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Edward Prescott Conference Proceedings

September 18, 2018
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Conference Agenda

On Friday, September 21, the Heller-Hurwicz Economics Institute hosted the Edward C. Prescott Fellowship Inauguration Conference. University of Minnesota graduate students were paired with conference presenters to summarize their remarks.

Livshits
Consumer Credit with Over-Optimistic Borrowers
Igor Livshits jointly with F. Exler, J. MacGee and M. Tertilt
Summary by Thomas J. May

Throughout the late 20th and early 21st centuries, the level of consumer credit grew dramatically due to expanding credit access. Significant debate has accompanied this growth, centered on the role of government regulation in consumer credit markets. One of the core discussions, fueled on by the experiences of the Global Financial Crisis, is the impact of financial mistakes made by borrowers and lenders using information asymmetry to exploit these borrowers. The authors refer to them as "behavioral borrowers" as opposed to fully rational borrowers). While existing research has offered little insight this paper provides an initial step towards determining optimal regulatory policy for the consumer credit market.

The authors focus on borrowers who are overly optimistic about their future income streams.  They develop a model with both rational and overly optimistic agents, who interact with lenders to borrow unsecured debt. The latter group of agents always believes that they are rational, but the lenders accrue information about the borrowers and attempt to distinguish the rational agents from them. Since the lenders cannot perfectly distinguish between the types of borrowers, the overly optimistic benefit from a subsidy for the risk premium of their loans. The model finds that these agents borrow too much and default on their debt too late relative to those who have a realistic view of their income stream. The fact that they are overly optimistic about incomes makes them overly optimistic about their ability to pay down their debt. The model does not predict predatory lending even though the lenders are better informed than the borrowers.

The model is employed to examine three common policy proposals: lowering the cost of default, loan taxation, and financial literacy education. For default costs, the model is inconclusive on the cost that is optimal for behavioral borrowers. This is due to the fact that, while the overly optimistic benefit from lower default cost, they also benefit from the lower interest rate associated with a higher default cost. For loan taxation, the authors find that taxes lower over-borrowing but result in all agents experiencing a deadweight welfare loss. Finally, they find that financial literacy education reduces the rate of financial mistakes. However, only rational agents benefit from education while behavioral agents are worse off due to losing the behavioral risk premium subsidy.

The debate over regulating consumer credit will continue to rage on, but this paper makes strides in our ability to assess the arguments of that debate.

Hansen

Reforming US Long Term Care Insurance
Gary Hansen jointly with E. Capatina and M. Hsu
Summary by Nicolò Russo

Rapid aging in the United States is sparking concern about the provision and financing of long term care (LTC). LTC expenditures are paid by private insurance or by Medicaid, when individuals are severely poor. Capatina, Hansen and Hsu aim at assessing the role of family structure in LTC and at evaluating possible reforms for LTC insurance. By building a lifetime consumption/savings model, they find that informal care received by a healthy spouse is a crucial determinant of LTC provision and of the way this is financed.

They underline the importance of marital status as a determinant of the risk associated with LTC faced by households and they find that individuals with highly disabled spouses have a higher probability of receiving Medicaid and that single individuals spend more on formal LTC than married ones.

The authors focus mainly on the informal care that can be provided by a healthy spouse. The presence of a spouse in old age is both a source of risk, for the possible increase in LTC needs, and a source of insurance, against an individual's own LTC needs. The role of family dynamics is a break with the previous literature on LTC, which has mainly focused on single individuals and which has mostly focused on care provided by children. The authors focus on the informal care provided by spouses, which, according to the Health and Retirement Study (HRS) data, accounts for 65% of the hours of care received by a disabled individual. Moreover, the authors build on the literature by modeling state-dependent utility and endogenous LTC expenditures.

