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Shiller (2003) and others have argued for the creation of financial instruments that allow households to insure risks associated with their lifetime labor income. In this paper, we argue that while the purpose of such assets is to smooth consumption across states of nature, one must also consider the assets' effects on households' ability to smooth consumption over time. We show that consumers in a realistically calibrated life-cycle model would generally prefer income-linked loans (with a rate positively correlated with income shocks) to an income-hedging instrument (a limited liability asset whose returns correlate negatively with income shocks) even though the assets offer identical opportunities to smooth consumption across states. While for some parameterizations of our model the welfare gains from the presence of income-linked assets can be substantial (above 1 percent of certainty-equivalent consumption), the assets we consider can only mitigate a relatively small part of the welfare costs of labor income risk over the life cycle.

Understanding the evolution of real-time beliefs about house price appreciation is central to understanding the U.S. housing crisis. At the peak of the recent housing cycle, both borrowers and lenders appealed to optimistic house price forecasts to justify undertaking increasingly risky loans. Many observers have argued that these rosy forecasts ignored basic theoretical and empirical evidence that pointed to a massive overvaluation of housing and thus to an inevitable and severe price decline. We revisit the boom years and show that the economics profession provided little such countervailing evidence at the time. Many economists, skeptical that a bubble existed, attempted to justify the historic run-up in housing prices based on housing fundamentals. Other economists were more uncertain, pointing to some evidence of bubble-like behavior in certain regional housing markets. Even these more skeptical economists, however, refused to take a conclusive position on whether a bubble existed. The small number of economists who argued forcefully for a bubble often did so years before the housing market peak, and thus lost a fair amount of credibility, or they make arguments fundamentally at odds with the data even ex post. For example, some economists suggested that cities where new construction was limited by zoning regulations or geography were particularly bubble-prone, yet the data shows that the cities with the biggest gyrations in house prices were often those at the epicenter of the new construction boom. We conclude by arguing that economic theory provides little guidance as to what should be the correct level of asset prices - including housing prices. Thus, while optimistic forecasts held by many market participants in 2005 turned out to be inaccurate, they were not ex ante unreasonable.

We document the fact that servicers have been reluctant to renegotiate mortgages since the foreclosure crisis started in 2007, having performed payment-reducing modifications on only about 3 percent of seriously delinquent loans. We show that this reluctance does not result from securitization: servicers renegotiate similarly small fractions of loans that they hold in their portfolios. Our results are robust to different definitions of renegotiation, including the one most likely to be affected by securitization, and to different definitions of delinquency. Our results are strongest in subsamples in which unobserved heterogeneity between portfolio and securitized loans is likely to be small, and for subprime loans. We use a theoretical model to show that redefault risk, the possibility that a borrower will still default despite costly renegotiation, and self-cure risk, the possibility that a seriously delinquent borrower will become current without renegotiation, make renegotiation unattractive to investors.

This paper analyzes the impact of the subprime crisis on urban neighborhoods in Massachusetts. The topic is explored using a dataset that matches race and income information from HMDA data with property-level transaction data from Massachusetts Registry of Deeds offices. With this data, we show that much of the subprime lending in the state was concentrated in urban neighborhoods, and that minority homeownerships created with subprime mortgages have proven exceptionally unstable in the face of rapid price declines. The evidence, in Massachusetts, suggests that subprime lending did not, as is commonly believed, lead to a substantial increase in homeownership by minorities, but instead generated turnover in properties owned by minority residents. Furthermore, we argue that the particularly dire foreclosure situation in urban neighborhoods actually makes it somewhat easier for policymakers to provide remedies.

