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Essays on credit booms and rational bubbles Pannella, Pierluca 2017

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Essays on Credit Booms and Rational BubblesbyPierluca PannellaB.Sc., Bocconi University, 2008M.Sc., Bocconi University, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Economics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2017© Pierluca Pannella 2017AbstractWhy are credit booms and bubbles harmful to the economy? A dominant view points tothe risk of bust. Traditional theories of bank runs and recent theories of rational bubblesdescribe the costs of jumping to a bad equilibrium when the economy accumulates too muchdebt. In this work, I propose a theory of rational bubbles where the boom, not the ensuingbust, reduces the output by promoting a misallocation of factors.In the model presented in Chapter 2, financial markets are imperfect and the rise of a bubblealleviates credit constraints and boosts capital accumulation. However, capital accumulationoccurs in unproductive sectors and aggregate output is reduced. The result is driven by thefact that heterogeneous borrowers have an advantage with respect to issuing different types ofdebt contracts. In normal times, High-productive borrowers have higher collateral and therebyattract most of the funds. In bubbly times, borrowers can also issue “bubbly debt,” a debtthat is repaid with future debt. The possibility to keep a pyramid scheme and raise bubblydebt depends on the probability of surviving in the market. Therefore, a bubble misallocatesresources towards borrowers with low fundamental risk, even if they invest in projects withlower productivity.In Chapter 3, I propose an augmented version of the model with nominal rigidities. Thegoal is to explain the timing of expansions and recessions during “bubbly episodes.” In thisversion of the model, the initial boom in output is caused by a positive demand effect; thelong run reduction in TFP is driven by a misallocation process. In this chapter, I also analyzethe optimal policy prescriptions. In particular, I stress the importance of the central bankmonopoly on the issuing of bubble-like instruments.Finally, Chapter 4 presents an investigation of American banks’ balance sheets motivatedby the theory of the previous chapters. I test models of credit bubbles versus models of liquiditytransformation. I provide evidence that the recent expansion in liquid debt instruments canbe interpreted by the emergence of a bubble on bank’s liabilities.iiLay SummaryBig financial crises typically burst in the midst of a credit boom. In traditional macroeconomictheories, this is explained by the fragility of financial markets: too much debt increases therisk of freezing in the supply of credit. According to this sources, credit booms are not badper se; the problem is the bust. In this dissertation, I provide support to the alternative viewthat credit booms are inherently harmful to the economy because they misallocate resourcestoward lower productive sectors. I propose a theory of credit bubbles in which the emergenceof the bubble induces a worse allocation of factors. From a theoretical and empirical point ofview, I show that bank debt can be interpreted as a credit bubble.iiiPrefaceThis dissertation is original, unpublished, independent work by the author, Pierluca Pannella.ivTable of ContentsAbstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Credit Bubbles and Misallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Credit Booms and Between-Industry Misallocation . . . . . . . . . . . . . . . . 92.3 A Model of Rational Bubbles with Capital Misallocation . . . . . . . . . . . . . 142.3.1 The Bubble-Free Environment . . . . . . . . . . . . . . . . . . . . . . . 142.3.2 Introducing Bubbly Debt . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Credit Bubbles and Misallocation in a Model with Risky Investments . . . . . . 232.4.1 OLG Workers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4.2 Risky Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4.3 Equilibrium and Steady State Solutions . . . . . . . . . . . . . . . . . . 252.4.4 The Dynamics of the Model . . . . . . . . . . . . . . . . . . . . . . . . . 292.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Credit Bubbles in a Model with Nominal Rigidities . . . . . . . . . . . . . . . . . 443.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2 A Model of Rational Bubbles with Nominal Rigidities . . . . . . . . . . . . . . 463.2.1 Workers with Elastic Labor Supply . . . . . . . . . . . . . . . . . . . . . 46v3.2.2 Investors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2.3 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3 Equilibrium and Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.4 Simulated Dynamics after Demand and Bubbly Shocks . . . . . . . . . . . . . . 503.5 Policy Prescriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 Liquidity Mismatch or Bubbly Mismatch? . . . . . . . . . . . . . . . . . . . . . . . 594.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.2 Theoretical Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.3 Empirical Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Appendix 1: Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Appendix 2: Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Appendix 3: Proof of Proposition 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Appendix 4: Proof of Proposition 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Appendix 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Appendix 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84viList of Tables2.1 The Effect of the Growth of Credit to the PNFS on Factors’ Allocation whenIndustry’s TFP Growth is Country Specific . . . . . . . . . . . . . . . . . . . . 322.2 The Effect of the Growth of Credit to NFC on Factors’ Allocation when Indus-try’s TFP Growth is Country Specific . . . . . . . . . . . . . . . . . . . . . . . 332.3 The Effect of the Growth of Credit to the PNFS on Factors’ Allocation whenthe US Industry’s TFP Growth is used as Proxy . . . . . . . . . . . . . . . . . 342.4 The Effect of the Growth of Credit to NFC on Factors’ Allocation when the USIndustry’s TFP Growth is used as Proxy . . . . . . . . . . . . . . . . . . . . . . 352.5 Summary of simulated dynamics experiments . . . . . . . . . . . . . . . . . . . 393.1 Summary of simulated dynamics experiments . . . . . . . . . . . . . . . . . . . 524.1 Balance Sheet Complementarities: shares of total assets . . . . . . . . . . . . . 674.2 Balance Sheet Complementarities: levels . . . . . . . . . . . . . . . . . . . . . . 704.3 Effect of Mismatch on Dividends: entire sample . . . . . . . . . . . . . . . . . . 704.4 Effect of Mismatch on Dividends: before and after 2001 . . . . . . . . . . . . . 714.5 Effect of Mismatch on Dividends: before and after 2001, excluding 2007-2009 . 714.6 Effect of Mismatch on Dividends: Deposits and Other Short Term Debt . . . . 724.7 Effect of Mismatch on Dividends: Deposits and Other Short Term Debt, ex-cluding 2007-2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72viiList of Figures1.1 Credit and Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Credit and Housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Credit and TFP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Total Credit to the Private Non-Financial Sector (% of GDP) . . . . . . . . . . 102.2 Average Growth in Credit (2001-2007) . . . . . . . . . . . . . . . . . . . . . . . 112.3 Steady state values of kH and kL as a function of Rb:  = 0.5 and 1  AL < AH 362.4 Steady state values of aggregate output and consumption as a function of Rb: = 0.5 and 1  AL < AH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.5 Steady state values of kH and kLas a function of Rb:  = 0.5 and AL < 1  AH 372.6 Steady state values of aggregate output and consumption as a function of Rb: = 0.5 and AL < 1  AH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.7 Steady state values of kH and kL as a function of Rb:  = 0.5 and AL < AH < 1 382.8 Steady state values of aggregate output and consumption as a function of Rb: = 0.5 and AL < AH < 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.9 Simulation of the dynamics for kH,t and kL,t (Experiment 1) . . . . . . . . . . 402.10 Simulation of the dynamics for hH,t and hL,t (Experiment 1) . . . . . . . . . . 402.11 Simulation of the dynamics for the total capital kH,t + kL,t (Experiment 1) . . 412.12 Simulation of the dynamics for the total output Yt = YH,t + YL,t (Experiment 1) 412.13 Simulation of the dynamics for kH,t , kL,t and total output: "H = "L and onlythe H-type investors issue unsecured notes (Experiment 2) . . . . . . . . . . . . 422.14 Simulation of the dynamics for kH,t , kL,t and total output: "H = "L and onlythe L-type investors issue unsecured notes (Experiment 3) . . . . . . . . . . . . 43viii3.1 Simulation of the dynamics for RNt , ht, Rt, ⇡t and Yt: shocks to the value ofbubbly debt (Experiment 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.2 Simulation of the dynamics for RNt , ht, Rt, ⇡t and Yt: demand shocks (Experi-ment 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.3 Simulation of the dynamics for RNt , ht, Rt, ⇡t and Yt: demand and bubblyshocks (Experiment 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.1 Balance Sheet Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Path of the Mismatch Ratio of Deposits and log Dividends for the aggregateeconomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3 Path of the Mismatch Ratio of Other Short Term Debt and log Dividends forthe aggregate economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73ixAcknowledgementsI am indebted to my supervisors, Paul Beaudry and Viktoria Hnatkovska. I wish to thankthem for their guidance and patience. I would also like to thank Amartya Lahiri, MichalSzkup, Yaniv Yedid-Levi and Michael Devereux for helpful comments.A special acknowledgement goes to Andrea Di Miceli and Hugo Jales for their supportduring these years. I also want to mention my comrades at UBC: Oscar Becerra, TimeaMolnar, Anujit Chakraborty, Adlai Newson, Jacob Schwartz, Nathan Canen and João Galindoda Fonseca.Infine, ringrazio mia madre e mio padre, che non hanno mai smesso di sostenermi nelle miescelte.xThis work is dedicated to Ana Luiza.Chapter 1IntroductionIn recent times, the macroeconomy of Western countries has been characterized by un-precedented fluctuations in aggregate credit. These credit cycles have been correlated withfluctuations in overall output and capital. Nonetheless, the housing sector was at the core ofthese expansions and contractions: it is widely documented how credit and property pricestended to strictly co-move. Observers from many different fields have often associated theseboom-and-bust cycles to the appearance of a bubble. Even though the concept of financialbubble often arises in the public debate, most macroeconomists have been reluctant to intro-duce bubbles in their formal models. One exception is represented by recent developments inthe literature on rational bubbles. This work wants to add to this new literature, by focusing,in particular, on the role of financial bubbles in the allocation of funding.In Figure 1.1 I report the dynamics of the total credit to the private non-financial sector,output and fixed capital formation in the United States, Spain, and Ireland, between 1995 and2015. The three countries have famously experienced boom-and-bust cycles in the credit andhousing markets in the beginning of the century and were at the origins of the 2008 GreatRecession. The images confirm a well-known fact: credit is correlated with economic funda-mentals. Another fact is documented in Figure 1.2: the fast rise and the sudden contractionin aggregate credit are similarly replicated by the dynamics of property prices. Finally, thegraphs in Figure 1.3 show the dynamics of credit and Total Factor Productivity in the threecountries. These last graphs are particularly interesting because they reveal an aspect that isnot accounted by traditional models of business and credit cycles: a higher amount of credit inthe economy can be associated with a reduction in the aggregate productivity. In the United1Figure 1.1: Credit and Growth05000100001500020000250001995 2000 2005 2010 2015YearGross Fixed Capital Formation GDPCredit to Private Non−Financial SectorUnited States050010001500200025001995 2000 2005 2010 2015YearGross Fixed Capital Formation GDPCredit to Private Non−Financial SectorSpain02004006001995 2000 2005 2010 2015YearGross Fixed Capital Formation GDPCredit to Private Non−Financial SectorIrelandNotes: Data on GDP and fixed capital formation are from OECD.Stat. Data on aggregate credit are from the "Total credit to thenon-financial sector" database by the Bank for International Settlements. The unit of measure is billions of national currency (USdollar for the United States, Euro for Spain and Ireland). All quantities are deflated by the CPI with 2010 as base year.States, and Ireland the growth in TFP stopped respectively two and four years before theaggregate credit reached its peak. In Spain, the TFP growth was negative for the entire periodof boom.In Chapter 2 I will start by showing that the negative relation between credit and produc-tivity can be explained by a causal effect from credit to productivity through a worsening inthe allocation of factors. Specifically, I reveal that those Western countries that experienceda larger credit boom allocated this funding toward less productive industries. Many observerswould interpret this fact as a proof that credit booms were associated with bubbles. Inter-estingly, the most prominent theory of bubbles, the rational bubble one, typically producesopposite predictions. Indeed, in both the original theory by Tirole (1985) and the recent papersby Kocherlakota (2009), Martin and Ventura (2012, 2016), and Miao and Wang (2012), bub-bles play an efficient role in the economy as they improve the intertemporal or intratemporalallocation of funding. In the same chapter, then, I propose a theory of rational credit bubbleswith misallocation of factors. I describe the necessary condition to have bubbles misallocatingcapital in the economy and simulate the dynamics for the rise and burst of a bubble in a simplemodel.2Figure 1.2: Credit and Housing150200250300Property Prices10000150002000025000Credit to PNFS1995 2000 2005 2010 2015YearCredit to PNFS Property PricesUnited States150200250300350Property Prices5001000150020002500Credit to PNFS1995 2000 2005 2010 2015YearCredit to PNFS Property PricesSpain100200300400500Property Prices100200300400500Credit to PNFS1995 2000 2005 2010 2015YearCredit to PNFS Property PricesIrelandNotes: Data on property prices are from the long series of the BIS “Residential Property Price” database. The quantities are theoriginal indices adjusted for inflation.Figure 1.3: Credit and TFP859095100TFP10000150002000025000Credit to PNFS1995 2000 2005 2010 2015YearCredit to PNFS TFPUnited States99100101102103TFP5001000150020002500Credit to PNFS1995 2000 2005 2010 2015YearCredit to PNFS TFPSpain708090100110TFP100200300400500Credit to PNFS1995 2000 2005 2010 2015YearCredit to PNFS TFPIrelandNotes: Data on TFP are the Multi-factor Productivity series from the OECD.Stat. The variable is built as a residual from GDP growthand re-expressed as an index.3In the framework presented in Chapter 2 the emergence of a bubble produces a negativeeffect on the aggregate productivity and output by promoting a misallocation of factors towardlower productivity sectors. While this outcome replicates the negative relation between creditand productivity, it also implies a counterfactual dynamics for the output. If the emergenceof a bubble is not the source for a better allocation of factors and a higher GDP, as suggestedby the recent literature, then there must be an alternative channel explaining the increase inGDP during “bubbly episodes”. In Chapter 3 I extend my model by adding nominal rigiditiesand shocks. I will show that a nominal increase in the value of credit assets, can trigger ademand effect that ultimately boosts the entire economy. When this demand effect is eventuallyabsorbed, real values may not return to their original levels by inducing the rise of a bubblescheme and a misallocation of factors. In the same chapter, I also analyze the optimal policyof a social planner. I show that the emergence of a bubble can be prevented by setting a capon debt creation.The theory of bubble I present in this work is suited to explain fluctuations in the valueof debt contracts. While recent papers have usually applied the theory of rational bubblesto stock and housing prices, in my model, a bubble is instead a money-like asset, as in theoriginal interpretation by Samuelson (1958). In Chapter 4, then, I test my theory of bubbleon banks’ balance sheet data. Specifically, I investigate if the mismatch between liabilities andassets is justified by the process of liquidity transformation, as described in the theories byDiamond and Dybvig (1983) or Dang, Gorton, Hölmstrom, and Ordoñez (2016), or if insteadit is associated with the issuing of bubbly debt. My analysis provides support to the secondhypothesis in the years after 2000.All the three main chapters composing this work introduce novel elements in the literature.The model in Chapter 2 provides a novel formal explanation for the relation between bubblesand misallocation. The addition of nominal rigidities in Chapter 3, allows for an originalinterpretation of the events associated with a credit boom-and-bust cycle. Finally, the exerciseproposed in Chapter 4 provides a new perspective to interpret the liquid debt instrumentsappearing on the liability side of banks’ balance sheets.4Chapter 2Credit Bubbles and Misallocation2.1 IntroductionIn recent decades modern economies have experienced large fluctuations in aggregate credit.Periods of high growth have typically been followed