Using data from the HRS the Medical Expenditure Panel Survey (MEPS) and the Panel Study of Income Dynamics (PSID), the authors estimate the external parameters of the model. They set some parameters to common values of the literature and calibrate the internal parameters. The authors' benchmark model simulates the existing LTC funding system.It also replicates two main features of insurance coverage and LTC expenditures observed in the data. First, the model predicts that single individuals have a higher probability of receiving Medicaid than married individuals, which is partly explained by the role of the informal care provided by spouses. Moreover, the model predicts that single individuals spend more on formal LTC than married ones, again confirming the crucial role of informal care provided by spouses.

Caucutt

Is Marriage for White People? Incarceration, Unemployment, and the Racial Marriage Divide
Elizabeth M. Caucutt joint with N. Guner and C. Rauh
Summary by Sang Min Lee

In 2006, the ratio of white women between 25 and 54 years old who had ever been married was 27 percentage points higher than that of their black counterparts. The Wilson Hypothesis suggests that this is because black men are more likely to go to prison or become unemployed.

The authors develop a dynamic equilibrium search model of marriage, divorce, and labor supply to verify this hypothesis. Their paper contributes to the frontier of this field in that it is the first to propose a dynamic equilibrium model that incorporates all three major possible explanations for the Wilson Hypothesis: incarceration, unemployment, and the low sex ratio (fewer men than women) among the black population.

In the model, men exogenously move among the three labor market states (employed, unemployed, and prison). There are exogenous job creation shocks for unemployed women and job destruction shocks for employed women. Given an opportunity to work, women can endogenously choose whether or not to work. Single men who are not in prison and single women meet (match) at the marriage market. For the marriage decision, they consider educational level, home value characteristics, and the history of incarceration, but they cannot know whether the partner will face unemployment, incarceration, or adverse income shocks in the future. The sex ratio affects the probability of matching and matched women have a fixed probability of meeting men with the same educational level as themselves. At the start of each new period, married couples decide whether to remain married or get divorced based on their most recent information.

The authors estimated the parameters of the model to make them consistent with the key marriage and labor market statistics. With these parameters, they were able to demonstrate that incarceration and unemployment can explain half of the marriage gap. Furthermore, incorporating the sex ratio along with these two factors explained 80% of the gap.

The talk presented by Professor Caucutt was well received by the audience. There were minor questions regarding the setup of the model. One of the questions was whether excluding interracial marriage in the model is reasonable. The author’s response was that interracial marriage is rare stating, “In 2006, only 0.3% of white husbands had black wives and 9.6% of black husbands had white wives.” Another question was whether the actual possibility of a black man being incarcerated can be calculated at an individual level. To which the author noted that the data does not provide enough detail to do so.

Parente

Development, Migration and Unemployment:  Harris-Todaro Meets Mortensen-Pissarides
Stephen L. Parente joint with D. Wiczer and H. Zhang
Summary by Ji-Heum Yeon

Countries experience a rural-urban migration when they go from a less developed economy to a modern, industrialized economy. However, neither the cross-section nor the time series data present a clear relationship between unemployment levels and the level of development (for example, as measured by GDP per capita). This paper seeks to determine if the positive relationship between unemployment and the level of development found in the steady-state analysis is consistent with the model's predictions along the structural transformation. The paper aims to demonstrate that search frictions are an important aspect of this phenomenon, in addition to productivity or income differentials.

Why does rural-urban migration occur as a country goes from an agriculture-based economy to a modern, industrialized economy? Fifty years ago, the Harris-Todaro model, a workhorse in the field of development economics, conjectured that productivity or income differentials are essential to explaining this migration pattern in less developed countries despite high levels of urban unemployment. Parente, Wiczer, and Zhang enrich the Harris-Todaro model by introducing Mortensen-Pissarides search-matching frictions into a two sector/region growth model.

The authors aim to demonstrate that the evolution of search-matching frictions is a crucial aspect of an economy’s structural transformation. This study contributes to the existing literature by providing a model that can analyze both transitional dynamics and comparative statics between the steady-state level of employment and other macroeconomic variables. Neither the cross-section nor the time series data present a clear relationship. Feng, Lagakos, and Rauch (2018) claim the relationship is positive. Turnham (1985) argued that unemployment was highest in middle income countries.

