Macroeconomics and Inequality (Macro III)

Transcription

1 October 1999, Jonathan Heathcote 1 and Kjetil Storesletten 2. Macroeconomics and Inequality (Macro III) 1 Syllabus The purpose of the course is to acquaint the students with the rapidly growing class of macroeconomic models that do not impose the ction of a representative agent. To address a large number of questions in macroeconomics it is very important to model heterogeneity explicity, and recent developments in numerical methods and computing power have made this possible. We recommend (but do not require) that students who have not already taken Lars Ljungqvist s Recursive Macroeconomic Theory class (Macro II) take both classes simulatenously, as these classes complement each other. The reading list below is more extensive than the lectures, which will focus on the starred items (several of which are in Marimon & Scott (1999), a new book we recommend). The applications discussed will to a certain extent depend on the interests of the students. 1.1 Introduction Some empirical facts oninequality, anda short surveyof some of the questions that can be addressed by incorporating heterogeneity into macro-models. R: Díaz-Giménez, Quadrini & Ríos-Rull (1997), Domeij & Klein (1998). 1.2 Basic numerical tools This will involve the review of more than one method. As the techniques are best learnt through hands-on experience, there will be several homeworks, which will involve writing and running computer-programs. 1. Local methods: methods for computing optimal decision rules and characterizing the behaviour of an economy at a particular point in the state space (usually the non-stochastic steady state). 1 jonathan.heathcote@hhs.se, Ph: (08) , Stockholm School of Economics 2 kjetil@iies.su.se, Ph: (08) , Institute for International Economic Studies, Stockholm University. 1

2 ² Iterating on a linear-quadratic approximation to the value function. R: Söderlind (1996), Cooley (1995) chapter 2. ² Solving systems of linearized rst order conditions (i.e. solving systems of linear expectational di erence equations). These methods are sometimes subdivided into the state space approach and the method of undetermined coe cients. R: Farmer (1993), Heathcote (1998), Klein (1997), Söderlind (1999), Marimon & Scott (1999) chapter Global methods: methods for computing decision rules that are (close to) optimal across the entire state space. ² Discretization of state space (brute force iteration). Marimon & Scott (1999) chapter 5. ² Iteration on (piecewise linear) policy functions. R: Coleman (1990) ² The nite element method. R: Marimon & Scott (1999) chapter 6, Heathcote (1997). ² The method of parameterized expectations. R: Marimon & Scott (1999) chapter 7, Christiano & Fisher (1997). 3. Methods for dealing with both aggregate and idiosyncratic risk. ² General methods. R: Marimon & Scott (1999) chapter 11, Krusell & Smith (1998), den Haan (1997). ² Special problems. R: Veracierto (1997) 1.3 Theory We start by considering the simplest case: inequality in models with complete markets. Then we move on to the main topic of the class: models withidiosyncratic risk, inwhichthis riskis assumedto be at leastpartially uninsurable. 1. Models withcomplete markets. ² Ini nitely-livedagent economies (heterogeneityininitial wealth). R: Chatterjee (1994)?, Maliar & Maliar (1999). 2

3 ² Overlapping generations economies (heterogeneity in age). This class of models assumes that a complete set of assets is traded within each generation, but that some markets for trade between generations do not exist. For example, it is usually not possible to trade with unborn agents. We consider the basic Auerbach and Kotliko model as a vehicle to study issues such as pension system reform, immigration, and the role of bequests. R: Auerbach & Kotliko (1987), Storesletten (2000), Kotliko & Summers (1981). 2. Models withuninsurable idiosyncratic risk. ² The stationary economy without capital. R: Huggett (1993)?, Aiyagari & Gertler (1991). ² The stationary economy with capital. R: Aiyagari (1994)?, Huggett (1997), Huggett & Ospina (1998), Krueger (1998). ² Overlapping generations economies. R: Huggett (1996)?, Storesletten, Telmer & Yaron (1999), De Nardi, Imrohoro¼glu & Sargent (1998), Imrohoro¼glu, Imrohoro¼glu & Joines (1995), Hubbard, Skinner & Zeldes (1994). ² Economies with both idiosyncratic and aggregate risk. R: Krusell & Smith (1998) : 1.4 Applications We then move on to study more closely various applications of heterogeneous agent models. ² 1. Understanding observed wealth andincome distributions R: Quadrini & Ríos-Rull (1997), Castaneda, Díaz-Giménez & Ríos-Rull (1998a), Castaneda, Díaz-Giménez & Ríos-Rull (1998b), Quadrini (1997), Huggett (1996), Hubbard et al. (1994). 2. Welfare costs of business cycles. R: Imrohoro¼glu (1989)? ; Krusell & Smith (1999). 3. Asset pricing. R: Storesletten et al. (1999)?, Krusell & Smith (1997), Constantinides & Du e (1996), Telmer (1993), Heaton & Lucas (1996). 3