This paper explores the question of whether market participants could have or should have anticipated the large increase in foreclosures that occurred in 2007 and 2008. Most of these foreclosures stemmed from loans originated in 2005 and 2006, leading many to suspect that lenders originated a large volume of extremely risky loans during this period. However, the authors show that while loans originated in this period did carry extra risk factors, particularly increased leverage, underwriting standards alone cannot explain the dramatic rise in foreclosures. Focusing on the role of house prices, the authors ask whether market participants underestimated the likelihood of a fall in house prices or the sensitivity of foreclosures to house prices. The authors show that, given available data, market participants should have been able to understand that a significant fall in prices would cause a large increase in foreclosures although loan-level (as opposed to ownership-level) models would have predicted a smaller rise than actually occurred. Examining analyst reports and other contemporary discussions of the mortgage market to see what market participants thought would happen, the authors find that analysts, on the whole, understood that a fall in prices would have disastrous consequences for the market but assigned a low probability to such an outcome.

A leading explanation for the lack of widespread mortgage renegotiation during the financial crisis is the existence of frictions in the mortgage securitization process. This paper finds little evidence that the securitization process impeded the ability of lenders to renegotiate home mortgages, in particular during the early part of the crisis. Using a nationally representative dataset on seriously delinquent mortgage borrowers from the first quarter of 2005 through the third quarter of 2008, we find similarly small renegotiation rates for securitized loans and loans held on banks' balance sheets. We offer an alternative theory that argues that information issues endemic to home mortgages, where lenders negotiate with large numbers of borrowers, lead to barriers in renegotiation that are fundamentally different from those present with other types of debt. Consistent with the theory, we show that as the informational asymmetries between borrowers and lenders became less severe over the course of the crisis, renegotiation rates increased dramatically, rising from approximately 3 percent of delinquent mortgages in early 2007 when subprime mortgages began to default in record numbers to approximately 20 percent in late 2009 at the peak of government intervention in the mortgage market.

This public policy brief presents a proposal, originally posted on the website of the Federal Reserve Bank of Boston in January of this year, designed to help homeowners who are unable to afford mortgage payments on their principal residence because they have suffered a significant income disruption and because the balance owed on their mortgage exceeds the value of their home. These homeowners represent a subset of the population of distressed homeowners, but according to our research they face an elevated risk of default and are unlikely to be helped by current foreclosure-reduction programs. The plan is a government payment-sharing arrangement that works with the homeowner's existing mortgage and provides a significant reduction in the homeowner's monthly mortgage payment. The plan does not involve principal reduction. Two options are presented; both are designed to help people with negative equity and a significant income disruption, such as job loss. In one version, the assistance comes in the form of a government loan, which must be repaid when the borrower returns to financial health. The second version features government grants that do not have to be repaid. In either case, the homeowner must provide evidence of negative equity in the home and of job loss or other significant income disruption. The costs of the plan are moderate, and the benefits should help not only the participating homeowners but also the housing industry, the financial markets, and the economy more broadly.

This public policy brief presents a proposal, originally posted on the website of the Federal Reserve Bank of Boston in January of this year, designed to help homeowners who are unable to afford mortgage payments on their principal residence because they have suffered a significant income disruption and because the balance owed on their mortgage exceeds the value of their home. These homeowners represent a subset of the population of distressed homeowners, but according to our research they face an elevated risk of default and are unlikely to be helped by current foreclosure-reduction programs. The plan is a government payment-sharing arrangement that works with the homeowner’s existing mortgage and provides a significant reduction in the homeowner’s monthly mortgage payment. The plan does not involve principal reduction. Two options are presented; both are designed to help people with negative equity and a significant income disruption, such as job loss. In one version, the assistance comes in the form of a government loan, which must be repaid when the borrower returns to financial health. The second version features government grants that do not have to be repaid. In either case, the homeowner must provide evidence of negative equity in the home and of job loss or other significant income disruption. The costs of the plan are moderate, and the benefits should help not only the participating homeowners but also the housing industry, the financial markets, and the economy more broadly. Chris Foote, Jeff Fuhrer, and Paul S. Willen are research economists at the Federal Reserve Bank of Boston. Eileen Mauskopf is a research economist at the Board of Governors of the Federal Reserve System.

