Research Database

A Welfare-to-Work (WTW) program is a mix of government expenditures on “passive” (unemployment insurance, social assistance) and “active” (job search monitoring, training, wage taxes/subsidies) labor market policies targeted to the unemployed. This paper provides a dynamic principal-agent framework suitable for analyzing the optimal sequence and duration of the different WTW policies, and the dynamic pattern of payments along the unemployment spell and of taxes/subsidies upon re-employment. First, we show that the optimal program endogenously generates an absorbing policy of last resort (that we call “social assistance”) characterized by a constant lifetime payment and no active participation by the agent. Second, human capital depreciation is a necessary condition for policy transitions to be part of an optimal WTW program. Whenever training is not optimally provided, we show that the typical sequence of policies is quite simple: the program starts with standard unemployment insurance, then switches into monitored search and, finally, into social assistance. Only the presence of an optimal training activity may generate richer transition patterns. Third, the optimal benefits are generally decreasing or constant during unemployment, but they must increase after a successful spell of training. In a calibration exercise based on the U.S. labor market and on the evidence from several evaluation studies, we use our model to analyze quantitatively the features of the optimal WTW program for the U.S. economy. With respect to the existing U.S. system, the optimal WTW scheme delivers sizeable welfare gains, by providing more insurance to skilled workers and more incentives to unskilled workers.

In a monetary model, it is shown that if there is a unique Pareto inefficient barter equilibrium, then a monetary equilibrium exists when traders are sufficiently patient.

The existence of fixed points for monotone maps on spaces of measures is established. The case of monotone Markov processes is analyzed and a uniqueness and global stability condition is developed. A comparative statics result is presented and the problem of approximation to the invariant distribution is discussed. The conditions of the theorems are verified for the cases of Optimal Stochastic Growth and Industry Equilibrium.

In social science research, household income is widely used as a stand-in for, or approximation to, the economic well-being of households. In a parallel way, income-inequality has been employed as a stand-in for inequality of economic well-being, or for brevity, "economic-inequality." But there is a force in market economies, ones with extensive amounts of monopoly, like the United States, which leads income-inequality to understate economic-inequality. This force has not been recognized before and derives from how monopolies behave. Monopolies, of course, raise prices. This reduces the purchasing power of households, or the value of their income. But monopolies, in fact, reduce the purchasing power of low-income households much more than high-income households. What has not been recognized is that, in many markets, as monopolies raise the prices for their goods, they simultaneously destroy substitutes for their products, low-cost substitutes that are purchased by low-income households. In these markets, then, while high-income households face higher prices, low-income households are shut out of markets, markets for goods and services that are extremely important for their economic well-being. It often leaves them with extremely poor alternatives, and sometimes none, for these products. Some of the markets we discuss include those for housing, financial services, and K-12 public education services. We also discuss markets for legal services, health care services, used durable equipment and repair services. Monopolies that infiltrate public institutions to enrich members, including those in foster care services, voting institutions and antitrust institutions, are also discussed.

This paper focuses on avoidable moral hazard and offers one explanation for limited insurance markets, for closely held firms, and for seemingly simple as opposed to contingent forms of debt. Agents have random endowments of a consumption good which are such that there are gains to trading contingent claims. But any realization of an endowment is known only by its owner unless a verification cost is borne. Contracts in such a setting are said to be consistent if agents submit to verification and honor claims in accordance with prior agreements. The Pareto optimal consistent contracts which emerge are shown to have familiar characteristics.

In this paper, we show that a substantial fraction of the volatility of real exchange rates between developed economies such as Germany, Japan, and the United Kingdom against the US dollar can be accounted for by shocks that affect the prices of primary commodities such as oil, aluminum, maize, or copper. Our analysis implies that existing models used to analyze real exchange rates between large economies that mostly focus on trade between differentiated final goods could benefit, in terms of matching the behavior of real exchange rates, by also considering trade in primary commodities.

We use a model of optimal portfolio choice to measure heterogeneity in risk aversion among households in Thai villages. There is substantial heterogeneity in risk preferences, positively correlated in most villages with alternative estimates based on a full risk-sharing model.

Forecasts are routinely revised, and these revisions are often the subject of informal analysis and discussion. This paper argues 1) that forecast revisions are analyzed because they help forecasters and forecast users to evaluate forecasts and forecasting procedures, and 2) that these analyses can be sharpened by using the forecasting model to systematically express its forecast revision as the sum of components identified with specific data revisions and forecast errors. An algorithm for this purpose is explained and illustrated.

