Jobless Recoveries and The Revolving Credit Revolution∗ (Preliminary) Kyle F. Herkenhoff† UCLA Department of Economics March 19, 2013

Abstract Access to revolving credit more than doubled between 1983 and 1992 among both employed and unemployed households, and new evidence suggests that close to 20% of unemployed households use revolving credit to replace lost income. Labor markets have also experienced sluggish recoveries following the 1991, 2001, and 2007 recessions. These two facts motivate the question posed in this study: how has access to ‘ondemand’ credit changed the way labor markets respond to downturns? To answer this question, I build a model with risk averse agents who face both search frictions in the labor market and search frictions in the credit market. In the model, easy credit conditions provide a safety net that incentivizes agents to search for better paying jobs. Following a downturn, I find that an economy with easy credit access experiences a 10% larger drop in employment per capita compared to an economy in which credit is tight (e.g. a 2.2% drop in employment per capita with easy credit access versus a 2% drop with tight credit access). ∗

I would like to thank Andy Atkeson, Gary Hansen, Seth Neumuller, Lee Ohanian, Ana Luisa Pessoa Araujo, and Pierre-Olivier Wiell and other UCLA seminar participants for useful comments. I am especially grateful to Yves Balasko for his helpful comments on the theory portion of this project. This paper was written in part at the Federal Reserve Bank of St. Louis during the summer Dissertation Fellowship Program, and I am especially grateful for their hospitality and financial support. I also thank the UCLA Ziman Center for Real Estate for funding this research. † Correspondence: [email protected]

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1

Introduction

Are credit access and default protection important for the unemployed? And if so, what are the implications of the long run rise in revolving credit access for the unemployed. Can this rise in self-insurance capacity and ability to borrow explain the changing nature of employment recoveries? What are the welfare implications of protecting default and what are the side effects? The present study is motivated by two stylized facts: (i) non-farm employment growth following the NBER dated trough of the 1991, 2001, and 2007 recessions is significantly slower than the postwar average, and (ii) revolving credit (e.g. credit cards with balances that can be rolled over) was essentially non-existent in the late 1970s and then approximately doubled in number and nominal balance between 1983 and 1992.1 The first fact is well-established in the literature (e.g., see Herkenhoff and Ohanian [2011] or Ohanian and Raffo [2011]). Figure 1 illustrates the anaemic employment growth in the 1991, 2001, and 2007 recessions as well as the healthy post-war average across previous business cycles.2 The second fact about revolving credit is also present in the literature and best illustrated by Figure 2 which shows that revolving credit to personal disposable income.3 Several authors have argued that the boom is largely driven by the post-1980 computerization of the banking sector, the advent of credit scoring, and the deregulation of credit markets.4 On a conceptually similar note, the secured side of the credit market, home equity credit lines also enjoyed a boom during the 1980s. As Canner et al. [1998] show in Survey of Consumer Finances data, the number of homeowners with equity credit was just 5 percent in 1977 and almost tripled to 13 percent of homeowners in 1993-1994. Ex-ante the question of how ‘on-demand’ credit interacts with unemployment is an important topic; as of February 2013, the Bureau of Labor Statistics reported 12.3m unemployed, of which 4.7m were long term unemployed, and a separate study conducted by Hurd and Rohwedder [2010] (RAND American Life Panel) found that 18% of unemployed households replace income by borrowing.5 In this paper, I argue that there are three channels through which unsecured credit acts as unemployment insurance. The first channel is (i) increased borrowing, the second channel is (ii) rolling over debts or balance transfers, and the third channel is (iii) outright default. 1

Consistent with past studies such as Durkin [2000], I will refer to bank cards as credit cards. Each of the later recoveries has also been marked by a protracted rise in the unemployment rate (not depicted here). 3 For more on the rise on of credit see Durkin [2000] or Livshits et al. [2007b]. Other types of unsecured credit were used heavily prior to the advent of revolving credit; however none of these types of credit looked anything like revolving credit. See Appendix E for more discussion. 4 See Sanchez [2010] or Drozd and Serrano-Padial [2012b] for discussion about technology, see Luzzetti and Neumuller [2012] for an alternative theory based on the great moderation. Appendix E contains additional evidence on major policy events and the IT revolution. 5 A little under 40% of their respondents claimed unemployment insurance to replace income. 2

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Figure 1: Percent Change in Non-Farm Employment Following NBER Dated Trough (BLS)

Figure 2: Revolving and Non-Revolving Credit to Disposable Income (Flow of Funds and BEA)

The first channel is evidenced by Sullivan [2008] who finds that unemployed households increase debt by 11-13 cents per dollar of lost income (this holds in both PSID and SIPP). The first channel is also evidenced in Hurd and Rohwedder [2010] who find that 18% of unemployed households report using unsecured credit replace lost income (RAND American Life Panel). The second channel through which unsecured debt can be used as self-insurance is rolling over debts and transferring balances between cards. Hurd and Rohwedder [2010] show that

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the average increase in credit card balance among households rolling over debt was 1,000$ (RAND American Life Panel). While their evidence is not specific to the unemployed, Drozd and Nosal [2008], via Evans and Schmalensee [2005], quote that balance transfers were 17% of total outstanding balances in 2002 and Drozd and Serrano-Padial [2012a] report that 60% of credit card offers allow for balance transfers. Thirdly, revolving credit balances (any type of credit, for that matter) can be defaulted upon indefinitely. As Figure 3 illustrates, many households use default to smooth consumption.6 Prior research by Herkenhoff and Ohanian [2012] illustrates the consumption smoothing importance of default for unemployed mortgagors.7 For unsecured credit, I establish that the unemployed are 11% more likely to default than the employed. Among other facts, I show that roughly 20% of the unemployed are 2mo+ late on payments (roughly 40% of the unemployed are 30+ days late on payments). Moreover, I show that credit denial increases the default probability by 43% (this is a local average treatment effect for those whose denial status in 2009 was influenced by their denial status in 2007). By deferring payments or inducing collection and subsequent charge-off, consumers do not need to file for bankruptcy and can supplement disposible income considerably.8 Government policies such as the 2009 CARD act limit penalties imposed on credit-card defaulters, and mortgage interventions such as HAMP and the Mortgage Servicer Settlement make secured default quite attractive for certain borrowers. On the theoretical side of the paper, in order to estimate the effects of this self-insurance on unemployment, I build a new GE model with labor frictions, credit frictions, and business cycle dynamics in which agents have varying access to each of the 3 channels of self-insurance. The experiment I run is to feed in productivity shocks to two economies from 1970-2012 where one economy receives the actual increase in credit access efficiency observed in the data while the economy has credit access efficiency stuck at 1970s levels, and then I compare recovery speeds.9 Following a downturn, I find that an economy with easy credit access experiences a 10% larger drop in employment per capita compared to an economy in which credit is tight (e.g. a 2.2% drop in employment with access versus 2% without). On the empirical side, I use new data from historical Survey of Consumer Finance (SCF) records to trace the evolution of credit access and credit use among population subgroups.10 6

The charge off rate is gross charge-offs minus recoveries to loan value. This is for banks with $300 million in assets or more. Smaller banks could optionally report these statistics. 7 Gerardi and Willen [2013] find that the majority of defaults are out of liquidity needs with only 10-20% of defaults actually being strategic. Borrowing while unemployed using secured credit is explored in Hurst and Stafford [2004] 8 See Herkenhoff [2012a] for more. 9 The model is broadly consistent with a slow increase in unemployment durations. Abraham and Shimer [2001] argue that much of the increase has to with an ageing population, and for the sake of interpreting this article, age and credit constraints are negatively correlated (see Jappelli [1990]). Mukoyama and S ¸ ahin [2009] argue that only a minor portion of the rise is due to demographics however. 10 Prior to 1983, the survey was called the Consumer Credit Survey. The sources are thus 1970-1977 Consumer Credit Survey and 1983-2010 Survey of Consumer Finances

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Figure 3: Consumer Credit Charge Off Rates (Flow of Funds)

I find that the growth in aggregate revolving credit access for the entire population mirrored the growth in revolving credit access among the unemployed.