by periods of decline or sudden busts. Whatdrives these cycles is a current subject of research and no consensus has yet been reached. Agrowing literature links these periods of extraordinary credit growth to the emergence of abubble. In particular, recent papers on rational bubbles point to the role of asset bubbles ineasing the transfer of funds when credit is constrained. According to these sources, bubblesboost the productive efficiency of the economy by improving the allocation of financing - theburst of the bubble initiates a recession. However, there exists an alternative view propos-ing that credit booms and bubbles actually induce a direct misallocation of resources in theeconomy.This work contributes to the debate in two ways. First, it provides evidence that favorsthe misallocation view by analyzing the between-industry allocation of factors across Westerncountries in the years prior to the 2008 financial crisis. Second, it builds on recent theories putforward in the literature on rational bubbles to support this alternative hypothesis. I proposethat it is the emergence of a bubble that reduces the output by promoting a misallocation ofresources.The original theory of rational bubbles was introduced by Tirole (1985). In Tirole’s frame-work, a bubble, defined as an asset with a zero market fundamental, can appear when theeconomy is dynamically inefficient; i.e., when the marginal return on capital is smaller than the5growth rate of the economy. Bubbles, then, enhance the inter-temporal allocation of resourcesand reduce the stock of capital. However, dynamic inefficiency was considered empiricallyirrelevant by most economists at the time.1 In addition, real bubbly episodes are typicallycharacterized by a boom in capital accumulation, a phenomenon that is counterfactual to thecapital crowding-out predicted by the model. Recent papers relax the condition for the exis-tence of rational bubbles and relate the arrival and burst of a bubble to credit dynamics. Infact, market returns can be lower than the growth rate even if the economy is dynamically effi-cient once we allow for imperfections in financial markets.2 According to Kocherlakota (2009),Martin and Ventura (2012, 2016), and Miao and Wang (2012) a bubble improves the intra-temporal allocation of funds, from unproductive agents to credit-constrained productive ones.3Intuitively, a bubble in the asset market raises the value of collateral, relaxes the borrowingconstraint, and therefore increases the amount of credit in the economy. In these models thepositive reallocation of investment supports a crowding-in of capital.These recent papers on rational bubbles can replicate aggregate macroeconomic facts, suchas the rise in investment rate during a credit boom and the start of a recession at the bust.Nonetheless, I question the reallocation channel which drives their result. My theory suggeststhat a bubble still alleviates credit constraints and raises the stock of capital. However, this isin favor of low productivity sectors.4In Section 2.2, I provide the evidence that motivates my model. I investigate the relationshipbetween credit growth and factor allocation in the years preceding the 2008 financial crisis.Specifically, I compare the change in between-industry allocation for a sample of Westerncountries that experienced a differential growth in credit. The result is that larger creditbooms favored the expansion of industries with low Total Factor Productivity growth. Inparticular, companies from less productive industries relatively increased their leverage in thecountries with a higher credit growth. In the following sections I place these facts inside therational bubble framework.51See Abel, Mankiw, Summers and Zeckhauser (1989) and Geerolf (2013) for an empirical investigation ondynamic inefficiency.2Woodford (1990) had already shown that financial frictions could relax the conditions for rational bubbles.3Kocherlakota (2009) and Miao andWang (2012) present models with infinite lived agents facing productivityshocks. Martin and Ventura (2012, 2016) rely on an Over-Lapping Generations model with generations ofproductive and unproductive agents.4To my knowledge, factor misallocation in a rational bubble environment has only been discussed in Miaoand Wang (2014). According to them a bubble can arise in a specific sector. However, a sector-specific bubbledoes not produce any direct misallocation. In keeping with the rest of the literature, the bubble still increasesthe productive efficiency of the sector. The overall productivity of the economy is negatively affected becausethe specific sector produces a negative externality on the rest of the economy.5There are alternative theories that link credit booms and misallocation. For example Cecchetti and Khar-roubi (2015) show that an expansion of the financial sector misallocates high-skilled workers from more pro-6The theoretical contribution is presented in two steps, described in Sections 2.3 and 2.4.First, in a stylized model I derive the necessary conditions for bubbles inducing a misallocationof factors. Second, in a richer model I introduce a motivation for bubbles appearing andboosting capital accumulation in low productivity sectors.My setup is based on the classical Over-Lapping Generations framework. In the modelthere are two types of agents: workers and investors. Workers earn their wage when young buthave no technology to store their income for consumption when old. Investors, on the otherhand, can invest today in order to obtain working capital tomorrow. A borrowing constraintlimits the credit between workers and investors. However, the latter can potentially expandthe funds they raise by issuing bubbly debt, a debt that will not be repaid with future incomebut with the purchase of this debt by a new generation of workers. It is worth noting that theemergence of bubbly debt is subject to workers’ beliefs regarding future repayment.A main feature in the model is heterogeneity in investor productivity. In Section 2.3,agents’ beliefs will not only determine the rise of bubbly debt but also the identity of theissuers. Notably, the ability to issue bubbly debt does not depend on the productivity of aninvestor, since he will not be responsible for repayment. If workers buy bubbly debt issued bylow productive investors, the outcome is a misallocation of resources away from more productiveinvestors.The mechanism described in Section 2.3 illustrates how a credit bubble can drag the econ-omy into an inefficient allocation of factors. There are, however, two drawbacks to this model.First, it does not explain how the borrowers issuing bubbly debt are selected. Second, itpredicts a reduction in aggregate capital when factors are misallocated. This prediction iscounterfactual to the large accumulation of capital that preceded the 2008 financial crisis.In Section 2.4, I address both issues by making a substantial addition to my model. I assumethat the possibility of sustaining a bubbly scheme is subject to the survival of the issuer onthe market: when a singular investor leaves the market, his bubbly debt must burst. In thissection, bubbly debt is effectively repaid with future debt until such a time that a borrowinginvestor dies or fails. In the real world, long-lived investors may be intermediaries that financetraditional sectors such as housing and real estate, activities with typically low productivitiesthat, nonetheless, have low fundamental risk. Assuming that low productive investors alsoductive sectors. Alternatively, Gopinath, Kalemli-Ozcan, Karabarbounis and Villegas-Sanchez (2015) describean environment in which larger firms have an advantage in accessing credit. However, neither paper takes intoaccount the boom-and-bust nature of credit cycles.7face a lower risk of leaving the market, they have a higher chance of issuing bubbly debt.6 Inaddition, their longer life expectancy allows them to accumulate more capital over time. Thisimplies that a bubble can boost aggregate capital even if resources are misallocated and theeconomy is contracting.A crucial aspect of both versions of my model is the possibility of initiating a new bubblyscheme by issuing bubbly debt. This possibility is also included in the framework set outby Martin and Ventura (2012) where the agent who issues a bubbly asset effectively earns arent. The authors identify two types of bubbly episodes: in contractionary episodes capitalis crowded-out as in Tirole’s framework; in expansionary episodes capital is crowded-in.7 Mymodel proposes a third type of bubbly episodes: capital is crowded-in while output is reduced.Besides the rational bubble literature, this work is related to the wider literature on creditcycles and financial crisis. Empirical works by Borio and Drehmann (2009), Reinhart andRogoff (2011), and Schularick and Taylor (2012) recognize that credit growth is a main predictorfor financial crises. More recently, additional papers have addressed the effect of credit boomson factor allocation. Gopinath, Kalemli-Ozcan, Karabarbounis and Villegas-Sanchez (2015)illustrate how the allocation of capital in Spain deteriorated during the period of rapid inflowsfollowing the introduction of the euro in 1999; alternatively Borio, Kharroubi, Upper andZampolli (2016) present a decomposition of labor productivity across Western economies andclaim that credit booms provoke a misallocation of the labor force.8 My theory is also relatedto the over-accumulation view of crises.9 Note that, in the model described here, a recessiondoes not originate from an over-accumulation of capital, but rather from an accumulation inthe wrong sector.Finally, the work is linked to the empirical and theoretical research on liquid debt. Indeed,our bubbly debt can be naturally interpreted as a short-term or liquid bank note. Growthin aggregate credit is associated with a near-symmetric increase in bank debt. For example,Krishnamurthy and Vissing-Jorgensen (2015) describe the relation between loans and liquiddebt on the two sides of the balance sheets for the US financial sector. From a theoreticalperspective, our bubbly debt has similarities to the information-insensitive bank debt described6A low fundamental risk, clearly, does not imply an overall low risk. Interestingly, the framework predictsa negative relation between fundamental and non-fundamental risk.7The crowd-in and crowd-out effects of bubbles is explored also in Hirano and Yanagawa (2016) in a modelwith infinite-lived agents. The authors analyze how the degree of financial imperfections influences the effectof bubbles on economy’s growth.8The first paper focus on within-industry misallocation, while the second one looks at between-industrymisallocation.9Friedrich Hayek was the most notable proponent of this view on recessions.8by Dang, Gorton, Hölmstrom, and Ordoñez (2016) where repayment does not depend on theborrower’s productivity. However, in the model set out here there is no liquidity mismatchbetween the assets and the liabilities of a borrower.The remainder of the chapter is organized as follows: Section 2.2 presents the empiricalresults that inform the theory. In Section 2.3, I describe the stylized version of the modelin which workers’ beliefs determine who can issue bubbly debt. In Section 2.4, I add a riskcomponent to the activity of investors which influences their survival on the market. Here lowrisk investors have an advantage in the issuing of bubbly debt. Section 4 also describes thedynamics of the model. Section 2.5 concludes.2.2 Credit Booms and Between-Industry MisallocationI motivate my theory on the basis of evidence on the allocation of factors across industriesin the US and western Europe prior to the 2008 financial crisis. In Figure 2.1, I show the pathof total credit to the Private Non-Financial Sector (PNFS) normalized by GDP. As we can see,from the late 1990s to 2008, the majority of sample countries experienced an unprecedentedcredit rise. For some countries, this boom was particularly dramatic: in Ireland the credit ratiorose from 100% at the end of the 1990s to over 300% at the peak of the cycle. In my empiricalanalysis I will exploit variation across countries to assess the impact of a credit boom on theallocation of factors.In recent years, a new literature focusing on factor misallocation has emerged. A cru-cial question is which measure should be considered to identify misallocation. Restuccia andRogerson (2008), and Hsieh and Klenow (2009) assess the within-industry misallocation bymeasuring the dispersion of marginal products. Alternatively, Bartelsman, Haltiwanger andScarpetta (2013) adopt a measure based on the covariance between size and productivity,where a weaker link denotes a worse allocation of factors. While the approach used here issimilar to the latter, the analysis follows a separate line of inquiry in at least two ways. First,I rely primarily on industry-level data to detect between-industry rather than within-industrymisallocation. Looking at the reallocation of factors between different industries is more appro-priate to motivate my theory; it is also better suited to support the causal claims made by theempirical model set out here. Studies that measure misallocation typically deal with firm-leveldata and avoid between-industry considerations for comparability issues. However, the goalhere is not to obtain an absolute measure of misallocation by doing an accounting of aggregateproductivity, but rather to compare the allocation pathway across countries exhibiting differ-9Figure 2.1: Total Credit to the Private Non-Financial Sector (% of GDP)Notes: Data are from the "Total credit to the non-financial sector" database by the Bank for International Settlements.ent credit growth. The problems related to the lack of comparability of different industriesare attenuated by the second point of departure from the literature: this analysis is based ongrowth rates rather than levels. Then, instead of looking at the correlation between size andproductivity, I examine the correlation between input/output growth and productivity growthacross industries and countries with a different credit growth prior to 2008.10 Specifically, themodel I will estimate is:Y_growthk,j = ↵k (industryk) + j (countryj)+ (TFP_growthk,j) +  (TFP_growthk,j ⇥ credit_growthj) + controlsk,j + "k,j .The dependent variables will include measures of growth in value added, capital, and laborfor industry k in country j. industryk and countryj are dummy variables respectively forindustries and countries. The measure of productivity I will use is the Total Factor Productivityof each industry k in country j, TFP_growthk,j . Finally, credit_growthj is the growthin aggregate credit in country j . While  tells us about the overall correlation betweenproductivity growth and input/output growth,  tells us how this relation changes with credit10Borio, Kharroubi, Upper and Zampolli (2016) provide the closest comparison to our study. The authors alsolook at the variation of between-industry allocation in relation to credit growth. However, they only focus onlabor productivity and follow the same decomposition used by Bartelsman, Haltiwanger and Scarpetta (2013),originally introduced by Olley and Pakes (1996).10Figure 2.2: Average Growth in Credit (2001-2007)Notes: Data are from the "Total credit to the non-financial sector" databases by the Bank for International Settlements.growth. A positive  would tell us that in those countries experiencing a larger credit boom,the effect of TFP growth on industry growth is higher. Conversely, a negative  would work inthe opposite direction: credit booms would be associated with a weaker relation between theproductivity and the performance of an industry.The measures of aggregate credit I use are from the BIS Statistics and include Creditto the Private Non-Financial Sector and Credit to Non-Financial Corporations (NFC).11 Allquantities are deflated by the CPI. To build the growth rate variables, I first took the year-by-year log-variation and multiplied by 100, and then computed the simple average from 2001 to2007.12 The results are reported in Figure 2.2.As we can see, all countries went through a period of general credit growth with the soleexception of Germany, which reports a slight decrease in the Credit to the PNFS and toNFC during the examined period.13 At the opposite extreme, Ireland and Spain, notably thetwo countries that suffered major banking crises, experienced an outstanding credit boom, asmeasured by both of the two quantities.Data on industries are derived from the EU KLEMS Growth and Productivity Accounts.11In this quantity the credit to households and non-profit institutions is excluded.12I chose 2001 as the starting year for my analysis since it corresponds to the bottom of business cycle formost of Western countries. However, results are robust to small changes in the starting year.13Notably, the credit boom similarly occurred in European countries, where bank loans are the main sourceof financing, as well as in the US where capital markets traditionally play a more relevant role.11The database contains industry-level measures of output, capital, employment, and TFP. Mea-surements and computations are based on the growth accounting methodology. Multifactorproductivity growth is computed as the residual contribution to output growth, under the as-sumption of competitive markets, full input utilization and constant returns to scale. Indicesfor capital service flows, labor service flows and intermediate inputs are built as weighted sumsof disaggregated components. In particular, in the labor index are weighted the hours workedby workers with different characteristics, such as educational attainment and age.14Industrial classification is based on the NACE1, up to 32 industries. Since the focus here ison the allocation of factors to the Non-Financial Sector, I exclude from my sample the entireFinance sector. Measures of Capital and Value Added are in volume indices. The growthvariables for