This paper takes a skeptical look at a leading argument about what is causing the foreclosure crisis and what should be done to stop it. We use an economic model to focus on two key decisions: the borrower's choice to default on a mortgage and the lender's subsequent choice whether to renegotiate or modify the loan. The theoretical model and econometric analysis illustrate that unaffordable loans, defined as those with high mortgage payments relative to income at origination, are unlikely to be the main reason that borrowers decide to default. In addition, this paper provides theoretical results and empirical evidence supporting the hypothesis that the efficiency of foreclosure for investors is a more plausible explanation for the low number of modifications to date than contract frictions related to securitization agreements between servicers and investors. While investors might be foreclosing when it would be socially efficient to modify, there is little evidence to suggest they are acting against their own interests when they do so. An important implication of our analysis is that policies designed to reduce foreclosures should focus on ameliorating the immediate effects of job loss and other adverse life events rather than modifying loans to make them more affordable on a long-term basis.

This paper takes a skeptical look at a leading argument about what is causing the foreclosure crisis and what should be done to stop it. We use an economic model to focus on two key decisions: the borrower’s choice to default on the mortgage and the lender’s choice on whether to renegotiate or “modify” the loan. The theoretical model and econometric analysis illustrate that “unaffordable” loans, defined as those with high mortgage payments relative to income at origination, are unlikely to be the main reason that borrowers decide to default. Rather, the typical problem appears to be a combination of household income shocks and an unprecedented fall in house prices. Regarding the small number of loan modifications to date, we show, both theoretically and empirically, that the efficiency of foreclosure for investors is a more plausible explanation for the low number of modifications than contract frictions related to securitization agreements between servicers and investors. While investors might be foreclosing when it would be socially efficient to modify, there is little evidence to suggest they are acting against their own interests when they do so. An important implication of our analysis is that policies designed to reduce foreclosures should focus on ameliorating the immediate effects of job loss and other adverse life events, rather than modifying loans to make them more “affordable” on a long-term basis.

We estimate a model of foreclosure using a data set that includes every residential mortgage, purchase-and-sale, and foreclosure transaction in Massachusetts from 1989 to 2008. We address the identification issues related to the estimation of the effects of house prices on residential foreclosures. We then use the model to study the dramatic increase in foreclosures that occurred in Massachusetts between 2005 and 2008 and conclude that the foreclosure crisis was primarily driven by the severe decline in housing prices that began in the latter part of 2005, not by a relaxation of underwriting standards on which much of the prevailing literature has focused. We argue that relaxed underwriting standards did severely aggravate the crisis by creating a class of homeowners who were particularly vulnerable to the decline in prices. But, as we show in our counterfactual analysis, that emergence alone, in the absence of a price collapse, would not have resulted in the substantial foreclosure boom that was experienced. JEL classification: D11, D12, G21 Key words: foreclosure, mortgage, house prices 1. Introduction There are two competing theories to explain the explosion of foreclosures in the United States in 2007 2009. The first focuses almost entirely on underwriting standards, and attributes the crisis to loans that borrowers had trouble repaying, either because they had bad credit and little income to begin with, or because the loans were unrealistically generous at the time of origination and later became unaffordable. There is persuasive prima facie evidence that is consistent with this theory. For example, subprime loans, which expanded credit by offering loans to borrowers who previously could not obtain any mortgage credit, and by offering large loans to those who previously could only obtain small loans, account for a disproportionate number of foreclosures. Subprime lending emerged as a major force in mortgage markets shortly before foreclosures began to accelerate, and were concentrated in communities that later became foreclosure hotspots. An alternative explanation focuses on house prices and points to the precipitous decline in prices that started in 2005 or 2006, depending on where in the country one looks, as an explanation for the crisis. There is prima facie evidence that is consistent with this theory as well. For example, until house prices began falling, subprime mortgages performed very well. In addition, states where house prices began declining sooner experienced foreclosure waves sooner than in states where prices began falling later. In this paper, we assess the merits of the "poor underwriting" and "falling house price" theories. We argue that, in a sense, both explanations are true, but that prices have primacy. We find that had prices not fallen, we would simply not have had a major foreclosure crisis, regardless of whether lenders had lowered underwriting standards in 2003 and 2004. By contrast, the observed fall in prices would have generated a substantial increase in foreclosures, even if lenders had retained the underwriting standards that prevailed in 2002. To be sure, the increase in foreclosures would have been substantially smaller without subprime lending because as we show that subprime loans are far more sensitive to a decline in house prices than prime loans, but the foreclosure rate would still have been very large relative to historical levels, and would have been still considered a major public policy problem. The central issue that any researcher must address in such an analysis is how to identify the effect of house prices on foreclosures. One natural explanation for the observed relationship is that the increase in foreclosures caused prices to fall. If that were the case, then the observed relationship between prices and foreclosures becomes evidence for the bad underwriting theory not the falling prices theory. The first contribution of this paper is to use a novel identification strategy to test this explanation of the crisis. …