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2

Related Literature

The two main channels often cited as consumption smoothing mechanisms for the unemployed include both (i) public insurance and (ii) precautionary saving. The first channel is empirically relevant as Gruber [1994] demonstrates. He finds that consumption would be 22% lower without government unemployment insurance Blundell and Pistaferri [2003] consider food stamps and find that the presence of food stamps dampens the consumption decline by as much as one third. More recently, Mulligan [2010, 2012] documents the growing public safety net and then uses a standard real business cycle model to show how rule-change induced expansions of the safety net are capable of explaining as much as half of the decline in hours per capita.11 The second channel of consumption smoothing is precautionary savings which has strong theoretical roots.12 In a well cited study, Gruber [2001] measures the wealth of the unemployed and shows that in the 1990s, almost 1/3 of workers were unable to cover even 10% of the income loss endured from unemployment. As opposed to the other two channels of consumption smoothing, Gruber [1994, 2001] and Sullivan [2008] both explain that private methods of unemployment insurance such as unsecured borrowing have received little attention in the unemployment insurance literature.13 In terms of debt and unemployment, Hurst and Stafford [2004] were the first to show that the unemployed used secured debt to smooth consumption. Using the PSID from 1991 to 1996, they showed that unemployed households were 25% more likely to have refinanced their home in order to extract equity and smooth consumption. In terms of unsecured debt, Sullivan [2008] finds similar behavior. Using the PSID, he finds that unemployed households outside of the bottom quintile of wealth borrow between 11-13 cents per dollar of lost income.14 In the lowest quintiles of wealth there is considerably less borrowing and he suggests that borrowing constraints are the most likely explanation for this result. Citing Sullivan [2008], Chetty [2008] shows that unemployment extensions increase unemployment durations which is consistent with borrowing constraints. Using Canadian data, Crossley and Low [2011] further examine the effect of borrowing constraints on consumption, and they find rapid consumption growth among the credit constrained unemployed who transit to employment. This evidence suggests that access to unsecured credit markets is important for households’ consumption smoothing while unemployed.15 Recently, Herkenhoff and Ohanian [2012] and 11 He also matches the decline in investment in this framework since with decreased employment comes decreased capital accumulation under standard assumptions. 12 A standard Bewley model actually over predicts the degree of precautionary saving in an economy. Hubbard et al. [1995] attempt to correct the over accumulation of assets in the Bewley model by allowing for social insurance. With this government sponsored lower bound in place, they are able to generate a mass of low asset households. 13 Bentolila and Ichino [2008] focus on private family transfer but find little role for these transfers in the US. 14 His sample is limited to those who experienced transitory unemployment shocks over the period 19892003. 15 Athreya et al. [2009] show that in the standard quantitative model of default, debt markets play little to no role in reducing the transmission of income shocks to consumption even after varying the information

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Herkenhoff [2012b] have pointed toward default (as opposed to bankruptcy) as an important unemployment insurance mechanism. Herkenhoff and Ohanian [2012] show how job finding rates change for homeowners in default that receive “free rent,” and Herkenhoff [2012b] uses micro data to show that job loss is the primary cause of mortgage default and that the skipped payments can raise mortgagor disposable income by 47% on average.16 In related work, Guerrieri and Lorenzoni [2011] and Carroll et al. [2012] model changes to household credit access. Both papers model a credit crunch by tightening the natural debt limit and a credit boom by loosening the natural debt limit, and both papers have a concept of unemployment. Guerrieri and Lorenzoni [2011] model employment opportunities as random and exogenous. Conditional on employment, households choose labor supply to operate their backyard technology. They find that credit crunches can generate reductions in labor supply with sufficiently low labor supply elasticities. Carroll et al. [2012] are concerned with explaining the savings rate decline, thus they take employment risk as an exogenous input in their model and make several other justifiable assumptions such as once an agent is unemployed, they cannot be re-employed. Their study suggests that unemployment risk and credit conditions are both vital to understanding the savings rate decline. While both models provide important conclusions and are intimately related to the present paper, neither model is capable of answering the questions posed in this paper since neither model allows credit frictions to feed back into employment on the extensive margin. In terms of default and the supply side of credit, Livshits et al. [2007b] provide strong evidence that an increase in credit market access is consistent with aggregate trends observed in the data. In a standard lifecycle model of bankruptcy, they analyze the rise in consumer bankruptcies and find that a combination of a decrease in the transaction costs of lending along with a decrease in the cost of filing for bankruptcy are capable of generating three stylized facts: (i) stable real costs of borrowing, (ii) a large rise in debt to incomes, and (iii) a rise in bankruptcies.17 . In their model, the transaction cost of lending is a proxy for credit access. Concurrent work by Drozd and Nosal [2008] explicitly models search and matching in credit markets and explores aggregate implications of this change. On the household side, endowments obey a Brownian law of motion and default occurs in cases where income is below a debt dependent threshold. They model the credit market using random search, allowing credit companies to send offers to agents. In a steady state analysis, they find that a decline in the cost of reaching out to customers is capable of matching the increased discharge rate and a rise in debt to income ratios. precision of the lender. The present study will provide a different form of market completeness with new implications for insurance. 16 See Gerardi and Willen [2013] for more on the determinants of default and the small role of strategic default (roughly 10% of default are truly strategic) which is not a consumption smoothing mechanism. 17 Their model actually allows for default following a bankruptcy and subsequent expense shocks; agents literally cannot pay the expense shock and they are not allowed to file for bankruptcy again, thus they must default. For models focused on default, see Benjamin and Wright (2008), Herkenhoff and Ohanian [2012], and Athreya et al. [2012] for more on modeling default as opposed to bankruptcy

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Several papers including Acemoglu and Shimer [1998], Lentz and Tranaes [2001], Athreya and Simpson [2006], Rendon [2006], Chetty [2008], Chen [2012] and Eeckhout [2013] include risk aversion and asset accumulation in a model of search and matching. Chetty [2008] like Rendon [2006] include borrowing constraints in a partial equilibrium setting; in a steady state counterfactual experiment, Rendon [2006] finds that relaxing the parametrized borrowing constraint increases unemployment durations.18 Rendon [2006] has no concept of downturns in his model and is thus an insufficient model to answer the question posed by this paper. Both Athreya and Simpson [2006] and Chen [2012] are useful steady state analyses in partial equilibrium models that incorporate search and matching as well as bankruptcy. Athreya and Simpson [2006] finds meaningful interactions between bankruptcy and unemployment insurance and Chen [2012] find moderate labor supply effects from default. Regarding search in credit markets and labor markets, Wasmer and Weil [2000] were the first to incorporate both frictions simultaneously in general equilibrium. Their analysis was primarily concerned with entrepreneurial behavior and job creation. Both Kaplan and Menzio [2013] and Rothstein and Bethune [2012] incorporate both labor search frictions and product market search frictions. Rothstein and Bethune [2012] is more closely related to the present study since the contracts in their product market resemble trade credit relationships. They model the interaction between credit crunches and labor slumps showing that the 2007 financial crises reduced trade credit and thus reduced aggregate demand, increasing unemployment. Their model yields two equilibria, one with low unemployment and high credit limits and one with high unemployment and low credit limits. The present study focuses on the supply side of credit, and shows that a rise in credit access increases self-insurance and slows down job finding rates (but increases match quality). At face value this seems like the exact opposite prediction of the above study, but the nature of production and the credit instruments used in Rothstein and Bethune [2012] is one that actually resembles trade credit between businesses rather than lending from intermediary institutions to households. In terms of jobless recoveries, there are many competing hypothesis. Aaronson et al. [2004] provide a nice summary of what has been mentioned (i) It is measurement error (see Hagedorn and Manovskii [2010]), (ii) sectoral labor reallocation and structural change (see Groshen and Potter [2003], Garin et al. [2011], and Jaimovich and Siu [2012]) (iii) changes in hiring patterns such as just-in-time hiring (see Bachmann [2009], and Berger [2012]), (iv) health care costs, (v) demographic changes that affect labor supply, and (vi) inadequate aggregate demand growth. Schultze [2009] looks at the role offshoring has played in generating jobless recoveries. He finds that the BLS numbers on multinational companies just dont account for enough of a decline in employment to explain the jobless recoveries. Jaimovich and Siu [2012] argue that missing middle-skill jobs account for the rise in jobless recoveries, while Foote and Ryan [2012] have argued against the role of job polarization Mitman and Rabinovich [2012] provide a closely related hypothesis to the present paper, arguing that 18 While Lentz and Tranaes [2001] is concerned with duration dependence and asset accumulation behavior, Eeckhout [2013] seeks to provide a theory as to why high asset individuals match with the most productive firms.

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countercyclical unemployment insurance extensions can explain the rise in jobless recoveries. Shimer [2010] argues that a capital destruction shock in combination with sticky wages may explain why labor markets are not clearing; ideally the wage would fall enough to clear markets, but the wage setting process prevents that from happening. Garin et al. [2011] argue that the nature of reallocation has changed over the recession pointing to the rise in mean squared deviations of employment shares across various sectors. On the nominal side, Hall [2011] argues that monetary policy is intimately related to labor market performance. Hall [2011], focusing on the most recent recession, argues that the zero lower bound is preventing monetary policy from stimulating the economy enough to jump-start hiring again.

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Evidence

The following 3 section include evidence regarding the use of unsecured credit by unemployed households over time. Section 3.1 looks at the time series of access to credit by the unemployed. Section 3.2 shows that 45% of the unemployed use their credit cards (unsurprisingly), but that close to 68% of the unemployed running balances on their cards have less than 500$ of liquid assets. Section 3.3 shows that default is an important consumption smoothing for the unemployed and that credit access is an important factor governing the default decision.19

3.1

Unemployed Access to Credit

Figure 4 depicts the revolving credit access rates among the total population and the unemployed. The unemployed doubled credit card access and doubled the balance held on credit cards between 1983 and 1992. Figure 6 depicts the fraction of the unemployed carrying positive balances. Of those who were unemployed and that carried a balance on their credit card, they increased their revolving credit holdings relative to monthly income by 40% (in levels) more than their employed counterparts in the 1991 recession. These borrowers carried revolving balances of roughly 100% of their prior monthly wages in 1991 and 200% of their prior monthly wages by 2001. Figure 5 depicts the ratio of revolving credit balance to monthly income (measured as an average over the prior year) for the sample of borrowers with positive balances. The interesting aspect of the gap between employed and unemployed debt to income ratios is that it is punctuated by recessions, growing much more in downturns. Figure 7 shows the average nominal balance for those with positive balances, the numerator of Figure 5. 19

Following Jappelli [1990], credit access is my proxy for credit constraints.