This paper seeks to determine if the positive relationship between unemployment and the level of development found in the steady state analysis is consistent with the model's predictions along the structural transformation. The paper also tries to offer some evidence suggestive of a hump shape.

They focus on the crucial choice of an agent who lives in the economy: whether a rural household decides to migrate to an urban region or stay put. In any equilibrium a marginal rural household must be indifferent between staying and migrating. The authors suggest that trade-offs between production and matching technologies drive such an indifference condition in equilibrium.

Huggett

Taxing Top Earners: A Human Capital Perspective
Mark Huggett joint with A. Badel and W. Luo
Summary by Fil Babalievsky

Mark Huggett and his coauthors Alejadro Badel and Wenlan Luo reconsider the consensus on the revenue-maximizing top income tax rate. They examine two elasticities not considered by most of the existing literature (the responses of one-percenters' non-labor incomes and non-one-percenters' total incomes to the top income tax rate) and find that both forces pull down the revenue-maximizing rate. They argue that endogenous skill accumulation strengthens both responses, and show that in their model the revenue-maximizing rate is 49 percent rather than the consensus estimate of 73.

The top of the Laffer curve is a key unknown quantity in public finance. How high can we raise tax rates on the top one percent before labor supply falls enough to reduce revenue? The consensus view in papers like Diamond and Saez (2011) is that the revenue-maximizing rate depends primarily on the elasticity of the labor supply of top earners with respect to wages and taxes. Plug in reasonable parameter values into a simple formula based on these elasticities, and you get a revenue maximizing rate of 73 percent. In “Taxing Top Earners: A Human Capital Perspective", Badel, Huggett, and Luo highlight two important ways in which this consensus view falls short and demonstrate that both of these mechanisms are strengthened when acquisition of skills is endogenous.

First, agents below the cutoff for the top tax rates might reduce their taxable income if the top rate rises. If workers get more productive as they put in more hours studying or on the job, then part of the return to today's effort is the increase in tomorrow's income. If taxes siphon off some of this increase, then workers currently far below the top one percent of the income distribution might reduce their work hours and studying in response. Second, federal and state governments also tax capital income and consumption, and those revenues will also fall if taxpayers work less and therefore have less income to invest and spend.

The authors' human capital model shows how these two forces are strengthened by skills acquisition. They consider a model where a worker can increase her skills not only by working longer hours but also by spending time to learn. They compare a benchmark case, calibrated to fit earnings data and the current tax system, to a simulated experiment that maximizes tax revenue from the one percent and find that work hours and learning time both drop in response to the tax hike. This pulls the top of the Laffer curve down to 49 percent instead of the widely-reported 73 (or the 65 that Huggett and coauthors get based on slightly different parameters.)

Next, they consider a different model where workers are forced to study for the same number of hours as they do under current taxes, even when they might want to study less as taxes rise. Because workers in this model are not allowed to cut back on training in response to taxes, they accumulate more human capital in the high-tax case than they would have done in the first model. However, workers still learn on the job and as such incomes outside the top one percent still respond to the top tax rate. Therefore, the revenue maximizing tax rate is still lower than Diamond and Saez's formula would imply. The top of the Laffer curve rises to 59 percent in this exogenous human capital model, higher than the endogenous case but still lower than the typical estimate.

The model accurately reproduces several features of the real economy and even makes good predictions about things like training time that were not used in the calibration. It assumes that learning is complementary to innate skill and generates a prediction that high-skill people will study more and the incomes of top earners will increase sharply throughout their lives. The data supports both predictions, lending more credibility to the model.

While there is still work to be done, in particular, future research could focus on alternative ways to estimate the two new elasticities, Huggett and his coauthors have moved the tax rate debate forward with their new paper.

