necessarily those of the World Bank, its Executive Directors or the countries they represent. Please send comments to meden@worldbank.org.

<mark>1</mark>
# **1 Introduction**

The patterns of global volatility over the last few decades have raised many questions regarding the consequences of globalization. For emerging economies, financial integration was typically associated with episodes of extreme volatility, often related to fluctuations in the supply of external funding. At the same time, for developed economies, fluctuations in the supply of funds did not seem to be an important source of volatility, at least not until the recent crisis<sup>1</sup> . Further, evidence suggests that the relative importance of non-technology shocks in developed economies was declining over the period of financial globalization, as many attributed the “Great Moderation” trend in output volatility to a decline in nonfundamental volatility<sup>2</sup> . Why were the initial effects of financial integration so different for emerging and developed economies?

The picture is complicated further by the recent crisis, that suggests that the consequences of financial integration on volatility in developed economies may have been highly complex. While fluctuations in external funding were not an important driver of volatility during normal times, it seems that the magnitude of flows towards developed economies may have led to an overflow of the financial system and a collapse from within. Many attribute the amplification of the crisis to the incapacity of the financial system to withstand even relatively small shocks, a fragility that was an equilibrium outcome of a global environment that flooded the financial system with liquidity. Did the global supply of funds play a role in setting the stage for the sub prime crisis?

This paper takes the view that the aggregate implications of financial distortions are central to these questions. I consider a model in which funding is the single input of production, and there are heterogenous projects. Distortions increase the sensitivity of relatively productive projects to aggregate fluctuations in the supply of funds. In reduced form, this type of misallocation can be represented as a 1See Demirguc-Kunt and Detragiache [1999], Kose et al. [2003] and Bekaert et al. [2006] for an empirical discussion of the differential effects of financial integration on emerging and developed economies. For literature emphasizing the importance of shocks to external funding to volatility in emerging markets, see Neumeyer and Perri [2005], Uribe and Yue [2006], Chang and Fernandez [2010] and Broner and Ventura [2010], among others.

> 2See Gali and Gambetti [2009] for a structural VAR decomposition of the components of the “Great Moderation”.

2
Figure 1: The Standard Deviation of Output Growh (a) Developed markets <!-- Start of picture text --> (b) Emerging markets<br><!-- End of picture text --> <!-- Start of picture text --> 2.5 2.5<br>ty in Developed and Emerging<br>2 2 Economies<br>1.5 1.5<br>1 1<br>0.5 0.5<br>0 0<br>1980-1989 1990-2003 2004-2011 1980-1989 1990-2003 2004-2011<br><!-- End of picture text --> The calculations are based on data from the IMF’s World Economic Outlook, September 2011. The calculation for developed markets are based on the series “Advanced Economies”, and the calculation for emerging markets are based on the series “Emerging and Developing Economies”. Growth rates are calculated based on the cumulative output produced by all countries in the group.

This figure plots the standard deviation of output growth in developed and emerging economies during three periods: the “pre-integration” period (1980-1989), the “integration” period (1990-2003) and the “post-integration” period (2004-2011) (see Chinn and Ito [2008] for a discussion of the timing of financial globalization). Two stylized facts are illustrated: (i) the initial divergence in volatility between emerging and developed economies upon financial integration, as illustrated by the decline in output volatility in developed economies between the periods 1980-1989 and 1990-2003, and the increase in output volatility in emerging economies over the same time; and (ii) the spike in volatility in both regions in the post integration period, that includes the subprime crisis.

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less steeply declining aggregate marginal return to funds: in efficient economies, projects are implemented in an order decreasing in their returns. The aggregate marginal return to funds is decreasing, as less and less productive projects are funded as the supply of funds increases. In distorted economies, the order in which projects are implemented is less correlated with their productivity. The marginal return to funding declines less steeply, as relatively productive projects are implemented with the marginal units of funding, while relatively unproductive projects are implemented inframarginally.

I embed this reduced form representation of distortions in a stylized general equilibrium model of financial integration. I begin by studying the closed economy equilibrium, and illustrate a tight link between financial distortions and aggregate output volatility. Shocks to the aggregate supply of funds are amplified by financial distortions, as distortions increase the vulnerability of relatively productive projects to aggregate fluctuations.

Next, I consider a global environment with a “distorted” emerging market region and an “efficient” developed market region, and characterize the integrated equilibrium under the short run assumption that the levels of distortion remain fixed. I show that financial integration leads to a further divergence in volatility between the two regions. In equilibrium, fluctuations in the global supply of funds adjust disproportionately through changes in the amount of funding supplied to emerging markets: an expansion in the supply of funds would lead to a larger expansion in emerging economies, as the projects implemented at the margin yield relatively higher returns. At the same time, a contraction in the supply of funds would lead to a larger contraction in emerging economies, as the set of projects funded inframarginally yield a relatively lower return. This presents a new and simple explanation for the divergence in volatility trends up to the recent crisis, based on an intuitive “conservation of volatility” law: the equilibrium counterpart of the increase in volatility in emerging economies is a decline in volatility in developed economies, as shocks to the domestic liquidity supply in developed economies adjust primarily through changes in the amount of funding supplied to emerging markets.

Finally, I study the medium run equilibrium in which the quality of the financial system in the developed world endogenously adjusts to the integrated environment.

4
I extend the model to allow banks to choose the level of distortion, where a higher level of distortion is associated with a lower cost. When financial integration is associated with a large drop in the price of funding, banks endogenously select a higher level of distortion. Intuitively, when funding is cheap, most projects should be implemented anyway; the returns to sustaining institutions that enable the differential contraction of productive and unproductive projects goes down. Interestingly, these endogenous institutional changes have a mixed effect on output and output volatility. While the output response to large contractions in the supply of funds is amplified, the deterioration in the financial system actually serves to increase and stabilize output during normal times. In the extreme case, the financial system implements all projects, regardless of small fluctuations in the price of funding, resulting in high and stable output. However, when the supply of funds contracts so much that the economy can no longer afford to run at full capacity, there is an efficiency loss resulting from the economy’s inability to absorb contractions through the discontinuation of the least productive projects.

The model’s predictions depend crucially on the assumption that the marginal return to funding is declining less steeply in more distorted economies. Formally, the key assumption is that the marginal return to funding is log supermodular in funding and the level of distortion. To assess the relevance of this assumption, one can ask (i) under which microfoundations it will hold and (ii) whether or not these microfoundations are themselves empirically relevant. I show that this assumption arises naturally in a wide variety of models in which the equilibrium is characterized by a stochastic matching between funding priorities and projects. Distortions create a mismatch, making better projects less likely to receive high priority, and relatively worse projects relatively more likely to receive a higher priority. I present empirical evidence for these properties using firm level data from emerging and developed economies. I find that in emerging economies, productive firms are relatively more sensitive to fluctuations in the aggregate supply of funds, and that the opposite is true for relatively less productive firms. I show that this type of mismatch can arise from many common sources of distortions, such as incomplete information, inefficient government intervention, collateral constraints and search frictions.

5
# **2 Related literature**

The results concerning the divergence in volatility between emerging and developed economies are related to several strands of literature. The idea that financial distortions exacerbate output volatility appears prominently in the context of collateral constraints. Kiyotaki and Moore [1997], Fostel and Geanakoplos [2008] and Caballero and Krishnamurthy [2001] are important examples, the latter two with specific applications to emerging market economies. The general formulation in this paper suggests that the link between financial distortions and volatility is not unique to collateral constraints, and is common to many forms of distortions. The mechanism in this paper is closest to Kiyotaki and Moore [1997], as the amplification of shocks is a result of a domestic inefficient allocation of resources that causes relatively productive projects to be more sensitive to aggregate fluctuations. However, the role of external funding in explaining emerging market volatility is closest to Fostel and Geanakoplos [2008]. In Fostel and Geanakoplos [2008], a small group of constrained investors hold emerging market assets. Shocks to the liquidity in the hands of these investors evidently translate into movements in the liquidity supply for emerging market projects. The focus of this paper is complementary to the one in Fostel and Geanakoplos [2008]: while their starting point is that emerging market projects are funded by a small group of “residual” investors, this paper uses financial distortions to endogenize the assumption that emerging market projects are “residual”.

