General Information Teaching Assistant and Tutorials: Diego Daruich. Office hours: Monday 4:00-5:00 pm in Room 720 in the Department of Economics. Again, contact Diego by e-mail to arrange an alternative time, if this does not work for you. Tutorials are on Friday 9:30-11:30 in 517. Homework: There will be weekly problem sets that are required for a passing grade. The problem sets are handed out on Thursdays and are due the next Thursday at the beginning of the class. You are allowed to cooperate with other students, but every student has to hand in his/her own uniquely written assignment. Examinations: There will be a final exam on Friday, May 16, 10-12 in room 517 Syllabus: Download it here. Summary: This last section of the core macro sequence is devoted to studying economies where agents are heterogeneous. These models are helpful to analyze a wide range of questions pertaining to business cycles, income distribution, asset pricing, consumption insurance, labor supply, the aggregate and redistributive effects of policies, etc. We will start with some "aggregation theorems" to show that in some cases a representative agent still exists. Next, we will move towards economies with "incomplete markets" where agents can only borrow and save through a risk-free bond. We begin by characterizing in detail the individual problem. Next, we proceed to the description of the stationary equilibrium. Then, we study an incomplete-markets model with aggregate shocks. The last set of classes are devoted to defining economies where there is default in equilibrium, and economies with heterogeneous firms. We may add one or two new topics, depending on the speed at which we settle.
Textbooks, Reading Material, and Website Background readings: Two useful background readings for this course are:
Finally, all the papers listed below, class by class, are required, with the exception of those marked with (XR) which are eXtra Readings, just for your own benefit, if you're interested in the topic.
Course website: Check regularly this web-page where announcements, readings, and notes will be regularly posted in PDF form to be downloaded. In what follows, I will outline the topics that we cover during the course, as we make progress. March 25: AggregationWe defined aggregation as a property of an economic model where the evolution of the aggregate equilibrium quantities and prices does not depend on the distribution of individual endowments. We briefly discussed aggregation of CRS production functions, and aggregation of preferences when every agent is the same along every dimension. We studied conditions under which Gorman (or demand) aggregation holds. We studied the equilibrium of the growth model with complete markets, quasi-homothetic utility, and household heterogeneity in endowments. In the presentation, we followed Chatterjee's article. We showed that a "representative agent" exists. The dynamics of aggregate quantities and prices are independent of the distribution of wealth, and are the same as in the representative agent economy you studied earlier. This is a stark example of Gorman aggregation.
We showed that in SS of the growth model with complete markets, heterogeneous endowments and homothetic preferences, the wealth distribution is indeterminate, but given an initial distribution the equilibrium dynamics are unique. We then covered the Negishi method, and derived the general aggregation with complete markets result by Constantinides (1982). The lecture notes contain an application based on the papers by Maliar-Maliar (2001, 2003). Finally, we discussed the two approaches one can take to modelling market incompleteness.
Lecture notes Homework 1 Solution to Homework 1 In the first
recitation on March 28th, Dario will teach some basic concepts of
measure theory from SLP, chapters 7, 8.1,11.1,11.2 and 12.4. We need
them from class 5 onwards. Note that the first recitation is in KMC 3-80 at the usual time because we need 517 for the Open House. April 1: Full Insurance and the Permanent Income Hypothesis
We have introduced the notion of precautionary saving (additional saving in the presence of uncertainty). We have related it to the convexity of marginal utility (prudence) and to the presence of borrowing constraints potentially binding in the future. We have defined a natural borrowing limit for the stochastic case. We have derived necessary conditions on the interest rate so that the optimal individual consumption sequence is bounded above, in the deterministic case and in the stochastic case. We have also shown, somewhat heuristically, that when income shocks are iid and BR<1 if absolute risk aversion declines monotonically with consumption, then the consumption sequence is bounded.
Homework 2 (note that the first problem is 17.2 in L-S_v3) Solution to Homework 2 April 8: Numerical Techniques to Solve the Stochastic Consumption-Saving Problem We have discussed how to discretize an AR1 process with the Tauchen method and the Rouwenhorst method. We have described in great detail a method to solve the income fluctuation problem based on iterating over the Euler equation and linearly interpolating the decision rule outside grid points.
April 10: The Neoclassical
Growth Model with Incomplete Markets I (LS 18.1-18.14)
April 15: Some Applications We have explained how to calibrate the model and and compute the steady-state equilibrium. Then we have illustrated how to use this class of models to analyze questions related to precautionary saving and wealth inequality. In particular, we outlined a model with entrepreneurs and workers and argued that it can generate a more skewed wealth distribution, since entrepreneurs have access to a higher return on their investment.
April 17: Optimal Ramsey Taxation with Incomplete Markets. Constrained Efficiency We began by studying the optimal level of government redistribution and the optimal quantity of government debt in the model. We then discussed the difference between the first-best allocation and the constrained-efficient (second-best) allocation in the Aiyagari model. We argued that the constrained planner, through saving decisions, will manipulate prices in order to raise wages (if the income of the poor is labor intensive), hence redistributing from the lucky-rich to the unlucky-poor.
Homework 4 Solution to Homework 4 April 22: Transitional Dynamics We defined a RCE of an economy undergoing a transition between two steady-states due to a tax reform, and studied how to compute the transitional dynamics by means of a shooting algorithm. We learned how to measure welfare changes from the tax reform.
April 24: Adding Aggregate
Risk: A Near-Aggregation Result (LS 18.15)
April 29: Micro
and Macro Labor Supply Elasticity
Lecture Notes May 1: Lifecycle Economies Wage inequality rises over the life-cycle. So does consumption inequality, but by much less. Hours inequality is flat. We argued that the complete-markets model (with separable utility) is unable to reproduce these facts. We studied an overlapping-generations version of the neoclassical growth model with incomplete market and we argued it can go a long way in matching the facts.
May 6: Aggregate shocks in lifecycle economies and default I have explained why the near-aggregation result of Krusell-Smith does not carry out to life cycle economies. Next, we have studied an incomplete-market economy where agents face borrowing constraints that are tight enough so that they never have the incentive to default in equilibrium. Then, we have formalized a model where agents can default and the financial sector takes into account the default probability and increases the prices of loans accordingly.
May 8: Industry
Dynamics
Final Exam: Friday May 16, 10-12 in room 517 Sample finals from past years: 2005, 2006, 2007, 2008, 2010, 2012 (in the missing years I did not teach the course) |
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