Grey Gordon

Nonlinear Adventures at the Zero Lower Bound

Motivated by the recent experience of the U.S. and the Eurozone, we describe the quantitative properties of a New Keynesian model with a zero lower bound (ZLB) on nominal interest rates, explicitly accounting for the nonlinearities that the bound brings. Besides showing how such a model can be efficiently computed, we find that the behavior of the economy is substantially affected by the presence of the ZLB. In particular, we document 1) the unconditional and conditional probabilities of hitting the ZLB; 2) the unconditional and conditional probabilty distributions of the duration of a spell at the ZLB; 3) the responses of output to government expenditure shocks at the ZLB, 4) the distribution of shocks that send the economy to the ZLB; and 5) the distribution of shocks that keep the economy at the ZLB.

Evaluating default policy: The business cycle matters

More debt forgiveness directly benefits households but indirectly makes credit more expensive. How does aggregate risk affect this trade‐off? In a calibrated general equilibrium life‐cycle model, aggregate risk reduces the welfare benefit of making default very costly when the costs are borne by all households at all times. The result does not necessarily extend to state‐contingent policies. The Bankruptcy Abuse Prevention and Consumer Protection Act of 2005 in particular generates a small welfare loss with or without aggregate risk.

Dynamics of Investment, Debt, and Default

How does physical capital accumulation affect the decision to default in developing small open economies? We find that, conditional on a level of foreign indebtedness, more capital improves the sovereign’s ability to meet its obligations, reducing the likelihood of default and the risk premium. This effect, however, is diminishing in the stock of capital because capital also tames the severity of the contraction following default, making autarky more appealing. Access to long-term debt and costly capital adjustment are crucial for matching business cycles. Our quantitative model delivers default episodes that mimic those observed in the data.

Computing Dynamic Heterogeneous-Agent Economies: Tracking the Distribution

Theoretical formulations of dynamic heterogeneous-agent economiestypically include a distribution as an aggregate state variable. This paperintroduces a method for computing equilibrium of these models by including a distribution directly as a state variable if it is finite-dimensional or a fine approximation of it if infinite-dimensional. The method accurately computes equilibrium in an extreme calibration of Huffmans (1987) overlapping-generations economy where quasi-aggregation, the accurate forecasting of prices using a small state space, fails to obtain. The method also accurately solves for equilibrium in a version of Krusell and Smiths (1998) economy wherein quasi-aggregation obtains but households face occasionally binding constraints. The method is demonstrated to be not only accurate but also feasible with equilibria for both economies being computed in under ten minutes in Matlab. Feasibility is achieved by using Smolyaks (1963) sparse-grid interpolation algorithm to limit the necessary number of gridpoints by many orders of magnitude relative to linear interpolation. Accuracy is achieved by using Smolyaks algorithm, which relies on smoothness, only for representing the distribution and not for other state variables such as individual asset holdings.

Optimal Bankruptcy Code: A Fresh Start for Some

What is the optimal consumer bankruptcy law? I answer this question using an incomplete markets life-cycle model with a planner who can choose state-contingent bankruptcy costs. I develop two main theoretical characterizations. First, whenever debt discharge is allowed, it should occur without cost. Second, bankruptcy should always be allowed for highly-indebted households. Quantitatively, the optimal policy can generate a welfare gain as large as 11.6%. However, attractive informal default, asymmetric information, and moral hazard can reduce the welfare gain to as little as 0.7%.

Accounting for the Rise in College Tuition

We develop a quantitative model of higher education to test explanations for the steep rise in college tuition between 1987 and 2010. The framework extends the quality-maximizing college paradigm of Epple, Romano, Sarpca, and Sieg (2013) and embeds it in an incomplete markets, life-cycle environment. We measure how much changes in underlying costs, reforms to the Federal Student Loan Program (FSLP), and changes in the college earnings premium have caused tuition to increase. All these changes combined generate a 106% rise in net tuition between 1987 and 2010, which more than accounts for the 78% increase seen in the data. Changes in the FSLP alone generate a 102% tuition increase, and changes in the college premium generate a 24% increase. Our findings cast doubt on Baumol’s cost disease as a driver of higher tuition.

A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity

A divide-and-conquer algorithm for exploiting policy function monotonicity is proposed and analyzed. To compute a discrete problem with n states and n choices, the algorithm requires at most 5n log2(n)n function evaluations and so is O(n log2 n). In contrast, existing methods for non-concave problems require n^2 evaluations in the worst-case and so are O(n^2). The algorithm holds great promise for discrete choice models where non-concavities naturally arise. In one such example, the sovereign default model of Arellano (2008), the algorithm is six times faster than the best existing method when n=100 and 50 times faster when n=1000. Moreover, if concavity is assumed, the algorithm combined with Heer and Maußner (2005)s method requires fewer than 18n evaluations and so is O(n).

A Practical Approach to Testing Calibration Strategies

A calibration strategy tries to match target moments using a model’s parameters. We propose tests for determining whether this is possible. The tests use moments at random parameter draws to assess whether the target moments are similar to the computed ones (evidence of existence) or appear to be outliers (evidence of non-existence). Our experiments show the tests are effective at detecting both existence and non-existence in a non-linear model. Multiple calibration strategies can be quickly tested using just one set of simulated data. Applying our approach to indirect inference allows for the testing of many auxiliary model speci�?cations simultaneously. Code is provided.