Rogerson

Hours, Occupations and Gender Differences in Labor Market Outcomes
Richard Rogerson joint with A. Erosa, L. Fuster, and G. Kambourov
Summary by Cristian Aguilera

Two central topics in the study of labor supply are time allocation and occupational choice. Typically, they are studied separately. The prime objective of this paper is to argue that there are important interactions between time allocation and occupational choice. The authors develop a model to account for these interactions. They document three patterns using data on the hours of work, occupations, and wages. First, there is a negative relationship between the mean annual hours in an occupation and the standard deviation of annual hours within that occupation. Second,occupations with high mean hours are associated with higher wages. Third, women are disproportionately represented in low mean hours occupations.

To conduct their analysis, the authors develop a unified model of occupational choice and labor supply that features heterogeneity across occupations in the return to working additional hours and show that it can match the key features of the data both qualitatively and quantitatively.

The core of the model is a standard two occupation version of the Roy (1951) model. Individuals are endowed with differential productivity across occupations and heterogeneity of occupational comparative advantage leads them to sort across occupations. They include a time allocation decision by assuming that individuals value leisure and have heterogeneous preferences over leisure. Another assumption is that the mapping from individual hours worked to the supply of efficiency units of labor is non-convex and the extent of this non-convexity is occupation-specific. They use the model to shed light on gender differences in labor market outcomes that arise because of gender asymmetries in home production responsibilities.

Their main results are as follows. Firstly, they find that assumptions about time devoted to home production has a large effect on occupational choice. Their quantitative results show that the share of females in high hours worked occupations by fourteen percentage points relative to males. Secondly, this asymmetry in home production time generates a gender wage gap of roughly eleven percentage points taking as given any difference due to productivity differences or gender wage discrimination. Lastly, the gender wage gap in their model reflects the direct effects of lower hours on wages, a change in occupational structure, and a selection effect. Their model generates a gender wage gap even in the occupations that feature no reward for longer hours. Lastly, they find that household interactions serve to significantly amplify the effect of these changes.

Rios Rull

Organizational Equilibrium with Capital
Jose-Victor Rios-Rull joint with M. Bassetto and Z. Huo
Summary by Joao Santos Lazzaro

The authors propose a new equilibrium concept useful for policy analysis when agents suffer from time inconsistency problems, the environment has state variables and agents make decisions sequentially. The Organizational Equilibrium has three conditions. The first is that no decision maker would rather become an earlier member of the decision making sequence. Secondly, no agent can do better by sitting out the system (playing Markov) and waiting for future agents to start a process. Finally, the third condition is optimality within the class of allocations that satisfy the previous two requirements.

This new equilibrium concept builds on existing literature but is restricted to a set of environments where preferences have a weak separability property. Another innovation is the inclusion of an additional equilibrium condition that precludes the delay of the implementation of the equilibrium strategy to future agents.

As an example of the new concept, the authors solve for organizational equilibrium in two benchmark economies: The growth model with quasi-geometric discounting and for the choice of a government that is financed via capital income taxes. In the benchmarks, the economy slowly moves towards a high/saving or low taxation behavior, respectively, that is, the model slowly overcomes the time consistency problem. In both environments the equilibrium allocation Pareto dominates that of the Markov perfect equilibrium.

According to the authors this behavior helps understand how modern institutions, such as governments or central banks benefit in showing that they have concerns over the long run, and hence do not take actions such as large capital levies or fast inflationary policies that may have been predicted by models with conventional equilibrium concepts. The authors interpret that Organizational Equilibrium is a notion of slowly building reputation.

Manuelli

Endogenous Debt Maturity: Liquidity Risk vs. Default Risk
Rody Manuelli joint with J. Sanchez
Summary by Robert Winslow

When agents make financing decisions, one factor they must consider is the maturity of the bonds which they issue. That is, a decision must be made between a loan that can be paid off far into the future and a loan that must be paid off very soon.