Many regional econometric models are estimated under the maintained assumption that certain national variables are exogenous with respect to the regional variables in the models. This exogeneity assumption is testable using time series methods of inference, yet, to my knowledge, no regional model has been so tested. In this paper, I test the national exogeneity assumption included in the specification of a particular regional forecasting model. Such a test is, I believe, a necessary and important step in the construction of any econometric model.

In this paper, we review the relationship between inflation rates, nominal interest rates, and rates of growth of monetary aggregates for a large group of OECD countries. We conclude that the low-frequency behavior of these series maintains a close relationship, as predicted by standard quantity theory models. In an estimated model, we show those relationships to be relatively invariant to alternative frictions that can deliver very different high-frequency dynamics. We argue that these relationships are useful for policy design aimed at controlling inflation.

It is commonly asserted that with excess plant capacity, expansive policy stimulates output and lowers unemployment without substantially boosting inflation, while at full capacity most of the impact is on inflation. This assertion is critically examined. First, two common definitions of capacity--engineering and economic—are examined and found to be nebulous. The concepts of supply and demand are older, but better. Full capacity is reinterpreted as points where the supply curve is steep and excess capacity as points where it is fairly flat. Then the "Keynesian" model in which stimulative policy shifts only the demand curve is compared to the "classical" model where stimulative policy shifts both demand and supply curves. For the former model the assertion on capacity utilization is correct, while in the latter it is not. Empirical tests are performed to determine whether measured capacity utilization is useful for predicting inflation. The tests are ambiguous, but certainly do not strongly favor capacity utilization.

This paper presents maximum likelihood estimates of a real business cycle model very similar to one Kydland and Prescott [1982] suggested. The results of the paper conflict with Kydland and Prescott’s. The model leaves unexplained much of the variance of two key investment series, namely, structures and equipment. Also, much of the variation in the differences of per capita hours can be generated assuming that past leisure choices do not affect current utility.

This paper is motivated by observations concerning the size of the banking sector and the growth rate of the economy before and after successful stabilizations of high inflations. The facts suggest that the relative size of the banking sector increases during a period of accelerating inflation and decreases immediately following a successful monetary stabilization. Furthermore, the GDP growth rate is lower during the high inflation period than after stabilization. The goal of this paper is to develop a monetary growth model which is qualitatively consistent with these observations. The model we use is a variant of the Lucas and Stokey (1987) model of cash and credit goods. The main innovation in our model is that while cash goods and credit goods are perfect substitutes in consumption we posit different technologies for their production. We show that the model’s predictions on the impact of a permanent stabilization are consistent with the main real and monetary observations on high inflation countries.

This paper develops a vector autoregression (VAR) for macroeconomic time series which are observed at mixed frequencies – quarterly and monthly. The mixed-frequency VAR is cast in state-space form and estimated with Bayesian methods under a Minnesota-style prior. Using a real-time data set, we generate and evaluate forecasts from the mixed-frequency VAR and compare them to forecasts from a VAR that is estimated based on data time-aggregated to quarterly frequency. We document how information that becomes available within the quarter improves the forecasts in real time.

This paper derives a variance bounds test for a broad class of linear rational expectations models. According to this test if observed data accords with the model, then a weighted sum of autocovariances of the covariance-stationary components of the endogenous state variables should be nonnegative. The new test reinterprets its forefather - West's [1986] variance bounds test - and extends its applicability by not requiring exogenous state variables in order to be tested. The possibility of the test's application to nonlinear models is also discussed.

This paper argues that versions of Samuelson/Cass-Yaari overlapping-generations consumption-loans models ought to be taken seriously as models of fiat money. The case is made by summarizing and interpreting what these models have to say about fiat money and by arguing that these properties are robust in the sense that they can be expected to hold in any model of fiat money. Two of the properties establish the connection between, on the one hand, the existence of equilibria in which value is attached to a fixed stock of fiat money and, on the other hand, the optimality of such equilibria and the nonoptimality of nonfiat-money equilibria. Other properties describe aspects of the tenuousness of monetary equilibria in such models: The nonuniqueness of such equilibria in the sense that there always exists a nonfiat-money equilibrium and the dependence of the existence of the monetary equilibrium on the physical characteristics of other potential assets and on other institutional features like the tax-transfer scheme in effect. Rather than being defects of these models, it is argued that this tenuousness is helpful in interpreting various monetary systems and, in any case, is unavoidable; it will turn up in any good model of fiat money. Still other properties summarize what these models imply about the connection—or, better, lack of such— between fiat money and private borrowing and lending (financial intermediation) and what they imply about country-specific monies.

