Collateral constraints and the amplification-persistence trade-off

Kiyotaki and Moore (1997) have stressed that an amplification-persistence trade-off arises when collateral constraints on borrowing interact with lumpy investment. In this paper, I confirm by way of example that collateral constraints are not by themselves responsible for such a deceptive trade-off. More precisely, I show in a standard general-equilibrium two-agent model that the amplification and persistence of the impact of temporary shocks go hand in hand. Unlike Kiyotaki-Moore's, the economy features concave utility and production functions, an endogenous interest rate and neo-classical input accumulationcollateral constraints; amplification and persistence of aggregate shocks

Is History a Blessing or a Curse? International Borrowing without Commitment, Leapfrogging and Growth Reversals

We develop a simple open-economy AK model with collateral constraints that accounts for growth-reversal episodes, during which countries face abrupt changes in their growth rate that lead to either growth miracles or growth disasters. Absent commitment to investment by the borrowing country, imperfect contract enforcement leads to an informational lag such that the debt contracted upon today depends upon the past stock of capital. The no-commitment delay originates a history effect by which the richer a country has been in the past, the more it can borrow today. For (arbitrarily) small deviations from perfect contract enforcement, the history effect offsets the growth benefits from international borrowing and dampens growth, and it leads to leapfrogging in long-run levels. When large enough, the history effect originates growth reversals and we connect the latter to leapfrogging. Finally, we argue that the model accords with the reported evidence on growth disasters and growth accelerations. We also provide examples showing that leapfrogging and growth reversals may coexist, so that currently poor but fast-growing countries experiencing sharp growth reversals may end up, in the long-run, significantly richer than currently rich but declining countries.Growth Reversals; Leapfrogging; International Borrowing; Open Economies

On the optimal control of a linear neutral differential equation arising in economics

In this paper, we apply two optimization methods to solve an optimal control problem of a linear neutral differential equation (NDE) arising in economics. The first one is a variational method, the second follows a dynamic programming approach. Due to the infinite dimensionality of the NDE, the second method requires the reformulation of the latter as an ordinary differential equation in an appropriate abstract space. It is shown that the resulting HJB equation admits a closed-form solution, allowing for a much finer characterization of the optimal dynamics compared to the alternative variational method. The latter is clearly limited by the nontrivial nature of asymptotic analysis of NDEs.Neutral differential equations; economic dynamics; optimal control; calculus of variations; dynamic programming; infinite dimension

Leapfrogging, Growth Reversals and Welfare

We show that leapfrogging and growth reversals entail sizeable welfare gains and losses, respectively, in an AK economy that cannot credibly commit to investment when borrowing from international financial markets. Small no-commitment delays originate a trade-off that has an ambiguous effect on welfare: they reduce the long-run consumption growth rate but increase the initial level of consumption that is optimally chosen. Essentially, the larger the delay, the tighter the borrowing constraint and the weaker the incentives to accumulate capital, so that smaller growth and larger initial consumption follow. We show under logarithmic utility and small delays that the short-run effect dominates the long-run effect and that welfare improves, provided that the economy has historically been growing fast enough, and numerical examples suggest that this benchmark result extends to CRRA utility. When relative risk aversion is larger than one, it follows that there exists a positive welfare-maximizing delay associated with slower growth relative to the no-delay case. We then apply our results to show that leapfrogging in consumption level typically imply large welfare gains. In contrast, growth reversals occur for large delays and lead to significant welfare losses. Finally, financial integration, as measured by the credit multiplier given the no-commitment delay, is welfare-improving only for economies that have historically been growing fast enough.Growth Reversals; Leapfrogging; International Borrowing; Open Economies; Welfare

Leveraged financing, over investment, and boom-bust cycles

It has long been argued in the history of economic thought that over investment through highly leveraged borrowing under elastic credit supply may generate large boom-bust business cycles. This paper rationalizes this idea in a dynamic general equilibrium model with infinitely lived rational agents. It shows that dynamic interactions between strong asset-accumulation motives (based on habit formation on the borrower side) and elastic credit supply (based on collateralized lending on the lender side) generate a multiplier-accelerator mechanism that can transform a one-time technological innovation into large and long-lasting boom-bust cycles. Such cycles share many features in common to investment bubbles observed in the history (such as the IT bubble in the 1990s and the 2000s housing bubble)

Are Progressive Fiscal Rules Stabilizing?

