Linearization about the Current State: A Computational Method for Approximating Nonlinear Policy Functions during Simulation

September 30, 2015

By Ricard Evans and Kirk Phillips

This paper presents an adjustment to commonly used approximation methods for dynamic stochastic general equilibrium (DSGE) models. Policy functions approximated around the steady state will be inaccurate away from the steady state. In some cases, this does not lead to substantial inaccuracies. In other cases, however, the model may not have a well-defined steady state, or the nature of the steady state may be at odds with its off-steady-state dynamics. We show how to simulate a DSGE model by approximating about the current state. Our method introduces an approximation error, but minimizes the error associated with a finite-order Taylor-series expansion of the model’s characterizing equations. This method is easily implemented using available simulation software and has the advantage of mimicking highly non-linear behavior. We illustrate this with a variety of simple models. We compare our technique with other simulation techniques and show that the approximation errors are approximately the same for stable, well-defined models. We also illustrate how this method can solve and simulate models that are not tractable with standard approximation methods.

(Log-)linearization clearly does not apply in some situations, and this paper details a relatively simple method that should help out those who want to stick with their standard solution tools. If you research question deals with large shocks or your model has an undefined steady-state, this paper is likely for you.


Optimally Sticky Prices

September 25, 2015

By William Zame and Jean-Paul L’Huillier

We propose a microfoundation for sticky prices. We consider a an environment in which a monopolistic firm has better information than its consumers about the nominal aggregate state. We show that, when many consumers are uninformed (and for some ranges of parameters), it is optimal for the firm to offer contracts/prices that do not depend on the state of the world; i.e. optimal contracts/prices are sticky. We establish this result first in a general mechanism design framework that allows for non-linear pricing and screening, and then show implementation under both contract-setting and price-setting. A virtue of our microfoundation is that it is compatible with a dynamic general equilibrium model with money. We analyze whether money is neutral in this framework, and discuss the implications of this microfounded friction for welfare.

Very ambitious and much needed work. Whether this model will stick or not will unfortunately depend on how easy it is to stick it in standard models…

Over consumption. A horse race of Bayesian DSGE models

September 22, 2015

By Amedeo Argentiero, Maurizio Bovi and Roy Cerqueti

Standard dynamic stochastic general equilibrium (DSGE) models are populated by fully-informed-optimising Muth-rational agents. This kind of agent is at odds with well-known psychological biases, not to mention real life people. In particular, there are strong theoretical and empirical reasons to believe that consumers are overly optimistic. Also, the size of over optimism is likely to show cyclical features. In this paper we simulate two DSGE models, one standard with Muth-rational consumers, the other different just because agents are allowed to over consume. We then compare them throughout different cyclical phases. Results show that taking into account psychological biases allows the DSGE to fit better actual data in the long-run and in an economic boom scenario. Recessions are instead characterized by pessimism. We also find that over consumption is a structural trait. Moreover, booms enlarge significantly the magnitude of the bias. These findings are in line with – and enrich – both the economic and psychological literature, implying i) that the business cycle has a non trivial psychological content, and ii) that the size of psychological biases is affected by macroeconomic evolutions.

This is interesting, but I would be careful before stating that such psychological biases are of macroeconomic importance. Indeed, the exercise here is to estimate a standard RE model, then re-estimate it with a bias parameter. The latter may be capturing any other model miss-specification, and to be honest it is difficult to get a worse fit when you add a parameter. Also, the result could also be consistent with self-fulfilling expectation, which may not be observationally different, and the latter can assume perfectly rational and unbiased agents.

Secular Labor Reallocation and Business Cycles

September 18, 2015

By Gabriel Chodorow-Reich and Johannes Wieland

We study the effect of mean-preserving idiosyncratic industry shocks on business cycle outcomes. We develop an empirical methodology using a local area’s exposure to industry reallocation based on the area’s initial industry composition and employment trends in the rest of the country over a full employment cycle. Using confidential employment data by local area and industry over the period 1980-2014, we find sharp evidence of reallocation contributing to worse employment outcomes during national recessions but not during national expansions. We repeat our empirical exercise in a multi-area, multi-sector search and matching model of the labor market. The model reproduces the empirical results subject to inclusion of two key, empirically plausible frictions: imperfect mobility across industries, and downward nominal wage rigidity. Combining the empirical and model results, we conclude that reallocation can generate substantial amplification and persistence of business cycles at both the local and the aggregate level.

The paper also shows that it is not sufficient to look at broad aggregates to determines the status of an economy. You also need to look at industry level data. Now the dilemma. Suppose there is some structural imbalance generating substantial unemployment. Higher inflation can then take care of the downward nominal rigidity friction in the affected industries and make the unemployed employable in those industries. But this does not solve the structural imbalance and just pushes the can down the road. Thus, should one inflate or not?

Collateral constraints and rental markets

September 16, 2015

By Hippolyte D’Albis and Eleni Iliopulos

We study a benchmark model with collateral constraints and heterogeneous discounting. Contrarily to a rich literature on borrowing limits, we allow for rental markets. By incorporating this missing market, we show that impatient agents choose to rent rather than to own the collateral in the neighborhood of the deterministic steady state. Consequently, impatient agents are not indebted and borrowing constraints play no role in local dynamics.

This short paper makes a very simple point that merits highlighting. Indeed, only few models include rental markets, and as this paper shows, this can have important implications on the results.

A Model of the Twin Ds: Optimal Default and Devaluation

September 11, 2015

By Vivian Yue, Stephanie Schmitt-Grohe, Martin Uribe and Seunghoon Na

This paper characterizes jointly optimal default and exchange-rate policy in a small open economy with limited enforcement of debt contracts and downward nominal wage rigidity. Under optimal policy, default occurs during contractions and is accompanied by large devaluations. The latter inflate away real wages thereby avoiding massive unemployment. Thus, the Twin Ds phenomenon emerges endogenously as the optimal outcome. By contrast, under fixed exchange rates, optimal default takes place in the context of large involuntary unemployment. Fixed-exchange-rate economies are shown to have stronger default incentives and therefore support less external debt than economies with optimally floating rates.

In other words, default is more likely to happen if a highly indebted economy joins a monetary union.

Disinflation and Inequality in a DSGE monetary model: A Welfare Analysis

September 9, 2015

By Maria Ferrara and Patrizio Tirelli

We investigate the redistributive effects of a disinflation experiment in an otherwise standard medium-scale DSGE model augmented for Limited Asset Market Participation, implying that a fraction of households do not hold any wealth. We highlight two key mechanisms driving consumption and income distribution: i) the cash in advance constraint on firms working capital needs; ii) the response of profit margins to disinflation, which is crucially dependent on the two most used pricing assumptions in the New-Keynesian literature, i.e. Calvo vs Rotemberg. Results show that disinflation softens the cash in advance constraint and raises the real wage in steady state. This, in turn, lowers inequality. While under the Calvo formalism this effect is reinforced by the fall of price markups, under Rotemberg it is more than compensated by the increase of price markups and, therefore, the opposite result obtains.

There are two lessons I learn from this paper: the standard price adjustment processes in the literature are seriously ill-equipped to help us with disinflation, and we know very little about the distribution impact of disinflation. This is all likely worse with deflation. Now that the latter has become the reality in several countries, and possibly for a longer time, macro theory has its work cut out.