Also related is the literature on volatility, development, and openness. The result that economies in earlier stages of development become more volatile with financial integration is in line with Obstfeld [1994], Greenwood and Jovanovic [1990], and Koren and Tenreyro [2009]. The focus in these papers is on the changes in the sectoral composition induced by better consumption diversification opportunities. If financial integration allows for better diversification, investors may be more inclined to take on high-risk projects, potentially increasing the aggregate riskiness of the economy. This mechanism is very different from the mechanism discussed in this paper, which does not rely on changes in sectoral composition. While sectoral composition seems like a plausible source for some shocks, particularly in lower stages of development, it seems like an unlikely explanation for 6
the heightened volatility of emerging markets associated with movements in external funds (such as sudden stops). Moreover, it provides a poor explanation for the common movements in emerging market economies, which have very different sectoral compositions.

Conceptually related is the work of Caballero et al. [2008], who study global imbalances as an outcome of financial integration in a world with heterogenous financial development. While the questions motivating these papers are different, both share the view that integration with a financially underdeveloped region is an important factor behind recent trends in the US economy. The work of Fogli and Perri [2006] links the Great Moderation with global imbalances by arguing that global imbalances are a natural artifact of the decline in volatility. In their model, the decline in volatility (relative to the rest of the world) reduces households’ relative incentives to accumulate precautionary savings. This paper proposes an alternative link between financial integration and the Great Moderation. In this model, financial integration decreases volatility in the developed world and increases volatility in emerging markets; it could be that as a result, through the mechanism in Fogli and Perri [2006], the external balance of the developed markets deteriorates. This combined mechanism demonstrates an additional channel through which financial underdevelopment in emerging markets may translate into global imbalances.

The results concerning the endogenous deterioration of the financial system in the developed world are broadly related to the literature on bubbles. As shown in Tirole [1985], environments in which the interest rate is low are fertile grounds for the formation of bubbles, and the presence of bubbles may lead to an expansion in output (as in Farhi and Tirole [2010] and Martin and Ventura [2010]). However, the mechanisms through which a low interest rate leads to an expansion are different: in the bubble literature, bubbles serve as additional sources of liquidity, which enable more economic activity. In this paper, low interest rates are indicative of a situation in which the global supply of liquidity is already high; the expansion results from an endogenous decision of intermediaries to implement projects indiscriminately, increasing the total amount of projects implemented.

Similar to the bubble-burst view of the crisis, this paper takes the view that the root of the crisis is a sudden contraction in the supply of liquidity. The contraction 7
in the supply of liquidity is not modeled here explicitly, and may be thought of as resulting from a burst of a bubble on an asset used for liquidity purposes (see Holmstrom [2008]). However, unlike the bubble-burst view of the crisis, in this model the burst of the bubble itself does not explain the full extent of the crisis. Rather, the crisis is amplified by the structural changes that the financial system underwent during the expansionary period. The emphasis on the role of financial frictions as an amplification mechanism of the crisis is shared with Hall [2009], Gertler and Kiyotaki [2010], and others. The view closest to this paper is the one expressed in Brunnermeier [2009] and Gorton [2008]. These papers discuss mechanisms through which a low interest rate environment led to a decline in lending standards and institutional changes which evidently amplified the subprime crisis. The model presented in this paper may be seen as a simple formalization grouping these phenomena.

This paper is also related to the empirical literature on the macroeconomic consequences of misallocation. Closest to this paper is Hsieh and Klenow [2009]. Similar to this paper, Hsieh and Klenow [2009] conduct an empirical study of the aggregate consequences of misallocation, without taking a stance on the type of distortion that causes resources to be allocated inefficiently. However, Hsieh and Klenow [2009] focus on the static productivity loss induced by misallocation, whereas I focus on the volatility induced by misallocation, or the amplification of contractions caused by the discontinuation of relatively productive projects.

Methodologically, this paper is related to the literature emphasizing the role of supermodularity and log supermodularity conditions in various economic fields. Prominent examples include, among others, Milgrom and Weber [1982] in auction theory; Bulow et al. [1985] in industrial organization; Jewitt [1987] and Athey [2002] in monotone comparative statics under uncertainty; and Costinot [2009] in international trade. Shimer and Smith [2000] consider a model in which heterogeneous agents search for partners for joint production, where the output produced by the match depends positively on each type. They use log supermodularity conditions on the joint production function to generate sufficient conditions for positive assortative matching. Broadly, the model in this paper is the inverse exercise: I characterize conditions on the matching process that deliver log supermodularity of the aggregate production function.

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# **3 An aggregate representation of misallocation**

There is a single consumption good and a single input of production called _funding_ and denoted _F ∈_ [0 _,_ 1]. Of course, this is a shortcut for a richer model in which funding is used to hire workers, rent capital and buy intermediate inputs. Fluctuations in _F_ can therefore be interpreted as fluctuations in employment; when _F_ = 1, all inputs are employed.

There is a set of _projects_ indexed _x ∈_ [0 _,_ 1]. Each project requires one unit of funding to implement. Projects are of heterogeneous productivity: if implemented, the project indexed _x_ produces _Ag_ ( _x_ ) units of output, where _A_ is the aggregate component of productivity and _g_ ( _x_ ) is the idiosyncratic component of productivity. Without loss of generality, I assume that _g_<sup>_′_</sup> ( _x_ ) _≤_ 0, so projects with lower indices are more productive.

Whether or not a project is implemented depends on the whether the aggregate supply of funding is high enough. For each project _x_ , there is a threshold _p_ = _p_ ( _x_ ), such that the project is implemented if and only if _F ≥ p_ . In principle, this threshold is an equilibrium object that is determined by a wide variety of factors, including the project’s productivity, its collateral, its connections to people in power, etc. Importantly for our purposes, this equilibrium object can be summarized as a _funding priority_ : when the aggregate supply of funds is _F_ , all projects with funding priorities _p ∈_ [0 _, F_ ] are implemented. The financial system is represented by a stochastic matching between funding priorities and projects. Let _φ_ be a reduced form parameter capturing the level of distortion. A higher _φ_ corresponds to a more distorted allocation. In an economy with distortion level _φ_ , the probability that project _x_ receives priority _p_ is given by _σφ_ ( _x, p_ ).

Aggregate output is denoted _Y_ . I assume that the matching takes place simultaneously in many different sub-locations, so aggregate output is deterministic and equal to the expected output produced by all implemented projects, that is, all projects with priorities _p ≤ F_ : 9
The aggregate marginal return to funding, denoted _y_ , is given by: I assume that better projects are relatively more likely to receive high priorities, so the marginal return to funding is weakly decreasing (<sup>_∂y_</sup> _∂F_<sup><u>(</u></sup><sup>_F,φ_</sup><sup><u>)</u></sup> _≤_ 0).

The key ingredient in the model is the following property, that states that the marginal return to funding is log supermodular<sup>3</sup> in the level of funding and the level of distortion:

**Property 1** _For any φ ≥ φ_<sup>_′_</sup> _and for any F ≥ F_<sup>_′_</sup> _,_

Property 1 can be understood as follows. Fix any two levels of funding, _F_<sup>_′_</sup> and _F_ , such that _F_<sup>_′_</sup> _≤ F_ . Property 1 requires that the ratio of the marginal returns to funding at _F_ and _F_<sup>_′_</sup> is relatively lower in more efficient economies; loosely stated, the (negative) slope of the marginal return to funding is relatively more steep in more economies.