4 4. Unemployment, search and heterogeneity. R: Gomes, Greenwood & Rebelo (1997)?. 5. The income distribution and development. R: Banerjee & Newman (1993), Benabou (1996), Galor & Zeira (1993). 6. Heterogeneous workers and rms. R: Krusell, Ohanian, Ríos-Rull & Violante (1995)?, Cooley & Quadrini (1999). 1.5 Class Schedule Date Time Place Thursday 4/11/ Frescati, F279 Thursday 11/11/ Frescati, A271 Monday 15/11/ Frescati, A271 Thursday 18/11/ Frescati, A279 Thursday 25/11/ Frescati, D279 Thursday 2/12/ Frescati, A279 Thursday 9/12/ Frescati, A279 Thursday 16/12/ Frescati, A239 2 Examination: project/term paper A central part of the class is an individual project or term paper. This is an alternative or addition to a regular exam. The intention is that each student should come up with an original research project that is small enough to make progress on within the scope of a class. The purpose is twofold: to get hands-on experience in solving current macroeconomic problems, and to get started on research. The stages involved in the project will be: 1. To think of well-posed economic question. 2. To describe a model well suited to addressing this question. 3. To describe a numerical algorithm well suited to solving this model. 4. To write a computer program (in MATLAB, GAUSS or FORTRAN) that is well suited to implementing this algorithm. 5. To perform numerical experiments on the model that are well suited to answering the initial question. 6. To present the results in class. 7. To write up a paper (optional). 4

5 2.1 Time schedule for term paper ² December 16, 1999: Well posed economic question and suitable model ready. ² January 17, 2000: Numerical algorithm ready. ² January 31, 2000: Project in presentable form. An outline of the question, the model, the solutionmethod, andat least some preliminary results are necessary components of this presentation. ² February 7, 2000: Half-hour presentation in front of the rest of the class. ² Students who are interested can complete their papers (for extra points). References Aiyagari, S. R. (1994), Uninsured idiosyncratic risk and aggregate saving, Quarterly Journal of Economics 109, Aiyagari, S. R. & Gertler, M. (1991), Asset returns with transactions costs and uninsured individual risk, Journal of Monetary Economics 27, Auerbach, A. & Kotliko, L. (1987), Dynamic Fiscal Policy, Cambridge University Press. Banerjee, A. & Newman, A. (1993), Occupational choice and the process of development, Journal of Political Economy 101(2), Benabou, R. (1996), Heterogeneity, strati cation and growth, American Economic Review 86, Castaneda, A., Díaz-Giménez, J. & Ríos-Rull, J.-V. (1998a), Earnings and wealth inequality and income taxation: Quantifying the trade-o s of switching the U.S. to a proportional income tax system. Mimeo, University of Pennsylvania. Castaneda, A., Díaz-Giménez, J. & Ríos-Rull, J.-V. (1998b), Exploring the income distributionbusiness cycle dynamics, Journal of Monetary Economics 42,

6 Chatterjee, S. (1994), Transitional dynamics and the distribution of wealth in a neoclassical growth model, Journal of Public Economics 54, Christiano, L. J. & Fisher, J. D. (1997), Algorithms for solving dynamic models with occasionally binding constraints. Mimeo, Northwestern University. Coleman, J. W. I. (1990), Solving the stochastic growth model by policy-function iteration, Journal of Business and Economic Statistics 8(1), Constantinides, G. M. & Du e, D. (1996), Asset pricing with heterogenous consumers, Journal of Political Economy 104, Cooley, T. F. (1995), Frontiers of Business Cycle Research, Princeton University Press, Princeton. Cooley, T. F. & Quadrini, V. (1999), Financial markets and rm dynamics. mimeo, Stern School of Business, NYU. De Nardi, M., Imrohoro¼glu, S. & Sargent, T. J. (1998), Projected U.S. demographics and social security. Unpublished manuscript. den Haan, W. (1997), Solving dynamic models with aggregate shocks and heterogeneous agents, Macroeconomic Dynamics 1(2), Díaz-Giménez, J., Quadrini, V. & Ríos-Rull, J.-V. (1997), Dimensions of inequality: Facts onthe U.S. distributions ofearnings, income andwealth, Federal Reserve Bank of Minneapolis Quarterly Review pp Spring. Domeij, D. & Klein, P. (1998), Inequality of income and wealth in sweden. Mimeo, Stockholm School of Economics. Farmer, R. E. A. (1993), The Macroeconomics of Self-Ful lling Prophecies, MIT Press. Galor, O. & Zeira, J. (1993), Income distribution and macroeconomics, Review of Economic Studies 60, Gomes, J., Greenwood, J. & Rebelo, S. (1997), Equilibrium unemployment. NBER Working Paper No