my regressions are built in the same way as those for total credit.Measures of input and output can tell us about the growth and allocation of productivefactors across industries. In order to verify that the results are driven by the credit allocationchannel, I integrated the data with a measure of financial leverage to be used as an additionaldependent variable. Given that balance sheets data by industry are not available, I constructeda summary variable from Compustat Global and North America. For each company in thedataset I computed the average debt-to-equity ratio and its annual growth.15 I then averagedacross companies in each industry and country. Finally, I computed the average from 2001to 2007. Note that the growth in leverage is only measured on the intensive margin withoutconsidering the entry and exit of firms in the dataset.16The results for our main specification are reported in Table 2.1 and 2.2, respectively whenwe use the Credit to the Private Non-Financial Sector and the Credit to Non-Financial Corpo-rations.17 For every regression I include as a control the initial share in 2001 of the dependentvariable in the total economy of the country. For the Debt-to-Equity ratio, the respectivecontrol is the initial level. I also show the results when controlling for the interaction with theinitial level of credit, measured as the ratio to GDP. This is to avoid the results are driven bya convergence in levels of aggregate credit.18 The growth in Debt-to-Equity ratio should helpreveal those industries that increased their dependence on external finance. In order to avoid14See O’Mahony and Timmer (2009) for a more detailed description of the dataset and the methodology.15The ratio is computed as (Total Liabilities)/(Total Assets-Total Liabilities). Negative values and outlyingvalues over 25 are dropped.16This is a reasonable restriction given that the Compustat database is limited to the small sub-sample ofpublicly traded firms.17Note that the different number of observations depends on the availability of data for the different industriesin the different countries. In particular, data on capital are not available for Belgium, France and Ireland.18For example high-growing credit countries may have started from lower levels of credit, which may implya negative relation between the productivity and performance of the various industries.12the variation from a change in the value of assets, I also control for the average asset growthfor the respective companies in the Compustat database.The interaction between the TFP growth and credit growth is significantly negative inall cases except for the regressions with Capital Growth as dependent variable.19 A likelyexplanation is that the sample is smaller since data on capital are not available for Belgium,France, and Ireland. In particular, all the remaining results are sensitive to the variationprovided by Germany, Ireland, and Spain. When excluding one of these three countries fromthe sample, the negative effect is weakened or it disappears.20Overall, these results play in favor of the hypothesis that credit booms are associated with aworse allocation of factors between the industries. In fact, those industries which experienceda bigger increase in productivity grew relatively less in countries which experienced a morerapid aggregate credit boomed. The effect is similar when we consider the increase in financialleverage of the Compustat companies. More productive industries showed a relative increasein their Debt-to-Equity ratio when the growth in aggregate credit was lower. This suggeststhat a misallocation of funds could be at the origin of the misallocation of factors.A possible critique to the results above is that they could be driven by reverse causality:those countries having a worse allocation of factors may need a bigger increase in aggregatecredit to reallocate resources between the industries. In particular, credit could be optimallyallocated to low productive sectors to boost long-term development and promote convergence.21In order to offset the likelihood of reverse causality, I proxy the TFP growth of the industriesin all countries with the TFP growth of the American industries, on the assumption thatthe growth in productivity of the American industries can be adopted as a measure of theirtechnological advancement. Consistent with the chosen proxy variable, it is argued that allcountries should optimally invest in those sectors showing the greatest progress. The model Iestimate here is similar to the previous estimation, but the productivity measure is no longercountry-specific, which means that the impact of the  is now captured by the industry-fixedeffects:19At the same time, the overall effect of the TFP growth is (most of the time) significantly positive.20Similarly, some industries have a bigger weight in driving the result. Construction and Real Estate areamong these industries.21Also note that there is an alternative hypothesis that the increase in credit to an industry reduces itsproductivity. This would still be in favor of the misallocation result, even though at the within-industry level.13Y_growthk,j = ↵k (industryk) + j (countryj)+ (US_TFP_growthk ⇥ credit_growthj) + controlsk,j + "k,j .The results are reported in Table 2.3 and 2.4, again for the Credit to the Private Non-Financial Sector and the Credit to Non-Financial Corporations. American industries are nowexcluded from the regressions. All the controls are similar to the previous specification. As wecan see the effect of the interaction between the TFP growth in the American industries andthe credit growth is significantly negative in almost all specifications.22The evidence set out here contradicts the proposition of the productive efficiency role ofbubbly credit advanced by recent literature on rational bubbles. However, in the followingsections, I will show that the emergence of a bubble can be a natural way to admit themisallocation of factors during a credit boom.2.3 A Model of Rational Bubbles with Capital Misalloca-tionIn this section, I will introduce the theory supporting the main claim of the paper. The cen-tral purpose is to describe the mechanism by which a rational bubble can induce a misallocationof factors and provide the necessary conditions for the misallocation result.I will first describe the framework and characterize the equilibrium without bubbles. ThenI will introduce the possibility of bubbly credit and analyze the bubbly equilibria. Note thatthe setup is deterministic. I will focus only on the steady state equilibria, given that the modelpresents trivial dynamics. I will introduce unexpected shocks and examine the dynamics forthe richer model proposed in Section 2.4.2.3.1 The Bubble-Free EnvironmentThe model is based on the classic Over-Lapping Generations framework set out by Diamond(1965) and Tirole (1985), with two-periods (young and old) lived agents.23 In the framework,there are three different types of agents, each of measure one:24 Workers, High-type investors22Interestingly, in this model, the negative effect appears also when Capital Growth is the dependent variable.The estimate is not significant only in the case of Debt-to-Equity ratio when I use the credit to Non-FinancialCorporations and control for the initial credit to GDP level.23Note that qualitatively similar results could be obtained in an environment with infinitely-lived agents hitby uninsurable idiosyncratic shocks. Woodford (1990), for example, proposes an elegant way to reproduceOver-Lapping Generations behavior starting from infinitely-lived agents.24Note that there is no population growth in the environment.14and Low-type investors. To make things more simple, I assume that all agents will onlymaximize their old-age consumption.When young, workers receive a wage w.25 While they may want to save their entire wageto consume when old, they have no technology to store it. Their only option is lending in thecredit market to earn an income in the following period.Investors, on the other hand, do not receive any wage. However, when they are born, theycan install capital and rent in the following period to competitive firms owning productiontechnologies of type H or L:26Ajkj,t for j 2 {H,L} . (2.1)Capital is specific for the two types of technologies: once installed, a given type of capitalcannot be intratemporally rented to a different technology. High-type and Low-type investorsdiffer in the type of capital they can install and, then, on the technology they can access. Weassume AH > AL. We will assume that capital fully depreciates in production.Finally, young agents in this economy can meet in a competitive credit market. Specifically,young investors can get external financing by selling credit contracts. However, in keepingwith the new literature on rational bubbles, a borrowing constraint limits the amount they canborrow:Rt+1dj,t+1  MRKj,t+1kj,t+1 for j 2 {H,L} (2.2)with  < 1. On the left-hand side, Rt+1 is the market interest rate, and dj,t+1 is the debtissued by investor of type j. The promised repayment Rt+1dj,t+1 cannot be higher than afraction  of the future capital income of the investor. Note that MRKj,t+1 is the price ofcapital for the two types of production. This constraint is quite standard in the literature andcan be interpreted as a limit on the pledgeable income of the borrower. In keeping with thisliterature, a binding borrowing constraint can push the interest rate below the growth rate ofthe economy and open the way for the existence of bubbles even if the economy is dynamicallyefficient.Finally the budget constraint for an investor is:kj,t+1 = dj,t+1 for j 2 {H,L} . (2.3)25In Section 4 workers will earn their wage by supplying labor.26In this chapter, the results of the model would not change if the investors also owned the productiontechnologies. However, in the next chapter, I will assume that the firms are owned by the workers in order tointroduce elastic labor supply and demand effects.15We can now define the equilibrium in this economy.DEFINITION: A competitive equilibrium is a list of consumption, debt, capital, labor,and prices such that:(i) Young workers maximize their old-age consumption by buying credit contracts in thevalue of w. Old workers consume Rtw(ii) Young investors choose kj,t+1 and dj,t+1, given prices (Rt+1,MRKj,t+1), maximizingfuture profitsMRKj,t+1kj,t+1 Rt+1dj,t+1 for j 2 {H,L} (2.4)subject to budget constraints (2.3), borrowing constraints (2.2) and resource constraintsdj,t+1  0.Old investors consume their profits(iii) Factors are paid at their marginal productivity:MRKj,t = Aj for j 2 {H,L} . (2.5)(iv) All markets clear in every period. In particular, it must be:dH,t+1 + dL,t+1 = w. (2.6)In this stylized economy with linear production technologies and borrowing constraints,High-type and Low-type investors can respectively offer rates AH and AL. In equilibrium,it must be R⇤ = AH with only High-type investors obtaining funds in the credit market.Then, all capital is optimally allocated to the High-type production: d⇤H = k⇤H = w. Aggregateproduction and consumption are Y ⇤ = AHw and C = R⇤w + (1 )Y ⇤ = Y ⇤ = AHw.In the next section, I will analyze how the emergence of a bubble distorts the allocation ofcapital in this economy. In order to introduce bubbles I will make the following assumption:ASSUMPTION 1:  < 1AH ! R⇤ < 1.This is the traditional condition for the existence of bubbles: the interest rate must belower than the growth rate of the economy. It is clear that R⇤ can be lower than 1, even if16the economy is dynamically efficient, i.e., AH > 1. In the following section, I will show howthe effect of a bubble on the allocation of capital depends on the market interest rate and thereturns on capital AH and AL.2.3.2 Introducing Bubbly DebtA bubble is an asset with no fundamental value, i.e., essentially a pyramid scheme. A youngagent would buy a bubbly asset only with the purpose of reselling it in the following period.Usually, according to the literature on rational bubbles, the stock of bubbly assets is given andthe analysis is focused on the exchange. Martin and Ventura (2012) introduced the possibilityof issuing new bubbly assets or starting a new pyramid scheme. This aspect is relevant becausethe agent that introduces a new bubbly asset in the economy earns a windfall. As we will see,the privilege of being an issuer of bubbly assets is crucial for our misallocation result.I will assume bubbles can be issued only by young investors.27 A bubble can be interpretedas a credit note, apparently identical to the other credit notes secured by the future pledgeableincome of the investors. The main difference is that the bubbly notes will not be repaid byborrowers, but will instead be repaid with the purchase by the future generation of workers.Credit markets are still competitive. However, now an investor can issue two types of debt,secured and unsecured. For j 2 {H,L}, these debt types are defined as:dSj,t+1 =8><>: dj,t+1 if Rt+1dj,t+1  MRKj,t+1kj,t+1Rt+1MRKj,t+1kj,t+1 if Rt+1dj,t+1 > MRKj,t+1kj,t+1(2.7)dUj,t+1 =8><>: 0 if Rt+1dj,t+1  MRKj,t+1kj,t+1dj,t+1  Rt+1MRKj,t+1kj,t+1 if Rt+1dj,t+1 > MRKj,t+1kj,t+1. (2.8)With the choice of secured funding, the investor will now face the following borrowing con-straint:Rt+1dSj,t+1  MRKj,t+1kj,t+1 for j 2 {H,L} . (2.9)It is worthy to stress that both secured and unsecured notes must promise the same returnRt+1 to be purchased in equilibrium.27The assumption does not affect the qualitative results of my analysis. In the next section I will introducea rationale for investors being the only possible issuers of bubbly debt.17When an investor can issue unsecured debt he earns a windfall, since he will not be respon-sible for its repayment. The budget constraint of an investor can now be rewritten as:kj,t+1 + lUj,t+1 = dSj,t+1 + dUj,t+1 for j 2 {H,L} (2.10)where lUj,t+1 represents the purchase of unsecured notes by investors of type j. It is relevant toobserve that the possibility of issuing unsecured debt depends on the beliefs of the agents inthe economy. In our framework an investor cannot actively influence these beliefs. This meansthat he can choose dSj,t+1 but not dUj,t+1.A bubbly scheme is sustainable if the future generations of agents have enough income torepurchase the unsecured notes issued in the market. The equilibrium interest rate is linkedto the path of the unsecured debt by the following market clearing relation:Rt+1lUH,t+1 + lUL,t+1 + wt  dSH,t+1  dSL,t+1= wt+1  (kH,t+2 + kL,t+2) . (2.11)The left-hand side represents the t+1-value of all unsecured notes issued before time t+1; theright-hand side represents the available income at time t + 1 that young agents do not investin capital.We can define the competitive equilibrium when there is bubbly debt in the economy.DEFINITION: A competitive equilibrium with bubbly debt is a list of consumption, securedand unsecured debt, capital, labor, and prices such that:(i) Young workers maximize their old-age consumption by buying credit contracts in thevalue of w. Old workers consume Rtw.(ii) Young investors choose kj,t+1, dSj,t+1 and lUj,t+1, given dUj,t+1 and prices (Rt+1,MRKj,t+1),maximizing future profitsMRKj,t+1kj,t+1 Rt+1dSj,t+1  lUj,t+1for j 2 {H,L} (2.12)subject to budget constraints (2.10), borrowing constraints (2.9) and resource constraintsdSj,t+1  dUj,t+1 and lUj,t+1  0.Old investors consume their profits18(iii) Factors are paid at their marginal productivity:MRKj,t = Aj for j 2 {H,L} . (2.13)(iv) Agents hold consistent beliefs about the path of dUH,t+1 and dUL,t+1(v) All markets clear in every period. In particular, it must be:RtlUH,t + lUL,t + wt1  dSH,t  dSL,t= wt  (kH,t+1 + kL,t+1) . (2.14)In this section, I will characterize the steady state equilibria with bubbly debt. An equi-librium with bubbly debt is supported by the beliefs of the agents, which in turn determinethe equilibrium rate Rb. Furthermore, these beliefs also determine who can issue bubbly debt.This aspect is critical to understanding our misallocation result. The investors issuing un-secured debt earn a rent which they can use to increase their investment. Particularly, thisissuing ability has nothing to do with the actual productivity of the issuer. In what followsI will assume that workers’ beliefs are such that H-type and L-type investors always issue afraction (1 ) and  of the total value of new unsecured notes dUH + dUL .In steady state, bubbly debt can exist only if the equilibrium rate Rb is higher than R⇤ =AH . In fact, if Rb = R⇤, we know from the previous section that it must be w = dSH , i.e., theH-type investors would be able to secure the entire lending amount from the workers.Investors choose to be borrowers or lenders in the credit market depending on whether theirreturn Aj is higher or lower than the market interest rate. I will describe the equilibria withbubbly debt in the following three cases: R⇤ < Rb  AL, AL < Rb  AH and AH < Rb.28CASE 1 : R⇤ < Rb  ALIf Rb is lower than AL, both H-type and L-type investors want to be net borrowers in thecredit market. This also implies lUH = lUL = 0, i.e., investors do not want to hold bubbly notes.The quantity w dSH  dSL then represents the aggregate value of bubbly debt in the economy,which is the value of newly and previously issued unsecured notes. Specifically, this quantitycannot be entirely transferred to the investors in the form of new unsecured debt - a part of itmust be used to repurchase the existing unsecured debt. From market clearing condition (2.14)28Note that the existence of the three intervals of equilibria is subject to Rb  1.19we can solve for the total steady state value of new unsecured debt issued by the investors:dUH + dUL =1Rb w  dSH  dSL . (2.15)In this last equation, we find the traditional necessary condition for the sustainability of abubbly equilibrium: Rb  g = 1. A higher Rb reduces the amount of new unsecured debt theinvestors can issue since the workers need to use a larger share of their income to buy existingcredit notes. This