It has been observed that prior to defaulting, countries tend to shorten the maturities of the debt they issue. A similar pattern has been observed among some firms, such as Lehman Brothers, in the days leading up to their bankruptcy. In his presentation, Manuelli sought to describe a model which could offer insight into this pattern of observations.

The model supposes that borrowing agents, conceptualized as firms, go through an initial period of illiquidity before randomly being able to expand and access equity markets. If the maturity arrives before the firm is able to expand, then in order to pay off their initial bonds, the firm must refinance and issue new bonds. There is a risk that the firm will be unable to do this, which is factored into the payment the risk-neutral lenders demand.

Once the firm expands, they are no longer at risk of being unable to gather the funds needed to pay their debts, but might strategically choose not to pay their debts if the benefits of defaulting outweigh the costs. The lender anticipates this possibility as well and factors it into the payoffs they demand.

Manuelli demonstrated in the model how the price of the “liquidity risk” can be separated from the other prices which the lending agents demand. He then showed the optimal maturity that firms should select for their bonds, given different values of various parameters in the model.

The main conclusion of the model is that a firm should issue shorter-maturity bonds if it is in an industry with higher variability of success. This is because if the firm is likely to face bad times, then the risk of strategic defaulting is increased, which increases the price the firm must pay to compensate the lender for strategic default risk. The firm should thus, decrease the maturity, and shift the costs of the total risk, by increasing the cost of defaulting from illiquidity while decreasing the costs associated with the risk of defaulting in the long run.

Krueger

Kehoe-Levine Meets Aiyagari-Bewley-Huggett-Imrohoroglu: Stationary Equilibrium in the Neoclassical Growth Model with One-Sided Limited Commitment
Dirk Krueger joint with H. Uhlig
Summary by Dhananjay Ghei

The authors develop a continuous time, neoclassical, growth model with limited commitment from households. They provide an analytically tractable alternative to the incomplete markets general equilibrium framework which was most famously developed by Aiyagari (1994).

To do so they dispense the assumption of incomplete markets and introduce endogenous limits to insurance of consumption. They use log preferences (under some restrictions on the parameters) to show that there is a unique equilibrium of the model however they also find that if the intertemporal elasticity of substitution is small there might be multiple stationary equilibria.

The authors have a standard neoclassical growth model with complete markets. Labor is supplied inelastically by the households. The households face idiosyncratic risk to their earnings due to risk in labor productivity. Which in turn generates the need for households to purchase insurance to smoothen out consumption in the future. The model also has risk-neutral intermediaries which offer long-term contracts to ensure consumption for the households. The authors introduce friction into the model by providing households with the ability to effortlessly switch from one intermediary to the other. The need for insurance also generates the need for savings by households which in turn finances the capital stock. This helps provide a link between the accumulation of capital stock in the economy and the ability of intermediaries to provide insurance to households against idiosyncratic risk. On the firm side, the capital is aggregated linearly and used with labor which is inelastically supplied in an aggregate Cobb-Douglas production function by a representative competitive firm.

Alverez

A Three Mutual Fund Separation Theorem
Fernando Alvarez jointly with A. Atkeson
Summary by Mahdi Ansari

Following the seminal work by Tobin (1958) of mutual fund separation, (that is, the mean-variance investors can be restricted to choose between two portfolios) several papers have shown the theorem in various setups with different preferences, wealth levels, and return distributions. However, only a tiny portion of the literature is on three mutual fund separation results. In their paper, Alvarez and Atkeson show that any efficient allocation can be decentralized with three assets: a noncontingent bond, a market portfolio, and a simple variance swap. One of their main contributions is to allow for heterogeneity of beliefs in aggregate output, and hence aggregate risk, which enables them to study variance swaps.

The authors develop a static, two-period model. In the first period, heterogeneous agents trade contingent assets whose payoffs are realized in the second period. The agents have CARA utility functions of contingent consumptions with different risk tolerances. Furthermore, each agent has a belief on the aggregate output as the exogenous source of uncertainty in the economy. All beliefs are normal distributions but with heterogeneous means and variances. Therefore, this CARA-Normal-Heterogeneous economy can be summarized by the vector of four elements for each type: its measure, risk tolerance, belief on expected output, and belief on variance. They analyze the complete market equilibrium with a complete set of time zero Arrow securities.