This simple setup is sufficient for producing all of the macroeconomic insights that follow. To motivate Property 1, in section 7 I show that it is consistent with a wide variety of standard microfoundations, including models of informational frictions, collateral constraints, inefficient government intervention and search frictions. The common feature of these microfoundations is that distortions cause relatively more productive projects to receive lower funding priorities, making their implementation outcome more sensitive to changes in _F_ .

For the time being, consider the following stark microfoundation, that will be used to illustrate the results throughout the paper:

> 3 _′_ Recall that a function _f_ ( _x_ 1 _, x_ 2) is log supermodular in _x_ 1 and _x_ 2 if for any _x_ 1<sup>_< x_1and</sup><sup>_x′_</sup> 2<sup>_<_</sup> _x_ 2, we have that _f_ ( _x_ 1 _, x_ 2) _f_ ( _x_<sup>_′_</sup> 1<sup>_, x′_</sup> 2<sup>)</sup><sup>_≥f_(</sup><sup>_x′_</sup> 1<sup>_, x_2)</sup><sup>_f_(</sup><sup>_x_1</sup><sup>_, x′_</sup> 2<sup>).If</sup><sup>_f_isstrictlypositive,thiscondition</sup> implies that<sup>_<u>f</u>_</sup> _f_<sup><u>(</u></sup> (<sup>_x_</sup> _x_<sup>1</sup><sup>_<u>′</u>_</sup> 1<sup>_<u>,,xx</u>_</sup> <u>2</u><sup>_′′_</sup> 2<sup><u>))</u></sup><sup>_≤_</sup> _f_<sup>_<u>f</u>_</sup> (<sup><u>(</u></sup> _x_<sup>_x′_</sup> 1<sup>1</sup><sup>_,x,x_22)).If</sup><sup>_f_isstrictlypositiveanddifferentiable,thiscorrespondsto</sup> _∂_<sup>2</sup> ln _<u>f</u>_ <u>(</u> _x_ 1 _<u>,x</u>_ 2) _∂x_ 1 _∂x_ 2 _≥_ 0.

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**Random allocation example.** There are two types of economies: efficient ( _eff_ ) and distorted ( _dis_ ). In efficient economies, projects are implemented in the order of their productivity; the funding priority of project x is _p_ ( _x_ ) = _x_ . This means that the probability of being assigned priority _p_ = _F_ is 0 for all _x_ = _F_ , and 1 for _x_ = _F_ :

Given an aggregate supply of _F_ units of funding, output is given by the cumulative output produced by the _F_ best projects: The marginal return to funding is given by the productivity of the marginal project: In distorted economies, projects are implemented in an arbitrary order. The probability that priority _p_ = _F_ is assigned to project _x_ is constant: This randomness can be thought of as resulting from a wide range of distortions; for example, it could be that the financial sector lacks the expertise to evaluate projects, and must implement projects arbitrarily. Alternatively, the randomness could be indicative of an economy with extreme corruption, in which the implementation outcome is orthogonal to productivity.

Output is equal to the expected cumulative output produced by _F_ randomly drawn projects: The marginal return to funding is constant and equal to the average return to projects: 11
It is easy to see that this model is consistent with Property 1, as the marginal return to funding is declining in efficient economies, but constant in distorted economies. Formally, it is easy to check that for any _F_<sup>_′_</sup> _≤ F_ :

# **4 Closed economy equilibrium**

In this section I characterize the effects of financial distortions on volatility under autarky, and show that more distorted economies are more sensitive to fluctuations in the aggregate supply of funding.

In the closed economy, the supply of funding is given by an exogenous domestic liquidity supply, _Q_ . Domestic households supply liquidity to the financial system, in exchange for future returns. In this model, liquidity is defined simply as the supply side of funding. The market clearing condition is: After production takes place, the financial system repays households at a rate of _r_ units of output per unit of liquidity. I assume that _r_ is equated with the marginal return to funding. This can be thought of as a result of a competitive banking system in which banks compete for liquidity supply from households.

There are two sources of volatility: shocks to the domestic technology level _A_ , and shocks to the supply of liquidity, _Q_ . I assume that these shocks are independent<sup>4</sup> . Appendix C presents a model of liquidity supply in which liquidity supply fluctuations are driven by three primitive shocks: shocks to the money supply, shocks to risk aversion, and shocks to the ability of the private sector to generate promises for future repayment.

It is straightforward to show that, in the closed economy, the sensitivity of

> 4The assumption that shocks to _A_ and to _Q_ are independent is, of course, unrealistic, as periods of high productivity may imply that it is easier for entrepreneurs to issue promises on future returns, as in Kiyotaki and Moore [1997]. The independence of the two shocks is not necessary for any of the results, however separating the two types of shocks is convenient for expositional purposes.

12
output to productivity shocks is unrelated to the degree of financial distortions. However, more distorted economies are more sensitive to shocks to liquidity supply:

**Proposition 1** _For any given processes of A and Q,_

_1. Output is more volatile in more distorted economies:_ _2. The average productivity of funded projects is more sensitive to liquidity supply shocks in less distorted economies:_ The proof of the above proposition, together with other omitted proofs, is in the appendix. The intuition follows directly from Property 1. In efficient economies, the decline in the average productivity of projects mitigates the effect of an increase in funding. In distorted economies, a suboptimal set of projects is implemented, so some low-yield projects are implemented before higher-yield projects. This implies two things. First, some projects that should have been implemented are not implemented; their implementation takes place only when the supply of funding is higher, intensifying the returns to funding. Second, some projects that should not have been implemented are implemented, lowering the average productivity of funded projects. These two facts put together imply that the ratio of the marginal return to funding and the average return to funding is higher in distorted economies. In other words, liquidity abundance increases the efficiency of distorted economies relative to efficient economies both by alleviating the inefficiency caused by implementing a suboptimal set of projects and by allowing for the implementation of higher-yield projects. Using the random allocation example, figure 2 illustrates the properties of the closed economy equilibria in a distorted “emerging market” economy and an efficient “developed market” economy.

13
<!-- Start of picture text --> y d (F) y em (F)<br>Y d Y d Y em Y em<br>Q d Q d F d Q em Q em F em<br>(a) Developed markets (b) Emerging markets<br><!-- End of picture text --> Figure 2: The figure on the left depicts the closed economy equilibrium in efficient “developed” economies, and the figure on the right depicts the closed economy equilibrium in distorted “emerging” economies. In both economies there is a positive shock to liquidity supply. The average productivity declines in efficient economies and remains constant in distorted economies. The output response is therefore larger in distorted economies (in the sense that<sup><u>∆</u></sup> _Y_<sup>_<u>Y</u>_</sup> is larger).

# **5 Volatility divergence**

In this section I present a set of results concerning the divergence of volatility between emerging and developed economies following financial integration. I first present the globally integrated equilibrium, and then discuss equilibrium implications for small open economies.

The setup of the model is as follows. There are two regions of equal size: an emerging market region ( _em_ ) and a developed market region ( _d_ ). For the time being, I assume that the only difference between emerging and developed economies is that emerging economies are more distorted than developed economies: For simplicity, I denote _Yi_ = _Y_ ( _Ai, Fi, φi_ ) and _yi_ = _y_ ( _Ai, Fi, φi_ ), for _i ∈{em, d}_ . I assume that _var_ (ln( _Ad_ )) = _var_ (ln( _Aem_ ))<sup>5</sup> and that liquidity supply _Qi_ is independent from both foreign and domestic technology, _Ai_ and _Aj_ .