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Figure 4: Fraction of Population with Access to Credit

Figure 5: Revolving Credit to Monthly Income Ratios, Conditional on Holding a Positive Balance

Figure 6: Fraction of Population Carrying Positive Balances

Figure 7: Average Nominal Balance, Conditional on Holding a Positive Balance

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3.2

Unsecured Credit Use While Unemployed (Evidence of Channel 1)

Table 1 shows the monthly Bankcard charges (as the the survey date) by people in the Survey of Consumer Finances according to their liquid assets and employment status (also both measured as of the survey date). From the table a few facts are apparent: i. The unemployed use credit cards less than the employed ii. However, 45% of the unemployed use credit cards iii. The monthly charges are roughly 25% of monthly income iv. And of those unemployed with credit charges, 43% have essentially zero liquid assets. In sum, almost 19% of the unemployed have less than 500$ in liquid assets and are using revolving credit lines to make purchases. Table 2 illustrates a similar set of tabulations for monthly Bankcard balances (what is rolled over).20 As with credit charges, the same set of facts holds when looking at unemployed revolving credit balances; an extraordinary fraction of unemployed with essentially zero liquid assets hold large revolving credit balances. Table 1: Bankcard Charges of the Unemployed by Liquid Assets (in 2010 $) Statistic Charges by Employed (2010 $’s) Charges by Unemployed Charges by Unemployed with Charges >0 Charges to Income by Unempl. w/ Charges >0 Fraction of Employed w/ Charges >0 Frac. of Unemployed w/ Charges >0 Frac. w/ Liquid Assets< $500 among Employed w/ Charges >0 Frac. w/ Liquid Assets< $500 among Unemployed w/ Charges >0

20

Mean 3120 548 1218 0.25 0.72 0.45 0.31 0.43

P10 0 0 60 0.02 0 0 0 0

The initial Bankcard balance is unknown, hence the focus on charges above.

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P25 0 0 200 0.04 0 0 0 0

P50 500 0 585 0.11 1 0 0 0

P75 3000 500 1500 0.25 1 1 1 1

P90 8000 1850 3000 0.60 1 1 1 1

Obs. 2322 200 90 79 2322 200 1661 90

Table 2: Bankcard Balances of the Unemployed by Liquid Assets (in 2010 $) Statistic Balance of Employed (2010 $’s) Balance of Unemployed Balance of Unemployed with Balance >0 Balance to Income by Unemployed with Balance >0 Fraction of Employed with Positive Balance Frac. of Unemployed with Positive Balance Frac. w/ Liquid Assets < $500 among Employed with Pos. Balance Frac. w/ Liquid Assets < $500 among Unempl. with Pos. Balance

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Mean 4662 2975 8041 2.65 0.38 0.37 0.45 0.68

P10 0 0 300 0.08 0 0 0 0

P25 0 0 1000 0.27 0 0 0 0

P50 0 0 2300 0.63 0 0 0 1

P75 2200 1400 5900 2.02 1 1 1 1

P90 12000 5000 25000 6.00 1 1 1 1

Obs. 2322 200 74 65 2322 200 871 74

3.3

Default as Insurance (Evidence of Channel 3)

As I argued in the introduction, default itself is an important method for boosting disposable income for those households with limited contemporaneous credit access. This third channel through which default can insure unemployed households is relatively unexplored in the literature due to data limitations. In the Survey of Consumer Finances (SCF), there is a considerable amount of information on both financial and non-financial household characteristics. I use the 2007-2009 SCF panel to assess whether or not the unsecured credit default channel (channel 3) is important for job losers and those denied access to credit by estimating a logit model of default on various employment and credit related covariates. I restrict the sample to working age heads of household who are labor force participants, have at least one unsecured loan, and are nonmortgagors.21 Table 3 describes the sample. Table 3: Summary Statistics Variable Unemployment Indicator, Survey Date Indicator 60+ Days Late over Last 12 mo. Indicator, Unemployment Spell Last 12 mo. Indicator Denied Credit Between 2007-2009 Indicator Denied Credit Between 2002-2007 Medical Loan Payments to Income Change in Medical Loan Payments 2007-2009 Total Income in 2006 College Degree Indicator Liquid Assets to Income < 5% Illiquid Assets to Income < 5% Divorce Indicator Unsecured Debt to Income ∈ [.25, .5] Unsecured Debt to Income ∈ [.5, .75] Unsecured Debt to Income ∈ [.75, ∞] Male Indicator Married Indicator Age

Obs 710 710 710 710 710 710 710 710 710 710 710 710 710 710 710 710 710 710

Mean 0.14 0.15 0.29 0.25 0.36 0.07 58 47614 0.30 0.69 0.88 0.03 0.04 0.01 0.08 0.74 0.45 40.85

Std Dev. 0.35 0.36 0.45 0.43 0.48 0.25 12669 117348 0.46 0.46 0.33 0.18 0.20 0.11 0.27 0.44 0.50 11.66

Min 0 0 0 0 0 0 -68000 0 0 0 0 0 0 0 0 0 0 24

Max 1 1 1 1 1 1 4510000 4900000 1 1 1 1 1 1 1 1 1 65

Table 4 illustrates the results from this analysis. Column (1) is a linear probability model, column (2) is the Average Marginal Treatment Effect for a logit model, and columns (3) and (4) implement the lagged instrument approach outlined in Arellano and Bond [1991]. Most importantly, I find that those who are unemployed as of the survey date are 11.4% more likely to have defaulted over the last 12 months than those who are employed. This number is roughly constant over the various specifications. In terms of modeling choices, I find that those who are denied credit between survey dates are 7.07% more likely to have defaulted than those who were not denied credit. 21

The last restriction is to to limit the effect of omitted variable bias that potentially arises from not actually observing house prices or equity (self-reported values are notoriously unreliable). See Gerardi and Willen [2013] for more.

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While the results in Column (1) and (2) are intuitive, the timing of the questions in the survey potentially results in simultaneity; it may be that the person was denied credit between the two survey dates (between 2007 and 2009) because the person defaulted. To get around this problem, I use Arellano and Bond [1991]’s idea of instrumenting an endogenous regressor with its own lagged values. It is likely that credit constraints are correlated over time, but that constraints over 3 to 8 years ago are unlikely to have caused recent default events except through their effect on recent constraints, especially among non-mortgagors.22 Since I am instrumenting a binary endogenous variable with another binary variable, the effect identified is a local average treatment effect. The estimates show that the probability of default is 43.8% greater for those who are denied credit in 2009 compared to those who were not denied credit in 2009 among the sub-population of ‘compliers’ (this sub-population includes those whose 2007 credit outcome changed their 2009 credit outcome).23 To better understand what is happening in columns (3) and (4), Table 5 follows Angrist et al. [1996] to construct an estimate of the important of credit denial on default using their identification strategy. The Table reveals that the sub-population for which the instrument influences behavior is quite large, roughly 30% of the population being studied (.414-.095=.319). The Table also reveals that the effect of credit denial on default (a .495 local average treatment effect) is in line with the estimates from columns (3) and (4) which include various controls and other instruments.

22

Apart from this intuition, both the J-Test and Under-Identification tests produce favorable results. In this empirical specification, the set of compliers is the set of people who get denied in 2009 because they were denied in 2007 but would not have been denied in 2009 otherwise. In other words, compliers are those whose ‘behavior’ changed in response to being denied in 2007. Since I assume a constant treatment effect, the model is identified under independence, monotonicity, and the standard exogeniety and relevance conditions. Conditional on the controls, given the sheer number of credit applications and errors in the process, it would be hard to argue that the instrument is not randomly assigned. The instrument also satisfies monotonicity, i.e. that those denied in 2007 are more likely to be denied in 2009. See Angrist et al. [1996] for more discussion about identification. 23

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Table 4: Dependent Variable is 60+ Days Late Default Indicator over Last 12 Months (1) LPM

Unemployment Indicator, Survey Date

0.114* (0.0605) Unemployed 1mo Over Prior Year 0.0522 (0.0851) Unemployed 2mo Over Prior Year 0.119 (0.103) Unemployed 3mo+ Over Prior Year 0.0292 (0.0460) Indicator Denied Credit Between 2007-2009 0.0707* (Instrumented in Columns (3) and (4)) (0.0395) Medical Loan Payments to Income -0.137 (0.110) Change in Medical Loan Payments 4.08e-08* (2.44e-08) Total Income in 2006 -2.01e-06 (9.36e-05) College Degree Indicator -0.0467* (0.0252) Liquid Assets to Income < 5% 0.0890*** (0.0226) Illiquid Assets to Income < 5% -0.00477 (0.0308) Divorce Indicator -0.0879* (0.0481) Unsecured Debt to Income ∈ [.25, .5] 0.0833 (0.0862) Unsecured Debt to Income ∈ [.5, .75] 0.00293 (0.122) Unsecured Debt to Income ∈ [.75, ∞] 0.163 (0.112) Demographic Controls Observations R-Squared (Logit-Pseudo R2) J-Test (P-Value) (H0:Valid Instr.) Under-identification (P-Value) (H0:Under ID)

Yes 710 0.110 NA NA

(2) Logit, Avg. Marg. Eff.