is in keeping with the characteristic crowding-out effect of rational bubbles.In the extreme case of Rb = 1, there is no unsecured transfer from the workers to the investorsin the steady state.The equilibrium H-type and L-type capital are given by:kH = dSH + dUH =RbAHkH + (1 )1Rb w  Rb(AHkH +ALkL)(2.16)kL = dSL + dUL =RbALkL + 1Rb w  Rb(AHkH +ALkL). (2.17)With respect to the equilibrium without bubbles, now the Low-type investors can raise financ-ing in the credit market as long as  > 0 and Rb < 1. Moreover, the Low-type investorswill invest their rent in L-type capital given that the market rate Rb is lower than AL. This,eventually, raises also the amount of secured debt issued by the Low-type investors. In the caseof Rb > AL, a Low-type investor who issues unsecured notes would use his rent to purchasecredit contracts in the market instead.We can solve further for kH and kLto obtain:kH =(1 ) 1RbRb RbAL1AL1 AHRb + (1 ) 1RbRbAHAL1ALw (2.18)kL = 1RbRbRbAH1AH1 ALRb +  1RbRbALAH1AHw. (2.19)In the bubble-free environment, the higher productivity was driving the allocation of financingand the installment of capital in the High-type sector. Here, secured debt still depends on AHand AL. However, the relative allocation of unsecured funding has no relation to the produc-tivity of the borrower - it is completely driven by the agents’ beliefs about . In particular, anincrease in  expands the relative allocation of capital in favor of the Low-type sector.20CASE 2 : AL < Rb  AHWhen Rb is higher than AL but lower than AH , only the High-type investors will be netborrowers in the credit market. Young Low-type investors will sell their unsecured notes topurchase credit contracts in the market, or they will simply keep their unsecured notes andsell them when old. In steady state, the market clearing condition (2.14) becomes:dUH +RbdUL =1Rb w  dSH . (2.20)Given dUL =1dUH , the value of new unsecured debt issued by the High-type investors is:dUH =1 1  (1Rb)1Rb✓w  RbAHkH◆. (2.21)Aggregate High-type capital is:kH = dSH + dUH =1  1RbRb1  (1Rb) AH w. (2.22)In this second case, there is no capital accumulated in the Low-type sector. A higher reduces the amount of High-type capital as it increases the rent consumed by the Low-typeinvestors.CASE 3 : AH < RbWhen the interest rate is higher than AH , both types of young investors want to be netlenders in the market. In this scenario it must be dSH = dSL = kH = kL = 0. From the marketclearing condition (2.14), all resources are employed to purchase existing unsecured notes inevery time:RbdUH + dUL=1Rbw. (2.23)We can now summarize our results:kH =8>>>>>>>>><>>>>>>>>>:w if Rb = R⇤(1) 1RbRbRbAL1AL1 RbAH+(1) 1RbRbAHAL1ALw if R⇤ < Rb  AL1(1Rb)Rb1(1Rb)AHw if AL < Rb  AH0 if Rb > AH, (2.24)21kL =8>>>>>>>>><>>>>>>>>>:0 if Rb = R⇤ 1RbRbRbAH1H1 RbAL+(1) 1RbRbALAH1AHw if R⇤ < Rb  AL0 if AL < Rb  AH0 if Rb > AH. (2.25)Figures 2.3, 2.5 and 2.7 plot the allocation of High-type and Low-type capital against Rb if1  AL < AH , AL < 1  AH and AL < AH < 1, given  = 0.5. The figures confirm thatthe emergence of a bubble misallocates capital only if Rb < AL. We can state the followingProposition.PROPOSITION 1: A necessary condition for bubbles inducing a misallocation of factorsis Rb < AL.We also want to examine how the bubble affects the aggregate accumulation of capital, theoutput and the welfare of the economy.PROPOSITION 2: The emergence of a bubble always reduces aggregate output and cap-ital. The effect on aggregate consumption can be positive only if AH < 1.The proof of Proposition 2 is in Appendix 1. Figures 2.4, 2.6 and 2.8 plot the steady statevalues of total output and consumption against Rb, given  = 0.5. In this model, a bubble isalways contractionary. This result does not only derive from the typical crowding-out effect.The model adds an additional contractionary effect associated with the misallocation of factors.However, a bubble may still increase aggregate consumption, but only when the economy isdynamically inefficient.29Finally, we can analyze how the identity of the investor that issues bubbly debt influencesthe aggregate economy.PROPOSITION 3: An increase in  always reduces aggregate output and capital. Theeffect on aggregate consumption can be positive only if AH < 1.Proposition 3 is proved in Appendix 2. Intuitively, when Low productivity investors issuea larger share of unsecured notes, factors are misallocated and output is lower. In addition,since Low-type investors earn lower returns, a larger share of the workers’ future endowmentmust be allocated to the repayment of bubbly debt. This, eventually, reduces the total stockof capital.29This is in line with the original theory by Tirole.22To conclude, the model described here adds a new dimension to existing theories of rationalbubbles. Bubbles do not only affect the aggregate accumulation of capital, they also have a re-allocation effect. Productive factors can be crowded out from specific sectors to be re-allocatedto others. For a given interest rate, the effect of a bubble depends on this re-allocation of factors.In particular, the cost of a bubbly episode may be higher if it involves a large misallocation ofcapital towards low productive sectors.This model, however, still does not tell us which investors would have an advantage inthe issuing of bubbly debt. In addition, the contraction in output is always associated with areduction in the stock of capital. In the next section, I will introduce some risk in the activityof the investors - which will affect their life expectancy on the market and, thereafter, theirability to maintain a bubbly scheme and accumulate capital over time. I will show that abubble can boost aggregate capital accumulation even if that induces a misallocation of factorsand a decrease in total production.2.4 Credit Bubbles and Misallocation in a Model withRisky InvestmentsIn this section I will extend the previous model by introducing a mechanism which predictsthe misallocation equilibrium in a unique way. Importantly, the same mechanism will alsoopen the doors for capital accumulation even if the bubble is contractionary. Here, investorswill live for more than two periods but they will face some risk in their investment activitywhich will affect their life expectancy on the market and, thereafter, their ability to maintaina bubbly scheme and accumulate capital over time. In addition, workers will now supply laborand make an intertemporal consumption choice when young.30 All agents are assumed to berisk neutral.I will describe the problem faced by workers and investors in the following subsection. Notethat, for simplicity, agents behave as if bubbles were deterministic. In looking at the dynamics,I will assume that the shocks to the system are unexpected.2.4.1 OLG WorkersWorkers live for two periods as in the previous version of the model. However, they nowchoose their total labor supply when young and their consumption in both young and old30This aspect will be relevant when introducing nominal rigidities in the second chapter.23periods, by maximizing the following utility:log (cY,t) 'ht + log (cO,t+1) (2.26)subject to cY,t = wtht  lt+1 and cO,t+1 = Rt+1lt+1, where lt+1 denotes lending in thecredit market. For simplicity I assume that the disutility from working is linear. The solutionto the problem gives the aggregate supply of labor and lending:ht =2'(2.27)lt+1 =12wtht =wt'. (2.28)2.4.2 Risky InvestmentsInvestors are still grouped into two categories of mass one - High-type and Low-type - butthey now live for more than two periods. Specifically, each investor has an i.i.d. probability of surviving in each period t. Then, in each period a mass (1 ) of old investors leave themarket and the same number of new investors enter the market with endowment e.31 Similarlyto the previous section, the investors want to maximize their consumption in their last periodof life.32 Then, in all the previous periods, they will always reinvest and continue to accumulatecapital.Again, the investors have a storing technology that will allow the installation of a specifickind of capital to rent in the following period to High-type or Low-type production. Unlikethe activities described in the previous section, here the storing activity is risky. In particular,with respective probabilities (1 "H) and (1 "L), the storing can fail and the investor canend up with no capital in the following period. I make the assumption that these shocks areidiosyncratic and not insurable.Production functions are now Cobb-Douglas combining capital and labor:Ajk↵j,th1↵j,t for j 2 {H,L} . (2.29)31Borrowing banks are modeled in a similar fashion in the model of bank runs described by Gertler andKiyotaki (2015).32Note that the same decision would derive if investors maximized a linear utility over consumption in differentperiods,P1t=0 cm,t, and the return from borrowing and investing was always higher than 1.24I make the following assumptions:ASSUMPTION 2: "H < "L.ASSUMPTION 3: "↵HAH > "↵LAL.Assumption 2 states that the probability of failing is higher for an H-type investor. Nonethe-less, Assumption 3 confirms that the overall H-type productivity is still higher. These premisesdescribe an environment in which higher productivity sectors are also riskier. Conversely, lowproductive sectors offer more stability over time. Then, the two types of investment offer adifferent combination in the risk-return spectrum.An investor m, of type H or L, raises external funding in the credit market and faces asimilar borrowing constraint:Rt+1dSm,t+1  MRKj,t+1"jim,t+1 for j 2 {H,L} , (2.30)where dSm,t+1 and im,t+1 are secured debt and investment. That is to say, an investor of typej can secure his borrowing up to a fraction  of his expected capital income. The investorscan also expand their borrowing by issuing bubbly debt. At this point, a further restriction isimposed:ASSUMPTION 4: A debt contract can be exchanged as long as the issuer has positiveequity.Assumption 4 comes with an important implication: when an investor fails or dies, allthe bubbly notes that he has issued will burst.33 This is a more accurate description of whathappens in the real world where tradable securities fail automatically with their issuers’ failure,or where financial institutions issue short-term notes which are rolled over under the same roof.Assumption 4 introduces a gap in the expected duration of H-type and L-type activities. It isworth pointing out that, given that H-type investors experience a shorter life expectancy onthe market, they have a lower probability of rolling over a bubbly scheme.2.4.3 Equilibrium and Steady State SolutionsThe equilibrium in the economy is now defined as follows:DEFINITION: A competitive equilibrium is a list of consumption, lending, secured andunsecured debt, capital, labor, and prices such that:33Note that an investor whose storage activity fails will also end up with zero consumption.25(i) Young workers maximize their utility (2.26) by choosing ht and lt+1. Old workersconsume Rtlt(ii) An investor m of type j who is still active in the market in period t chooses im,t+1,lUm,t+1 and dSm,t+1, given dUm,t+1 and prices (Rt+1,MRKj,t+1), maximizing profits in the lastperiod of his life1Xq=1(1 )q1"j⇥MRKj,t+qim,t+q Rt+qdSm,t+q  lUm,t+1⇤for j 2 {H,L} (2.31)subject to budget constraintcm,t + im,t+1 + lUm,t+1 = MRKj,tim,t RtdSm,t + dSm,t+1 + dUm,t+1, (2.32)borrowing constraint (2.30) and resource constraintsdSm,t+1  MRKj,tim,t RtdSm,t + dUm,t+1and lUm,t+1  0.An investor who dies in period t, consumes his final income cm,t = MRKj,tim,tRtdSm,t  lUm,t,while an investor who fails leaves the market with no final consumption(iii) Factors are paid at their marginal productivity:wt = (1 ↵)AH✓kH,thH,t◆↵= (1 ↵)AL✓kL,thL,t◆↵(2.33)MRKj,t = ↵Aj✓hj,tkj,t◆1↵for j 2 {H,L} (2.34)with kj,t = "j´m2j im,t for j 2 {H,L}(iv) Agents hold consistent beliefs about the path of dUj,t+1 for j 2 {H,L}(v) All markets clear in every period.As described in the previous section, the necessary condition to have bubbles misallocatingresources is that both borrowing constraints are binding. Therefore, I make the followingassumption.ASSUMPTION 5: Rt+1 < "LMRKL,t+1 8 t. 3434The condition is on variables endogenously determined in the model. Therefore, it implicitly sets restrictionson parameters so that all the equilibria we will characterize (with or without bubbles) respect the inequality.26Note that Assumption 5 implies Rt+1 < "HMRKH,t+1 a fortiori. All investors will try toborrow until their constraints bind and only the workers will lend in the credit market.I begin by characterizing the steady state equilibria of the economy. Without bubbles inthe economy, the steady state interest rate is:35R⇤ = 2↵1 ↵ . (2.36)The previous section described bubbly debt equilibria as possible if Rb was lower than thegrowth rate of the economy. This was possible because a debt security could also be exchangedafter the death of the issuer. Here a bubbly scheme will burst if the issuer dies or fails, whichmeans that in a steady state with bubbles, High-type and Low-type investors cannot promisea return higher than "H and "L.36 From now on, I will make the following assumption:ASSUMPTION 6: "H  R⇤ < "L.Assumption 6 implies that only L-type investors can run a bubbly scheme in steady state.By backward induction, only L-type investors can credibly initiate a bubbly scheme becausetheir survival rate in the market is higher given a lower probability of failure. A rationalbubbly scheme relies on the expectation that the agents will continue to buy in the longrun. Borrowers with riskier projects have a lower probability of survival and cannot sustaina long term pyramid scheme. In this course of event, a bubble will necessarily prompt themisallocation of resources from higher to lower productive borrowers. The interest rate Rb inthis bubbly equilibria will be such that R⇤  Rb  "L < 1.The dynamics of aggregate capital can now be set out in both sectors:kH,t+1 = "H⇢(1 ) e+  (1 ) ↵1 ↵wthH,t +Rt+1↵1 ↵wt+1hH,t+1(2.37)kL,t+1 = "L⇢(1 ) e+  (1 ) ↵1 ↵wthL,t +Rt+1↵1 ↵wt+1hL,t+1+"L⇢lt+1  Rt+1↵1 ↵wt+1ht+1 Rt✓lt  Rt↵1 ↵wtht◆. (2.38)35We can solve by plugging (33) inR⇤w'= ↵⇣AHk↵Hh1↵H +ALk↵Lh1↵L⌘. (2.35)36Note that the implicit assumption is that unsecured funds are randomly allocated inside the mass of H-typeand L-type investors who are in the market at time t.27The curly braces refer to the H-type and L-type aggregate investments in time t. Newly-arrivedinvestors of both types invest their endowment e. Pre-existing investors who remain in the mar-ket in period t, on aggregate reinvest their income: (1 )MRKj,tkj,t = (1 ) ↵1↵wthj,t,for j 2 {H,L}. All investors in the market will also invest all external funding they are ableto raise in the credit market: Rt+1MRKj,t+1kj,t+1 =Rt+1↵1↵wt+1hj,t+1, for j 2 {H,L}. Inaddition, L-type investors can invest the rent they obtain from issuing unsecured debts. In thelast line we can see that the rent is given by the portion of current unsecured debt that is notallocated to the repayment of past unsecured debt. In an equilibrium with no bubbles, therent is equal to 0. Finally, both types of aggregate investments are fractioned by the respectivestorage survival rate.In steady state the two equations can be simplified:kH = "H⇢(1 ) e+ (1 ) + Rb↵1 ↵whH(2.39)kL = "L⇢(1 ) e+ (1 ) + Rb↵1 ↵whL +1Rb Rb R⇤Rbw'. (2.40)Substituting into (2.33), the steady state labor allocation is finally obtained as a function ofw:hH =(1 ) e⇣w(1↵)"↵HAH⌘ 1↵ h (1 ) + Rbi↵1↵w(2.41)hL =(1 ) e+ 1Rb RbR⇤Rb w'⇣w(1↵)"↵LAL⌘ 1↵ h (1 ) + Rbi↵1↵w. (2.42)It is easy to see that in the bubble-free equilibrium, i.e. when Rb = R⇤, the allocation ofcapital and labor is driven by the aggregate productivities "↵HAH and "↵LAL. Since the latter issmaller, High-type investors receive more capital and labor. The rise of a bubble misallocatesfactors in favor of the Low-type investors.The following Proposition can now be stated.PROPOSITION 4: A bubble always reduces total output.A formal proof is provided in the Appendix. Intuitively, it would seem that a bigger Rb in-creases the amount of unsecured debt in the economy, which would raise both the misallocationand the crowding-out of capital. As expected, bubbles in this section are always contractionary.Nevertheless, this does not necessarily imply a reduction in the aggregate stock of capital as28it did in the previous section.PROPOSITION 5: There exist steady state equilibria with bubbles in which aggregatecapital increases.The proposition is proved in Appendix 4. The bubbly episodes preceding a financial crisisare typically characterized by a fast accumulation in capital. In particular, in the years priorto 2008 we saw a boom in housing and mortgage loans. The original theory of rational bubblescould not explain this phenomenon. In Tirole’s framework, a bubble would reduce capitalwhen the economy is dynamically inefficient. The addition of credit constraints in the newliterature on rational bubbles, has introduced a new class of bubbly equilibria: by improvingthe intratemporal allocation of funding, bubbles can boost output and capital. In this sectionI introduced a further type of bubbly episode. This bubble reduces output and increasescapital by misallocating resources towards low productive sectors which, nonetheless, have ahigher propensity to accumulate. Our result is driven by the assumption that low productivesectors have a lower fundamental risk. Interestingly, the model predicts the emergence ofnon-fundamental risk in sectors that are fundamentally more stable.2.4.4 The Dynamics of the ModelThis section will set out the simulated dynamics of the model when the system is hit byunexpected shocks to the interest rate Rt. A summary of the three experiments proposed inthis section is presented in Table 2.5.I start by analyzing the transition dynamics between the bubble-free steady state, charac-terized by R⇤, and the bubbly steady state with Rb = "L. The model is solved numerically.The share of capital is in line with data from developed countries: ↵ = 0.35. The selection ofthe remaining parameters respects the assumptions set out in the previous section. Specifically,I set AH = 1.9, AL = 1.1, "H = 0.13, "L = 0.6,  = 0.75,  = 0.4, e = 0.001, ' = 1.  