> 5The results trivially generalize to _var_ (ln( _Ad_ )) _< var_ (ln( _Aem_ )).

14
In order to isolate the effects of financial heterogeneity on the global equilibrium environment, it is convenient to assume that _Qd_ and _Qem_ are perfectly correlated. Assuming that liquidity supplies are perfectly correlated isolates the effects of financial heterogeneity because, under this assumption, financial integration between two _identical_ economies would have no effect on liquidity-supply driven output volatility. In contrast, independent liquidity supplies would imply that financial integration between two identical regions has a moderating effect on output in both regions, as shocks to liquidity supply are shared across regions. Replacing the assumption that _Qd_ and _Qem_ are perfectly correlated with the assumption that they are independent would therefore decrease volatility in both regions; however, the result that volatility induced by financial integration would be relatively higher for emerging economies would still hold.

# **5.1 Integrated equilibrium**

Assume that liquidity can move freely across regions. The global equilibrium is characterized by two equations: The first equation is a market clearing condition, stating that the total amount of funding, _Fem_ + _Fd_ , must be equal the global supply of liquidity, _Qw_ = _Qem_ + _Qd_ . The second condition is the optimality condition of the financial system, requiring that there is no gain from reallocating liquidity from one region to another<sup>6</sup> .

I denote autarkic values with superscript _a_ ( _F_<sup>_a_</sup> , _Y_<sup>_a_</sup> , etc). Denote by ∆the absolute value of the _average_ change in funding levels induced by financial integration: The value of ∆is determined in equilibrium as a function of the average sup-

> 6The results easily generalize if there is a constant wedge in marginal returns, that is, the second equilibrium condition is replaced with a condition of the form _yd_ ( _Fd_ ) = _wyem_ ( _Fem_ )

15
ply of liquidity, the financial distortions, and the relative productivities _AAemd_<sup>.In</sup> particular, there is always a value of _AAemd_<sup>forwhich∆=0.Forthepurposeof</sup> this exercise, I assume that ∆is small. The importance of this assumption is in assuring that the sensitivity of output to funding remains similar to its autarkic level. If this assumption is violated, the implications of financial integration on macroeconomic volatility depend more specifically on how the sensitivity of output with respect to funding changes with the level of funding.

The main result is stated in the proposition below:

**Proposition 2** _For_ ∆ _sufficiently small, financial integration exacerbates the volatility differences between emerging and developed markets:_

Financial integration leads to a divergence in volatility levels for two reasons<sup>7</sup> . First, financial integration is associated with a new source of fluctuations in funding, which is shocks to the relative productivity of emerging and developed economies (<sup>_<u>A</u>_</sup> _A_<sup>_<u>em</u>_</sup> _d_<sup>).Theseshocksleadtoasubstitutionoffundingacrossregions.</sup> Since, by proposition 1, financially-distorted emerging markets are more sensitive to fluctuations in funding than developed markets, this works towards exacerbating the differences in output volatility across regions.

Second, it turns out that shocks to the global supply of liquidity adjust disproportionately through changes in the supply of funding to emerging markets. This equilibrium property is closely related to the feature of financial distortions emphasized by Property 1. In developed markets, projects are implemented in an order decreasing in their returns: most implemented projects generate returns which well exceed _r_ , while most unimplemented projects generate returns which are well below _r_ . Fluctuations in the implementation threshold therefore have a relatively small impact on the amount of projects implemented in developed 7Proposition 2 easily generalizes to an equilibrium with many countries with different levels of distortions. In an integrated equilibrium, the sensitivity of each economy to shocks to the global supply of liquidity or to TFP will be an increasing function of its level of financial distortions. Differences in volatility levels will magnify upon financial integration.

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economies. In contrast, in emerging markets, the order in which projects are implemented is more arbitrary; this implies that the return generated by the next unit of funding is similar to the return generated by the previous unit. The same fluctuations in _r_ therefore induce larger fluctuations in the amount of implemented projects. Figure 3 illustrates this equilibrium property in the random allocation example<sup>8</sup> .

Generically, abstracting from productivity shocks, financial integration leads to less variation in _r_ from the developed market’s perspective, and more variation in _r_ from the emerging market’s perspective. Consequently, there is a divergence in liquidity-driven output volatility between emerging and developed economies.

<!-- Start of picture text --> y d (F) y em (F)<br>r<br>Y d Y em Y em<br>F d F em F em<br>Q w Q w<br><!-- End of picture text --> Figure 3: In this figure, the origin of the developed economy is on the left corner, and the origin of the emerging economy is on the right corner. The market clearing condition states that the distance between the two corners is equal to the global liquidity supply, _Qw_ . The intersection of the marginal returns to funding determines _r_ , and hence the division of _Qw_ into _Fd_ and _Fem_ . Shocks to the global liquidity supply adjust entirely through changes in the funding levels supplied to emerging markets, _Fem_ . An increase in _Qw_ of size ∆ _Qw_ is illustrated as a shift of the emerging economy’s origin to the right.

# The direction in which volatility levels change following financial integration is

> 8In the random allocation example, the equilibrium level of _r_ does not change following a shock to global liquidity supply. Rather, the shock is adjusted entirely through changes in the quantity of funding supplied to the emerging market region.

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potentially different in emerging and developed economies. In emerging economies, the volatility of funding necessarily increases upon integration. This is because funding becomes vulnerable to two new shocks: shocks to foreign liquidity supply ( _Qd_ ) and shocks to relative technology levels (<sup>_<u>A</u>_</sup> _A_<sup>_<u>em</u>_</sup> _d_<sup>).Indevelopedeconomies,</sup> funding also becomes vulnerable to shocks to relative technology, which works towards increasing volatility. However, funding becomes less sensitive to shocks to domestic liquidity supply ( _Qd_ ), since shocks to liquidity supply adjust primarily through movements in the funding supplied to emerging markets. The net effect on volatility depends on the relative importance of technology shocks and liquidity shocks. Specifically, if movements in the level of funding result primarily from variation in the supply of liquidity, financial integration will decrease the volatility of output in developed economies.

Under stronger assumptions regarding the relative importance of liquidity and technology shocks, it is possible to obtain stronger results concerning the direction in which volatility levels change following financial integration:

# **Proposition 3** _For_ ∆ _sufficiently small,_

_1. Financial integration increases the volatility of funding and the volatility of output in emerging markets:_ _2. If the variance of liquidity supply is sufficiently large compared to the variance of relative TFP, financial integration decreases the volatility of funding and the volatility of output in developed markets:_ These results provide some insight into the distinct behavior of emerging and developed markets following globalization. The theory above suggests that the 18
divergence in liquidity-driven output fluctuations may have been a result of developed markets effectively exporting their liquidity shocks to emerging markets.

# **5.2 Small open economies**

Given that much of the literature on the excess volatility of emerging markets has focused on small open economies, it is useful to study small open economies in the context of this global equilibrium environment.

I assume that each region is composed of a continuum of small open economies, identical within regions. Small open economies are subject to idiosyncratic productivity shocks, as well as to exogenous shocks to _r_ which result from changes in the global liquidity supply.

The first thing to note is that this model naturally implies comovements in emerging market economies. Compared to their developed counterparts, small open emerging markets are more severely affected by shocks to the global liquidity supply. The importance of global liquidity supply as a source of emerging market fluctuations naturally implies common movements in emerging market output levels. Similar to Fostel and Geanakoplos [2008], comovements in emerging market economies result from a common sensitivity to an external supply of funding.

