Useful results for the simulation of non-optimal economies with heterogeneous agents

This paper deals with infinite horizon non-optimal economies with aggregate uncertainty and a finite number of heterogeneous agents. It derives sufficient conditions for the existence of a recursive structure,an ergodic, a stationary, and a non-stationary equilibria. It also gives an answer to the following question: is it possible to derive a general framework which guarantees that numerical simulations truly reflect the behavior of endogenous variables in the model? We provide sufficient conditions to give an affirmative answer to this question for endowment economies with incomplete markets and uncountable exogenous shocks. These conditions guarantee the ergodicity of the process and hold for a particular selection mechanism. For economies with finitely many shocks or for an arbitrary selection in economies with uncountable shocks, it is only possible to show that a computable, time independent and recursive representation generates a stationary Markov process. The results in this paper suggest that often a well defined stochastic steady state in heterogenous agent models is sensitive to the initial conditions of the economy; a fact which imply that heterogeneity may have irreversible long-lasting effects

Accuracy in recursive minimal state space methods

The existence of a recursive minimal state space (MSS) representation is notalways guaranteed. However, because of its numerical efficiency, this type of equilibrium is frequently used in practice. What are the consequences of computing and simulating a model without a constructive proof? To answer this question, we identify a condition which is associated with a convergent and computable MSSrepresentation in a RBC model with state contingent taxes. This condition ensures the existence of a benchmark equilibrium that can be used to test frequently used algorithms. To verify the accuracy of simulations even if this condition does not hold, we derive a closed form recursive equilibrium which contains the MSS representation. Both benchmark representations are accurate and ergodic. We showthat state of the art algorithms, even if they are numerically convergent, may underestimate capital (and thus overestimate the benefits of capital taxes) by at least 65%, a figure which is in line with recent findings using accurate benchmarks. When an existence proof is not available, we found 2 sources of inaccuracy: the lack of a convergent operator and the absence of a well-defined (stochastic) steady state.Moreover, we identify a connection between lack of convergence and the equilibrium budget constraint which implies that simulated paths may be distorted not only in the long run but also in any period. When we have a constructive proof, inaccuracy is generated by the lack of qualitative properties in the computed policy functions

Memory, multiple equilibria and emerging market crises

We present a new Generalized Markov Equilibrium (GME) approach to studying sudden stops and financial crises in emerging countries in the canonical small open economy model with equilibrium price-dependent collateral constraints. Our approach to characterizing and computing stochastic equilibrium dynamics is global, encompasses recursive equilibrium as a special case, yet allows for a much more flexible approach to modeling memory in such models that are known to have multiple equilibrium. We prove the existence of ergodic GME selections from the set of sequential competitive equilibrium, and show that at the same time ergodic GME selectors can replicate all the observed phases of the macro crises associated with a sudden stop (boom, collapse, spiralized recession, recovery) while still being able to capture the long-run stylized behavior of the data. We also compute stochastic equilibrium dynamics associated with stationary and nonstationary GME selections, and we find that a) the ergodic GME selectors generate stochastic dynamics that are less financially constrained with respect to stationary non-ergodic paths, b) non-stationary GME selections exhibit a great range of fluctuations in macroeconomic aggregates compared to the stationary selections. From a theoretical perspective, we prove the existence of both sequential competitive equilibrium and (minimal state space) recursive equilibrium, as well as provide a complete theory of robust recursive equilibrium comparative statics in deep parameters. Consistent with recent results in the literature, relative to the set of recursive equilibrium, we find 2 stationary equilibrium: one with high/over borrowing, the other with low/under borrowing. These equilibrium are extremal and “selffulfilling” under rational expectations. The selection among these equilibria depend on observable variables and not on sunspots

Life cycle, financial frictions and informal labor markets: the case of Chile

We study the implications of economic policies on household's decisions. We focus on Chile in 2019. Using a life-cycle search model and survey data, we found that an equivalent change in labor tax rates and non-contributory pensions (NCP) have opposite effects on labor markets, specifically on informality and unemployment duration. NCP offers a milder trade-off as it produces a second-order increase in informality. However, due to the presence of informal labor markets and financial frictions, non-retired agents increase their current consumption only after a tax cut. That is, a positive wealth shock can reduce consumption. When we consider the impact on welfare, as households are assumed to value only consumption, cutting taxes seems to be preferred. We characterize labor market and consumption-savings decisions. We found two effects operating in opposite directions: substitution and wealth. The latter prevails suggesting that the life cycle aspects of the labor market are critical.This work was supported by the Inter-American Development Bank [ATN/OC -14728 RG (T2528)]

An ergodic theory of sovereign default

We present the conditions under which the dynamics of a sovereign default model of private external debt are stationary, ergodic and globally stable. As our results are constructive, the model can be used for the accurate computation of global long run stylized facts. We show that default can be used to derive a stable unconditional distribution (i.e., a stable stochastic steady state), one for each possible event, which in turn allows us to characterize globally positive probability paths. We show that the stable and the ergodic distribution are actually the same object. We found that there are 3 type of paths: non-sustainable and sustainable; among this last category trajectories can be either stable or unstable. In the absence of default, non-sustainable and unstable paths generate explosive trajectories for debt. By deriving the notion of stable state space, we show that the government can use the default of private external debt as a stabilization policy

Persistent current account deficits and balance of payments crises

Persistent current account defficits are common among low- andmiddle-income countries. We evaluate when this situation triggers acrisis and characterize it. Using a non-parametric estimator, we finda critical value for the yearly current account defficit just before thecrisis sets of. These findings give rise to a different type of crises:countries that have increased their external indebtedness by an accumulated amount of at least 26%-31% of the GDP in a time span of 3 to 5 years, when they are hit by a crisis, they suffer a more severe recession than an average sudden stop. We call these events persistent balance of payment crises. This generates a consumption fall of 3.1% and a current account reversal 4.9 percentage points. We also contribute to the structural characterization of balance of payment crises. Using a canonical model augmented with an endogenous interest rate, given enough persistence of the GDP, we can replicate these stylized facts. In this sense, the variability of national income in countries which are external net debtors is critical