This paper studies how income-based, progressive taxes and transfers may reduce aggregate volatility by protecting the economy against expectation-driven business cycles. Eliminating “local” sunspots that are arbitrarily close to an indeterminate steady state requires, for sensible parameter values, strong levels of progressivity so as to make labor supply close to inelastic. However, progressive taxes and transfers are shown to be ineffective to rule out stable deterministic cycles (and the associated “global” sunspots) that are located close to a determinate steady state. Our results are formalized within two benchmark models and show how the efficiency of progressive fiscal schemes as local automatic stabilizers depends on the fiscal base. In the first setting with heterogeneous agents and segmented asset markets in which wage income mostly finances consumption, we show that progressive taxes and transfers should be made dependent on labor income, so as to rule out local indeterminacy. On the contrary, progressive fiscal rules should be applied to capital income in an overlapping generations economy where consumption comes from savings income. Incidentally, the latter results suggest that capital income taxes may be desirable, when progressive, to make local expectation-driven fluctuations less likely. In both frameworks, key to the results is the property that progressive fiscal rules provide insurance in the presence of imperfect capital markets

Local Determinacy with Non-separable Utility

Journal of Economic Literature Classification Numbers: C62, D58, D91, E32.This paper introduces general formulations for both technology (with input substitution) and non-separable utility (compatible with balanced growth and stationary worked hours) into a benchmark RBC model. It is shown that intertemporal substitution and input substitutability lead to local determinacy and rule out stationary sunspot equilibria when labor demand is downward-sloping, in contrast with recent results obtained under the assumption of separable utility. The main intuition behind this result is shown to work as follows: in contrast with separable preferences, increasing the elasticity of intertemporal substitution in consumption necessarily implies decreasing the elasticity of constant-consumption labor supply, when utility is non-separable and concave, which affects unfavorably the occurrence of local indeterminacy

Leapfrogging, Growth Reversals and Welfare

We show that leapfrogging and growth reversals entail sizeable welfare gains and losses, respectively, in an AK economy that cannot credibly commit to investment when borrowing from international financial markets. Small no-commitment delays originate a trade-off that has an ambiguous effect on welfare: they reduce the long-run consumption growth rate but increase the initial level of consumption that is optimally chosen. Essentially, the larger the delay, the tighter the borrowing constraint and the weaker the incentives to accumulate capital, so that smaller growth and larger initial consumption follow. We show under logarithmic utility and small delays that the short-run effect dominates the long-run effect and that welfare improves, provided that the economy has historically been growing fast enough, and numerical examples suggest that this benchmark result extends to CRRA utility. When relative risk aversion is larger than one, it follows that there exists a positive welfare-maximizing delay associated with slower growth relative to the no-delay case. We then apply our results to show that leapfrogging in consumption level typically imply large welfare gains. In contrast, growth reversals occur for large delays and lead to significant welfare losses. Finally, financial integration, as measured by the credit multiplier given the no-commitment delay, is welfare-improving only for economies that have historically been growing fast enough

CREDIT MARKET FRICTIONS AND THE AMPLIFICATION-PERSISTENCE TRADE-OFF

The issue of how endogenous borrowing constraints lead to the amplification and persistence of aggregate shocks is revisited in this paper. Specifically, I show that an amplification-persistence trade-off is embodied in the setting proposed by Kiyotaki and Moore (1997). The key point is that while complex unit roots associated with persistence of temporary shocks require the fraction of credit-constrained firms to be small enough, large amplification relies on the opposite condition. Incidentally, I confirm the occurrence of periodic and quasi-periodic cycles around the determinate steady state

Collateral constraints and the amplification-persistence trade-off

Kiyotaki and Moore (1997) have stressed that an amplification-persistence trade-off arises when collateral constraints on borrowing interact with lumpy investment. In this paper, I confirm by way of example that collateral constraints are not by themselves responsible for such a deceptive trade-off. More precisely, I show in a standard general-equilibrium two-agent model that the amplification and persistence of the impact of temporary shocks go hand in hand. Unlike Kiyotaki-Moore's, the economy features concave utility and production functions, an endogenous interest rate and neo-classical input accumulatio