Second, it is interesting to note that both in emerging and in developed markets, funding responds similarly to idiosyncratic productivity shocks and to shocks to the price of liquidity. This suggests a link between the heightened sensitivity of emerging markets to interest rate shocks (as in Neumeyer and Perri [2005] and Uribe and Yue [2006]) and the amplification of shocks to productivity (as in Caballero et al. [2005]). To see this link, note that in a small open economy, the level of funding is pinned down by a single indifference condition, equating the marginal product of funding with the world rate of return: From the formulation above, it is easy to see that funding is affected similarly by shocks to _r_ and shocks to _Ai_ . Essentially, in this model, the responsiveness of funding to either type of shock captures the density of projects which are implemented at the margin and collectively yield a return equal exactly to _r_ . A 19
small shock to the returns of these projects will shift them above or below the implementation threshold; similarly, small shocks to _r_ will determine whether or not the projects at the margin generate a return which justifies implementation. The result that small open emerging markets are relatively more sensitive to both shocks is closely tied to Property 1, as it guarantees that the density of projects implemented at the margin is higher.

The model presented in this section suggests the following conclusions regarding the role of financial institutions in determining the effects of financial integration on output volatility. Poor financial institutions in emerging markets exacerbate their sensitivity to funding, as well as increase the volatility of funding supplied to them. At times in which financial institutions are intact in developed markets, their superior ability to implement projects differentially serves both to stabilize equilibrium funding levels and to mitigate the effects of fluctuations in funding on output.

# **6 The endogenous deterioration of the financial system**

In section 5 it was assumed throughout that the quality of financial institutions remains fixed upon financial integration. While this may be a valid short-run assumption, the recent subprime crisis comes as a reminder that the quality of financial institutions may evolve with changing circumstances.

In section 6.1 I consider a model in which the financial system in the developed world deteriorates endogenously following financial integration. In section 6.2 I discuss the implications of the deterioration during “normal times”. I show that in the absence of large shocks, the deterioration of the financial system actually increases and stabilizes output in the developed world. In section 6.3 I show that the deterioration in the financial system amplifies large adverse shocks.

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# **6.1 Endogenous deterioration**

I extend the setup to allow for an endogenous adjustment in the quality of the financial system in the developed world. Banks can choose the level of financial distortions out of some finite set. There is a cost _λ_ ( _φ_ ) associated with choosing the level of distortions _φ_ , where _λ_ ( _·_ ) is decreasing. This cost should be thought of as the cost of sorting projects and overcoming other obstacles which stand in the way of an efficient allocation. For simplicity, I assume that banks consider only the mean price of liquidity when choosing the level of financial distortions, and do not take into account any uncertainty.

Given a price of liquidity _r_ , the banks choose the level of funding, _Fd_ , and the level of distortion, _φd_ , to maximize profits. The bank’s profits are given by: The following proposition characterizes the equilibrium response of the financial system to a global environment with the following two features: first, liquidity supply is high. The role of this assumption can be understood as follows. At low levels of funding, there is little incentive to invest in creating an efficient matching, as the scale of activity does not justify the cost. A marginal increase in funds will work towards countering this effect: the benefits of an efficient matching increase as there is more funding to be allocated efficiently. At some point, as we increase the level of funding, this type of scale effect works in the opposite direction: the returns to knowing which projects to exclude go down, as there are less projects to be excluded. The assumption that liquidity supply is sufficiently high restricts attention to this region.

The second feature of the global equilibrium environment is that _AAemd_<sup>isrela-</sup> tively large. Note that _AAemd_<sup>capturestherelativereturnsgeneratedbythesame</sup> project in developed and emerging economies. The presence of limited enforcement in emerging economies would tend to imply a positive wedge between the productivity of a project and its return to investors. The role of the assumption that _Ad_<sup>largeistogenerateaflowoffundsfromemergingtodevelopedeconomies,</sup> _Aem_<sup>is</sup> 21
broadly consistent with the view of global imbalances expressed in Caballero et al. [2008].

**Proposition 4** _For Qw and AAemd_<sup>_sufficientlylarge,financialintegrationleadsto_</sup> _an endogenous deterioration of the financial system in the developed market region._

It is straightforward to show that the objective of banks in this model coincides with the objective of a social planner trying to maximize domestic output minus the costs of differentiation (taking _r_ as given). The deterioration in the financial system can therefore be interpreted more broadly as an outcome of _endogenous_ lax regulation.

In the context of the recent crisis, the above proposition formalizes the popular claim according to which financial integration increased the equilibrium level of financial distortions by lowering the price of liquidity from the developed market’s perspective<sup>9</sup> . Intuitively, if liquidity is sufficiently cheap so that nearly all projects are implemented anyway, the benefits of differentiating between projects may not be worth the cost. Broadly interpreted, the financial system will gravitate towards various institutional arrangements that tie the implementation of high quality projects with the implementation of low quality projects.

# **6.2 Normal**

What are the implications of the deterioration of the financial system on output and on output volatility? Under autarky, the implications would be fairly intuitive: a weakening of the financial system would decrease output and increase subsequent output volatility<sup>10</sup> . However, these intuitive results breakdown under financial integration. The following proposition states that the deterioration in the quality

> 9A note is in order regarding the applicability of these results to emerging market economies. The analysis in this section relies heavily on the assumption that financial integration is associated with a decline in the price of liquidity from the domestic perspective. The results are therefore not applicable for emerging markets. For emerging markets, the mirror image is the relevant one: financial integration is associated with an increase in _r_ , potentially leading to an endogenous increase the the quality of financial institutions. The characterization of the long run general equilibrium environment, in which financial institutions are allowed to adjust in both emerging and developed economies, is beyond the scope of this paper. I leave this interesting issue for future research.

> 10To see this, note that by Lemma 7 in the Appendix, holding funding fixed, output is higher when financial institutions are intact (because a superior set of projects are implemented). Thus,

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of the financial system in the developed world will increase funding in that region, and may increase and stabilize output as well:

**Proposition 5** _An endogenous weakening of the financial system in the developed market will:_

_1. Increase the flow of funds from emerging to developed economies._ _2. If the increase in flows is sufficiently large (which will be the case for a sufficiently large AAemd_<sup>_),developedmarketoutputwillincreaseandstabilize_</sup> _conditional on small fluctuations._ Abandoning the higher standard of differentiation causes inefficient projects that were implemented at the margin to be implemented inframarginally, while more productive projects become marginal. This lowers the average return to funding, but increases the _marginal_ return to funding. In the integrated equilibrium, this increase in domestic marginal returns leads to additional inflows of funding. If these flows are sufficiently large, domestic output will rise.

The increase in the marginal return also serves to stabilize output, as domestic funding adjusts less to fluctuations in the interest rate. Intuitively, when the domestic marginal return is higher, a larger fraction of the economy becomes globally inframarginal. Of course, section 4 illustrates that the economy becomes more sensitive to fluctuations in domestic funding: so, while _F_ becomes less volatile, the economy becomes more sensitive to fluctuations in _F_ . Conditional on small global fluctuations, the first effect dominates and volatility declines.

Proposition 5 can shed light on the seemingly “irrational” behavior that led up to the subprime crisis, in which many bad loans were given to subprime borrowers, and, while the financial system behaved “irresponsibly”, the demand for US assets seemed only to increase. This result suggests that this type of indiscriminate lending raised the expected marginal return to funds in the US, leading to additional Finally, does the fact that output in the developed world increases with the deterioration of its financial system mean that such a deterioration is “good”?

a weakening of the financial system constitutes an adverse shock to output. The fact that subsequent output volatility increases is immediate from the comparison between closed emerging and developed economies in section 4.