(3) 2SLS

(4) 2SLS (Over-ID)

0.0826* (0.0491) 0.0343 (0.0568) 0.0773 (0.0766) 0.0275 (0.0366) 0.0486

0.146** (0.0651) 0.0366 (0.0931) 0.0550 (0.0985) 0.0283 (0.0470) 0.438***

0.149** (0.0656) 0.0354 (0.0941) 0.0503 (0.0988) 0.0282 (0.0474) 0.465***

(0.0312) -0.0913 (0.0886) -6.21e-07 (3.58e-06) -0.00177 (0.00220) -0.0515** (0.0259) 0.101*** (0.0289) 0.00137 (0.0544) -0.0853* (0.0439) 0.0794 (0.0691) 0.00928 (0.114) 0.182 (0.113)

(0.144) -0.0498 (0.0917) 1.33e-08 (2.15e-08) 4.69e-05 (9.61e-05) -0.0349 (0.0278) 0.0502* (0.0290) -0.0261 (0.0337) -0.0678 (0.0562) 0.00455 (0.0939) 0.0437 (0.135) 0.0412 (0.0970)

(0.140) -0.0434 (0.0907) 1.12e-08 (2.11e-08) 5.05e-05 (9.68e-05) -0.0340 (0.0279) 0.0474* (0.0287) -0.0277 (0.0339) -0.0664 (0.0574) -0.00122 (0.0949) 0.0467 (0.137) 0.0322 (0.0955)

Yes 710 .151 NA NA

Yes 710 0.0850 NA 1.96e-10

Yes 710 0.0641 0.463 1.01e-09

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

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Table 5: Imbens and Angirst Analysis E(Default 09 | Denied 07) 0.202 E(Default 09 | Not Denied 07) 0.044 E(Denied 09 | Denied 07) 0.414 E(Denied 09 | Not Denied 07) 0.095 Imbens and Angirst IV Estimator

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0.495

4

General Flow of Events

The timing of the model is illustrated in Figure 8. Initially agents enter the frictional credit market and, based on their income, employment status, and debt, are matched to a creditor. Agents then make default decisions and borrowing decisions. And finally, unemployed agents make job search decisions. Figure 8: Model Timing

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5

Model

Environment: Time is discrete and runs forever, t = 0, 1, 2, .... The economy is comprised of a unit measure of risk-averse heterogeneous households who face both idiosyncratic and aggregate risk. There are two frictional markets: a labor market and a credit market.24 Both markets are characterized by directed search and matching. In the labor market, households choose which jobs to apply for based on salary as in Menzio and Shi [2009, 2010] and Karahan and Rhee [2011]. In the credit market, households are passive, but upon matching with a lending institution, they make borrowing decisions over one-period, non-contingent, and nonenforceable bonds.25 Credit relationships last for 1 period.26 Households who wish to save always have access to risk-free savings institutions. Households are free to default, and default occurs in general equilibrium. Since there is default in general equilibrium, default risk is priced like in Eaton and Gersovitz [1981] and Chatterjee et al. [2007], and furthermore, default risk is also reflected in credit market matching probabilities. Over time, aggregate labor productivity fluctuates and aggregate credit market access fluctuates. Aggregate credit market access is modeled as changes in the matching efficiency parameter in the front of the credit market matching function. As aggregate conditions in both markets change, household job search decisions change. Mechanism: All unemployed households post wages today anticipating tomorrow’s credit market access.27 If they remain unemployed then it is important that they can borrow either to roll over debt or increase their balance. If they cant borrow, its important to be able to default. With more self-insurance they optimally post higher wages (see Herkenhoff [2012a] for a proof by hand under simple assumptions) ...but the side effect is that joblessness goes up.28

6

Household Problem

There is a unit measure of risk averse households that face both idiosyncratic and aggregate risk. Consumers make borrowing/saving decisions, default decisions, and job search decisions to maximize lifetime utility. As in Dubey et al. [1990, 2005], consumers maximize preferences 24

The final good is taken as the numeraire. The credit market is directed in the sense that lending institutions choose which types of households to offer credit to based on projected revenues. 26 In Equifax, close to 30% of households opened a new credit card over the last 6 months. Households operate on the extensive margin quite often given their high utilization rates of existing credit cards, see Herkenhoff [2012a] for more. 27 This induces behavioral changes across many different asset levels. 28 But, it is important to note that long run differences are dampened by the fact that households save more with poor credit access. 25

18

over non-durable consumption, u(ct ), net of any utility penalties incurred by defaulting, x(Dt ), where Dt is the default fraction.29 Let β be the discount factor, then the problem is to maximize,

E0

X ∞

t


β u(ct ) − x(Dt )



t=0

The idiosyncratic risk faced by households include employment risk, credit market access risk, and stochastic unemployment benefit expiration. The aggregate risk faced by households includes, aggregate productivity risk, and aggregate credit market access risk.  A household’s state vector includes the current employment status e ∈ W, U ≡ W (thevalue function will be denoted W if employed, U if unemployed), credit access status a ∈ C, N , the current wage w ∈ W ≡ [w, w] ⊆ [0, 1] if employed or unemployment benefits z ∈ Z ≡ [γw, γw] ⊆ [0, 1] where γ ∈ (0, 1) if unemployed, net assets b ∈ B ≡ [b, b] ⊆ R, and the aggregate state Ω.30 The aggregate state Ω includes three components. The first component is aggregate productivity y ∈ Y, the second component is aggregate credit conditions A ∈ A, and the third component is an infinite dimensional object µ which the distribution of   summarizes households across ass state variables, i.e. µ : W, U × C, N × W × B → [0, 1]. An unemployed (U ) household’s access to credit is determined by their past asset accumulation b and unemployment benefit income z. Ω = (y, A, µ) summarizes aggregate labor productivity y and the distribution of households across states µ. Let Aψ(θUC (z, b; Ω)) be the probability that an unemployed person with assets b and benefits z is extended credit. θUC (z, b; Ω) is the tightness of submarket for unemployed agents with benefits z and assets b:
U (z, b; Ω) = Aψ(θUC (z, b; Ω))U C (z, b; Ω) + 1 − Aψ(θUC (z, b; Ω)) U N (z, b; Ω) For those with access to credit (i.e. credit application is approved). Let B denote the set of available asset market contracts. Let D ∈ [0, 1] denote the fraction of debts defaulted upon. In the case of default, there is a utility penalty of default x(D) ≤ 0 where full repayment D = 0 is not penalized x(0) = 0.31 At the end of the period, after realizing the aggregate state, unemployed agents look for jobs paying w. ˜ Each submarket is indexed by 29

See appendix C for more about the default assumptions. In the data, default is a continuous choice and banks sell defaulting non-bankrupt accounts to collection agencies for 5 cents per 1 dollar Furletti [2003]. While this is expected net revenue, it reflects the idea that banks essentially write off defaults regardless of bankruptcy. 30 From now on, I will omit time subscripts and use primes to indicate tomorrow’s variables since I will be focusing on a recursive equilibrium. 31 Utility penalties of default were introduced by Dubey et al. [2005] and have been calibrated in the past to levels of asset exemption across states Araujo and Funchal [2006]. The calibration strategy below will be to match the histogram of default rates as well as default sizes which are taken from Herkenhoff [2012a].

19


a wage and p θL (w; ˜ Ω0 ) is the probability of successfully matching to an employer paying w. ˜ The function θL (w; ˜ Ω0 ) is the submarket tightness (vacancy to looker ratio) in market w ˜ 0 given the aggregate state Ω . Thus, the problem solved by an unemployed agent (U ) with credit access (C) is given below: C

U (z, b; Ω) =

max

b0 ∈B,D∈[0,1]

  
 0 0 L 0 0 0 L 0 b (z, b ; Ω ) u(c) − x(D) + βE max p(θ (w; ˜ Ω ))W (w, ˜ b ; Ω ) + 1 − p θ (w; ˜ Ω) U w∈W ˜

Such that the laws of motion for Ω and z hold and the budget constraint is satisfied, c + qU (z, b0 ; Ω)b0 ≤ z + (1 − D)b the household takes the law of motion for the aggregate state as given, Ω0 µ0 y0 A0

= (µ0 , A0 , y 0 ) = Φ(Ω, A0 , y 0 ) ∼ F (y 0 | y) ∼ G(A0 | A)

(1)

and the household anticipates that unemployment benefits expire with probability pz at which point agents are given z, b (z, b0 ; Ω0 ) = pz U (z, b0 ; Ω0 ) + (1 − pz )U (z, b0 ; Ω0 ) U

(2)

For those without access to credit (i.e. credit application is rejected), the problem is similar, except the household’s asset choice b0 is restricted to be positive. N