Using a variety of datasets, we document some basic facts about the current subprime crisis. Many of these facts are applicable to the crisis at a national level, while some illustrate problems relevant only to Massachusetts and New England. We conclude by discussing some outstanding questions about which the data, we believe, are not yet conclusive.

Millions of Americans have negative housing equity, meaning that the outstanding balance on their mortgage exceeds their home's current market value. Our data show that the overwhelming majority of these households will not lose their homes. Our finding is consistent with historical evidence: we examine more than 100,000 homeowners in Massachusetts who had negative equity during the early 1990s and find that fewer than 10 percent of these owners eventually lost their home to foreclosure. This result is also, contrary to popular belief, completely consistent with economic theory, which predicts that from the borrower's perspective, negative equity is a necessary but not a sufficient condition for foreclosure. Our findings imply that lenders and policymakers face a serious information problem in trying to help borrowers with negative equity, because it is difficult to determine which borrowers actually require help in order to prevent the loss of their homes to foreclosure.

Using a variety of datasets, we document some basic facts about the current subprime crisis. Many of these facts are applicable to the crisis at a national level, while some illustrate problems relevant only to Massachusetts and New England. We conclude by discussing some outstanding questions about which the data, we believe, are not yet conclusive.

This paper analyzes the impact of the subprime mortgage crisis on urban neighborhoods in Massachusetts. We explore the topic using a data set that matches race and income information from Home Mortgage Disclosure Act data with property-level, transaction data from Massachusetts Registry of Deeds offices. With these data, we show that much of the subprime lending in the state was concentrated in urban neighborhoods and that minority homeownerships created with subprime mortgages have proved exceptionally unstable in the face of rapid price declines. The evidence in Massachusetts suggests that subprime lending did not, as commonly believed, lead to a substantial increase in homeownership by minorities but instead generated turnover in properties owned by minority residents. Furthermore, we argue that the particularly dire foreclosure situation in urban neighborhoods actually makes it somewhat easier for policymakers to provide remedies.

This paper analyzes the impact of the subprime mortgage crisis on urban neighborhoods in Massachusetts. We explore the topic using a data set that matches race and income information from Home Mortgage Disclosure Act data with property-level, transaction data from Massachusetts Registry of Deeds offices. With these data, we show that much of the subprime lending in the state was concentrated in urban neighborhoods and that minority homeownerships created with subprime mortgages have proved exceptionally unstable in the face of rapid price declines. The evidence in Massachusetts suggests that subprime lending did not, as commonly believed, lead to a substantial increase in homeownership by minorities but instead generated turnover in properties owned by minority residents. Furthermore, we argue that the particularly dire foreclosure situation in urban neighborhoods actually makes it somewhat easier for policymakers to provide remedies.

This paper explores the question of whether market participants could have or should have anticipated the large increase in foreclosures that occurred in 2007 and 2008. Most of these foreclosures stemmed from loans originated in 2005 and 2006, leading many to suspect that lenders originated a large volume of extremely risky loans during this period. However, the authors show that while loans originated in this period did carry extra risk factors, particularly increased leverage, underwriting standards alone cannot explain the dramatic rise in foreclosures. Focusing on the role of house prices, the authors ask whether market participants underestimated the likelihood of a fall in house prices or the sensitivity of foreclosures to house prices. The authors show that, given available data, market participants should have been able to understand that a significant fall in prices would cause a large increase in foreclosures although loan-level (as opposed to ownership-level) models would have predicted a smaller rise than actually occurred. Examining analyst reports and other contemporary discussions of the mortgage market to see what market participants thought would happen, the authors find that analysts, on the whole, understood that a fall in prices would have disastrous consequences for the market but assigned a low probability to such an outcome.