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<!-- Start of picture text --> y d (F) y em (F)<br>r<br>Y d Y em<br>F d F d F em<br>Q w<br><!-- End of picture text --> Figure 4: The origin of the developed economy is on the left corner, and the origin of the emerging economy is on the right corner. The market clearing condition states that the distance between the two corners is equal to the global liquidity supply, _Qw_ . The intersection of the marginal products of funding determines _r_ . A deterioration of the financial system in the developed world causes funding to flow towards that region. In this figure, the deterioration of the financial system is illustrated by the “flattening” of the marginal return to funding. The size of the increase in _Fd_ is given by ∆ _Fd_ , the distance between the intersection of the autarkic (sloping) marginal return to funding and _r_ , and the point of satiation ( _Fd_ = 1).

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From a global perspective, no. The generic adverse effect of a deterioration in the financial system is that it decreases world output, both under autarky and under financial integration:

**Lemma 1** _A weakening of the financial system in the developed world decreases world output._

This lemma is immediate from the fact that intact financial institutions allow for a differential implementation of projects based on their returns; the set of projects implemented when differentiation is not possible is necessarily inferior to the set of projects implemented when some differentiation is possible.

# **6.3 Large adverse shocks**

In the global environment described in this paper, the deterioration of the financial system in the developed world serves to increase and stabilize output in that region during normal times. However, while the response to small shocks is mitigated, the output response to large negative shocks is amplified:

**Proposition 6** _In the developed world, the weakening of the financial system amplifies the output response to large adverse shocks to Qw or AAemd_<sup>_._</sup>

Intuitively, cheap liquidity leads to structural changes in the financial system that disable the separation of high-quality projects from low-quality projects. During normal times, this increases the amount of low-quality projects being implemented, and output increases as a result. However, sufficiently large contractions in liquidity are amplified by the inability to separate the discontinuation of lowquality projects from the discontinuation of high-quality projects.

This result suggests that the deterioration in the quality of financial institutions preceding the sub-prime crisis may have indeed precipitated it by creating an amplification mechanism for large adverse shocks. This amplification mechanism is consistent with many inefficiencies that seem important for understanding the extent of the crisis. A straightforward interpretation is the mortgage market itself. The creation of mortgage backed securities enabled the pooling of idiosyncratic risk of subprime loans. Once housing prices declined, issuing new subprime loans 25
became difficult, perhaps in part because the process of issuing subprime loans did not allow for differentiation between relatively promising borrowers and relatively unpromising borrowers. A more subtle interpretation is in balance sheet effects (as in Brunnermeier [2009]). The heavy reliance of banks’ balance sheets on mortgage backed securities forced them to disengage from productive lending activities once the subprime crisis hit. This can be viewed as an additional mechanism that ties the implementation of productive projects to the implementation of unproductive projects.

**Corollary 1** _Financial integration may lead to the amplification of large adverse shocks in the developed world._

Corollary 1 is immediate from the analysis in this section: by Proposition 4, financial integration leads to the deterioration of the financial system. By Proposition 6, the deterioration in the financial system amplifies the output response to large adverse shocks.

Note that this analysis also suggests that the subprime crisis cannot be explained solely in terms of a breakdown in the financial system; rather, a complete explanation would require either an additional large shock to TFP or to liquidity supply.

The results in this section present a modification to the view presented in section 5 according to which financial integration mitigates output fluctuations in the developed world. If financial integration with a distorted emerging market region is coupled with a decline in the price of liquidity, financial institutions may deteriorate in accordance with Proposition 4. As a result, the sensitivity of output with respect to small shocks will decline, but large adverse shocks will be amplified.

# **7 The financial system as a matching mechanism**

The results presented in the previous sections rely heavily on Property 1. In this section, I derive Property 1 from two primitive assumptions on the effect of financial distortions on the matching between funding priorities and projects. I present empirical evidence for these assumptions, and show that Property 1 can be derived from a variety of microfoundations.

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Before proceeding to the general case, it is useful to consider the following simplified example. Assume that there are only two funding priorities, “high” and “low”, and only two types of projects, “good” and “bad”. The good project produces 3 if implemented, and the bad project only produces 1 if implemented ( _g_ (good) = 3 and _g_ (bad) = 1; for simplicity, I’ve assumed _A_ = 1).

In an efficient economy, the good project would be prioritized higher than the bad project. However, in a distorted economy, there may be frictions that prevent the efficient matching between funding priorities and projects: with some probability _φ_ , the bad project will be prioritized higher than the good project:

# _σφ_ (bad project _,_ high priority) = _φ_

Note that _φ_ = 0 corresponds to the efficient case; a higher _φ_ corresponds to a more distorted economy, in which the probability of implementing the bad project before the good project is higher. Given _φ_ , the marginal return to the first unit of funding is equal to the expected productivity of the project that receives the high funding priority: The marginal return to the second unit of funding is the expected productivity of the project that receives a low funding priority: The ratio of the marginal return to the second unit of funding and the marginal return to the first unit of funding is therefore increasing in _φ_ , in accordance with 27
the log supermodularity condition in Property 1: Note that the log supermodularity condition holds both because the return to the second unit funding is increasing in _φ_ , and because the return to the first unit of funding is decreasing in _φ_ . In other words, the ratio of the marginal returns increases with _φ_ both because good projects are more likely to receive a low priority, and because bad projects are more likely to receive a high priority.

For the general case, I am going to present two assumptions on the set of matching functions _{σφ}φ∈_ Φ that loosely correspond to these conditions, which guarantee that the resulting marginal return to funding is log supermodular, consistent with Property 1.

For this purpose, it is convenient to fix two funding priorities, _p_<sup>_′_</sup> and _p ≥ p_<sup>_′_</sup> , and two levels of distortions, _φ_<sup>_′_</sup> and _φ ≥ φ_<sup>_′_</sup> . We will be interested in comparing the two matching functions ( _σφ_ and _σφ′_ ) in terms of the relative likelihood that projects of certain types are assigned funding priorities _p_ and _p_<sup>_′_</sup> . Given the choices of _p_ , _p_<sup>_′_</sup> , _φ_ , and _φ_<sup>_′_</sup> , for a measurable subset _X_ , let _D_ ( _X_ ) be a given by: The measure _D_ ( _X_ ) compares _φ_ and _φ_<sup>_′_</sup> in terms of the relative likelihood that projects of types _x ∈ X_ receive higher funding priority. To develop intuition, consider for example the statement _D_ ( _X_ ) _<_ 0. Assuming that all measures are strictly positive, this statement holds true if and only if: In words, this means that the ratio of the likelihood that projects of types _x ∈ X_ receive priority _p_<sup>_′_</sup> (a high priority) and the likelihood that they receive priority _p_ (a low priority) is relatively smaller in less distorted economies. This statement seems reasonable for _X_ that is composed of relatively “bad” projects: in an efficient economy, these projects are unlikely to receive a high funding priority. In a distorted economy, this type of mistake can happen sometimes.

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The above suggests that a reasonable assumption is that _D_ ( _X_ ) _<_ 0 for a set _X_ that is composed of “bad” projects. Similarly, it is reasonable to assume that for a set _X_ composed of “good” projects, _D_ ( _X_ ) _>_ 0: In words, good projects are relatively _more_ likely to receive higher priority in less distorted economies.

But what is a set of “good” projects? Given the restriction to a decreasing _g_ ( _·_ ), we know that projects of types _x ∈_ [0 _,_ ̄ _x_ ] are relatively better than projects of types _x ∈_ [ ̄ _x,_ 1]. A set of the form _X_ = [0 _,_ ̄ _x_ ] is therefore a set of relatively good projects. The first assumption is as follows:

# **Assumption 1** _Let X be of the form X_ = [0 _,_  ̄ _x_ ] _. Then, D_ ( _x_ ) _≥_ 0 _._

For the purpose of the second assumption, it is convenient to impose a partial ordering on the set of subsets of the form _X_ = [ _<u>x,</u>_ ̄ _x_ ]: it will be said that _X > X_<sup>_′_</sup> if all elements in _X_ are larger than all elements in _X_<sup>_′_</sup> <u>(</u> _<u>x</u> ≥ x_ ̄<sup>_′_</sup> ).