We develop a theory of outsourcing in which there is market power in one factor market (labor) and no market power in a second factor market (capital). There are two intermediate goods: one labor-intensive and the other capital-intensive. We show there is always outsourcing in the market allocation when a friction limiting outsourcing is not too big. The key factor underlying the result is that labor demand is more elastic, the greater the labor share. Integrated plants pay higher wages than the specialist producers of labor-intensive intermediates. We derive conditions under which there are multiple equilibria that vary in the degree of outsourcing. Across these equilibria, wages are lower the greater the degree of outsourcing. Wages fall when outsourcing increases in response to a decline in the outsourcing friction.

Under certain assumptions, monopolistic competition with CES preferences is efficient, as first discovered by Dixit and Stiglitz. One assumption, invariably left implicit, is that there are, at any given point in time, no bounds on the number of products that can be discovered. But square wheels do not work, and round wheels keep getting rediscovered. Giving away patents to entrepreneurs who happen to be the first to discover a product generates an inefficiently large amount of variety. The stock of undiscovered products is a commons that can attract too many discovery attempts. Perpetual patents can be efficient, but only when combined with just the right tax on patent-protected monopoly profits. Such a tax is, however, too crude an instrument in an economy with even the least amount of heterogeneity.

The key question asked by standard monetary models used for policy analysis is, How do changes in short-term interest rates affect the economy? All of the standard models imply that such changes in interest rates affect the economy by altering the conditional means of the macroeconomic aggregates and have no effect on the conditional variances of these aggregates. We argue that the data on exchange rates imply nearly the opposite: the observation that exchange rates are approximately random walks implies that fluctuations in interest rates are associated with nearly one-for-one changes in conditional variances and nearly no changes in conditional means. In this sense, standard monetary models capture essentially none of what is going on in the data. We thus argue that almost everything we say about monetary policy using these models is wrong.

Recent developments in the theory of economies with private information permit a re-examination of the issues raised in the "real bills-quantity theory" debate. A model is developed here in which there are banks, in which fiat money is present, and in which agents possess private information. Two regulatory regimes are then considered. In the first, banks are essentially unregulated. In the second, banks face 100 percent reserve requirements. Issues related to existence and optimality of equilibrium are addressed, and problems with existence are given an interpretation in terms of the "stability" of the banking system. Existence (stability) problems which arise under laissez-faire banking can be rectified by a 100 percent reserve requirement. However, unless there is private information regarding access to investment opportunities, there are typically better ways to accomplish this. Finally, it is shown that even in the presence of 100 percent reserve requirements banks are not simply "money warehouses." Bank deposits and money bear different (real) return streams, even under 100 percent reserves.

Wage inequality between education groups in the United States has increased substantially since the early 1980s. The relative number of college-educated workers has also increased dramatically in the postwar period. This paper presents a unified framework where the dynamics of both skill accumulation and wage inequality arise as an equilibrium outcome driven by measured investment-specific technological change. Working through equipment-skill complementarity and endogenous skill accumulation, the model does well in capturing the steady growth in the relative quantity of skilled labor during the postwar period and the substantial rise in wage inequality after the early 1980s. Based on the calibrated model, we examine the quantitative effects of some hypothetical tax-policy reforms on skill accumulation, wage inequality, and welfare.

Starting in the early 1990s, countries in southern Europe experienced low productivity growth alongside declining real interest rates. We use data for manufacturing firms in Spain between 1999 and 2012 to document a significant increase in the dispersion of the return to capital across firms, a stable dispersion of the return to labor, and a significant increase in productivity losses from capital misallocation over time. We develop a model with size-dependent financial frictions that is consistent with important aspects of firms’ behavior in production and balance sheet data. We illustrate how the decline in the real interest rate, often attributed to the euro convergence process, leads to a significant decline in sectoral total factor productivity as capital inflows are misallocated toward firms that have higher net worth but are not necessarily more productive. We show that similar trends in dispersion and productivity losses are observed in Italy and Portugal but not in Germany, France, and Norway.