The U.S. mortgage market has experienced phenomenal change over the last 35 years. Most observers believe that the deregulation of the banking industry and financial markets generally has played an important part in this transformation. This paper develops and implements a technique for assessing the impact of changes in the mortgage market on individuals and households. Our analysis is based on an implication of the permanent income hypothesis: that the higher a household?s future income, the more it desires to spend and consume, ceteris paribus. If we have perfect credit markets, then desired consumption matches actual consumption and current spending on housing should forecast future income. Since credit market imperfections mute this effect, we can view the strength of the relationship between housing spending and future income as a measure of the ?imperfectness? of mortgage markets. Thus, a natural way to determine whether mortgage market developments have actually helped households by decreasing market imperfections is to see whether this link has strengthened over time. We implement this framework using panel data going back to 1969. We find that over the past several decades, housing markets have become less imperfect in the sense that households are now more able to buy homes whose values are consistent with their long-term income prospects. One issue that has received particular attention is the role that the housing Government Sponsored Enterprises (GSEs), Fannie Mae and Freddie Mac, have played in improving the market for housing finance. We find no evidence that the GSEs? activities have contributed to this phenomenon. This is true whether we look at all homebuyers, or at subsamples of the population whom we might expect to benefit particularly from GSE activity, such as lowincome households and first-time homebuyers.

This paper provides the first rigorous assessment of the homeownership experiences of subprime borrowers. We consider homeowners who used subprime mortgages to buy their homes, and estimate how often these borrowers end up in foreclosure. In order to evaluate these issues, we analyze homeownership experiences in Massachusetts over the 1989-2007 period using a competing risks, proportional hazard framework. We present two main findings. First, homeownerships that begin with a subprime purchase mortgage end up in foreclosure almost 20 percent of the time, or more than 6 times as often as experiences that begin with prime purchase mortgages. Second, house price appreciation plays a dominant role in generating foreclosures. In fact, we attribute most of the dramatic rise in Massachusetts foreclosures during 2006 and 2007 to the decline in house prices that began in the summer of 2005.

How much should a family save for retirement and for the kids' college education? How much insurance should they buy? How should they allocate their portfolio across different assets? What should a company choose as the default asset allocation for a mandatory retirement saving plan? We believe that the life-cycle model developed by economists over the last fifty years provides guidance for making such decisions. The theory teaches us to view financial assets as vehicles for transferring resources across different times and outcomes over the life cycle, and that perspective allows households and planners to think about their decisions in a logical and rigorous way. This paper lays out and illustrates the basic analytical framework from the theory in nonmathematical terms, with the aim of providing guidance to financial service providers, consumers, and policymakers.

This paper provides the first rigorous assessment of the homeownership experiences of subprime borrowers. We consider homeowners who used subprime mortgages to buy their homes, and estimate how often these borrowers end up in foreclosure. In order to evaluate these issues, we analyze homeownership experiences in Massachusetts over the 1989-2007 period using a competing risks, proportional hazard framework. We present two main findings. First, homeownerships that begin with a subprime purchase mortgage end up in foreclosure almost 20 percent of the time, or more than 6 times as often as experiences that begin with prime purchase mortgages. Second, house price appreciation plays an important role in generating foreclosures. In fact, we attribute much of the dramatic rise in Massachusetts foreclosures during 2006 and 2007 to the decline in house prices that began in the summer of 2005.

How much should a family save for retirement and for the kids’ college education? How much insurance should they buy? How should they allocate their portfolio across different assets? What should a company choose as the default asset allocation for a mandatory retirement saving plan? We believe that the life-cycle model developed by economists over the last fifty years provides guidance for making such decisions. The theory teaches us to view financial assets as vehicles for transferring resources across different times and outcomes over the life cycle, and that perspective allows households and planners to think about their decisions in a logical and rigorous way. This paper lays out and illustrates the basic analytical framework from the theory in nonmathematical terms, with the aim of providing guidance to financial service providers, consumers, and policymakers.