# **Assumption 2** _For every two segments X_<sup>_′_</sup> _and X > X_<sup>_′_</sup> _, D_ ( _X_<sup>_′_</sup> ) _≥ D_ ( _X_ ) _._

This assumption loosely implies that relatively better projects are relatively more likely to receive higher funding priority in less distorted economies. As we’ve seen above, for _X_ composed of “bad” projects, we are likely to see _D_ ( _X_ ) _<_ 0, whereas for _X_ composed of “good” projects, we are likely to see _D_ ( _X_ ) _>_ 0. This assumption essentially states that _D_ ( _X_ ) is monotone; if all projects _x_<sup>_′_</sup> _∈ X_<sup>_′_</sup> are better than all projects _x ∈ X_ , then _D_ ( _X_<sup>_′_</sup> ) _≥ D_ ( _X_ ).

**Theorem 1** _Assumptions 1 and 2 imply compliance with Property 1 for any positive and decreasing g_ ( _·_ ) _._

Assumptions 1 and 2 essentially state that distortions make it less likely for good projects to be matched with high funding priorities, and that as we decrease the quality of projects they become relatively more likely to be prioritized higher in more distorted economies. The theorem then states that when funding 29
priorities are distorted in this fashion, the average quality of projects with high funding priorities is relatively closer to the average quality of projects with low funding priorities. As the aggregate marginal return to funds is equal to the average productivity of projects with marginal funding priority (equation 2), this implies compliance with Property 1.

# **7.1 Empirical interpretation**

How plausible are Assumptions 1 and 2? In this section I present empirical evidence that is consistent with Assumptions 1 and 2, and is hence supportive of Property 1 (by Theorem 1) .

As illustrated in the previous sections, there are many general equilibrium implications of Property 1 that are consistent with empirical regularities. However, there are obvious problems with testing Property 1 directly. Essentially, it would require an exogenous source of variation in the supply of funding that does not also affect the productivity of funding. This is problematic, as we would expect that periods of high productivity would imply both that the returns to funding are higher and that the supply of funding is larger. Using the standard small open economy trick and restricting attention on global variation in the supply of funding is not helpful here, as it may capture variation in global productivity that also affects the domestic marginal return to funds.

Appendix A presents an empirical investigation of Assumptions 1 and 2. I use the AMADEUS data set<sup>11</sup> , that includes balance sheet data for all formal sector firms for several European and Eastern European countries, between the years 1990-2011. For each firm, I construct a measure of the marginal productivity of funding ( _Ai_ ). In the appendix I illustrate how this measure maps into the productivity of projects ( _Ag_ ( _x_ )).

I divide the set of countries into “distorted” and “efficient” based on the crude measure of GDP per capita. I choose the cutoff to be the GDP per capita in Cyprus. After removing countries with insufficient data, the list of “efficient” economies includes Austria, Belgium, Finland, France, Germany, Iceland, Italy, Luxembourg, Netherlands, Norway, Spain, Sweden and Switzerland. The list of “distorted”

> 11The AMADEUS database (Analyze Major Databases from European Sources) is published by Bureau van Dijk Electronic Publishing.

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economies includes Belarus, Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic, Estonia, Greece, Hungary, Latvia, Lithuania, Malta, Moldova, Poland, Portugal, Romania, Russia, Serbia, Slovakia, Slovenia and the Ukraine.

**Testing Assumption 1.** Assumption 1 states that in less distorted economies, productive projects are more likely to receive higher funding priorities. Of course, funding priorities are not observable so this assumption cannot be tested directly. However, we can get a crude measure of funding priority by calculating the extent to which the implementation of the project depends on the aggregate supply of funding. If a project has high priority, its implementation will depend little on the aggregate supply of funds. Projects with lower funding priorities will be more vulnerable to shocks to the aggregate supply of funds (unless of course they are not implemented at all; these projects, however, will not show up in the data).

I test whether in less distorted economies, relatively more productive projects are less sensitive to fluctuations in the aggregate supply of funds. For each country, I divide the set of projects in each year into “high productivity” and “low productivity” projects, depending on whether their productivity is in the top _k_ percentile. Denote the set of high productivity projects by _X_ ( _k_ ).

I regress the funding of firm _i_ on aggregate funding, adding an interaction term for productive projects. I then test weather the coefficient on the interaction term is smaller for less distorted economies, that is, for efficient economies the implementation of productive projects depends less on the aggregate supply of funds. I consider the following specification: I then calibrate the empirical counterpart of _D_ ( _X_ ( _k_ )) as: Where the superscripts indicate the coefficients estimated on the efficient and distorted subsamples. I then test the hypothesis _D_<sup>ˆ</sup> ( _X_ ( _k_ )) _≥_ 0.

I do this exercise for _k_ = 25%, _k_ = 50%, and _k_ = 75%. In all three cases, I find support for the hypothesis (at least at the 5% confidence level). The results 31
are summarized in figure 5.

<!-- Start of picture text --> Estimates of D(X) with 95% Confidence Intervals<br>0.6<br>0.5<br>0.4<br>0.3<br>0.2<br>0.1<br>0<br>X=[0,0.25] X=[0,0.5] X=[0,0.75]<br>max 0.4107914 0.4472499 0.5569949<br>min 0.2232662 0.3292569 0.4780644<br>point 0.3170288 0.3882534 0.5175296<br><!-- End of picture text --> Figure 5: The estimated values of _D_ ( _X_ ( _k_ )). The figure illustrates that the data is consistent with the assumption that _D_ ( _X_ ) _≥_ 0 for all _X_ of the form _X_ = [0 _,_ ̄ _x_ ]. 24,026,371 observations; standard errors adjusted for 392 clusters representing country-year pairs.

**Testing Assumption 2.** Assumption 2 loosely states that relatively better projects are relatively more likely to receive high funding priority in more efficient economies. In similar spirit, I divide the projects in each country and each year into 4 (disjoint) groups based on the quartile of their productivity. The quartiles correspond to the sets of projects _X_ 1 = [0 _,_ 0 _._ 25], _X_ 2 = [0 _._ 25 _,_ 0 _._ 5], _X_ 3 = [0 _._ 5 _,_ 0 _._ 75] and _X_ 4 = [0 _._ 75 _,_ 1].

For each quartile _q_ = 1 _, ...,_ 4, I run the following regression: Similarly, the empirical counterpart of _D_ ( _Xq_ ) is given by: 32
Assumption 2 would suggest that for _X_<sup>_′_</sup> _< X_ (or _q_<sup>_′_</sup> _< q_ ), The results are summarized in figure 6. Consistent with the hypothesis, the estimates _D_<sup>ˆ</sup> ( _Xq_ ) are weakly monotone in the sense that for _q_<sup>_′_</sup> _< q_ , the 95% confidence interval of _D_<sup>ˆ</sup> ( _Xq′_ ) either overlaps with the 95% confidence interval of _D_<sup>ˆ</sup> ( _Xq_ ) or is strictly above it. As we would expect, the estimate is positive for the first quartile but negative for the last quartile.