7 Heathcote, J. (1997), Notes on the nite element method. Mimeo. Heathcote, J. (1998), Notes on solving systems of linear di erence equations. Mimeo. Heaton, J. & Lucas, D. (1996), Evaluating the e ects of incomplete markets on risk sharing and asset pricing, Journal of Political Economy 104(3), Hubbard, G., Skinner, J. & Zeldes, S. (1994), The importance ofprecautionary motives in explaining individual and aggregate saving, Carnegie- Rochester Conference Series on Public Policy 40, Huggett, M. (1993), The risk-free rate in heterogeneous-agent incompletemarkets economies, Journal of Economic Dynamics and Control 17(5/6), Huggett, M. (1996), Wealth distribution in life-cycle economies, Journal of Monetary Economics 38(3), Huggett, M. (1997), The one-sector growth model with idiosyncratic shocks: Steady states and dynamics, Journal of Monetary Economics 39(3), Huggett, M. & Ospina, S. (1998), On aggregate precautionary saving: when is the third derivative irrelevant? ITAM Discussion Paper Imrohoro¼glu, A. (1989), The cost of business cycles with indivisibilities and liquidity constraints, Journal of Political Economy 97(6), Imrohoro¼glu, A., Imrohoro¼glu, S. & Joines, D. (1995), A life cycle analysis of social security, Economic Theory 6(1), Klein, P. (1997), Using the generalized schur form to solve a system of linear expectational di erence equations. Mimeo, Institute for International Economic Studies, Stockholm University. Kotliko, L. & Summers, L. (1981), The role of intergenerational transfers in aggregate capital accumulation, Journal of Political Economy 89(4),

8 Krueger, D. (1998), Risk sharing in economies with incomplete markets. mimeo, Stanford University. Krusell, P., Ohanian, L., Ríos-Rull, J.-V. & Violante, G. (1995), Capital-skill complementarity and inequality. Mimeo. Krusell, P. & Smith, A. (1997), Income and wealth heterogeneity, portfolio choice, and equilibrium asset returns, Macroeconomic Dynamics 1(2), Krusell, P. & Smith, A. (1998), Income and wealth heterogeneity in the macroeconomy, Journal of Political Economy 106(5), Krusell, P. & Smith, A. (1999), On the welfare e ects of eliminating business cycles, Review of Economic Dynamics 2(1), Maliar, L. & Maliar, S. (1999), Heterogeneity in capital and skills in a neoclassical stochastic growth model. mimeo, Universtitat Pompeu Fabra. Marimon, R. & Scott, A. (1999), Computational Methods for the Study of Dynamic Economies, Oxford University Press. Quadrini, V. (1997), Entrepreneurship, saving and social mobility. Mimeo, University of Pennsylvania. Quadrini, V. & Ríos-Rull, J.-V. (1997), Understanding the U.S. distribution of wealth, Federal Reserve Bank of Minneapolis Quarterly Review pp Spring. Söderlind, P. (1996), Lecture notes. Mimeo. Söderlind, P. (1999), Solution and estimation of R.E. macromodels with optimal policy, European Economic Review 43, Storesletten, K. (2000), Sustaining scal policy through immigration. Storesletten, K., Telmer, C. & Yaron, A. (1999), Asset pricing with idiosyncratic risk and overlapping generations. Working Paper, GSIA Carnegie Mellon University. Telmer, C. I. (1993), Assetpricing puzzles andincomplete markets, Journal of Finance 48,

9 Veracierto, M. (1997), Plant level irreversible investment and equilibrium business cycles. Federal Reserve Bank of Minneapolis Discussion Paper No