U (z, b; Ω) =

max

b0 ≥0,D∈[0,1]

  
 0 0 L 0 0 0 L 0 b u(c) − x(D) + βE max p(θ (w; ˜ Ω ))W (w, ˜ b ; Ω ) + 1 − p θ (w; ˜ Ω ) U (z, b ; Ω ) w∈W ˜

c+

1 b0 ≤ z + (1 − D)b 1 + rf

such that (1)- (2) are taken as given. Employed agents in this economy face a similar credit constraint to unemployed agents. At the start of the period, employed agents are able to obtain access to credit markets with C probability Aψ(θW (w, b; Ω)) that depends on the vector households attributes. Households therefore have the following value function:
C C (w, b; Ω)) W N (w, b; Ω) W (w, b; Ω) = Aψ(θW (w, b; Ω))W C (w, b; Ω) + 1 − Aψ(θW δ(w; y) is the state contingent job separation rate and there is a γ replacement rate on wage income upon job loss. If they have access to the credit market, their dynamic programming problem is given by: C

W (w, b; Ω) =

max

b0 ∈B,D∈[0,1]

  0 0 0 0 0 0 u(c) − x(D) + βE (1 − δ(w; y ))W (w, b ; Ω ) + δ(w; y )U (γw, b ; Ω )

20

Such that the laws of motion for Ω and z (the equations are given by (1)) hold and the budget constraint is satisfied: c + qW (w, b0 ; Ω)b0 ≤ w + (1 − D)b For those who are employed and without access to credit (i.e. credit application is rejected), they face the same problem except their asset choice is restricted to be positive, b0 ≥ 0. N

W (w, b; Ω) =

max

b0 ≥0,D∈[0,1]

  0 0 0 0 0 0 u(c) − x(D) + βE (1 − δ(w; y ))W (w, b ; Ω ) + δ(w; y )U (γw, b ; Ω )

Such that equations (1) hold and the budget constraint is satisfied:

c+

7

1 b0 ≤ w + (1 − D)b 1 + rf

Saving Institutions and Lending Institutions

There is a competitive loanable funds market with a unit measure of saving institutions and a unit measure of lending institutions. Saving institutions are competitive and face a frictionless market where they accept deposits each period. These institutions have access to a risk-free technology that yields rf on deposits. With free entry, the yield on savings offered to consumers is this risk free rate rf . Lending institutions on the other hand must look for customers. To look for a customer, lenders send out an offer to a given submarket a at cost of κC . If a lender meets a customer, the customer makes a take it or leave it offer to the lender taking into account the minimum servicing cost τ , set by regulation and levied 0 0 on resources lent.32 Let b ∗ (w, b; Ω) be the bond policy of the household and Dea0 (w0 , ˆb; Ω0 ) be the default decision of the household, then the expected profits accruing to a matched lender are given by:    1 0 E (1 − Dea0 (w0 , ˆb; Ω0 )) · ˆb ∀e ∈ W, U b ∈ B Q(e, w, b; Ω) = qe (w, ˆb; Ω)ˆb − ˆ 0 ∗ 1 + rf b=be (w,b;Ω)

To ensure an expected minimum servicing fee of τ on the resources lent, the expected yield on the loan must be (1 + rf + τ ):   0 E (1 − Dea0 (w0 , ˆb; Ω0 )) · ˆb  (1 + rf + τ ) ≤ ∀e ∈ W, U ˆb ∈ B− qe (w, ˆb; Ω)ˆb 32

In the model, τ covers the vanacy cost and yields an incentive for lending institutions to look for customers. In the literature, imposing this wedge τ is common; see Livshits et al. [2007a] for an example.

21

With  free entry the general menu of prices is given by (indexed by employment status e ∈ W, U ) :

qe (w, ˆb; Ω) =

    0   E (1−Dea0 (w0 ,ˆb;Ω0 )) (1+rf +τ )

  

1 , (1+rf )

, ˆb ∈ B− ˆb ∈ B+

(3)

Substituting, Q(e, w, b; Ω) = −

τ 0 0 · qe (w, b ∗ (w, b; Ω); Ω) · b ∗ (w, b; Ω) 1 + rf

The free entry condition for lenders will bind for every submarket of consumers that takes loans: κC = Aψ(θeC (w, b; Ω))Q(e, w, b; Ω)

(4)

Under certain invertibility conditions, the tightness can be expressed as: ! κ C θeC (w, b; Ω) = ψ −1 A · Q(e, w, b; Ω) The expected repayment of an unemployed agent is given below:   0 E (1 − Dea0 (w0 , ˆb; Ω0 )) · ˆb | e = U, b, Ω = "  
C C C N EΩ0 p(θL (w; ˜ Ω0 )) Aψ(θW (w, ˜ ˆb; Ω0 ))(1 − DE (w, ˜ ˆb; Ω0 )) + 1 − Aψ(θW (w, ˜ ˆb; Ω0 )) (1 − DE (w, ˜ ˆb; Ω0 ))   
C 0 C 0 C 0 N 0 ˆ ˆ ˆ ˆ + 1 − p(θ (w; ˜ Ω )) (1 − pz ) Aψ(θU (z, b; Ω ))(1 − DU (z, b; Ω )) + 1 − Aψ(θU (z, b; Ω )) (1 − DU (z, b; Ω )) # 
C C C N (z, ˆb; Ω0 )) + 1 − Aψ(θU (z, ˆb; Ω0 )) (1 − DU (z, ˆb; Ω0 )) · ˆb + pz Aψ(θU (z, ˆb; Ω0 ))(1 − DU ˆ 0 ∗ ˆ L

0




b=bU (w,b;Ω) w= ˜ w(z, ˜ b;Ω0 )

The expected repayment of an employed agent is given below:   0 E (1 − Dea0 (w0 , ˆb; Ω0 )) · ˆb | e = W, b, Ω = "  
C C C N EΩ0 (1 − δ(w; y)) Aψ(θW (w, ˆb; Ω0 ))(1 − DE (w, ˆb; Ω0 )) + 1 − Aψ(θW (w, ˆb; Ω0 )) (1 − DE (w, ˆb; Ω0 ))  #
C C C N + δ(w; y) Aψ(θU (γw, ˆb; Ω0 ))(1 − DU (γw, ˆb; Ω0 )) + 1 − Aψ(θU (γw, ˆb; Ω0 )) (1 − DU (γw, ˆb; Ω0 )) · ˆb ˆ

0

∗ (w,b;Ω) b=bW

22

8

Firms

There is free entry of firms, and the vacancy posting cost κ(y) : Y → R++ potentially varies with aggregate productivity.33 As in Moen (1997) and Menzio and Shi (2007, 2009) firms direct their search by posting vacancies in certain submarkets that are indexed by w ∈ W ⊂ R++ . The posted wage w is fixed once an employee is found. The submarket v(w;Ω) where v(w; Ω) is the number of vacancies posted in tightness is given by θ(w; Ω) = u(w;Ω) the w submarket and u(w; Ω) is the number of unemployed people in that submarket.34 The constant returns to scale of the matching function will guarantee that the ratio of unemployment and vacancies is all that matters for determining job finding rates. Let the (w;Ω) and let the job finding rate be given vacancy filling rate be given by p(θ(w; Ω)) = Mv(w;Ω) by p(θ(w; Ω)) = below:35

M (w;Ω) . u(w;Ω)

The value to a firm of posting a vacancy in submarket w is given

V (w; Ω) = −κ(y) + p(θ(w; Ω))J(w; Ω) With free entry it must be the case that profits are competed away. Thus V (w; Ω) = 0 for any submarket that is visited with positive probability. Thus, the free entry condition is given below: κ(y) = p(θ(w; Ω))J(w; Ω) if θ(w; Ω) > 0

(5)

Given a sufficiently well behaved function p(·), it is possible to invert this equation to solve for the market tightness θ(w; Ω): ! κ if θ(w; Ω) > 0 (6) θ(w; Ω) = p−1 J(w; Ω) The value of an ongoing match is similar to Menzio and Shi [2009, 2011], where I use several key simplifying assumptions similar to Karahan and Rhee [2011], except in the model below, there is a state contingent job destruction rate δ(y, z) preventing firms from operating in negative surplus matches and a state contingent vacancy cost κ(y).36 Notice that the expectation EΩ0 is over the aggregate state vector which includes the distribution of people across states (I will omit the subscript from now on): h i J(w; Ω) = y − w + βEΩ0 (1 − δ(w; y 0 ))J(w; Ω0 ) 33

See Hagedorn and Manovskii [2008] for more on cyclical vacancy costs. Off equilibrium path markets will have a tightness of 0. 35 Notice the timing- the firm is not subject to risk at posting 36 This will correct for the irregular Beveridge curve common in directed search models without on-thejob-search. See Menzio and Shi [2011] and the Appendix for more. 34

23

Where the aggregate law of motion for Ω0 is, Ω0 µ0 y0 A0

= (µ0 , A0 , y 0 ) = Φ(Ω, A0 , y 0 ) ∼ F (y 0 | y) ∼ G(A0 | A)

And I will assume that zero profit matches are destroyed with probability 1:37 ( δ¯ if y > w δ(w; y) = 1 if y < w

9

Equilibrium

Definition of Recursive Competitive Equilibrium: A recursive  competitive equilibrium for this economy is a list of household policy functions for assets b0∗ (w, b; Ω) e,a e=W,U a=C,N ∗ (which depends on employment status e and credit access a), wages w ˜ (w, b; Ω), and de ∗,a fault De (w, b; Ω) e=W,U a=C,N , a bond price qe (w, b; Ω) e=W,U for those with credit acL cess  C , a labor market tightness function θ (w; Ω), and a credit market tightness function θe (w, b; Ω) e=W,U , distributions for the aggregate shocks (F and G), and an aggregate law of motion Ω0 = (Φ(Ω, A0 , y 0 ), A0 , y 0 ), such that: i. Given the prices, shock processes, and the aggregate law of motion, the household’s policy functions are consistent with their respective dynamics programming problems. ii. The labor market tightness is consistent with free entry (i.e., labor market tightness satisfies equation (5)). iii. The credit market tightness is consistent with free entry (i.e., credit market tightness satisfies equation (4)). iv. Debt is priced consistent with take-it-or-leave-it-offers (i.e., bond prices satisfy (3)). v. The law of motion of the aggregate state is consistent with household policy functions.