We study a variation of the standard model of sovereign default, as in Aguiar and Gopinath (2006) or Arellano (2008), and show that this variation is consistent with multiple interest rate equilibria. Some of those equilibria correspond to the ones identified by Calvo (1988), where default is likely because rates are high, and rates are high because default is likely. The model is used to simulate equilibrium movements in sovereign bond spreads that resemble sovereign debt crises. It is also used to discuss lending policies similar to the ones announced by the European Central Bank in 2012.

In this paper we explain why markets in noncontingent debt securities might be a stable form of market organization for intermediation to households. Efficient-contract allocation might be supported by these markets because households' relationships with their intermediaries do not exactly parallel the explicit form of the noncontingent contracts that they explicitly sign with one another. Also we show that the efficient-contract model can be distinguished from alternative models within the time-series framework that has been widely used to study households' consumption patterns.

Entrepreneurship is a key determinant of investment, saving, wealth holdings, and wealth inequality. We study the aggregate and the distributional effects of several tax reforms in a model that recognizes the key role played by the entrepreneurs, and that matches very well the extreme degree of wealth inequality observed in the U.S. data. We find that the effects of tax reforms on output and capital formation can be particularly large when they affect the majority of small and medium-size businesses, which face the most severe financial constraints, rather than a small number of big businesses. We show that the consequences of changes in the estate tax depend heavily on the size of its exemption level. The current effective estate tax system seems to insulate most of the businesses from the negative effects of estate taxation thus minimizing the aggregate costs of redistribution. Abolishing the current estate tax would generate a modest increase in wealth inequality and slightly reduce aggregate output. Decreasing progressivity of the income tax can generate large increases in output, as this stimulates entrepreneurial savings and capital formation, but at the cost of large increases in wealth concentration.

We produce a theoretical framework that helps explain the co-evolution of the real and financial sectors of an economy in the growth process, as described by Gurley and Shaw. According to them, self-financed capital investment first gives way to debt finance and later to the emergence of equity as an additional instrument for raising funds externally. As the economy develops further, the aggregate ratio of debt to equity will generally fall. We analyze that portion of their account concerning the evolution of equity markets. We show that in an important sense, debt equity are complementary sources for the financing of capital investments.

In a repeated game of incomplete information, myopic players form beliefs on next-period play and choose strategies to maximize next-period payoffs. Beliefs are treated as forecast of future plays. Forecast accuracy is assessed using calibration tests, which measure asymptotic accuracy of beliefs against some realizations. Beliefs are calibrated if they pass all calibration tests. For a positive Lebesgue measure of payoff vectors, beliefs are not calibrated. But, if payoff vector and calibration test are drawn from a suitable product measure, beliefs pass the calibration test almost surely.

The main substantive finding of the recent structural vector autoregression literature with a differenced specification of hours (DSVAR) is that technology shocks lead to a fall in hours. Researchers have used these results to argue that business cycle models in which technology shocks lead to a rise in hours should be discarded. We evaluate the DSVAR approach by asking, is the specification derived from this approach misspecified when the data are generated by the very model the literature is trying to discard? We find that it is misspecified. Moreover, this misspecification is so great that it leads to mistaken inferences that are quantitatively large. We show that the other popular specification that uses the level of hours (LSVAR) is also misspecified. We argue that alternative state space approaches, including the business cycle accounting approach, are more fruitful techniques for guiding the development of business cycle theory.

We use scanner data to estimate inflation rates at the household level. Households' inflation rates are remarkably heterogeneous, with an interquartile range of 6.2 to 9.0 percentage points on an annual basis. Most of the heterogeneity comes not from variation in broadly defined consumption bundles but from variation in prices paid for the same types of goods - a source of variation that previous research has not measured. The entire distribution of household inflation rates shifts in parallel with aggregate inflation. Deviations from aggregate inflation exhibit only slightly negative serial correlation within each household over time, implying that the difference between a household's price level and the aggregate price level is persistent. Together, the large cross-sectional dispersion and low serial correlation of household-level inflation rates mean that almost all of the variability in a household's inflation rate over time comes from variability in household-level prices relative to average prices for the same goods, not from variability in the aggregate inflation rate. We provide a characterization of the stochastic process for household inflation that can be used to calibrate models of household decisions.