<!-- Start of picture text --> Estimates of D(Xq) with 95% Confidence Intervals<br>0.6<br>0.4<br>0.2<br>0<br>-0.2<br>-0.4<br>-0.6<br>-0.8<br>X=[0,0.25] X=[0.25,0.5] X=[0.5,0.75] X=[0.75,1]<br>max 0.4107914 0.2426918 0.0686512 -0.4781197<br>min 0.2232662 0.15859 -0.069732 -0.5570674<br>point 0.3170288 0.2006409 -0.0005404 -0.5175936<br><!-- End of picture text --> Figure 6: The estimated values of _D_ ( _Xq_ ). The figure illustrates that the data is consistent with _D_ ( _Xq_ ) being weakly monotone decreasing in _q_ . 24,026,371 observations; standard errors adjusted for 392 clusters representing country-year pairs.

# **7.2 Microfoundations**

In this section I present different microfoundations of distortions that comply with Property 1. These microfoundations are intended to illustrate both the plausibility of compliance with Property 1, and the flexibility that Property 1 allows in specifying the sources of distortions.

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**Incomplete information.** Projects’ types are unobservable; instead, implementation decisions are made based on a signal that is correlated with the project’s quality, _s_ ( _x_ ). There are two signals: half the projects receive the signal _G_ (“good”) and the other half receive the signal _B_ (“bad”). The average quality of projects receiving the signal _G_ is higher than the average quality of the projects receiving the signal _B_ ; thus, all projects with _G_ signals will be implemented before any projects with _B_ signals will be implemented.

The parameter _φ_ governs the noisiness of the signal. If _φ_<sup>_′_</sup> _≤ φ_ , the signal _φ_<sup>_′_</sup> is more informative in the sense that for every _x_ ̄: In other words, the distribution of projects that receive a good signal under _φ_<sup>_′_</sup> stochastically dominates the distribution of projects that receive a good signal under _φ_ ; the distribution of projects that receive a bad signal under _φ_ stochastically dominates the distribution of projects that receive a bad signal under _φ_<sup>_′_</sup> .

**Lemma 2** _In this model of incomplete information, Assumptions 1 and 2 are satisfied. Hence, Property 1 is satisfied for any g_ ( _·_ ) _._

**Government intervention.** The government owns a fraction _φ_ of the economy: a fraction _φ_ of each project is owned by the government, and the government controls a fraction _φ_ of the funds. The government distributes its funds among government-owned projects; I assume that it does so inefficiently, and that the likelihood that a project receives government funding is uncorrelated with its productivity.

The private sector efficiently distributes its funds among privately-owned projects, financing the more productive projects before allocating funds to the less productive projects. The matching function _σφ_ ( _·, ·_ ) therefore satisfies: Where _σeff_ ( _·, ·_ ) is defined by equation 4. Here, the value of _φ_ determines the 34
level of distortion: a higher _φ_ implies that the government runs a larger part of the economy, so more funds are being allocated randomly.

**Lemma 3** _In this model of government intervention, Assumptions 1 and 2 are satisfied. Hence, Property 1 is satisfied for any g_ ( _·_ ) _._

**Collateral constraints.** Consider a model in which projects are characterized by their type, _x_ , and by their collateral type, _b_ . Assume that collateral types ( _b_ ) are distributed independently from the project type ( _x_ ). Conditional on any project type, collateral is uniformly distributed on [0 _, φ_ ]. The collateral level of the project is given by the following decreasing function:

That is, collateral is decreasing in _b_ , and is bounded from below by the productivity of the least productive project.

A project with features ( _x, b_ ) is implemented if and only if both its return and its collateral level exceed the price of funding: The mismatch between the quality of projects and their collateral changes the order in which projects are implemented. Note that a higher _φ_ implies that the aggregate collateral is lower. It is easy to see that _φ →_ 0 corresponds to the efficient allocation, as all projects have sufficient collateral to be implemented when their return is high enough. The case _φ →∞_ corresponds to an extremely distorted economy, in which essentially all projects are collateral constrained and can be implemented only when the market return is equal to the productivity of the least productive project; in this case, the marginal product of funding is close to constant, as projects are implemented essentially in a random order (as in the previous example).

**Lemma 4** _Assume that g_ ( _x_ ) = _αx_<sup>_−_(1</sup><sup>_−α_)</sup> _. In this model of collateral constraints, Property 1 is satisfied._

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Note that in this model, Property 1 is guaranteed only for the given functional form of _g_ ( _·_ ). I leave the question of generality for future exploration.

**Search frictions.** Consider a model in which economies differ in the search technology available to their banks. In each economy there are _φ_ local banks indexed _i_ = 0 _, ..., φ −_ 1. Projects owners are unaware of their project’s type until right before production decisions must be made. Local banks are modeled as risk sharing arrangements among project owners. Each local bank shares risk among <u>1</u> _φ_<sup>projectowners.Thebankindexed</sup><sup>_i_isarisksharingarrangementbetweenthe</sup> owners of projects indexed _x ∈_ ( _φ_<sup>_<u>i</u>,_</sup><sup>_<u>i</u>_</sup><sup><u>+1</u></sup> _φ_<sup>](for</sup><sup>_i_=0,thesegmentofprojectsisthe</sup> closed set [0 _, φ_<sup><u>1</u>]).Theprocessofdistributingfundsfromhouseholdstoprojectsis</sup> as follows:

1. Households supply funds to a large savings bank. The savings bank has direct access to projects (but is unaffiliated with the local banks, and is unaware of projects’ types).

2. The savings bank distributes funds randomly among projects owners.

3. Project owners handover their funds to their local bank. When the productivity of projects is revealed, the local bank uses the funds in its hands to implement the best set of projects among those owned by the bank’s members.

The parameter _φ_ can be thought of as a measure inversely related to the integration of the domestic financial system. A high _φ_ captures a situation in which there are some banks with access to highly productive projects that lack liquidity to implement them, and some banks with high liquidity without access to good projects. The case _φ_ = 1 corresponds to the efficient allocation: there is only one bank in charge of allocating the entire supply of funds, and the bank has access to the entire set of projects. The optimal set of projects is therefore implemented. The case _φ →∞_ corresponds to the random allocation example: project owners are essentially in autarky, as they must use their own funds to implement their own project. The implementation of projects is therefore random, as it does not depend on the level of productivity.

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**Lemma 5** _Assume that g_ ( _x_ ) = _e_<sup>_−x_</sup> _. In this model of search frictions, Property 1 is satisfied._

Similar to the model of collateral constraints, Property 1 is guaranteed only for a given functional form of _g_ ( _·_ ). Similarly, I leave the question of generality for future exploration.

# **8 Conclusion**

This paper studies the effects of financial distortions on the global equilibrium environment. I present a reduced form formulation of financial distortions according to which the marginal return to funding is log supermodular in funding and the level of distortion. This formulation is consistent with a class of microfoundations in which the distortion creates a mismatch between projects and funding priorities, in a way which results in an order of implementation which is less indicative of the relative quality of projects.

Upon financial integration, financial distortions affect global volatility patterns through two related channels: first, financial distortions determine the sensitivity of output to liquidity supply. Output in emerging markets is more sensitive to liquidity supply, because the projects implemented at the margin have high returns compared to the projects implemented infra-marginally. Second, in the integrated economy, the higher level of distortion in emerging markets causes them to absorb a larger fraction of the volatility of global liquidity supply. As a result, financial integration increases liquidity-driven output volatility in emerging markets, and decreases liquidity-driven output volatility in developed markets.

In the long run, a global environment in which liquidity is cheap is conducive to a deterioration in the financial system in the developed world. In the integrated economy, a deterioration in the quality of the financial system has a mixed effect on output in developed economies: in the absence of large liquidity or TFP shocks, it serves to increase output and to reduce output volatility. However, the response of output to large adverse liquidity shocks is amplified. This offers a modified view regarding the long run effect of financial integration on developed market output volatility. As the quality of financial institutions adjusts downward, the economy 37