Sargent Reading Group Notes

Model This is a general equilibrium trade model that focuses on producer export, entry, expansion, and exit. The structure of the model nests other standard models such as Krugman, Melitz and others. In the model there are two symmetric countries. Within each country there are consumers, final goods producers, intermediate goods producers, and a government. Consumers A unit mass of identical consumers live in each country and inelastically supple one unit of labor Choose sequences of capital, risk free one period bond holdings, and consumption to maximize expected present discounted value of CRRA utility over consumption.

Model Firm Problem The model has a representative firm that uses capital and labor within CRS Cobb Douglas production technology, subject to TFP shock. Capital evolution is standard: kt + 1 = (1 − δ)kt + it Firms also raise resources through debt and equity financing: Debt financing comes through the issuance of a non-state contingent one period bond. Debt financing has a tax advantage relative to equity (Rt = 1 + rt(1 − τ)) Equity financing comes through dividend payments (or receipts) from shareholders Total cost to firms of dividend payouts is the payment amount plus a quadratic term in deviation of payout from target (steady state).

Outline The authors of this paper do 3 main things: Describe a particular class of Dynamic economic games Describe two algorithms for computing Markov perfect equilibria of those games Give two detailed, non-trivial examples of how to apply the algorithms to games in this class We won’t have time to touch on the examples, but my goal today is to describe the class of models and explain the key components of the algorithms.

Model Mechanics Two agents, infinite horizon, discrete time, and each agent has a common discount factor δ. Each period agent 1 can choose to enter or exit. Player 2 has a countably finite set of actions, represented as the set 𝒜, which is equal to the natural numbers. Each period an i.i.d subset of A ⊂ 𝒜 is drawn. This is both the state of the economy in each period and agent 2’s feasible actions set for the period.

Intro Goal: Characterize the main conceptual composition of risk and shock elasticities and provide an example of their interpretation in a macro model. Outline: General continuous time framework Stochastic process for state Growth processes and cash flows Perturbations Elasticities Simple example Do the BL model. Can talk about choosing αd = ei for i = 1, 2, 3. Mathematical Framework I will briefly explain the mathematical framework used in this and related papers.

Model The model in this paper is fairly simple. The interesting analysis in this paper has to do with the information structure Setup Agents in the model either live in the mainland or on one of a continuum of islands Each island: Is populated by a continuum of workers and a continuum of monopolistic firms. Within each island all firms are identical, as are workers Firms: Hire workers through competitive labor markets Use labor in a linear production technology: product of labor supply island specific TFP The log of TFP in each period is the sum of an aggregate and an idiosyncratic shock All shocks in the model are mean zero Gaussians, unless otherwise specified.

Outline This is paper is more empirical than theoretical. Theoretical contributions are to specify more flexible stochastic environment than in other long run risk models a la Bansal et al. (2007) Empirical contributions are form a linear approximation of the stochastic environment to apply state space methods within an MCMC algorithm Show how to incorporate data of various frequencies and accuracy in the inference algorithm Overview of this talk:

Model This is two-type agent, continuous time model of financial intermediaries. He and Krishnamurthy (2013) Agents are either households or specialists. Distinction will be made clear once we understand the market structure Market structure One risk-free short run bond in zero net supply All agents can freely buy this asset Specialists can also short One risky asset whose dividends evolve as GBM Only specialists can purchase this asset, however they can do so in behalf of households via an intermediary mechanism to be explained shortly Net supply normalized to 1 Technology (how markets work) Each period between t and t + dt is split into 5 mini-periods:

Section 1 (intro): Two channels: productivity channel says move from low productivity to high productivity country risk-sharing channel says move from low marginal utility (MU) to high MU country Section 2 (lit review): Differ from Tretvol on three dimensions: (1) look at long run shocks, (2) Tretvoll considers standard BKK capital accumulation (TODO: what is used here) (3) parameter values are closer to asset pricing than RBC literature (RRA = 10, IES > 1 where tretvoll has RRA=100, IES < 1) Section 3 (empirics): Used data on G7 countries to show three main results: Positive short run productivity news leads to net inflow of capital Positive long run productivity news leads to net outflow of captial Did estimation for US vs UK and then for US vs all other G6.