We use an extended Barro-Becker model of endogenous fertility, in which parents are heterogeneous in their labor productivity, to study the efficient degree of consumption inequality in the long run. In our environment a utilitarian planner allows for consumption inequality even when labor productivity is public information. We show that adding private information does not alter this result. We also show that the informationally constrained optimal insurance contract has a resetting property—whenever a family line experiences the highest shock, the continuation utility of each child is reset to a (high) level that is independent of history. This implies that there is a non-trivial, stationary distribution over continuation utilities and there is no mass at misery. The novelty of our approach is that the no-immiseration result is achieved without requiring that the objectives of the planner and the private agents disagree. Because there is no discrepancy between planner and private agents' objectives, the policy implications for implementation of the efficient allocation differ from previous results in the literature. Two examples of these are: 1) estate taxes are positive and 2) there are positive taxes on family size.

This paper investigates whether there are simple versions of the permanent income hypothesis which are consistent with the aggregate U.S. consumption and output data. Our analysis is conducted within the confines of a simple dynamic general equilibrium model of aggregate real output, investment, hours of work and consumption. We study the quantitative importance of two perturbations to the version of our model which predicts that observed consumption follows a random walk: (i) changing the production technology specification which rationalizes the random walk result, and (ii) replacing the assumption that agents' decision intervals coincide with the data sampling interval with the assumption that agents make decisions on a continuous time basis. We find substantially less evidence against the continuous time models than against their discrete time counterparts. In fact neither of the two continuous time models can be rejected at conventional significance levels. The continuous time models outperform their discrete time counterparts primarily because they explicitly account for the fact that the data used to test the models are time averaged measures of the underlying unobserved point-in-time variables. The net result is that they are better able to accommodate the degree of serial correlation present in the first difference of observed per capita U.S. consumption.

We show that much of the recent reported decrease in interstate migration is a statistical artifact. Before 2006, the Census Bureau's imputation procedure for dealing with missing data inflated the estimated interstate migration rate. An undocumented change in the procedure corrected the problem starting in 2006, thus reducing the estimated migration rate. The change in imputation procedures explains 90 percent of the reported decrease in interstate migration between 2005 and 2006, and 42 percent of the decrease between 2000 (the recent high-water mark) and 2010. After we remove the effect of the change in procedures, we find that the annual interstate migration rate follows a smooth downward trend from 1996 to 2010. Contrary to popular belief, the 2007–2009 recession is not associated with any additional decrease in interstate migration relative to trend.

A definition of a transactions medium is proposed. This is that a transactions medium permits the attainment of otherwise unattainable resource allocations. It is shown that by this definition money can be a transactions medium in a pure exchange, overlapping generations economy. It is also shown that money is a transaction medium only if there are informational asymmetries of a particular type. Finally, it is shown that the set of economies for which money is a transactions medium is not isolated, in a well-defined sense.

The normal linear model, with sign or other linear inequality constraints on its coefficients, arises very commonly in many scientific applications. Given inequality constraints Bayesian inference is much simpler than classical inference, but standard Bayesian computational methods become impractical when the posterior probability of the inequality constraints (under a diffuse prior) is small. This paper shows how the Gibbs sampling algorithm can provide an alternative, attractive approach to inference subject to linear inequality constraints in this situation, and how the GHK probability simulator may be used to assess the posterior probability of the constraints.

The classic explanation for the persistence and volatility of real exchange rates is that they are the result of nominal shocks in an economy with sticky goods prices. A key implication of this explanation is that if goods have differing degrees of price stickiness then relatively more sticky goods tend to have relatively more persistent and volatile good-level real exchange rates. Using panel data, we find only modest support for these key implications. The predictions of the theory for persistence have some modest support: in the data, the stickier is the price of a good the more persistent is its real exchange rate, but the theory predicts much more variation in persistence than is in the data. The predictions of the theory for volatility fare less well: in the data, the stickier is the price of a good the smaller is its conditional variance while in the theory the opposite holds. We show that allowing for pricing complementarities leads to a modest improvement in the theory’s predictions for persistence but little improvement in the theory’s predictions for conditional variances.