In order to solve the problem numerically, I will focus on a subset of competitive equilibria called Block Recursive Equilibria. In the sections that follow, I will establish existence 37

There is efficiency loss here since future surplus might be positive even though today’s profits are zero. I can no longer solve the social planners problem, but this assumption allows me to ignore the household’s surplus (which depends on several states) in calculating the equilibrium market tightness.

24

and propose a new solution method for block recursive models that can be applied to environments with on the job search. Definition of Block Recursive Competitive Equilibrium: A block recursive competitive equilibrium is a recursive competitive equilibrium in which the resulting decision rules and prices do not depend on the aggregate distribution of agents across states (i.e µ is not a state variable for the household or the firm).

10

Existence

I will use arguments similar to Balasko and Shell [1980] and Levine [1989] in order to establish existence. The basic premise of the proof is as follows. i. Introduce a finite life span for every agent and store age as a state variable. The only function of age is to provide a finite date at which the household value function is zero. ii. Guess that all value functions in the final stage of life are independent of the distribution of agents across states. Solve backwards to age 0. The solution should be independent of the distribution of households across states. iii. This price vector is compact and non-empty.38 iv. Now increase the lifespan by 1 year. Repeat the above steps. The new price vector is compact and non-empty, but more importantly, it is nested in the previous price vector. v. As the life span tends to infinity, the limiting price vector is the intersection of these nested compact non-empty sets, and is therefore non-empty. To proceed with the proof, I must make some basic assumptions to guarantee boundedness and unique interior solutions. Basic Assumptions: A.i Boundedness: (a) w ∈ W ≡ [w, w] ⊆ [0, 1] (b) z ∈ Z ≡ [γw, γw] ⊆ [0, 1] where γ ∈ (0, 1) (c) b ∈ B ≡ [b, b] ⊆ R 38

Conditions to ensure all potential t-span prices lie in a compact space are given below. Technically, as will be explained below, the price vector is also defined to include the irrelevant ages from -1,-2,-3, and onward.

25

(d) y ∈ Y ∈ [y, y] (e) A ∈ A ∈ [A, A]   (f) µ : W, U × C, N × W × B → [0, 1]. A.ii Inada Conditions: (a) The utility function is twice continuously differentiable, u00 < 0, u0 > 0, limc→0 u0 (c) = +∞, and limc→+∞ u0 (c) = 0. (b) The penalty function is also twice continuously differentiable x00 > 0, x0 > 0, limD→D x0 (D) = ∞, limD→0 x0 (D) = 0. Solution Method for t-span Economy: The firm’s problem is now indexed by t which is the age of the employee. This is necessary to include in the firm’s state space because the firm must forecast the household’s life span. In the last period of life JT (w; Ω) = y − w = JT (w; y) is independent of the distribution across types. Moving backward in time, the firm problem yields solutions independent of the distribution across types. 

 Jt (w; y) = y − w + βE (1 − δt (w, y ))Jt+1 (w; y ) Such that

0

0

( 1 if t = T or y < w δt (w, y 0 ) = δ¯ otherwise

and the shock follows the process y 0 ∼ F (y 0 | y) For any given lifespan, it is possible to construct an equilibrium following Menzio et al. [2012]: i. In the last period of life, qe,T (w, b; A, y) = 0 ∀b ∈ B− (anyone that borrows in their last period of life will not repay anything next period because they will be dead). Thus, C θe,T (w, b; A, y) = 0 and no one gets credit in the last period. Neither object depends on the distribution. ∗,a 0∗,a ii. Obtain the default rule De,T (z, b; A, y) and the degenerate asset accumulation rule be,T (z, b; A, y) from the household problem at date T :

WTC (w, b) = UTC (z, b) =

max

u(w − (1 − D)b) − x(D)

max

u(z − (1 − D)b) − x(D)

D∈[0,1],b0 ≥0

D∈[0,1],b0 ≥0

26

iii. Obtain the labor market tightness θTL (w; y) from the free entry condition and using the fact that JT (w; Ω) = JT (w; y) = y − w.39   κ −1 L θT (w; y) = p JT (w; y) ∗,a iv. Given the household default rule De,T (z, b; A, y) and the fact that it never makes sense C to lend to someone in their last period of life (θe,T (w, b; A, y) = 0), the household makes new take-it-or-leave-it bond offers qT −1,e (w, b; y, A) based on the date T default policies.

v. Solve HH problem at date T − 1: C

W (w, b; A, y) =

max

b0 ∈B,D∈[0,1]

  0 0 0 0 0 0 0 0 u(c) − x(D) + βE (1 − δ(w; y ))W (w, b ; A , y ) + δ(w; y )U (γw, b ; A , y )

Such that: c + qT −1,W (w, b0 ; A, y)b0 ≤ w + (1 − D)b y 0 ∼ F (y 0 | y) A0 ∼ G(A0 | A) UTC−1 (z, b; A, y) =

 u(c) − x(D) + βE max p(θTL (w; ˜ A0 , y 0 ))W (w, ˜ b0 ; A0 , y 0 ) w∈W ˜ b0 ∈B,D∈[0,1]  
 0 0 0 L 0 0 b + 1 − p θT (w; ˜ A , y ) UT (z, b ; A , y ) max

Such that: c + qT −1,U (z, b0 ; Ω)b0 ≤ z + (1 − D)b y 0 ∼ F (y 0 | y) A0 ∼ G(A0 | A) and bT (z, b0 ; A0 , y 0 ) = pz UT (z, b0 ; A0 , y 0 ) + (1 − pz )UT (z, b0 ; A0 , y 0 ) U ∗,a 0∗,a These problems imply optimal rules for default De,T −1 (z, b; A, y), assets be,T −1 (z, b; A, y) , and, in the case of the unemployed, the optimal wage posting rule w˜T∗ −1 (w, b; A, y).

vi. Now move back to T − 1 for the firm to obtain JT −1 (w; y):   0 0 JT −1 (w; y) = y − w + βE (1 − δT −1 (w, y ))JT (w; y ) 39

This object is only well defined if JT > 0 which is discussed below. In general JT > 0 since δ(y, w) = 1 if y ≥ w, and JT ≥ mini,j s.t. y(i)>w(j) y(i) − w(j) . Notice that the tightness does not depend on credit conditions but the weighted average tightness of visited submarkets will fluctuate with credit access.

27

Such that

( 1 if t = T or y < w δt (w, y 0 ) = δ¯ otherwise

and the shock follows the process y 0 ∼ F (y 0 | y) vii. Obtain the labor market tightness θTL−1 (w; y) from the free entry condition:   κ −1 L θT −1 (w; y) = p JT −1 (w; y) ∗,a 0∗,a viii. Given qT −1 (w, b; A, y), use De,T −1 (z, b; A, y), be,T −1 (z, b; A, y) to solve for QT −1 (e, w, b; A, y). The free entry condition can then be inverted to obtain the credit market tightness: ! κ C C −1 θe,T −1 (w, b; A, y) = ψ A · QT −1 (e, w, b; A, y)

ix. Repeat this process for t=T − 2, · · · , 1 to obtain a sequence of equilibrium prices that do not depend on the distribution. This process results in a unique vector of equilibrium prices for agents aged 1 through T. I will call these prices the determinate prices. For technical reasons, I must define indeterminate prices for ages −1, −2, . . .. Even though these prices are irrelevant for the t-span economy, I must define these prices in a way such that they take values in compact intervals that are consistent with t+n-span economies, n ∈ N+ arbitrary. For these reasons, I must make several additional assumptions: Assumptions to Ensure Equilibrium Prices Contained in Compact Set: n o B.i Labor Tightness: Define Jmax = 1/(1 − β) Jmin = mini,j s.t. y(i)>w(j) y(i) − w(j) Then labor market tightness lies in a closed and bounded interval. "    # κ κ , p−1 ∀t θtL (w; y) ∈ ΘL ≡ [θ, θ] = p−1 Jmin Jmax B.ii Credit Tightness: Assume there is a minimum loan size B = [b, −b ] ∪ [0, b] and further assume that repayment is strictly positive D ≤ D < 1, but small enough that even the worst-off unemployed agents with expired benefits can obtain positive τ τ consumption (1 − D )b < z. Define Qmax = 1+r b and Qmin = − 1+r b · (1 − D ) Then f f the credit market tightness lies in a closed and bounded interval, A ∈ [A, A]. "    # κ κ C C θtC (w; y, A) ∈ ΘC ≡ [θ, θ] = ψ −1 , ψ −1 ∀t AQmin AQmax

28

D , 1 ]≡ B.iii Bond Price: Since D ∈ [D , 1] and D > 0 it must be the case that q ∈ [ 1+r f 1+rf Q.