We examine the effects of collateralized borrowing in a realistically parameterized life‐cycle portfolio choice problem. We provide basic intuition in a two‐period model and then solve a multi‐period model computationally. Our analysis provides insights into life‐cycle portfolio choice relevant for researchers in macroeconomics and finance. In particular, we show that standard models with unlimited borrowing at the riskless rate dramatically overstate the gains to holding equity when compared with collateral‐constrained models. Our results do not depend on the specification of the collateralized borrowing regime: The gains to trading equity remain relatively small even with the unrealistic assumption of unlimited leverage. We argue that our results strengthen the role of borrowing constraints in explaining the portfolio participation puzzle, that is, why most investors do not own stock.

We examine the effects of collateralized borrowing in a realistically parameterized life-cycle portfolio choice problem. We provide basic intuition in a two-period model and then solve a multi-period model computationally. Our analysis provides insights into life-cycle portfolio choice relevant for researchers in macroeconomics and finance. In particular, we show that standard models with unlimited borrowing at the riskless rate dramatically overstate the gains to holding equity when compared with collateral-constrained models. Our results do not depend on the specification of the collateralized borrowing regime: The gains to trading equity remain relatively small even with the unrealistic assumption of unlimited leverage. We argue that our results strengthen the role of borrowing constraints in explaining the portfolio participation puzzle, that is, why most investors do not own stock.

In this paper, we show that incomplete markets lead to trade imbalances. We use a two‐period general equilibrium model with countries composed of heterogeneous households. We look at a world where, when markets are complete, countries engage in balanced trade; and we show that when some of those markets are absent, trade imbalances emerge. Market incompleteness across countries causes trade imbalances because national income in some countries is more sensitive to risky asset payoffs than in others. Market incompleteness within countries causes trade imbalances because superior risk‐sharing in one country leads to a lower precautionary demand for saving.

In this paper, we show that incomplete markets lead to trade imbalances. We use a two-period general equilibrium model with countries composed of heterogeneous households. We look at a world where, when markets are complete, countries engage in balanced trade and we show that when some of those markets are absent, trade imbalances emerge. Market incompleteness across countries causes trade imbalances because national income in some countries is more sensitive to risky asset payoffs than in others. Market incompleteness within countries causes trade imbalances because superior risk-sharing in one country leads to a lower precautionary demand for saving.

Most young households simultaneously hold both unsecured debt on which they pay an average of 10 percent interest and social security wealth on which they earn less than 2 percent. We document this fact using data from the Panel Study of Income Dynamics. We then consider a life-cycle model with "tempted" households, who find it impossible to commit to an optimal consumption plan and "disciplined" households who have no such problem, and we explore ways to reduce this inefficiency. We show that allowing households to use social security wealth to pay off debt while exempting young households from social security contributions (but in both cases requiring higher contributions later) leads to increases in welfare for both types of households and, for disciplined households, to significant increases in consumption and saving and reductions in debt.

Affordable higher education is, and has been, a key element of social policy in the United States with broad bipartisan support. Financial aid has substantially increased the number of people who complete university - generally thought to be a good thing. We show, however, that making education more affordable can increase income inequality. The mechanism that drives our results is a combination of credit constraints and the 'signaling' role of education first explored by Spence (1973). When borrowing for education is difficult, lack of a college education could mean that one is either of low ability or of high ability but with low financial resources. When government programs make borrowing easier or tuition more affordable, high-ability persons become educated and leave the uneducated pool, driving down the wage for unskilled workers and raising the skill premium.

Since World War II, the United States government has made improved access to higher education a priority. This effort has substantially increased the number of people who complete college - generally thought to be a good thing. We show, however, that such policies can actually increase income inequality. The mechanism that drives our results is the "signaling" role of education first explored by Spence (1973). We focus on government policies that reduce the effective interest rate on borrowing for education. When borrowing for education is difficult, lack of a college education could mean that one is either of low ability or high ability but has low financial resources. Wages and income reflect the presence of high ability individuals in the uneducated pool. When government programs make borrowing easier, high ability types get educated and leave the uneducated pool. We demonstrate our argument by solving for the relationship between the effective interest rate and income inequality in the steady state of a dynamic asymmetric information model.

