Sargent Reading Group Notes

This paper presents a stochastic simulation method for solving dynamic economic models. The ideas in this paper lean on a literature sometimes known as approximate dynamic programming and can enable us to solve models with many state variables and non-convexities in objectives and constraints. My intent is to summarize the core theoretical ideas behind the algorithm. Main idea: Post decision states Notation: classic Bellman equation Consider a stationary economic model where at time t the state is summarized by a vector st of endogenous state variables and a vector xt of exogenous state variables.

This paper looks at the class of equations used to represent and solve heterogenous agent models in continuous time and presents a solution approach that is efficient and tractable. Model A few models were presented in the paper. Here we’ll take the simplest one: a continuous time version of the Huggett economy. In this economy there are a continuum of individuals that are heterogeneous in their wealth and income. Individuals value streams of consumption using CRRA preferences and a constant discount factor ρ.

This paper extends the Meltiz framework to allow for optimal tariff policies. Model This model extends a two country Melitz framework in two ways: Allows for heterogeneity in variable and fixed costs. This will be a policy instrument where governments can set firm specific tariffs The representative consumer in each country has a constant elasticity of substitution across all varieties procued within a country, but that elasticity can differ across countries.

Overview A primarily empirical paper that studies how allowing exporting firms to learn about demand for their product impacts firm dynamics in a Melitz style trade model. Data and stylized facts Let’s start with the data. The data set used in this paper describes all imports by US buyers from Colombian exporters from 1992-2009. The source is the U.S. Census Bureau’s Longitudinal Foreign Trade Transactions Database (LFTTD). Using this data, the authors report the following stylized facts:

Intro This introduces heterogenous banks into a general equilibrium trade model in the flavor of Melitz. There are also empirical exercises that show that the model can generate some features of German banking data. Model We will describe the model in two stages: Closed economy, where we will characterize economic setting and the optimization problem of each agent. Open economy, where combine 2 closed economies and allow them to trade Closed economy The economy consists of the following agents:

Intro This paper takes an empirical look at a variant of the Melitz model from last week. Model Assumptions: Domestic and foreign product markets are monopolistically competitive and segmented. In Melitz we got segmentation from CRS production. Marginal costs do not respond to output shocks: domestic shocks do not impact optimal export levels Firms are heterogeneous in marginal production costs and foreign demand functions (so profits differ) Future exchange rate, production costs, and foreign demand shifters are unkown, but Markov Firms must pay an up-front cost to enter export market in addition to per period fixed operating costs For a firm already in the export market, export profits are characterized by log-linear (Cobb Douglass in levels) function of firm-specific characteristics, the real exchange rate, and a random disturbance.

Intro An early paper that introduced a now common framework for thinking about firm entry, export decision, and exit in trade models. Model I’ll describe the model in two stages: A closed economy version of the model with a single country An open economy version with many similar countries Closed economy Consumers There is a representative consumer with CES a utility function over a continuum of goods. The elasticity of substitution between any two goods is σ > 1.

Model The model is a search and matching model in the flavor of DPM, with a few modifications. Consumers There are a continuum of identical consumers that have the following characteristics: They face both idiosyncratic and aggregate risk (both productivity shocks that are AR(1) in logs) Have a constant hazard probability ϕ of dying each period Are organized into families that pool all idiosyncratic risk and exhibit perfect idiosyncratic risk sharing within the family The family problem:

Outline An empirical paper that examines the relationship between the real exchange rate and the relative price of non-traded vs traded goods. Modes of thought At the time of writing the paper, there were two main modes of thought for thinking about real exchange rate movements Traditional view: all movements in bilateral real exchange rate between two countries are due to fluctuations in the bilateral relative price of non-traded to traded goods.

Intro The authors did some empirical work with data on Columbian firms to arrive at two stlyized facts about new exporters (firms who recently began exporting): On average, entrant exporters are smaller than long-time exporters The probability of exiting the export market falls with tenure The goal of the paper is to write a model that can match the data on these two dimensions. Model Partial equilibrium version of the model I presented last week.