(preliminary) with Paul Beaudry and Franck PortierAbstract: We propose a reduced form model of accumulation and interactions between agents. The model can be seen either as an Agent-Based model or as the DSGE one, depending on how forward-looking the agents are. When complementarities between agents are increased (but stay weak in the sense that there are no multiple period-t equilibria), non-trivial dynamic properties can emerge, depending on three mechanisms: the sign of the effect of past accumulation for current actions, the strength of sluggishness in actions and the strength of the forward looking behaviour of economic agents. Depending on the relative strength of those three forces, hysteresis,limit cycles of sunspot equilibria can emerge. Our results show that complementarities in actions are key for the emergence of fluctuations in otherwise stable and non-oscillating economies.
(preliminary) with Paul Beaudry and Franck PortierAbstract: We study the type of equilibria that emerges when one increases the level of interactions between agents in a dynamic extension of the Cooper and John's  model. In the model, agents exert an effort that accumulates into a stock. The payoff function V depends on individual effort, individual stock, but also possibly on the aggregate level of effort, as capturing interactions between agents. Three features of the payoff function will be relevant: how does the agregate level of effort impact marginal value of individual effort or marginal value of individual stock; whether interactions are under the form of complementarities or substitutabilities; and finally whether past accumulation increases or decreases current incentives to make effort. Depending on those properties, we show how hysteresis, limit cycles and sunspots can emerge from interactions.
Quantitative Economics, 12(3)Abstract: Unlike linear ones, non-linear business cycle models can generate sustained fluctuations even in the absence of shocks (e.g., via limit cycles/chaos). A popular approach to solving non-linear models is perturbation methods. I show that, as typically implemented, these methods are incapable of finding solutions featuring limit cycles or chaos. Fundamentally, solutions are only required not to explode, while standard perturbation algorithms seek solutions that meet the stronger requirement of convergence to the steady state. I propose a modification to standard algorithms that does not impose this overly strong requirement.
Online Appendix Code (Supplement for Mac users, courtesy of Mariano Kulish)
with Paul Beaudry and Franck Portier American Economic Review, 110(1) (lead article)
[Copyright American Economic Association; reproduced with permission of the American Economic Review]Abstract: Are business cycles mainly a response to persistent exogenous shocks, or do they instead reflect a strong endogenous mechanism which produces recurrent boom-bust phenomena? In this paper we present new evidence in favor of the second interpretation and, most importantly, we highlight the set of key elements that influence our answer to this question. In particular, when adopting our most preferred estimation framework, we find support for the somewhat extreme notion that business cycles may be generated by stochastic limit cycle forces; that is, we find support for the notion that business cycles may primarily reflect an endogenous propagation mechanism buffeted only by temporary shocks. The three elements that tend to favor this type of interpretation of business cycles are: (i) slightly extending the frequency window one associates with business cycle phenomena, (ii) allowing for strategic complementarities across agents that arise due to financial frictions, and (iii) allowing for a locally unstable steady state in estimation. We document the sensitivity of our findings to each of these elements within the context of an extended New Keynesian model with real-financial linkages.
with Paul Beaudry and Franck Portier The Review of Economic Studies, 85(1)Abstract: Recessions often happen after periods of rapid accumulation of houses, consumer durables and business capital. This observation has led some economists, most notably Friedrich Hayek, to conclude that recessions often reflect periods of needed liquidation resulting from past over-investment. According to the main proponents of this view, government spending or any other form of aggregate demand policy should not be used to mitigate such a liquidation process, as doing so would simply result in a needed adjustment being postponed. In contrast, ever since the work of Keynes, many economists have viewed recessions as periods of deficient demand that should be countered by activist fiscal policy. In this paper we reexamine the liquidation perspective of recessions in a setup where prices are flexible but where not all trades are coordinated by centralized markets. The model illustrates why liquidations likely cause recessions characterized by deficient aggregate demand and accordingly suggests that Keynes' and Hayek's views of recessions may be closely linked. In our framework, interventions aimed at stimulating aggregate demand face a trade-off whereby current stimulus postpones the adjustment process and therefore prolongs the recessions, but where some stimulative policies may nevertheless remain desirable.
with Paul Beaudry and Franck Portier NBER Macroeconomics Annual 31Abstract: In most modern macroeconomic models, the steady state (or balanced growth path) of the system is a local attractor, in the sense that, in the absence of shocks, the economy would converge to the steady state. In this paper, we examine whether the time series behavior of macroeconomic aggregates (especially labor market aggregates) is in fact supportive of this local-stability view of macroeconomic dynamics, or if it instead favors an alternative interpretation in which the macroeconomy may be better characterized as being locally unstable, with nonlinear deterministic forces capable of producing endogenous cyclical behavior. To do this, we extend a standard AR representation of the data to allow for smooth nonlinearities. Our main finding is that, even using a procedure that may have low power to detect local instability, the data provide intriguing support for the view that the macroeconomy may be locally unstable and involve limit-cycle forces. An interesting finding is that the degree of nonlinearity we detect in the data is small, but nevertheless enough to alter the description of macroeconomic behavior. We complete the paper with a discussion of the extent to which these two different views about the inherent dynamics of the macroeconomy may matter for policy.