We analyze consumption and portfolio behavior in a life-cycle model with realistic borrowing costs and income processes. We show that even a small wedge between borrowing costs and the risk-free return dramatically shrinks the demand for equity. When the cost of borrowing equals or exceeds the expected return on equity the relevant case according to the data households hold little or no equity during much of the life cycle. The model also implies that the correlation between consumption growth and equity returns is low at all ages, and that risk aversion estimates based on the standard excess return formulation of the consumption Euler Equation are greatly upward biased. The demand for equity in the model is non-monotonic in borrowing costs and risk aversion, and the standard deviation of marginal utility growth is an order of magnitude smaller than the Sharpe ratio.

We analyze consumption and portfolio behavior in a life-cycle model with realistic borrowing costs and income processes. We show that even a small wedge between borrowing costs and the risk-free return dramatically shrinks the demand for equity. When the cost of borrowing equals or exceeds the expected return on equity the relevant case according to the data households hold little or no equity during much of the life cycle. The model also implies that the correlation between consumption growth and equity returns is low at all ages, and that risk aversion estimates based on the standard excess return formulation of the consumption Euler Equation are greatly upward biased. The demand for equity in the model is non-monotonic in borrowing costs and risk aversion, and the standard deviation of marginal utility growth is an order of magnitude smaller than the Sharpe ratio.

This paper develops and applies a simple graphical approach to portfolio selection that accounts for covariance between asset returns and an investor's labor income. Our graphical approach easily handles income shocks that are partly hedgable, multiple risky assets, many periods and life cycle considerations. We apply the approach to occupation-level components of individual income innovations estimated from repeated cross-sections of the current population survey. We characterize several properties of these innovations, including their covariance with aggregate equity returns, long-term bond returns, and returns on several other assets. Aggregate equity returns are uncorrelated with the occupation-level income innovations, but a portfolio formed on firm size is significantly correlated with income innovations for several occupations, and so are selected industry-level equity portfolios. An application of the theory to the empirical results shows (a) large predicted levels of risky asset holdings compared to observed levels, (b) considerable variation in optimal portfolio allocations over the life cycle, and (c) large departures from the two-fund separation principle.

This paper develops and implements a framework for quantifying the gains to international trade in risky financial assets. The framework can handle may agents, many assets, incomplete markets and limited participation in asset markets. It delivers closed-form analytic solutions for consumption, portfolio allocations, asset prices and the gains to trade. We find enormous gains to trade when asset returns are calibrated to observed risk premia and all agents participate in asset markets. The gains-to-trade puzzle is closely related to, but distinct from, the equity premium puzzle. High risk aversion merely alters the form of the gains-to-trade puzzle, but limited participation in asset markets goes a long way towards addressing both puzzles. We also identify three reasons for limited international risk sharing. First, the requirement that asset markets span the space of national output shocks fails in a serious way. Second, for many countries the cost of using financial assets to hedge national output shocks greatly exceeds the benefits. Third, limited asset market participation reduces the feasible gains from international risk sharing.

This paper develops and applies a simple graphical approach to portfolio selection that accounts for covariance between asset returns and an investor's labor income. Our graphical approach easily handles income shocks that are partly hedgable, multiple risky assets, many periods and life cycle considerations. We apply the approach to occupation-level components of individual income innovations estimated from repeated cross sections of the Current Population Survey. We characterize several properties of these innovations, including their covariance with aggregate equity returns, long-term bond returns and returns on several other assets. Aggregate equity returns are uncorrelated with the occupation-level income innovations, but a portfolio formed on firm size is significantly correlated with income innovations for several occupations, and so are selected industry-level equity portfolios. An application of the theory to the empirical results shows (a) large predicted levels of risky asset holdings compared to observed levels, (b) considerable variation in optimal portfolio allocations over the life cycle, and (c) large departures from the two-fund separation principle.