The model provides some interesting results. First, there exists one agent that represents the economy, that is the price of the contingent claims is a function of her risk tolerance and beliefs for any arbitrary distribution of aggregate output. Furthermore, these representative parameters are the weighted averages of all agents’ corresponding parameters. Second, the complete market allocation can be decentralized using three assets: risk free bond, market portfolio, and simple variance swap with constant, linear, and quadratic returns respectively. While the prices of these assets are determined solely by the representative agent’s parameters, the relative share of assets for each agent is a function of their relative risk tolerance and beliefs compared to the representative agent’s. The authors, also, find expressions for trade volume of each asset. Finally, they extend their results to the dynamic, multi-period case.

Hopenhayen

The Rise and Fall of Labor Force Growth: Implications for Firm Demographics and Aggregate Trends
Hugo Hopenhayn joint with J. Neira and R. Singhania
Summary by Mateus Santos

Hopenhayn, Neira and Singhania (2018) raise the question whether unexpected behavior in aggregates since the 1980's is related to firm's demographics data. More specifically, it seeks to answer if declines in the rate of business formation, firm exit rate(corporate), labor share, and increase in business concentration, are related to firm's demographics data. Bringing data that shows that increases in both average firm's size and age, they propose a firms model with demographic elements to try to explain the behavior observed in the aggregates. To do so they bring data that shows increases in both average firm's size and age. Their argument follows from a feedback loop between firm and population demographics.

The literature in the field has presented links between either firm or population demographics and these aggregates. Karahan, Pugsley and Sahin (2018), focusing in the past years decline in firm entry rate, argue that there exists a correlation between the decline in the labor force growth and the movement in firm entry. Pugsley and Sahim (2018) focus on the fall in the entry rate in the last years to discuss its effects to the firm age distribution, and a joint effect on what they call jobless recoveries.

Karabarbounis and Neiman (2014) document the fall in the labor share for a period of over 20 years and argue that this may be the result of firms moving away from labor and toward capital, due to a relative fall in the price of investment goods. Grullon, Larkin and Michaely (2017) document an increase in concentration among the majority of U.S. Barkai (2017) argues that increases in competition are correlated with reduction in labor and capital share. Autor, Dorn, Katz, Patterson and Van Reeren (2017) relate increase in concentration with the fall in average labor share, due to the increase in the number of successful firms that have a smaller labor share than the average firm. Hopenhayn, Neira and Singhania (2018) propose a model of firm dynamics, with explicit elements of firm demographics and effects of population demographics, and changes in labor force growth, in order to conciliate the documented facts.

In the structural model of firm dynamics, firms will produce a single good using labor. Incoming firms pay an entry cost (in labor units) and make their goods, given an expectation of their future value, which depends on their draw of an initial productivity. Productivity has a stochastic process, and exit happens when productivity is smaller than a certain threshold, which is the smallest productivity such that expected profits are positive. Firms take prices as given. They show that if labor force is non-decreasing, and the share of firms of all cohorts that survived times the average size of that cohort is non-increasing, then over a period of time average firm size increases and exit rate decreases. Calibrating the model to match data from the 1980's onwards, they are able to reproduce most of its behavior. The model's results on firm demographics show that firm's size is positively correlated with age, while exit rates are negatively correlated. The model's time series mimics part of the data they presented.

Their conclusion is that labor force growth is an important driver in the change of the aggregates. Also, the model outputs decrease in entry rates and labor share, and increase in firm age and concentration. Furthermore, there may exist an important connection between population and firm demographics, as changes in the labor force may affect firm demographics which in turn may affect aggregates, with decreasing entry and exit rates, and population dynamics, as bigger firms may absorb the growth of the labor force.