Consider equilibrium prices vectors that extend from −∞ to T , where q0,e (w, b; A, y), L C C q−1,e (w, b; A, y),. . . ∈ Q, θ0 (w, b; A, y),θ−1,e (w, b; A, y),. . . ∈ ΘL , and θ0,e (w, b; A, y), θ−1,e (w, b; A, y), C 40 . . . ∈ Θ . The price vector is thus given below:   · · · q−1,e (w, b; A, y) q0,e (w, b; A, y) q1,e (w, b; A, y) · · · qT,e (w, b; A, y) L (w, b; A, y) θ0L (w, b; A, y) θ1L (w, b; A, y) · · · θTL (w, b; A, y)  pT,e (w, b; A, y) =  · · · θ−1,e C C C C (w, b; A, y) θ1,e (w, b; A, y) θ0,e (w, b; A, y) · · · θT,e (w, b; A, y) · · · θ−1,e Define p+ T as the sub matrix of equilibrium prices for ages 1 through T. This vector is unique and pinned down using the solution method outlined above.   q1,e (w, b; A, y) · · · qT,e (w, b; A, y)  θ1L (w, b; A, y) · · · θTL (w, b; A, y)  p+ T,e (w, b; Ω) = C C θ1,e (w, b; A, y) · · · θT,e (w, b; A, y) Define p− T as the sub matrix of ages less than or equal to zero. In a T-period economy, the vector of prices for ages less than 1 are arbitrary so long as they live in the compact intervals implied by assumption A.i-A.iii:   · · · q−1,e (w, b; A, y) q0,e (w, b; A, y) L  · · · θ−1,e (w, b; A, y) θ0L (w, b; A, y)  p− T,e (w, b; Ω) = C C · · · θ−1,e (w, b; A, y) θ0,e (w, b; A, y) Suppose instead consumers live until age T + 1. The price vector for the T+1 economy is given below:

 · · · q0,e (w, b; A, y) q1,e (w, b; A, y) · · · qT,e (w, b; A, y) qT +1,e (w, b; A, y) pT +1,e (w, b; A, y) =  · · · θ0L (w, b; A, y) θ1L (w, b; A, y) · · · θTL (w, b; A, y) θTL+1 (w, b; A, y)  C C C · · · θ0,e (w, b; A, y) · · · θT,e (w, b; A, y) θ1,e (w, b; A, y) θTC+1,e (w, b; A, y) 

Relabel the elements such that T˜ = T + 1 (it is always possible to relabel the elements such that T˜ = T + N as N → ∞). Define p+ as the sub matrix for agents whose transformed T˜ age is between 1 and T˜. Based on the equilibrium construction method, p+ = p+ T . In other words, the prices T˜ implied by solving the model in the last period of life are the same across different life spans. 40

I have partitioned the matrix in a particular way to isolate the determinate portion from the indeterminate portion.

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It does not matter if the life span is 10 years or 20 years, in the last period of life the problem is always the same. Now notice that when T˜ < 1, the implied prices (qT˜,e (w, b; A, y), θTL˜ (w, b; A, y), θTC˜,e (w, b; A, y)))∈ Q × ΘL × θC must lie in the compact intervals outlined in assumptions A.i-A.iii. Thus, the equilibrium price vectors are nested since the elements of p− T can assume any value in the set Q × ΘL × θC . Definition: Let P(t) be the equilibrium vector of prices for an economy in which agents live t periods:  − L C P(t) = pt | p+ solves equilibrium conditions age 1 to age t and all elements of p ∈ Q×Θ ×θ t t As outlined above, pt = (q, θL , θC )0 summarizes the age specific equilibrium prices and p+ t a determinate vector of the sub-coordinates of pt for attainable ages. Lemma 10.1. Under assumptions A.i-A.ii and B.i-B.iii, P(t) is non-empty and compact. − Proof. Non-emptiness: The above solution method yields a unique vector for p+ t . Let pt − + L C have arbitrary elements selected from the set Q × Θ × θ . Then p = [pt , pt ] ∈ P(t) is an equilibrium price vector.

Compactness: Under assumptions B.i-B.iii, all possible t-span equilibrium price vectors have elements that reside in the compact set Q × ΘL × θC . p+ t is uniquely defined thus, those coordinates are compact. The arbitrary price vector − pt is forced to live in a closed and bounded interval. Thus P(t) is compact for every t = 0, 1, 2, · · · .

Lemma 10.2. The equilibrium price vectors are nested such that P(t + 1) ⊂ P(t) ∀i > 1 Proof. Implied by construction. Proposition 10.3. Under assumptions A.i-A.ii and B.i-B.iii, there exists a block recursive competitive equilibrium. Proof. Following Balasko and Shell [1980] it is sufficient to show that P(∞) is non-empty to establish existence. Note that P(∞) = ∩∞ t=1 P(t) by construction. Since P(∞) is the intersection of nested, non-empty, compact intervals, P(∞) is non-empty.

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11

Calibration (Preliminary)

The calibration is preliminary. I set the period to be one quarter. The discount factor is β = .97 which corresponds to a risk free annual rate of ∼ 12%. The aggregate productivity fluctuates over time according to an AR(1) process, discretized using Tauchen’s method. ln(y 0 ) = ρ ln(y) +   ∼ N (0, σe2 ) I take the standard business cycle parameters from Hansen [1985], ρ = .95, σe2 =.007. I also assume the aggregate credit process follows an AR(1). ln(A0 ) = ρA ln(A) + A A ∼ N (0, σA2 ) Using the access rate for unemployed agent in the SCF, I find ρA = .98, σA2 =.059.41 For both the credit market and labor market, I use the matching function popularized by Haan et al. [1997]:  u·v M (u, v) = l ∈ 0, 1) (u + v l )1/l I follow Schaal [2011] and set the matching function parameter to l = 1.6 in both markets. As in the real world, I set the benefit replacement rate to 50%, thus γ = 50%, and I calibrate the chance of losing benefits to match the 26 week average duration of benefits. I set the lowest possible benefit received at z = .25 (this corresponds to a lowest possible replacement rate of 25% for those with the highest wage – Krueger and Mueller [2010] use a slightly lower minimum consumption). For job destruction, I use a 3.5% quarterly firing rate which is consistent with Shimer [2005]’s postwar separation rate data. Using the numbers in Shimer [2005] and Haan et al. [1997], I set firm entry costs to target θ = .85 (see Hagedorn and Manovskii [2008]). The quarterly job filing rate is 1−(1−.71)3 = .9756 and the quarterly job finding rate is 1 − (1 − .45)3 = .833 which implies θ = pU /pV = .833/.9756 = .85. Preferences are given below: r−r c1−σ − 1 − (κD ) × 1−σ +r−r I follow the literature and set the risk aversion parameter to 2, σ = 2, (see Arellano [2008]). I set κD = 1/5 to match the average default rate [In progress], and I set credit entry costs κC = .000175 to match the probability of obtaining a credit card [In progress]. I set the minimum servicing revenue to τ =50 basis points. 41

I must assume here that the rate is constant in the quarters for which there is no survey, and I look at the unemployed access rate since the only people to initiate new borrowing in my model are job losers.

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Appendix F describes how the cyclical vacancy cost in the model is calibrated to match the countercyclical corporate paper spread (it actually fixes the irregular Beveridge curve in models with directed search and no on-the-job search, see Menzio and Shi [2010] for further dicussion about this generic problem in directed search models).

12

Experiment

The main experiment is to compare labor market recoveries across economies with varying degrees of access to on-demand credit. One challenge is measuring credit market access; I use new data from the SCF regarding the fraction of unemployed households with credit access as a proxy for the search and matching efficiency in the credit market. The details are explain below: i. Feed in productivity shocks (and job destruction, for now) from 1974-I to 2012-IV. - Productivity is log deviations of output per hour in non-farm business sector (BLS). ii. Feed in credit access shocks from 1974-I to 2012-IV. - Unemployed credit access, A, is normalized to 1 in 2001 which is the peak access of credit among the unemployed (1970-2012 SCF) iii. Compare employment recoveries with and without access following downturn.