islow enough so that Assumption 5 is respected. Similarly, the choice for , "H and "L is madeto meet Assumption 6. In particular, to confirm Proposition 5, "H is set sufficiently smallrelatively to "L that a reallocation of funding towards L-type investors would boost capitalaccumulation. In this simulation the economy starts from a bubble-free steady state: in period11 the interest rate rises from R⇤ to Rb = "L; in period 71 the bubble bursts, the returndrops and converges to R⇤.Figure 2.9 and 2.10 report the path for the allocation of capital and labor for the firstexperiment. While the reallocation in the labor market is symmetrical, given a fixed total labor29supply, we can see how the increase in the amount of L-type capital overtakes the reduction inH-type capital when the bubble appears. This can also be observed in the path for aggregatecapital presented in Figure 2.11. However, the rise in the aggregate stock of capital is notreflected in a long run expansion in output. Total production gradually decreases at theemergence of the bubble and only returns to its initial steady state level when the bubblebursts (Figure 2.12).In the two remaining exercises, I analyze the system in the case in which Assumption 6 isnot respected and both types of investors can potentially issue unsecured notes. With respectto before, I assume "H = "L = 0.13 and  = 1 ⇥ 10100 and I study the transition betweenthe bubble-free steady state and a bubbly steady state characterized by Rb = R⇤ + 1⇥ 105.Note that R⇤ and Rb are now set extremely small in order to minimize the crowding-outeffect of bubbles and reproduce the positive growth result proposed by the recent literatureon rational bubbles. In Figure 2.13, I report the path for H-type capital, L-type capital andaggregate output when assuming that only H-type investors issue unsecured notes. As we cansee, when the bubble emerges, the high productivity sector increases its capital while the lowproductivity one reduces it. In particular, the crowding-out in investment does not offset thispositive reallocation of capital and the aggregate output increases. Finally, in Figure 2.14, Ireplicate the same exercise in the case in which only the L-type investors issue unsecured notes.As in the initial simulation, the bubble induces a recession given that the negative reallocationof capital is summed to the crowd-out effect. However, aggregate capital can not increase giventhat the two sectors now face the same risk.An apparent drawback of this model is the timing of the expansion and the recession.Bubbly times are generally expansionary, at least in the short run; recessions typically startat the burst of the bubble. In the second chapter of the dissertation, I will add nominalrigidities to our environment and show how a rise and drop in nominal returns can induce botha short-run demand effect and a long-run reallocation of factors.2.5 ConclusionsFinancial crises are typically preceded by a credit boom. According to a widespread view,the cost of a crisis originates in the sudden freezing of the credit markets. Recent contributionsto the literature on rational bubbles associate these fluctuations in credit to bubbly episodes.In these papers, bubbles expand output and capital by improving the allocation of fundingwhen productive agents are financially constrained. The burst of the bubble would then lead30to a recession.The evidence, however, shows that a rapid growth in credit promotes a misallocation ofresources towards low productive industries. For example, housing and real estate sectors arethe usual recipients of an increased share of capital in a credit boom. This chapter shows howthis phenomenon can be explained in the rational bubble framework. Here, investors withdifferent productivities can borrow by pledging their future income as collateral or by pledgingthe repurchase of debt by future lenders. The key intuition for the misallocation result is thatborrowing through unsecured debt does not require high productivity. Instead, a credit bubblefavors those borrowers who have a low probability of exiting the market in the future and canmaintain a long-lived scheme.An important result of the theory is that bubbles can promote capital accumulation even ifthey are contractionary. Funding would be reallocated towards lower productive sectors whichhave a higher propensity for accumulation. This explains both the investment misallocationand the growth in capital stock that can be observed during a credit boom.31Table 2.1: The Effect of the Growth of Credit to the PNFS on Factors’ Allocation when Industry’s TFPGrowth is Country Specific(1) (2) (1) (2) (1) (2) (1) (2) (1) (2)0.794*** 2.312*** 0.004 *0.187 0.076** 0.039 0.046 0.170 0.538*** 1.175**(0.051) (0.119) (0.044) (0.146) (0.032) (0.102) (0.032) (0.133) (0.137) (0.567)*0.072*** *0.051*** *0.003 *0.008 *0.014*** *0.014*** *0.015*** *0.014*** *0.074*** *0.073***(0.007) (0.006) (0.006) (0.007) (0.004) (0.004) (0.004) (0.004) (0.021) (0.021)*0.010*** 0.001 0.000 *0.001 *0.005(0.001) (0.001) (0.001) (0.001) (0.004)0.132 0.260*(0.178) (0.143)*0.043* *0.044*(0.026) (0.026)*0.026 *0.026(0.055) (0.055)*0.026 *0.027(0.060) (0.060)*0.325 *0.258(0.598) (0.601)*0.109*** *0.110***(0.032) (0.032)Number6of6observations 384 384 284 284 379 379 378 378 312 312R2 0.639 0.766 0.629 0.631 0.765 0.765 0.749 0.750 0.272 0.275Debt*to*Equity6Ratio6in62001Average6Asset6Growth6of6Compustat6CompaniesInteraction6(TFP6Growth6X6Credit6Growth6PNFS)Interaction6(TFP6Growth6X6Credit6PNFS6to6GDP6in62001)Industry's6share6of6total6Value6Added6in62001Industry's6share6of6total6Capital6in62001Industry's6share6of6total6Employment6in62001Industry's6share6of6total6Hours6Worked6in62001Value&Added&Growth Capital&Growth Employment&Growth Hours&worked&growth Debt<to<Equity&Ratio&GrowthTFP6Growth6Notes: Data on credit are from the "Total credit to the non-financial sector" database by the Bank for International Settlements. Data on industry growthand productivity are from the "EU KLEMS" database by the Groningen Growth and Development Center. Debt-to-Equity ratios are average across companiescomputed from Compustat Global and North America.32Table 2.2: The Effect of the Growth of Credit to NFC on Factors’ Allocation when Industry’s TFP Growthis Country Specific(1) (2) (1) (2) (1) (2) (1) (2) (1) (2)0.819*** 1.610*** (0.030 0.045 0.059* 0.057 0.034 0.110 0.534*** 0.508*(0.047) (0.088) (0.044) (0.117) (0.031) (0.064) (0.031) (0.070) (0.135) (0.282)(0.078*** (0.100*** 0.002 0.004 (0.011*** (0.011*** (0.013*** (0.017*** (0.081*** (0.080***(0.006) (0.006) (0.006) (0.006) (0.004) (0.004) (0.004) (0.005) (0.022) (0.024)(0.008*** (0.001 0.000 (0.001 0.000(0.001) (0.001) (0.001) (0.001) (0.003)0.077 0.415***(0.170) (0.153)(0.043* (0.043(0.026) (0.026)(0.025 (0.025(0.056) (0.056)(0.025 (0.025(0.060) (0.060)(0.347 (0.350(0.597) (0.598)(0.108*** (0.108***(0.032) (0.032)Number6of6observations 384 384 284 284 379 379 378 378 312 312R2 0.668 0.745 0.628 0.629 0.763 0.763 0.748 0.749 0.273 0.273Debt(to(Equity6Ratio6in62001Average6Asset6Growth6of6Compustat6CompaniesInteraction6(TFP6Growth6X6Credit6Growth6NF6Corp.)Interaction6(TFP6Growth6X6Credit6NF6Corp.6to6GDP6in62001)Industry's6share6of6total6Value6Added6in62001Industry's6share6of6total6Capital6in62001Industry's6share6of6total6Employment6in62001Industry's6share6of6total6Hours6Worked6in62001Value&Added&Growth Capital&Growth Employment&Growth Hours&worked&growth Debt<to<Equity&Ratio&GrowthTFP6Growth6Notes: Data on credit are from the "Total credit to the non-financial sector" database by the Bank for International Settlements. Data on industry growthand productivity are from the "EU KLEMS" database by the Groningen Growth and Development Center. Debt-to-Equity ratios are average across companiescomputed from Compustat Global and North America.33Table 2.3: The Effect of the Growth of Credit to the PNFS on Factors’ Allocation when the US Industry’sTFP Growth is used as Proxy(1) (2) (1) (2) (1) (2) (1) (2) (1) (2)!0.033** !0.037*** !0.026*** !0.027*** !0.032*** !0.034*** !0.030*** !0.032*** !0.056** !0.055**(0.013) (0.013) (0.009) (0.009) (0.006) (0.006) (0.006) (0.006) (0.026) (0.027)!0.004*** !0.001 !0.002*** !0.002*** 0.000(0.002) (0.001) (0.001) (0.001) (0.003)0.190 0.225(0.254) (0.252)!0.046* !0.047*(0.026) (0.026)!0.062 !0.074(0.057) (0.056)!0.053 !0.065(0.063) (0.062)!0.450 !0.449(0.665) (0.666)!0.114*** !0.115***(0.035) (0.035)Number5of5observations 348 348 255 255 346 346 345 345 284 284R2 0.331 0.345 0.640 0.641 0.768 0.776 0.749 0.756 0.244 0.244Average5Asset5Growth5of5Compustat5CompaniesInteraction5(TFP5Growth5in5the5US5X5Credit5PNFS5to5GDP5in52001)Industry's5share5of5total5Value5Added5in52001Industry's5share5of5total5Capital5in52001Industry's5share5of5total5Employment5in52001Industry's5share5of5total5Hours5Worked5in52001Debt!to!Equity5Ratio5in52001Value&Added&Growth Capital&Growth Employment&Growth Hours&worked&growth Debt<to<Equity&Ratio&GrowthInteraction5(TFP5Growth5in5the5US5X5Credit5Growth5PNFS)Notes: Data on credit are from the "Total credit to the non-financial sector" database by the Bank for International Settlements. Data on industry growthand productivity are from the "EU KLEMS" database by the Groningen Growth and Development Center. Debt-to-Equity ratios are average across companiescomputed from Compustat Global and North America.34Table 2.4: The Effect of the Growth of Credit to NFC on Factors’ Allocation when the US Industry’s TFPGrowth is used as Proxy(1) (2) (1) (2) (1) (2) (1) (2) (1) (2)!0.025* !0.062*** !0.021** !0.022** !0.027*** !0.041*** !0.026*** !0.037*** !0.052** !0.046(0.013) (0.015) (0.009) (0.009) (0.006) (0.007) (0.006) (0.007) (0.026) (0.030)!0.008*** !0.002 !0.003*** !0.002*** 0.001(0.002) (0.001) (0.001) (0.001) (0.004)0.178 0.277(0.255) (0.250)!0.046* !0.046*(0.026) (0.026)!0.057 !0.072(0.058) (0.057)!0.050 !0.063(0.063) (0.063)!0.468 !0.473(0.665) (0.666)!0.114*** !0.115***(0.035) (0.035)Number6of6observations 348 348 255 255 346 346 345 345 284 284R2 0.326 0.363 0.634 0.637 0.763 0.772 0.746 0.752 0.243 0.244Average6Asset6Growth6of6Compustat6CompaniesInteraction6(TFP6Growth6in6the6US6X6Credit6NF6Corp.6to6GDP6in62001)Industry's6share6of6total6Value6Added6in62001Industry's6share6of6total6Capital6in62001Industry's6share6of6total6Employment6in62001Industry's6share6of6total6Hours6Worked6in62001Debt!to!Equity6Ratio6in62001Value&Added&Growth Capital&Growth Employment&Growth Hours&worked&growth Debt<to<Equity&Ratio&GrowthInteraction6(TFP6Growth6in6the6US6X6Credit6Growth6NF6Corp.)Notes: Data on credit are from the "Total credit to the non-financial sector" database by the Bank for International Settlements. Data on industry growthand productivity are from the "EU KLEMS" database by the Groningen Growth and Development Center. Debt-to-Equity ratios are average across companiescomputed from Compustat Global and North America.35Figure 2.3: Steady state values of kH and kL as a function of Rb:  = 0.5 and 1  AL < AH0 R* 1k*kHkLFigure 2.4: Steady state values of aggregate output and consumption as a function of Rb: = 0.5 and 1  AL < AH0 R* 1Y*YC36Figure 2.5: Steady state values of kH and kLas a function of Rb:  = 0.5 and AL < 1  AH0 R* AL 1k*kHkLFigure 2.6: Steady state values of aggregate output and consumption as a function of Rb: = 0.5 and AL < 1  AH0 R* AL 1Y*YC37Figure 2.7: Steady state values of kH and kL as a function of Rb:  = 0.5 and AL < AH < 10 R* AL AH 1k*kHkLFigure 2.8: Steady state values of aggregate output and consumption as a function of Rb: = 0.5 and AL < AH < 10 R* AL AH 1Y*YC38Table 2.5: Summary of simulated dynamics experimentsPermanent positiveshock to Rt at t = 11Permanent negativeshock to Rt at t = 71"H "L  Who issuesunsecured notes1) From R⇤ = 0.43 toRb = 0.45From Rb = 0.45 toR⇤ = 0.430.13 0.6 0.4 L-type, given"H  R⇤ < "L2) From R⇤ ⇡ 0 toRb = R⇤ + 1⇥ 105From R⇤ + 1⇥ 105to R⇤ ⇡ 00.13 0.13 1⇥ 10100 H-type, byassumption3) From R⇤ ⇡ 0 toRb = R⇤ + 1⇥ 105From R⇤ + 1⇥ 105to R⇤ ⇡ 00.13 0.13 1⇥ 10100 L-type, byassumptionNotes: All remaining parameters are the same in the three experiments: ↵ = 0.35, AH = 1.9, AL = 1.1,  = 0.75, e = 0.001 and ' = 1.39Figure 2.9: Simulation of the dynamics for kH,t and kL,t (Experiment 1)0 20 40 60 80 100 120 14000.010.020.030.040.050.060.070.080.090.1← rise← burst kH,tkL,tThe dynamics is initiated by an unexpected positive shock to Rt at time 11 and a negative shock at time 71.Figure 2.10: Simulation of the dynamics for hH,t and hL,t (Experiment 1)0 20 40 60 80 100 120 14000.20.40.60.811.21.41.61.82← rise← bursthH,thL,tThe dynamics is initiated by an unexpected positive shock to Rt at time 11 and a negative shock at time 71.40Figure 2.11: Simulation of the dynamics for the total capital kH,t + kL,t (Experiment 1)0 20 40 60 80 100 120 1400.080.090.10.110.120.130.140.150.16← rise← bursttotal capitalThe dynamics is initiated by an unexpected positive shock to Rt at time 11 and a negative shock at time 71.Figure 2.12: Simulation of the dynamics for the total output Yt = YH,t + YL,t (Experiment 1)0 20 40 60 80 100 120 1401.2051.211.2151.221.225← rise← bursttotal outputThe dynamics is initiated by an unexpected positive shock to Rt at time 11 and a negative shock at time 71.41Figure 2.13: Simulation of the dynamics for kH,t , kL,t and total output: "H = "L and only the H-typeinvestors issue unsecured notes (Experiment 2)0 20 40 60 80 100 120 1400.1067650.1067660.1067670.1067680.1067690.1067700.1067710.1067720.1067730.1067740.106775kH,t0 20 40 60 80 100 120 1400.0000350.0000360.0000370.0000380.0000390.0000400.0000410.0000420.0000430.0000440.000045kL,t0 20 40 60 80 100 120 1401.36271.36271.36271.36271.36271.36271.36271.3627← rise← bursttotal outputThe dynamics is initiated by an unexpected positive shock to Rt at time 11 and a negative shock at time 71. The bubble induces a positive reallocation ofcapital that boosts output. Note that the scale in the first two graphs is the same.42Figure 2.14: Simulation of the dynamics for kH,t , kL,t and total output: "H = "L and onlythe L-type investors issue unsecured notes (Experiment 3)0 20 40 60 80 100 120 14000.020.040.060.080.10.12← rise← burstkH,tkL,t0 20 40 60 80 100 120 1400.80.911.11.21.31.4← rise← bursttotal outputThe dynamics is initiated by an unexpected positive shock to Rt at time 11 and a negative shock at time 71.43Chapter 3Credit Bubbles in a Model withNominal Rigidities3.1 IntroductionFinancial bubbles typically have a bad reputation among the general public. However,boom-and-bust cycles in credit and housing prices are correlated with output and investments.For this reason, recent papers in the literature of rational bubbles have suggested that bubblesthemselves are beneficial to the economy; the problem is that they burst. In the first chapter, Ichallenged the productive efficiency role of bubbles and proposed a theory of rational bubbleswith misallocation of factors. In this chapter, I will propose a different channel by which theincrease in asset prices potentially produce a positive effect on output.Adding to the previous chapter, here the main contribution is the introduction of a demandeffect associated to nominal rigidities. Specifically, this demand effect will be consistent withshort-run variations in the real return Rt. The main intuition is that a boom in prices canbe sustained by two different forces: a higher demand and the emergence of a bubble. Acombination of the two effects can explain both the positive correlation with output and thenegative correlation with TFP.In Section 3.2 I describe the mechanism driving the demand effect. A nominal rise in thecredit market return, given price rigidities, implies a higher demand and an optimal increasein the labor supply. This, ultimately, boosts the returns on capital and confirms the original44rise in the credit market rate. In Section 3.3 I characterize the equilibrium of the model, whilein Section 3.4 I show how the return can fluctuate because of a monetary shock or a change ina bubble scheme. The simulations of the model report the opposite effect on output inducedby a monetary shock and the rise of a bubble. In particular, given a zero inflation path, aninitial increase supported by aggregate demand can turn into a bubble. Then, the output isboosted in the short run but falls toward a lower steady state in the long run.Finally, in Section 3.5, I analyze the optimal policy prescriptions. In my environment,stabilizing the output gap is not enough to prevent the emergence of a bubble. A socialplanner should limit the issuing of unsecured credit notes by the private sector and keep themonopoly power to create bubbly notes.The role of nominal prices in an environment with asset bubbles has been already studiedin Galí (2014) and Asriyan, Fornaro, Martin, and Ventura (2016). However, my frameworkdeparts from both papers. In Galí (2014) the presence of nominal rigidities allows a centralbank to manage the short-run real interest rate, and through this, to influence the short-runfluctuations of an asset bubble. However, similarly to my model, the monetary policy doesnot affect the long run conditions for the existence of bubbles. In Asriyan, Fornaro, Martin,and Ventura (2016) there are no price rigidities. The authors focus on the role of inflationwhen expectations on bubble returns are set in nominal terms. In their framework moneyis an additional asset with no fundamental value; then, agents are exogenously constrainedto hold it. By controlling the money supply the monetary authority determine the inflationrate and, ultimately, it influences the growth rate of bubbles. In my model, inflation may stillinfluence the real price of bubbly notes, but the monetary authority cannot generate it byprinting money. Importantly, the demand effect introduced in my model is not present in anyof the previous works.The