This paper uses an estimated structural model to argue that the option to move in and out of the parental home is an important insurance channel against labor market risk for youths who do not attend college. Using data from the NLSY97, I construct a new monthly panel of parent-youth coresidence outcomes and use it to document an empirical relationship between these movements and individual labor market events. The data is then used to estimate the parameters of a dynamic game between youths and their altruistic parents, featuring coresidence, labor supply and savings decisions. Parents can provide both monetary support through explicit financial transfers, and non-monetary support in the form of shared residence. To account for the data, two types of exogenous shocks are needed. Preference shocks are found to explain most of the cross-section of living arrangements, while labor market shocks account for individual movements in and out of the parental home. I use the model to show that coresidence is a valuable form of insurance, particularly for youths from poorer families. The option to live at home also helps to explain features of aggregate data for low-skilled young workers: their low savings rates and their relatively small consumption responses to labor market shocks. An important implication is that movements in and out of home can reduce the consumption smoothing benefits of social insurance programs.

Previous literature has shown that the study and characterization of constrained efficient allocations in economies with limited enforcement is useful to understand the limited risk sharing observed in many contexts, in particular between sovereign countries. In this paper we show that these constrained efficient allocations arise as equilibria in an economy in which private agents behave competitively, taking as given a set of taxes. We then show that these taxes, which end up limiting risk sharing, arise as an equilibrium of a dynamic game between governments. Our decentralization is different from the existing ones proposed in the literature. We find it intuitively appealing and we think it goes farther than the existing literature in endogenizing the primitive forces that lead to a lack of risk sharing in equilibrium.

We construct a vintage capital model of economic growth in which the decision to replace old technologies with new ones is modeled explicitly. Depreciation in this environment is an economic, not a physical concept. We describe the balanced growth paths and the transitional dynamics of this economy. We illustrate the importance of vintage capital by analyzing the response of the economy to fiscal policies designed to stimulate investment in new technologies.

In this paper, we consider an environment in which agents’ productivities are private information, potentially multi-dimensional, and follow arbitrary stochastic processes. We allow for arbitrary incentive-compatible and physically feasible tax schemes. We prove that it is typically Pareto optimal to have positive capital taxes. As well, we prove that in any given period, it is Pareto optimal to tax consumption goods at a uniform rate.

One of the long-standing issues in the literature on transfer programs for the U.S. low-income population concerns the high cumulative marginal tax rate on earnings induced by participation in the multiplicity of programs offered by the government. Empirical work on the issue has reached an impasse partly because the analytic solution to the choice problem is intractable and partly because the model requires the estimation of multiple sets of equations with limited dependent variables, an estimation problem which until recently has been computationally infeasible. In this paper we estimate a model of labor supply and multiple program participation using methods of simulation estimation that enable us to solve both problems. The results show asymmetric wage and tax rate effects, with fairly large wage elasticities of labor supply but very inelastic responses to moderate changes in cumulative marginal tax rates, implying that high welfare tax rates do not necessarily induce major reductions in work effort.

How much discretion is it optimal to give the monetary authority in setting its policy? We analyze this mechanism design question in an economy with an agreed-upon social welfare function that depends on the randomly fluctuating state of the economy. The monetary authority has private information about that state. In the model, well-designed rules trade off society’s desire to give the monetary authority flexibility to react to its private information against society’s need to guard against the standard time inconsistency problem arising from the temptation to stimulate the economy with unexpected inflation. We find that the optimal degree of monetary policy discretion is decreasing in the severity of the time inconsistency problem. As this problem becomes sufficiently severe, the optimal degree of discretion is none at all. We also find that, despite the apparent complexity of this dynamic mechanism design problem, society can implement the optimal policy simply by legislating an inflation cap that specifies the highest allowable inflation rate.

This paper examines the optimal debt contract between lenders and a sovereign borrower when the borrower is free to repudiate the debt and when his decision to invest or consume borrowed funds is unobservable. We show that recurrent debt crises are a necessary part of the incentive structure which supports the optimal pattern of lending.

We construct a sequence of pure exchange, stationary OLG economies in which generations have longer and longer life spans and all agents maximize a discounted sum of utilities with a fixed, positive, and common discount rate. Period utility functions and endowment patterns are subject to mild restrictions and within generation heterogeneity is permitted. We show that: (i) Every sequence of equilibrium interest rates converges to the discount rate. (ii) Eventually every nonmonetary steady state is optimal and a monetary steady state will never exist. (iii) For any agent consumption at any fixed age converges to permanent income evaluated using the utility discount rate.