The experiment illustrated below is quite stark. One economy has growing credit access over the 4 decades spanning 1970 to 2012 while the other economy is stuck with 1970s credit access (zero revolving credit access). Definition of Economy with Access: Access grows from 1970-2010 Definition of Economy without Access: Access at 1970 levels (zero access)

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13

Results (Preliminary)

Figure 9 illustrates employment deviations from trend following the 1981 recession. The employment drops are the same in the two economies since credit access for the unemployed is quite low. The safety nets are essentially the same in both economies. Figure 9: Simulated 1981 Recession

Figure 10 illustrates employment deviations from trend following the 2001 recession. 2001 was the peak of credit card access for the unemployed. The figure illustrates the affect of self-insurance on the employment recovery. There is actually very little borrowing in the economy, but the mere presence of a safety-net induces all agents to behave differently. Knowing that they can borrow if they dont get the job (and they do get the job 60-75% of the time in the present calibration), they post higher wages. Clearly, with credit market access, employment takes longer to recover and there is a persistent wedge between the two economies almost 3 years after the recession. Figure 11 shows that credit market access results in a precipitous decline in the savings rate. Here, I plot model net worth to income, which is proportional to the savings rate. Figure 12 illustrates revolving credit to income in the model and the data. Even though Figure 10 illustrates quite large effects from the safety-net, the actual realized use of borrowing is quite small. Many households anticipate the use of the credit line if the job search goes poorly, but few actually realize bad outcomes and resort to borrowing to smooth consumption.

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Figure 10: Simulated 2001 Recession

Figure 11: Household Liquid Assets to Income (∼ Saving Rate)

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Figure 12: Revolving Credit to Income

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14

Reservation Wage Mechanism

Figure 13 is the wage policy function for the unemployed. In the case of limited credit access, the wage policy function shifts downward [interpolate over wages]. The effect is strongest for those with low assets.42 As a result, unemployed agents take longer to find jobs while unemployed when credit is easy. However, they tend to find higher paying jobs. Of course, any sort of policy that expands the budget set of the consumer is welfare improving [add formal welfare analysis]. Figure 13: Wage Policy by Aggregate Credit Access

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The nature of the discrete state space solution method currently employed mutes the effect considerably and introduces ‘rounding-errors’ due to the discreteness of the grid. See the appendix for policy functions.

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15

Conclusions

The analysis started with a question about how access to on-demand credit changes labor market recoveries. In both the data and the model, unemployed households use unsecured debt in 3 ways to smooth consumption: (i) borrowing (ii) rolling over debt or transferring balances, and (iii) default. I used existing evidence to establish the use of the first two channels, and I used new evidence from the SCF to establish the widespread use of the third channel during the 2007-2009 recession. I then built a structural model to show that even with limited realized borrowing, unemployed households of all asset positions change their behavior as on-demand credit becomes available. Households rationally expect that if their job search fails and they consume all the assets they have, they will still be able to smooth consumption by borrowing. If they cant afford to pay they can roll over their debts. And, if they cant roll over their debts, they can default. In the numerical experiments, all three of these insurance possibilities change job search decisions, resulting in an additional reduction in employment per capita of 10% (as a fraction of the total deviation) following a recession.

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A

Unemployment Duration

The model is consistent with the broad rise in unemployment durations shown in Figures 14 and 15. Table 6 shows that unemployment durations went up significantly since the 1980s at a low frequency whether or not the 2007-2009 recession is included in the sample. Figure 15: Mean Unemployment Duration, 1948-2007 (Source: CPS)

Figure 14: Mean Unemployment Duration, 1948-2012 (Source: CPS)

Table 6: Unemployment Durations Recession Trough

Average Unemployment Duration

Unempl. Duration HP Filtered (λ=1600)

1975-I 1982-IV 1991-I 2001-IV 2009-II

11.4 17.5 12.6 14.0 22.6

12.5 16.0 14.4 15.2 25.2

Unempl. Duration HP Filtered, Up to 2006IV (λ=1600) 12.5 16.0 14.4 15.4 NA

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Unempl. Duration HP Filtered (λ=10e5) 12.3 13.4 14.8 19.1 24.8

Unempl. Duration HP Filtered, Up to 2006IV (λ=10e5) 12.7 13.9 15.1 16.6 NA

B

Policy Functions and Prices

Figure 16 illustrates the job finding rate by wage where each curve corresponds to a different aggregate shock. Figure 16: Job Finding Rate

Figure 17 is the revenue function for a lender. Figure 18 is access probability for an unemployed agent. Figure 19 is the bond price for an employed agent. Figure 20 is the wage policy function. Figure 21 is the bond policy function.

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Figure 17: Service Revenue

Figure 18: Credit Access Probability

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Figure 19: Bond Price

Figure 20: Wage Policy

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Figure 21: Asset Policy

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C

Discussion of Default Assumptions

In the data, default is a continuous choice. Herkenhoff [2012a] shows that consumers default on roughly 50% of their credit lines (2 out of 4), on average. Herkenhoff [2012a] also shows that over 30% of these defaults end up in collection – essentially ‘informal bankruptcies.’ Likewise, banks sell defaulting non-bankrupt accounts to collection agencies for 5 cents per 1 dollar Furletti [2003]. While this is expected net revenue, it reflects the idea that banks essentially write off defaults regardless of bankruptcy. In terms of one period contracts, Figure 22 illustrates that the model generates credit access persistence through employment persistence and aggregate state persistence. For those who default, their probability of getting credit the next period falls dramatically. Figure 24 compares the model default fraction against the data, and the model does quite well. Figure 22: Default and Credit Access, Model v. Data

Figure 23 is a plot of the average default episode. Time 0 is the default, and the window includes 4 quarters prior to default and 4 quarters following default. Income is already recovering at the time of default which is typical in defaultable debt models. The unemployment rate is thus relatively low at the time of default.

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Figure 23: Default

Figure 24: Default Fraction, Model v. Data

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D

The Saving Rate

One feature of the model that is broadly consistent with the data is the change in the saving rate over the postwar period. Figure 25 shows personal saving rates over the post-war period along with NBER dated business cycles. Figure 25: Personal Savings Rate (BEA)

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E

Structural Change in Lending Markets

Banking Efficiency: As Berger et al. [1995] show, banking efficiency changed dramatically over the course of the 1980s. Figure 27 shows how banking digitized relatively rapidly from the late 1970s to the early 1990s. Mester [1997] explains that prior to credit scoring, loans took 3 to 4 weeks to process. After the introduction of credit scoring, loans took a few mere hours to process. Credit scoring grew dramatically during the 1980s, culminating in Equifax going public in 1987. Other Types of On-Demand Credit: Figure 26 plots revolving credit relative to other forms of unsecured credit. Considering the cyclicality of other unsecured credit and strong countercyclical pattern of consumer durables, many of which are bought on credit, it is amazing that Figure 26 does not have a strong countercyclical pattern. While there was significant unsecured borrowing prior to the advent of the bankcard, on-demand credit was scant. Payday lending, also called a cash advance, was non-existant prior to the 1980s (the deceptive nature of this naming convention is that these loans are actually not contingent on employment). Stegman [2007] explains that “California went from zero payday lenders in 1996 to 2300 in 2004, with almost 450 new outlets opened in California in 2003 alone.” In terms of regulations, there were many changes to credit markets that favored consumers and led to a boom in credit. I have compiled a list of several of the important laws and a brief description of their effect: i. Regulation Z (Truth in Lending) 1968- Standardized the credit industry to increase transparency on credit terms ii. Fair Credit Reporting Act 1970 - Consumers entitled to receive free credit reports once a year to dispute information iii. Bankruptcy Reform Act of 1978-Chapter 13 strengthened significantly iv. Equal Credit Opportunity Act of 1974- Ban on redlining v. Fair Credit Billing Act of 1974- Means for consumers to dispute credit charges

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Figure 26: Revolving and Non-Revolving Credit to Disposable Income (Flow of Funds and BEA)

Figure 27: Banking Efficiency (Kashyap et al 1995 via Harken 2005)

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F

Vacancy Cost

In order to correct for the irregular Beveridge curve, I assume that firms must borrow to finance the costs of recruiting employees. The intraperiod loan is size κ ¯ subject to an interest rate r˜(y) that fluctuates over time with aggregate productivity, y. The interest rate will be further decomposed as follows, r˜(y) = r¯(1 − σs (y)) where r¯ is a base interest rate. I will take this rate as exogenous, and calibrate it to the BofA Merrill Lynch US High Yield Master II Option-Adjusted Spread. This spread reflects borrowing costs for risky small businesses, is highly countercycical (corr(yt , σs (yt )) = −.48), and has a standard deviation, expressed in log percentage points, that is nearly 5 times greater than that of productivity, σs (y)/σ = 4.77. Define σ ¯s ≡ 4.77 and denote the deviations of productivity as ly . The borrowing cost can then be written as follows, κ(y) = r¯(1 − σs (y))¯ κ σs (y) = σ ¯s ly ln(κ(y)) = ln(¯ rκ ¯ ) + ln(1 − σs (y)) ≈ ln(¯ rκ ¯ ) − σs (y) ≈ ln(¯ rκ ¯) − σ ¯s ly

Let lκ be log deviations of the vacancy posting cost. Then to log deviation is proportional to that of output, as desired: ∆ ln(¯ κ) ≈ σ ¯s ∆ly As a result, the free entry condition is now given as follows: ! κ(y) if θ(w; Ω) > 0 θ(w; Ω) = p−1 V J(w; Ω)

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(7)

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