chapter is also related to the literature on credit booms and financial crises. In anumber of papers, the cost of a financial crisis has been associated with the freezing of creditmarkets because of adverse selection. For example, in Gorton and Ordoñez (2014), the boom-ing period is characterized by an increasing opacity regarding the quality of collateral; thecrisis bursts when the lenders have the incentive to collect information about the true qualityof the investments. In Boissay, Collard, and Smets (2016), credit supply collapses after an ex-pansion in which less efficient banks self-select on the borrowing side of the interbank market.Differently from these papers, in my model, the deep recession that follows the credit boom israther explained by the misallocation of factors resulting from a credit bubble, combined with45a negative demand effect.The chapter is organized as follows. Section 3.2 describes the additions to the modelpresented in Chapter 2. In Section 3.3 I characterize the equilibrium. Section 3.4 describes howthe return on secured notes is related to both the existence of bubbles and the aggregate demandand reports the simulations of the model under three different scenarios: shocks to a bubblescheme, demand shocks and a mix of the two. Section 3.5 analyzes the policy prescriptions.Section 3.6 concludes.3.2 A Model of Rational Bubbles with Nominal RigiditiesThe model described in this section is an extension of the one exposed in Section 2.4 ofthe previous chapter. The economy is still populated by OLG workers, High-type investorsand Low-type investors. Workers supply labor, while investors produce capital goods. Laborand capital are combined by firms of type H and L to produce consumption goods. Tointroduce demand effects associated to nominal rigidities I will now assume that firms producedifferentiated goods and compete in a monopolistic fashion. Specifically, agents in the economyconsume two perfectly substitutable composite goods produced by firms of type H and L:Yt = YH,t + YL,t =ˆn2Hy⌘1⌘n,t dn ⌘⌘1+ˆn2Ly⌘1⌘ dn ⌘⌘1(3.1)for ⌘  1, where yn,t is the output of a single firm, while YH,t and YL,t are the aggregate outputsof High-type and Low-type firms. I assume that the firms in each of two sectors compose acontinuum of mass one. The implied composite prices are:Pt = PH,t = PL,t =ˆn2Hp1⌘n,t dn 11⌘=ˆn2Lp1⌘n,t dn 11⌘. (3.2)In equilibrium, the two composite prices must be equal, given that the two goods are perfectsubstitutes.I will describe the decisions of the workers, investors, and firms in separate subsections.For simplicity, I still assume that agents behave as if there were no shocks. In what follows,all variables in nominal terms will have a superscript N .3.2.1 Workers with Elastic Labor SupplyWorkers live for two periods and choose their total labor supply and consumption by max-46imizing the utilitylog (cY,t) 'ht + log (cO,t+1) (3.3)subject to cY,t = wNtPtht+⇧NtPtlt+1 and cO,t+1 =⇣RNt+1PtPt+1⌘lt+1. lt+1 denotes the real amountof lending in the credit market. wNt and ⇧Nt respectively denote the nominal wage and profits.RNt+1 is the nominal return. I am assuming that young workers own the monopolistic firmsand earn their profits. Then, the optimal supply of labor and lending are:ht =wNt ht⇧Nt + wNt ht2'(3.4)lt+1 =12✓wNtPth+⇧NtPt◆=wt'. (3.5)It is worthy to note that the labor supply increases with the relative share of labor income toprofits. This is crucial to generating demand effects in the economy.3.2.2 InvestorsInvestors of type H and L behave as in Subsection 2.4.2 of the previous chapter. Everytime they invest to obtain a specific type of capital to rent in the following period. I keepAssumption 2, 3 and 4 to reproduce the correlation between bubbles and misallocation.Finally, the borrowing constraint can be rewritten in nominal terms:RNt+1PtPt+1dSm,t+1  QNj,t+1Pt+1"jim,t+1 for j 2 {H,L} . (3.6)3.2.3 FirmsEach firm n maximizes its profitspn,tAjk↵n,th1↵n,t QNj,tkn,t  wNt hn,t for j 2 {H,L} (3.7)given prices QNj,t and wNt , and demand constraint yn,t =⇣pn,tPt⌘⌘Yj,t. Note that the priceof capital Qj,t can now be different from the marginal return on capital MRKj,t, given thepresence of monopolistic rents. I assume that the price of a good is set one period in advance:as long as no shock hits the economy, a firm will set the price at a constant markup ⌘⌘1 over47his marginal cost. Optimal capital and labor demand will be such thatn,tpn,t↵Aj✓hn,tkn,t◆1↵= QNj,t for j 2 {H,L} (3.8)n,tpn,t (1 ↵)Aj✓kn,thn,t◆↵= wNt for j 2 {H,L} , (3.9)where n,t is the portion of revenues allocated to the payment of factors. Note that, when afirm can optimally set his price, it must be n,t = ⌘1⌘ 8 n1. The aggregate t in period t canbe defined ast = H,tYH,tYt+ L,tYL,tYt, (3.10)where H,t and L,t are the respective shares of High and Low type firms. Fluctuations in twill be associated to demand effects. The incomes and profits in the economy can be rewrittenas a function of t and aggregate output Y Nt :QNH,tkH,t +QNL,tkL,t = t↵YNt , (3.11)wNt ht = t (1 ↵)Y Nt , (3.12)⇧Nt = (1 t)Y Nt . (3.13)Then, from (3.4), I can express the labor supply as an increasing function of t:ht =(1 ↵)t(1 t) + (1 ↵)t2'. (3.14)The workers are willing to increase their labor supply when the share of revenues allocated tothe payment of factors is larger.3.3 Equilibrium and Steady StateThe equilibrium in the economy is now defined as follows:DEFINITION: A competitive equilibrium is a list of consumption, lending, secured andunsecured debt, capital, labor, and prices such that:(i) Young workers maximize their utility (3.3) by choosing ht and lt+1. Old workers consumeRtlt1n,t is indeed the inverse of the firm’s markup.48(ii) An investor m of type j who is still active in the market in period t chooses im,t+1,lUm,t+1 and dSm,t+1, given dUm,t+1 and pricesRNt , QNj,t, Pt, maximizing profits in the last periodof his life1Xq=1(1 )q1"j"QNj,t+qPt+qim,t+q RNt+qPt+q1Pt+qdSm,t+q  lUm,t+1#(3.15)for j 2 {H,L}, subject to budget constraintcm,t + im,t+1 + lUm,t+1 =QNj,tPtim,t RNtPt1PtdSm,t + dSm,t+1 + dUm,t+1, (3.16)borrowing constraint (3.6) and resource constraintsdSm,t+1   QNj,tPtim,t RNtPt1PtdSm,t + dUm,t+1!and lUm,t+1  0.An investor who dies in period t, consumes cm,t =QNj,tPtim,t  RNt Pt1PtdSm,t  lUm,t, while aninvestor who fails leaves the market with no final consumption(iii) Each firm n chooses kn,t, hn,t at time t and pn,t at time t 1, maximizing (3.7)(iv) Agents hold consistent beliefs about the path of dUj,t+1 for j 2 {H,L}(v) All markets clear in every period.As in the previous chapter, I keep the assumption that the credit market return is lower thanthe marginal return of both types of investors. In addition, I still assume that "H  R⇤ < "L,so that only L-type investors can issue unsecured debt.In a deterministic world, nominal rigidities cannot play any role. If firms optimally settheir price, it must be:ht =(⌘  1) (1 ↵)1 + (⌘  1) (1 ↵)2'. (3.17)Given (3.17), the bubble-free steady state equilibrium interest rate is pinned down from thebinding borrowing constraint:R⇤ = 2↵1 ↵(⌘  1) (1 ↵)1 + (⌘  1) (1 ↵) . (3.18)49The dynamics of capital is the same as in Subsection 2.4.3:kH,t+1 = "H⇢(1 ) e+  (1 ) ↵1 ↵wthH,t +Rt+1↵1 ↵wt+1hH,t+1(3.19)kL,t+1 = "L⇢(1 ) e+  (1 ) ↵1 ↵wthL,t +Rt+1↵1 ↵wt+1hL,t+1+"L⇢lt+1  Rt+1↵1 ↵wt+1ht+1 Rt✓lt  Rt↵1 ↵wtht◆. (3.20)The steady state capital allocation is then:kH = "H⇢(1 ) e+ (1 ) + R↵1 ↵whH(3.21)kL = "L⇢(1 ) e+ (1 ) + R↵1 ↵whL + (1R)1R⇤ 1R↵1 ↵wh. (3.22)From the last equations we solve for the steady state labor allocation as a function of w andaggregate labor supply h:hH =(1 ) e⇣ ⌘⌘1w(1↵)"↵HAH⌘ 1↵ h (1 ) + Ri↵1↵w(3.23)hL =(1 ) e+ (1R) ⇥ 1R⇤  1R⇤ ↵1↵wh⇣ ⌘⌘1w(1↵)"↵LAL⌘ 1↵ h (1 ) + Ri↵1↵w. (3.24)Finally, the steady state wage w can be pinned down from the labor market clearing:hH + hL =(⌘  1) (1 ↵)1 + (⌘  1) (1 ↵)2'. (3.25)In the next section, I will study how the system behaves when hit by unexpected shocks tothe credit market return. I will show that, in this version of the model, the return is subject totwo shocks of different nature. First, as in the previous chapter, the interest rate can changebecause of the emergence and burst of a bubble. Second, a monetary shock can induce ademand effect because of the presence of nominal rigidities.3.4 Simulated Dynamics after Demand and Bubbly ShocksIn a deterministic environment, there is no difference between the expected and realized50returns. This also implies that both secured and unsecured notes would be associated withthe same interest rate, both ex-ante and ex-post. In order to properly analyze the effect ofunexpected shocks in the model, we need to formally introduce a distinction between theserates. In what follows I denote the ex-ante interest rate with REA,t. In equilibrium, this returnmust be the same across secured and unsecured notes. The realized returns from secured andbubbly notes are denoted instead with Rt and RB,t. Obviously, the two returns can diverge.For example, in the time in which a bubble bursts, RB,t collapses, while Rt does not.The relation between Rt and fluctuations to the aggregate demand can be derived from thebinding borrowing constraint:RNt = R¯t tYt⌘1⌘ Y¯t!✓PtPt1◆. (3.26)In Appendix 5 I describe how to obtain the formula above. The realized nominal return is afunction of a natural rate R¯t, a gap in the repayment of factors✓tYt⌘1⌘ Y¯t◆and inflation. R¯t isthe return that prevails without any demand shock. Then, it must be R¯t = REA,t. For oursimulations, I will set:  tYt⌘1⌘ Y¯t!✓PtPt1◆= ⌫t. (3.27)An unexpected change in ⌫t can be interpreted as a monetary or demand shock. A positiveshock will induce an increase in✓tYt⌘1⌘ Y¯t◆and, ultimately, in Rt. Intuitively, a higher supplyof labor given a same amount of capital would raise Qj,t and, by a relaxation of the borrowingconstraint, Rt. In normal times, on a path with zero inflation, it must be ⌫t = 1.The emergence and burst of a bubble influences Rt through R¯t. We can write:R¯t = REA,t = 2↵1 ↵(⌘  1) (1 ↵)1 + (⌘  1) (1 ↵)w¯twt1+ ⇠t. (3.28)The first element in the sum is the return we pin down from the binding borrowing constraintin the absence of monetary shocks and bubbles. The additional component ⇠t  0 appearsduring a bubbly episode. In normal times, it must be ⇠t = 0. Therefore, an increase in thereal return Rt can be associated with an economy contraction when driven by a change in R¯t,and an economy expansion when driven by a positive monetary shock. In this section, I willanalyze the effect of both types of shock.I will simulate the dynamics of the model under three different scenarios. First, I will51Table 3.1: Summary of simulated dynamics experimentsPermanent rise in RNt at t = 11 Permanent falls in RNt at t = 511) Driven by permanent positive shock to⇠t (bubble rise)Driven by permanent negative shock to⇠t (bubble burst)2) Driven by permanent positive shock to⌫t (positive demand effect)Driven by permanent negative shock to⌫t (negative demand effect)3) Driven by temporary positive shock to⌫t and permanent positive shock to ⇠tDriven by temporary negative shock to⌫t and permanent negative shock to ⇠tdescribe how the system reacts in response to a change in ⇠t. This is the scenario described inChapter 2 where a change in the real return is associated with the emergence and the burst ofa bubble. In the second simulation, I will analyze instead the effect of a permanent shock to⌫t. In this scenario, the shocks will only produce temporary deviations from the same steadystate. Finally, I will propose a simulation in which a temporary monetary shock turns into along run change in R¯t. A summary of three experiments is presented in Table 3.1.The model is solved numerically. ⌘ is set equal to 11, in order to have a 10% markup.The remaining parameters are similar to the ones chosen in Chapter 2: ↵ = 0.35, AH = 1.9,AL = 1.1, "H = 0.13, "L = 0.6,  = 0.75,  = 0.45, e = 0.001, ' = 1. In all three simulationsI analyze the effects of a positive and a negative shock to RNt . In particular, I assume thatin period 11 the changes in ⇠t and ⌫t induce a permanent rise in the nominal rate RNt , fromR⇤ = 0.42 to 0.43; then, from period 51 the rate RN falls back to 0.42. Specifically, the startingand final values are always ⇠t = 0 and ⌫t = 1. It is worthy to note that Rt will be differentfrom REA,t only in periods 11 and 51.In Figure 3.1, I plotted the path for RNt , Rt, ht, inflation ⇡t = PtPt1 and total output Ytfor the first simulation. Here the change in the nominal return is associated with an identicalchange in the real return: prices are constant along the entire interval. Moreover, nominalrigidities do not play any role since there is no demand shock: the labor supply is constant.This scenario is similar to the one described in Chapter 2. The emergence of the bubble inperiod 11 induces a misallocation of factors reducing the total output. The burst of the bubblebrings the economy back to the higher original steady state.Figure 3.2 reports the path for the same variables when the shocks to RNt is driven by apermanent change in ⌫t. In this case, there are no bubbles appearing in the economy. Thesudden increase in RNt triggers a demand effect in the time of the shocks, given that prices are52rigid. The real return reacts in an identical way only in the time of the unexpected shocks.Starting from the periods that follow the positive (negative) shock, the inflation rises (drops)and the real interest rate returns to the bubble-free steady state level. The monetary shocksproduce a temporary real effect. In the period of the increase (fall) in RNt , the labor supplyreacts in a positive (negative) way. The total output is boosted in period 11 because of thehigher labor supply. Then it gradually goes back to its original steady state. The oppositedynamics is triggered from period 51 on. Note that Rt and ⇡t do not follow a smooth pathafter the shocks. For example, Rt falls below the steady state level after the initial positiveshock. The reason can be seen in equation (3.28): a positive monetary shock that boosted theoutput at time t 1, induces a reduction in R¯t given an increase in the total lending.Finally, in Figure 3.3 I present the results of the third simulation. In this last experiment,the initial rise (drop) in RNt is driven by a positive (negative) change in ⌫t and induces animmediate demand effect as in the previous case. However, in the following periods, I assumethat prices do not adjust, ⌫t falls (jumps) back to 1, and the higher (lower) real return issupported by a change in ⇠t, i.e., by the emergence (burst) of a bubble. Such a dynamics maybe justified by a coordination on zero-inflation equilibria.2 Therefore, inflation keeps stationaryas in the first scenario; the total labor reacts in period 11 and 51 as in the second scenario.This experiment allows me to reproduce a situation in which the initial boom in market returnsinduces an immediate positive demand effect which gradually vanishes and gets replaced bya long run misallocation of factors. The output boom in period 11 turns into a recession inthe following periods. Similarly, the output drop in period 51 is followed by an expansion thatbrings the system back to the initial steady state.The last exercise proposed in this section provides a potential interpretation for the dy-namics of output and TFP that we observed in the recent times of low inflation. While aninitial boom is associated with a positive demand effect triggered by higher market returns,the reduction in TFP is driven by the emergence of a bubble and a misallocation of factors.In the next section, I will study the policy implications suggested by the model.3.5 Policy PrescriptionsIn this section, I will discuss how a social planner can restore an optimal equilibrium in theeconomy. A monetary authority, controlling the nominal value of the secured credit contracts,can effectively close the gap between the output Yt and its natural level Y¯t. However, this has2For example, a central bank may play the role of coordination device in supporting this equilibrium selection.53no effect on R¯t.In order to influence the real return R¯t and the allocation of factors, other instrumentsare needed. Given the simple structure of the framework set out here, an optimal allocationof factors is one in which all credit and labor are assigned to high productive investors.3 Inthis context, a planner would promote a reallocation by discouraging L-type activity. A simpleroute to this would be to tax the capital income of the L-type investors. In particular, for aproportional tax ⌧L,t, L-type investors would prefer to lend to H-type investors if(1 ⌧L,t) "LQL,t < Rt; (3.29)i.e., if the equilibrium interest rate was higher than the expected return from the L-typeinvestment.4 In the following I assume ⌧L,t is large enough to allow the condition to berespected.Bubbles are still possible even if high productive borrowers obtain the entire funds. In along run steady state, the social planner would like to target the return R¯g that maximizes theaggregate welfare of the economy:log12✓1 ↵⌘  1⌘◆YHR¯g+ log12R¯g✓1 ↵⌘  1⌘◆YHR¯g+(1 )↵⌘  1⌘YHR¯g+ R¯g1 1 R¯g e. (3.30)The first line refers to the utility of the workers; the second line reports the utility of the H-type investors and L-type investors. Given an optimal allocation of factors, a bubbly schemeis certainly contractionary - the only effect is to crowd-out H-type capital. However, by trans-ferring resources from younger to older agents, the consumption of the latter may increase ifthe economy is dynamically inefficient.A social planner can target an optimal rate R¯gt+1 by imposing its monopoly on the creationof bubbly notes. The planner would set a cap on the debt creation by the private sector: itmust be dH,t+1  R¯gt+1↵YH,t+1R¯gt+1 8 t. In addition he can directly introduce bubbly noteswhen R¯gt+1 is larger than the bubble-free rate R⇤t+1 and the workers have extra resources tolend. An optimal amount of unsecured notes dUt+1R¯gt+1can be issued by a government in3Since "↵HAH > "↵LAL, it is always "HMRKH,t > "LMRKL,t.4Note that a policy which reallocates resources towards productive borrowers is also desirable in the absenceof a bubble in the economy, as long as e > 0.54the form of government bonds,5 or by a central bank in the form of bank notes. Clearly, thefraction that the planner earns as a rent would be transferred to subsidize H-type investment.3.6 ConclusionsBoom-and-bust cycles in credit and asset prices can be associated with different effects.While we usually label these events as bubbly episodes, they may also be supported by a changein the aggregate demand. In this chapter, I showed how the actual emergence (burst) of abubble can be anticipated by an initial increase (fall) in the aggregate demand. Such a dynamicscan explain why, during the recent cycles, output and credit were positively correlated, whileTFP and credit were not.From a policy perspective, targeting the output gap is not enough to prevent the emergenceof a bubble in the private sector. In order to control bubbles, a monetary or fiscal authorityneeds to retain the monopoly on the creation of bubbly assets. Caps on the debt creation byprivate entities is a possible instrument to reach this goal.5A similar policy is suggested by Woodford (1990).55Figure 3.1: Simulation of the dynamics for RNt , ht, Rt, ⇡t and Yt: shocks to the value of bubbly debt(Experiment 1)0 10 20 30 40 50 60 70 80 90 1000.4180.420.4220.4240.4260.4280.430.432 RNt0 10 20 30 40 50 60 70 80 90 1000.511.522.53total labor0 10 20 30 40 50 60 70 80 90 1000.4180.420.4220.4240.4260.4280.430.432 Rt0 10 20 30 40 50 60 70 80 90 10000.20.40.60.811.21.41.61.82πt0 10 20 30 40 50 60 70 80 90 1001.041.0421.0441.0461.0481.051.052 total outputThe dynamics is initiated by an unexpected positive shock to R¯t at time 11 and a negative shock at time 51. Nominal rigidities play no role.56Figure 3.2: Simulation of the dynamics for RNt , ht, Rt, ⇡t and Yt: demand shocks (Experiment 2)0 10 20 30 40 50 60 70 80 90 1000.4180.420.4220.4240.4260.4280.430.432 RNt0 10 20 30 40 50 60 70 80 90 1001.71.711.721.731.741.751.761.77total labor0 10 20 30 40 50 60 70 80 90 1000.4050.410.4150.420.4250.430.435Rt0 10 20 30 40 50 60 70 80 90 1000.970.980.9911.011.021.03πt0 10 20 30 40 50 60 70 80 90 1001.0351.041.0451.051.0551.061.065total outputThe dynamics is initiated by an unexpected positive shock to RNt at time 11 and a negative shock at time 51. Nominal rigidities play a role only in theperiods of the shocks.57Figure 3.3: Simulation of the dynamics for RNt , ht, Rt, ⇡t and Yt: demand and bubbly shocks (Experiment3)0 10 20 30 40 50 60 70 80 90 1000.4180.420.4220.4240.4260.4280.430.432 RNt0 10 20 30 40 50 60 70 80 90 1001.711.721.731.741.751.761.77total labor0 10 20 30 40 50 60 70 80 90 1000.4180.420.4220.4240.4260.4280.430.432 Rt0 10 20 30 40 50 60 70 80 90 10000.20.40.60.811.21.41.61.82πt0 10 20 30 40 50 60 70 80 90 1001.031.0351.041.0451.051.0551.061.065total outputThe dynamics is initiated by an unexpected positive shock to RNt at time 11 and a negative shock at time 51. Nominal rigidities play a role only in theperiods of the initial shocks.58Chapter 4Liquidity Mismatch or BubblyMismatch?4.1 IntroductionThe 2008 financial crisis was triggered by a systemic run on unconventional short-term debtsecurities such as commercial papers and repurchase agreements. This has raised new concernsabout the risk of liquidity mismatch between assets and liabilities of financial institutions.The last Basel Accord has introduced explicit liquidity ratios for banks; recent papers byBrunnermeier, Gorton, and Krishnamurthy (2012) and Bai, Krishnamurthy, and Weymuller(2016) have proposed a new measure to assess the liquidity risk of an institution. According tothe traditional theories of liquidity mismatch, banks issue short-term debt to finance long-terminvestments. This process is beneficial to the economy, but it exposes financial institutions tothe risk of runs. However, a run on short-term debt can also be explained by the collapse of abubbly scheme on bank debt. The appearance of such a bubble would still raise a mismatchbetween assets and liabilities, but not to support the financing of long-term projects.In this chapter, I investigate the balance sheets of American Bank Holding Companies totest theories of liquidity transformation versus theories of bubbles. In particular, I want tofind out if periods of rising mismatch between assets and liabilities are associated with thetransformation of illiquid assets into liquid debt, or rather with the emergence of a bubble onliabilities. Answering this question is particularly relevant, given that the two hypothesis imply59different policy prescriptions. While traditional deposits are, to a large extent, insured by thegovernment, new types of liquid debt contracts are not. An extension of government insurancemay be justified if that supports a process of liquidity transformation. On the contrary, agovernment should typically prevent the appearance of a bubble, as I discussed in the previouschapters.In Section 4.2, I will rely on stylized theories of liquidity creation to obtain testable predic-tions. I compare two scenarios: a first one in which the bank can temporarily roll-over its debtto finance projects that are currently illiquid, but that will pay out in a future time; a secondone in which the bank can roll-over its debt forever, by effectively issuing bubbles. I will showthat in both scenarios, a mismatch arises between the cash from assets that the bank earnsand the repayment of debt. However, this mismatch is supported by a different underlyingmotivation and produces different predictions. The bank investing in illiquid projects can issuenew debt to pay the old one, but not to increase its current dividends. The bank issuing bub-bles has no such a constraint and will increase its dividend payouts. Although oversimplified,the framework captures some relevant features of the traditional models with rolling-over ofdebt. In particular, in models of liquidity transformation and bank runs such as Diamondand Dybvig (1983), Gertler and Kiyotaki (2015), and Dang, Gorton, Hölmstrom, and Ordoñez(2016), banks do not roll-over forever, and they eventually use their funds to repay the debt.In Section 4.3, I present the results of my empirical investigation over the balance sheetsof American Bank Holding Companies from 1986 to today. First, I analyze the balance sheetcomplementarities of financial institutions. I show that new types of short-term debt contractare more likely to be backed by securities rather than loans, while traditional deposits arethe usual complement of illiquid loans. Second, I test the previous theories by looking at thecorrelation between the cash-flow mismatch, measured as the ratio between the repayment ofshort-term debt and the cash from assets, and the payment of dividends. While the correlationis typically negative, it is flattened when focusing on the years after 2001 and controlling fortime and bank fixed effect. In particular, I show that the issuing of non-traditional short-termdebt securities is correlated with higher dividends.To the best knowledge of the author, the analysis proposed in this chapter is novel. Mostempirical papers try to measure the liquidity mismatch of financial institutions by lookingat the stock values from balance sheet data (generally combined with market price data). Atypical problem with liquidity ratios based on stock information is that they cannot report60the actual liquidity mismatch in case of emergency asset liquidation.1 In this paper, I donot attempt to provide a correct measure of the unobservable liquidity mismatch of a bank.Instead, I look at the actual cash flow from assets and its allocation to infer variations in thetransformation of illiquid assets or the build-up of a bubbly scheme.The chapter is organized as follows. In Section 4.2 I describe the theoretical motivationand derive the testable predictions. In Section 4.3 I report the empirical results. Section 4.4concludes.4.2 Theoretical PredictionsIn this section, I will describe the decision of an infinitely lived bank and derive the predictionsto be tested on the data. The bank’s optimal decision is restrained by a pledgeability constraint,similar to the one described in the previous chapters. The constraint sets a limit to therepayment of debt that the bank can credibly promise, based on the cash flow from assetsthat it will earn. I will describe two different scenarios in which this constraint is violatedand a mismatch between assets and liabilities arises. In the first scenario, the bank can investin an illiquid project, which is an asset that pays in T > 1 periods and it is not pledgeable.However, the constraint is temporarily relaxed and the bank can effectively roll-over its debtuntil the project pays off. In this scenario, I want to depict a process of liquidity transformationconducted by a financial institution. In the second scenario, the bank is allowed to violate thepledgeability constraint by issuing bubbly debt. In this scenario, the bank is not responsiblefor the repayment of its debt in excess.The bank maximizes its utility:1Xt=0t1t1  , (4.1)where t are the dividends at time t. Every time, the bank can invest in a liquid asset at+1,and obtain Qat+1 in the following period. In addition, it can raise external debt dt+1 at a fixedinterest rate R. When not investing in illiquid assets nor issuing bubbly debt, the decision issubject to constraint:Rdt  Qat. (4.2)1Bai, Krishnamurthy, and Weymuller (2016) try to do that by inferring liquidation prices from the market.However, this remains an imperfect way given that market prices in case of a systemic bank run are not reallyobservable.61The constraint imposes that the total repayment on debt must be lower than a fraction  of therevenues. It is worthy to note that such a constraint prevent the bank from engaging in Ponzi-schemes. However, the condition is stricter than a usual no-Ponzi game one. In particular,in this environment, the bank cannot be punished in case of default. Then, Qat should beinterpreted as the fraction of future income that the bank can credibly pledge.Assuming Q > R and Q < R, the constraint must be binding. This means that, withoutinvestment in illiquid assets and bubbly debt, the mismatch ratio must beRdtQat= . (4.3)In the two cases that I will describe below, the pledgeability constraint is violated and themismatch ratio increases for two different reasons. In the first case, at time 0, the bank canalso invest in an illiquid asset zT that pays at time T . Between 0 and T , the constraint isrelaxed and the bank can temporarily raise more debt. In the second case, between 0 andT , the bank can increase the mismatch by issuing bubbly debt. Then, at time T , the bubblebursts and the mismatch goes back to . The goal is to derive how the bank optimally changesits path of dividends when having the option of creating a liquidity or a bubbly mismatch.LIQUIDITY MISMATCH :At time 0, I assume that the bank can invest zT in an illiquid asset paying in T periods. Theasset is illiquid not just because it does not pay off immediately; it also cannot be efficientlytraded by the lenders.2 Therefore, the bank cannot use it as a pledge until the time in whichit pays off. However, I will assume that banks own a technology to relax their pledgeabilityconstraint when investing in the illiquid asset. Effectively, the bank can temporarily roll-overits debt. The scheme ends when the illiquid asset finally pays off.In what follows, I will assume that the illiquid asset pays QzzT at time T . The bank choosesat+1, zT and dt+1. The problem can be expressed in the following way:max1Xt=0tQat + 1{t=T}Qzz Rdt + dt+1  at+1  1{t=0}zT11  (4.4)2For example, in Dang, Gorton, Hölmstrom, and Ordoñez (2016), the consumers cannot efficiently hide theinformation regarding the investment outcome. In Gertler and Kiyotaki (2015), the households must pay amanagement cost if directly holding capital; however, in this last paper, the asset is not per-se illiquid, since itpays out in every period.62subject to constraintRdt  Qat + 1{0<tT} 1RTtQzzT . (4.5)The bank can effectively pledge the repayment from the illiquid asset only at time T . However,from 0 to T 1, the constraint is relaxed and the bank is allowed to issue more debt by holdingthe illiquid asset. A simple interpretation is that the bank can pledge a part of its future debtto repay the current one. Note that, even if the asset cannot be pledged, I am assuming that,for any 0 < t < T , the debt in excess is a discounted amount of the final pledgeable repayment.Therefore, debt can be rolled-over as long as it helps the bank to invest in zT .The problem is solved in Appendix 6. From 0 to T 1 and from T onwards, the bank musthold some liquid assets. In fact, they are the only instruments available to smooth consumptionacross these periods. Given that Q > R and Q < R, the constraint is binding and the optimaldividends path is such that:t+1t= Q1 1 QR! 18 0  t < T  1 and t  T. (4.6)Dividends would grow at a constant rate, which depends on the prices Q and R, and thetightness of the borrowing constraint.Between T  1 and T , it must be:TT1= max8>><>>: Q1 1 QR! 1;0B@ Qz⇢ (Q,Qz, R, T )T1  ⇣Q 11QR⌘T1  Qz⇢(Q,Qz,R,T )R1CA19>>=>>; ,(4.7)where ⇢ (Q,Qz, R, T ) < 1 is a function of the prices and the number of periods T . The bankdoes not invest in the illiquid asset if the second term in the curly brackets is smaller. Thisis the case in which the illiquid asset is not profitable enough. If instead the second term islarger, it must be zT > 0. In this case, the bank optimally reduces its stock of liquid assetbetween 0 and T  1, expecting for time T in which the illiquid asset is finally liquidated.When the bank invests in the illiquid asset a mismatch between debt repayment and incomefrom assets arises. Specifically, it isRdtQat=Qat +1RTtQzzTQat>  8 0 < t  T  1. (4.8)63In addition, the dividends jump to a higher level at time T , when the mismatch ratio goesback to . By investing in the illiquid asset, the bank keeps its dividends at a lower level inthe initial periods to raise them when the project pays off. Therefore, the analysis predicts anegative correlation between a liquidity mismatch and the level of dividends.BUBBLY MISMATCH :In the second scenario, I assume that the bank is allowed to violate the borrowing constraintby issuing bubbly notes as in the framework described in the previous chapters. However, attime T , I assume that the bubble bursts unexpectedly and the bank stops issuing bubbly notes.The bank now chooses both secured dSt+1 and unsecured debt dUt+1, solving the problem:max1Xt=0tQat RdSt + dSt+1 + dUt+1  !t  at+111  (4.9)subject to constraintsRdSt  Qat (4.10)anddUt  d¯Ut . (4.11)The borrowing constraint is still binding for secured debt. However, by issuing dUt+1, thebank can raise its financing beyond the pledgeability limit without being responsible for itsrepayment. Every time, the bank would maximize its unsecured debt until the supply limitd¯Ut+1. The quantity !t is taken as exogenous and must be equal to Rd¯Ut .3 From 0 to T  1,it is d¯Ut+1  Rd¯Ut > 0 ; from T onwards it is d¯Ut+1 = 0 and !t = 0. Therefore, the bank earnspositive rents until T  1; from T onwards, the rents unexpectedly drop to 0.By violating the pledgeability constraint, the mismatch ratio must beRdtQat=RdSt + dUtQat=Qat +Rd¯UtQat>  8 0 < t  T  1, (4.12)as in the liquidity case. At time T it falls back to . In addition, the optimal path for dividendsis still:t+1t= Q1 1 QR! 18 0  t < T  1 and t  T . (4.13)3Note that, with respect to the previous chapters, in this specification, dUt+1 includes the resources necessaryto repurchase the existing unsecured notes.64Figure 4.1: Balance Sheet Summary StatisticsLoans&to&Banks 5.3%&(0.04) 80%&(0.1) DepositsReverse&Repos 1.8%&(0.04) 2.8%&(0.05) Other&Short&Term&Debt&(Commercial&Papers&and&Repos)Loans 62.5%&(0.14) 0.1%&(0.01) Tradable&LiabilitiesNon&Government&Securities 11%&(0.09) 6.3%&(0.07) Other&BorrowingGovernment&Securities 10.3%&(0.09) 2.5%&(0.05) Other&LiabilitiesOther&Assets 5.8%&(0.04) 9%&(0.04) EquityASSETS LIABILITIESNotes: Data are from the FRY-9C Consolidated Report of Condition and Income, completed on a quarterly basis by Bank HoldingCompanies.However, when the bubble bursts at time T , if the bank expected positive rents d¯Ut+1Rd¯Ut > 0for t  T , the level of dividends must be reduced:TT1< Q1 1 QR!. (4.14)Since the bank obtains a rent when issuing bubbly debt, a bubbly mismatch must be positivelycorrelated to dividends.In the next section, I will verify if the correlation between the mismatch ratio and thedividends is positive or negative, by analyzing the balance sheet of the American Bank HoldingCompanies over the last thirty years. Given the theoretical predictions of this section, a positivecorrelation would likely be associated with the appearance of a bubble rather than with thetransformation of illiquid assets into liquid debt.4.3 Empirical TestIn this section, I will report the results of my empirical test. Data are from the FRY-9C report completed by American Bank Holding Companies. Observations are quarterly andavailable from 1986 for almost 3000 banks. Figure 4.1 shows the structure of the balance sheet.65For each item, I report the average share across all banks over time (with relative standarddeviations). Deposits represent by far the largest component. Repos and Commercial Papersrepresent less than 3% of the total assets.4 In Table 4.1 and 4.2 I report the correlation betweenthe two sides of the balance sheet. The variables are measured respectively as fractions of totalassets and levels. I regress the total Deposits and Other Short-Term Debt on the Loans toBanks, Reverse Repos, Loans, Government Securities, Non-Government Securities and OtherAssets. Regressions include time and bank fixed effects. The results show that while traditionaldeposits are mainly backed by loans, other short-term liabilities require a relatively largershare of securities.5 The expansion in liquid debt contracts that preceded the 2008 crisiswas primarily driven by a surge in Repos and Commercial Papers. A preliminary analysisreveals that these contracts are not typically backed by illiquid loans as it happens instead fortraditional deposits.In order to test the theories presented in the previous section I start by estimating thefollowing model:logb,t = bankb + quartert + ✓RtDb,tQb,tAb,t◆+ "b,t. (4.15)The goal is to evaluate the correlation between the cash-flow mismatch and the ratio of divi-dends to assets. The variable b,t is given by the total dividends from preferred and commonshares. The repayment on debt RtDb,t is given by the total amount of short-term debt (De-posits and Other Short Term Debt) multiplied by the quarterly interest rate on T-bills. FinallyQb,tAb,t is equal to the total income from assets. In Table 4.3 I present the results of my es-timation.6 The coefficient  is always significantly negative. However, when we include bothtime and bank fixed effect the magnitude of the effect is much smaller. The main reason is thelarge size heterogeneity of the banks included in the sample.7In the following tables I investigate if the relation between the two ratios has changed in4Unfortunately, our data do not include the large amount of short-term securities issued by investment banksthrough their off-balance sheet conduits. Gorton and Metrick (2012) provide an analysis of the unregulatedrepo market relying on survey data. They estimate that in 2004 the size of the total bilateral repo market,which was dominated by unregulated institutions, was $3.857 trillion. In a 2008 speech, Timothy Geithner, atthe time President of the FED New York, assessed the combined size of the asset-backed commercial paperconduits in the beginning of 2007 at $2.2 trillion.5The coefficients for Government Securities appear to flip between the table with shares of total assets andthe one with levels. A possible explanation comes from the weak correlation between Government Securities andLoans, the largest asset component, where the remaining asset items are highly correlated with it. Therefore,an increase in the Government Securities to Total Asset ratio may also be induced by an independent reductionin the level of Loans. This would explain the relatively higher effect on Other Short-Term Debt and the lowereffect on Deposits when moving from the levels to the shares analysis.6Outlier observations with⇣RtDb,tQb,tAb,t⌘> 100 are dropped from the analysis.7Indeed, the magnitude of the coefficient with no fixed effects can be halved by excluding the largest 10%of Total Assets observations.66Table 4.1: Balance Sheet Complementarities: shares of total assetsDeposits(on(Total(Assets Other(STD(on(Total(AssetsLoans&to&Banks&on&TA 0.555*** 00.055***(0.010) (0.005)Reverse&Repos&on&TA 0.584*** 0.053***(0.011) (0.006)Loans&on&TA 0.499*** 00.012**(0.009) (0.005)Government&Securities&on&TA 0.418*** 0.078***(0.009) (0.005)Non&Government&Securities&on&TA 0.400*** 0.058***(0.009) (0.005)Bank&Fixed&Effects Yes YesQuarter&Fixed&Effects Yes YesNumber&of&observations 70,379 74,115R2 0.160 0.085Notes: Data are from the FRY-9C Consolidated Report of Condition and Income.the years of the boom-and-bust cycle associated with the 2008 crisis. In Table 4.4 I replicatethe previous exercise including a dummy identifying the quarters starting after 2001 and itsinteraction with⇣RtDb,tQb,tAb,t⌘:logb,t = bankb+quartert+dummy_2001p+pdummy_2001p ⇥✓RtDb,tQb,tAb,t◆+"b,t. (4.16)The choice of the 2001 threshold is justified by the appearance of Repos and CommercialPapers in the balance sheets of the companies. In all cases, the coefficient is significantly lessnegative when considering the period after 2001. In Table 4.5 I estimate the model in (4.16)excluding the quarters between 2007 and 2009 in which many banks suffered a run. This is inorder to exclude the possibility that our results are driven by the banking crisis. The resultsare similar to before. In particular, the total effect disappears in the period after 2001 whenincluding both bank and quarter fixed effects.The years preceding the 2008 financial crisis were characterized by a boom in non conven-tional deposits. In the last exercise, I want to isolate the effects of a variation in traditionalDeposits and Other Short Term Debt. In Figure 4.2 and 4.3 I plotted the aggregate path of⇣RtdtQtAt⌘and⇣RtotQtAt⌘, where dt and ot are respectively the aggregate amount of Deposits and67Other Short Term Debt, with Dt = dt + ot. In both graphs I also included the path of the logaggregate dividends. As we can see, on aggregate the mismatch ratio⇣RtotQtAt⌘is more positivelycorrelated than⇣RtdtQtAt⌘. In the model we now include both mismatch ratios as explanatoryvariables:logb,t = bankb + quartert + d✓Rtdb,tQb,tAb,t◆+ o✓Rtob,tQb,tAb,t◆+ "b,t. (4.17)Note that the data on Other Short Term Debt start only from 2002; then, the regressionscover only this period. The results are presented in Table 4.6 and 4.7, including or not the2007-2009 period. The tables reveal that non-conventional deposits have a relevant impact forthe near-zero correlation of the after-2001 period.8 While traditional Deposits still induce anegative effect,⇣Rtob,tQb,tAb,t⌘tends to be positively correlated to dividends.Overall, the empirical investigation shows that the relation between the mismatch ratioand dividends have become more positive during the years of the recent credit cycle. Thosebanks that increased their cash-flow mismatch did not reduce the payment of dividends. Theseresults support the claim that the increased leverage and mismatch were not entirely justifiedby the transformation of illiquid assets into liquid instruments but could also be explained bythe emergence of a debt bubble.4.4 ConclusionsThe recent financial crisis was anticipated by an increase in the mismatch between assetsand liabilities of banks. The transformation of illiquid loans into liquid debt instruments isone of the main roles of the financial sector. For this reason, most countries in the worldhave introduced government insurance schemes to prevent the risk of a bank run. However,in this chapter, I showed that an increasing cash-flow mismatch could also be associated withthe emergence of a bubble on bank debt. From a stylized model, I derived a simple conditionto test theories of liquidity transformation versus theories of bubbles in bank’s balance sheet.Specifically, I showed that the correlation between dividends and cash-flow mismatch is negativewhen a bank is running a liquidity mismatch and positive when it is running a bubbly mismatch.Importantly, the condition does not require any analysis of the assets’ composition.I find evidence that the boom in short-term debt that preceded the 2008 crisis could havebeen fed by the emergence of a bubble. Specifically, those banks with a higher mismatch were8Observations with⇣Rtob,tQb,tAb,t⌘> 0.15 are dropped from the analysis.68not reducing their dividends payout.The results depend on the simple definition of mismatch that my theory provides. Fu-ture research efforts should aim to relax the definition of mismatch taking into account theheterogeneous degree of pledgeability of different types of asset.From a normative point of view, a regulatory authority should identify when an expansionin short-term debt is matched by illiquid long-term investment or if instead it is supportedby the build-up of a bubbly scheme. In this second case, government insurance may not bethe optimal policy. A stricter regulation controlling the issuing of short-term debt by financialinstitutions would be desirable instead.69Table 4.2: Balance Sheet Complementarities: levelsDeposits( Other(Short(Term(DebtLoans&to&Banks 0.874*** 0.030***(0.004) (0.001)Reverse&Repos 0.255*** 0.028***(0.005) (0.001)Loans 0.814*** 0.013***(0.002) (0.000)Government&Securities 1.164*** B0.221***(0.010) (0.002)Non&Government&Securities 0.666*** 0.039***(0.005) (0.001)Other&Assets B0.245*** B0.010***(0.004) (0.001)Bank&Fixed&Effects Yes YesQuarter&Fixed&Effects Yes YesNumber&of&observations 70,377 74,114R2 0.960 0.205Notes: Data are from the FRY-9C Consolidated Report of Condition and IncomeTable 4.3: Effect of Mismatch on Dividends: entire sampleMismatch)Ratio ,0.029*** ,0.024*** ,0.048*** ,0.001***(0.000) (0.000) (0.001) (0.000)Bank)Fixed)Effects No Yes No YesQuarter)Fixed)Effects No No Yes YesNumber)of)observations 84,425 84,425 84,425 84,425R2 0.050 0.138 0.110 0.505log$DividendsNotes: Data are from the FRY-9C Consolidated Report of Condition and Income.70Table 4.4: Effect of Mismatch on Dividends: before and after 2001Mismatch)Ratio ,0.051*** ,0.045*** ,0.052*** ,0.037*** ,0.200*** ,0.005***(0.001) (0.001) (0.000) (0.000) (0.002) (0.001)Mismatch)Ratio)X)Dummy_after2001 0.025*** 0.018*** 0.034*** 0.012*** 0.170*** 0.004***(0.001) (0.001) (0.000) (0.000) (0.003) (0.001)Dummy_after2001 0.224*** 0.759***(0.025) (0.011)Bank)Fixed)Effects No No Yes Yes No YesQuarter)Fixed)Effects No No No No Yes YesNumber)of)observations 84,425 84,425 84,425 84,425 84,425 84,425R2 0.074 0.075 0.285 0.324 0.153 0.505log$Dividends$Notes: Data are from the FRY-9C Consolidated Report of Condition and Income.Table 4.5: Effect of Mismatch on Dividends: before and after 2001, excluding 2007-2009Mismatch)Ratio ,0.048*** ,0.045*** ,0.050*** ,0.037*** ,0.200*** ,0.005***(0.001) (0.001) (0.000) (0.000) (0.002) (0.001)Mismatch)Ratio)X)Dummy_after2001 0.023*** 0.020*** 0.033*** 0.013*** 0.173*** 0.005***(0.001) (0.001) (0.000) (0.000) (0.003) (0.001)Dummy_after2001 0.112*** 0.701***(0.026) (0.011)Bank)Fixed)Effects No No Yes Yes No YesQuarter)Fixed)Effects No No No No Yes YesNumber)of)observations 76,765 76,765 76,765 76,765 76,765 76,765R2 0.069 0.069 0.281 0.315 0.150 0.510log$Dividends$Notes: Data are from the FRY-9C Consolidated Report of Condition and Income.71Table 4.6: Effect of Mismatch on Dividends: Deposits and Other Short Term DebtMismatch)Ratio)))))))))))))))))))))))(Deposits)10.027*** 10.027*** 10.063*** 10.007***(0.000) (0.000) (0.001) (0.001)Mismatch)Ratio)))))))))))))))))))))))))(Other)Short)Term)Debt)42.286*** 10.811 38.727*** 2.081***(0.888) (0.546) (0.850) (0.492)Bank)Fixed)Effects No Yes No YesQuarter)Fixed)Effects No No Yes YesNumber)of)observations 44,794 44,794 44,794 44,794R2 0.116 0.299 0.206 0.435log$Dividends$Notes: Data are from the FRY-9C Consolidated Report of Condition and Income. Observations for Other Short Term Deposits areavailable only from 2002.Table 4.7: Effect of Mismatch on Dividends: Deposits and Other Short Term Debt, excluding2007-2009Mismatch)Ratio)))))))))))))))))))))))(Deposits)10.025*** 10.026*** 10.061*** 10.006***(10.001) (0.000) (10.001) (10.001)Mismatch)Ratio)))))))))))))))))))))))))(Other)Short)Term)Debt)44.079*** 10.705 40.377*** 2.787***(11.005) (10.626) (10.959) (10.554)Bank)Fixed)Effects No Yes No YesQuarter)Fixed)Effects No No Yes YesNumber)of)observations 37,328 37,328 37,328 37,328R2 0.109 0.295 0.205 0.452log$Dividends$Notes: Data are from the FRY-9C Consolidated Report of Condition and Income. Observations for Other Short Term Deposits areavailable only from 2002.72Figure 4.2: Path of the Mismatch Ratio of Deposits and log Dividends for the aggregateeconomy16.51717.51818.5log Dividends7891011Mismatch Ratio2001 2006 2011 2016Mismatch Ratio (Deposits) log DividendsFigure 4.3: Path of the Mismatch Ratio of Other Short Term Debt and log Dividends for theaggregate economy16.51717.51818.5log Dividends.05.1.15.2Mismatch Ratio2001 2006 2011 2016Mismatch Ratio (Other Short Term Debt) log Dividends73Bibliography[1] A.B. Abel, N.G. Mankiw, L.H. Summers, and R.J. Zeckhauser. Assessing dynamic effi-ciency: theory and evidence. Review of Economic Studies, 1989.[2] V. Asriyan, L. Fornaro, A. Martin, and J. Ventura. Monetary policy for a bubbly world.NBER working paper, 2016.[3] E. Bartelsman, J. Haltiwanger, and S. Scarpetta. Cross-country differences in productiv-ity: the role of allocation and selection. American Economic Review, 2013.[4] F. Boissay, F. Collard, and F. Smets. 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The dynamics of productivity in the telecommunications equip-ment industry. Econometrica, 1996.[30] M. O’Mahony and M. P. Timmer. Output, input and productivity measures at the indus-try level: the eu klems database. Economic Journal, 2009.[31] C.M. Reinhart and K.S. Rogoff. From financial crash to debt crisis. American EconomicReview, 2011.[32] D. Restuccia and R. Rogerson. Policy distortions and aggregate productivity with hetero-geneous plants. Review of Economic Dynamics, 2008.[33] P. Samuelson. An exact consumption-loan model of interest with or without the socialcontrivance of money. Journal of Political Economy, 1958.[34] M. Schularick and A.M. Taylor. Credit boom gone bust: monetary policy, leverage cyclesand financial crises, 1870-2008. American Economic Review, 2012.[35] J. Tirole. Asset bubbles and overlapping generations. Econometrica, 1985.[36] M. Woodford. Public debt as private liquidity. American Economic Review, 1990.76Appendix 1: Proof of Proposition 2We will prove that aggregate capital and output is always lower if Rb > R⇤. When it isRb  AL, the aggregate capital isK =⌥w =⇣1 RbAL + qbALAH1AH⌘(1 ) qb RbAL1AL +⇣1 Rb + (1 ) qbAHAL1AL⌘qb RbAH1AH⇣1 RbAL + qbALAH1AH⌘⇣1 RbAH + (1 ) qbAHAL1AL⌘ w.(4.18)with qb = 1RbRb . The denominator is bigger than the numerator if Rb > AH = R⇤. In fact,it is⌥ = +✓Rb  AHRbRb  ALRb◆⇢1 1Rb 1  [(1 )AH + AL](1 AH) (1 AL), (4.19)where both the quantities in the round and curly brackets are positive. Then it must beK < w = K⇤. When it is AL < Rb  AH , the aggregate capital isK = kH =1  1RbRb1  (1Rb) AH w. (4.20)Also in this case the ratio is lower than one as long as Rb > R⇤, and it must be K < K⇤.The result trivially follows for the aggregate output, given that Y = AHkH + ALkL AH (kH + kL) < AHw = Y ⇤.77Appendix 2: Proof of Proposition 3We will start showing that @K@ and@Y@ are negative for both cases with R⇤ < Rb  AL andAL < Rb  AH . In the first case the aggregate capital K can be expressed as a function of kHor kL:K =1Rbw +  (AL AH) kL1 AH =1Rbw +  (AH AL) kH1 AL . (4.21)Given that@kL@=1RbRb(RbAH)(RbAL)Rb(1AH)⇣1 RbAL +  1RbRb ALAH1AH⌘2w > 0, (4.22)it must be @K@ < 0. The result follows for the aggregate output, since it is Y =K(1Rb)w .In the case of AL < Rb  AH we can derive@kH@=1Rb AH Rb[1  (1Rb) AH ]2w < 0. (4.23)Then, it must be @K@ < 0 and@Y@ < 0, since Y = AHK = AHkH .The effect of an increase in  on the aggregate consumption varies in the two cases withR⇤ < Rb  AL and AL < Rb  AH . Aggregate consumption in steady state is given by:C =8>>>>>>>><>>>>>>>>:AHw if Rb = R⇤Rbw + (1 )Y if R⇤ < Rb  ALRbw + (1 )Y +RbdUL if AL < Rb  AHw if Rb > AH. (4.24)When R⇤ < Rb  AL, it is @C@ = (1 ) @Y@ < 0. In the case of AL < Rb  AH we can78simplify the derivative:@C@=1Rb[1  (1Rb) AH ]2Rb  AH(1AH)w. (4.25)A higher  increases the aggregate consumption only if AH < 1.79Appendix 3: Proof of Proposition 4We will prove that an increase in Rb always reduces the steady state wage. From labor marketclearing it is:(1 ) e⇣w(1↵)"↵HAH⌘ 1↵ h (1 ) + Rbi↵1↵w+(1 ) e+ 1Rb RbR⇤Rb w'⇣w(1↵)"↵LAL⌘ 1↵ h (1 ) + Rbi↵1↵w=2'.(4.26)Taking derivatives with respect to Rb, we get:264 R⇤2(Rb)2w⇣w(1↵)"↵HAH⌘ 1↵  p (Rb, w)R⇤2(Rb)2w⇣w(1↵)"↵LAL⌘ 1↵  p (Rb, w)375hH w'⇣w(1↵)"↵LAL⌘ 1↵  p (Rb, w)=1w@w@Rb8>><>>:1↵⇣w(1↵)"↵HAH⌘ 1↵  p Rb, whH⇣w(1↵)"↵HAH⌘ 1↵  p (Rb, w)+1↵⇣w(1↵)"↵LAL⌘ 1↵  p Rb, whL  q R⇤, Rb, w⇣w(1↵)"↵LAL⌘ 1↵  p (Rb, w)9>>=>>;(4.27)with qR⇤, Rb, w=1Rb RbR⇤Rb w' and p Rb, w = h (1 ) + Rb i ↵1↵w. The equationalways implies @w@Rb < 0. In fact, the left hand side is negative for sure, given "↵HAH > "↵LAL.80Appendix 4: Proof of Proposition 5Aggregate capital in steady state is given by:K = ("H + "L) (1 ) e+("HhH + "LhL) (1 ) + Rb↵1 ↵w+ "L1Rb Rb R⇤Rbw'.(4.28)Taking derivatives with respect to Rb at Rb = R⇤ we obtain:@K@Rb= "L⇢ (1 ) + R⇤↵1 ↵h⇤L@w@Rb w⇤ @hH@Rb+1R⇤'R⇤ 12R⇤h⇤Lw⇤+"H⇢ (1 ) + R⇤↵1 ↵h⇤H@w@Rb+ w⇤@hH@Rb 12R⇤h⇤Hw⇤. (4.29)It is easy to see that @K@Rb would certainly be negative if "H = "L.In what follows we will show that @K@Rb would be positive for small  and "H . For simplicity,we will prove the claim for the case "↵HAH = "↵LAL. We start by taking the limit of@K@Rb for "Happroaching 0 given a constant ⇢ = "↵HAH = "↵LAL , i.e. by assuming AH = AH ("H) =⇢"↵H.Note that, as soon as "↵HAH and "↵LAL are constant, h⇤H , h⇤L, w⇤,@w@Rb and@hH@Rb do not changeas "H goes to 0. Then it will be:lim"H!0@K@Rb= "L⇢ (1 ) + 1 ↵↵↵1 ↵1'@w@Rb w⇤ @hH@Rb+1 2R⇤2'R⇤w⇤. (4.30)h12R⇤2'R⇤iwould be positive for a small R⇤. Moreover, we can rewriteh1'@w@Rb  w⇤ @hH@Rbias:(w⇤)22'81264 1+R⇤R⇤⇣w⇤(1↵)"↵HAH⌘ 1↵ h (1 ) + R⇤i↵1↵w⇤ 11↵⇣w⇤(1↵)"↵HAH⌘ 1↵ h (1 ) + R⇤i↵1↵w⇤375 ,(4.31)where the quantity in the square brackets is always positive.82Appendix 5From the binding borrowing constraint we can find the real return at time t:Rt =2'↵t(1 t) + (1 ↵)twtdSt; (4.32)with flexible prices it must be:R¯t =2'↵ (⌘  1)1 + (1 ↵) (⌘  1)w¯tdSt. (4.33)Then, we can rewrite:Rt = R¯ttwt(1 t) + (1 ↵)t1 + (1 ↵) (⌘  1)(⌘  1) w¯t . (4.34)From the equilibrium in the labor market it is:wt ='2[(1 t) + (1 ↵)t]Yt; (4.35)then, we finally obtainRNt = Rt✓PtPt1◆= R¯t tYt⌘1⌘ Y¯t!✓PtPt1◆. (4.36)83Appendix 6The first order conditions of the problem with respect to at+1, zT and dt+1 are:t = Qt+1 + t+1Q (4.37)0 = TQzT + QzTXi=1iRT1(4.38)t = Rt+1 + t+1R. (4.39)For 0 < t  T  1 and t > T the bank must invest in at+1. Combining the first and thirdequation we obtain:t = QRR Qt . (4.40)In addition, it must bet+1t= Q1 1 QR! 18 0  t < T  1 and t  T. (4.41)We can solve recursively in (35):0 = T Qz⇢ (Q,Qz, R, T )T + Qz⇢ (Q,Qz, R, T )T , (4.42)with⇢ (Q,Qz, R, T ) = 1 QzRTQRR QT1Xi=1 Q1 1 QRR!i. (4.43)84Combining (36), (38) and (39), finally we obtain:0 = ⇣ (Q,Qz, R, T )T = T Qz⇢ (Q,Qz, R, T )T1   ⇣Q 11QR⌘T1⇣Q 11QR⌘T1  Qz⇢(Q,Qz,R,T )RT . (4.44)If ⇣ (Q,Qz, R, T ) is larger than⇣Q 11QR⌘T, then it must be:TT1=0B@ Qz⇢ (Q,Qz, R, T )T1  ⇣Q 11QR⌘T1  Qz⇢(Q,Qz,R,T )R1CA1> Q1 1 QR! 1. (4.45)85

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