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I. USEFUL REFERENCES Cooley, Chapter 1: Economic Growth and Business Cycles by Thomas F. Cooley and Edward C. Prescott Cooley, Chapter 2: Recursive Methods for Computing Equilibria in Business Cycle Models by Gary D. Hansen and Edward C. Prescott The Poverty of Nations: A Quantitative Investigation by V.V. Chari, Patrick J. Kehoe, and Ellen R. McGrattan Intertemporal General Equilibrium Models by Timothy J. Kehoe Barro and Sala-i Martin Book: Introduction Chapter 1: Growth Models with Exogenous Saving Rates (the Solow-Swan Model) References Ponzi :Where Did Ponzi Schemes Get Their Name? Lecture notes on the Solow Growth model. Lecture notes #1, #2, #3, #4 #5, #6 by Dirk Kruger Kydland and Prescott: Nobel citation Prescott's lecture Levine on Kydland and Prescott's contribution Lucas: Nobel lecture Chari on Lucas' contribution Weekly Session Notes: Theory Notes Matlab Notes II. USEFUL TEXTBOOKS Acemoglu, Daron. Introduction to modern economic growth. Cambridge, Princeton University Press, 2009. Adda, Jérôme and Cooper, Russell. Dynamic economics: Quantitative methods and applications. Cambridge, Massachusetts: The MIT Press, 2003 Cooley, Thomas F. (Eds.). “Frontiers of Business Cycle Research.” Princeton University Press, 1995. Heer, Burkhard and Maussner, Alfred. Dynamic general equilibrium modeling: computational methods and applications. Berlin; New York, NY: Springer, 2005. Judd, Kenneth L. Numerical methods in economics. Cambridge, MA: MIT Press, 1998. Ljungqvist, Lars and Sargent, Thomas J. Recursive Macroeconomic Theory. Cambridge, MA: MIT Press, 2004. Marimon, Ramon and Scott, Andrew (Eds.). “Computational Methods for the Study of Dynamic Economies.” Oxford: Oxford University Press, 1999. Miranda, Mario J. and Fackler, Paul L. Applied computational economics and finance. Cambridge, Massachusetts: The MIT Press, 2002. Pissarides, Christopher A. Equilibrium Unemployment Theory. Cambridge, MA: MIT Press, 2000. Press, William H.; Teukolsky, Saul A.; Vetterling, William T. and Flannery, Brian P. (Eds.) Numerical Recipes in C. New York, N.Y.: Press Syndicate of the University of Cambridge, 1992. Ralston, Anthony and Rabinowitz, Philip. A first course in numerical analysis. Mineola, New York: Dover Publications, Inc. 1978 (2nd edition). Stokey, Nancy L.; Lucas, Robert E., Jr. and Prescott, Edward C. Recursive Methods in Economic Dynamics. Cambridge, MA: Harvard University Press, 1989. III. HISTORY OF MACROECONOMICS, DATA AND THE NEOCLASSICAL MODEL OF DEVELOPMENT Macroeconomic issues are central concerns in economics. Macroeconomics underwent a revolution in the 1970s and 1980s, due to the introduction of the methods of rational expectations, dynamic optimization, and general equilibrium analysis into macroeconomic models, to the development of new theories of economic fluctuations, and to the introduction of sophisticated methods for the analysis of economic time series Slides by Murat Blanchard, Olivier. “What Do We Know about Macroeconomics that Fisher and Wicksell Did Not?” Quarterly Journal of Economics, November 2000, 115(4), pp. 1375-1409. Blanchard, Olivier. “The State of Macro.” Annual Review of Economics, 2009, 1, pp. 209-228. Kydland, Finn E. “Quantitative Aggregate Economics.” American Economic Review, December 2006, 96(5), pp. 1373-83. Phelps, Edmund S. “Macroeconomics for a Modern Economy.” American Economic Review, June 2007, 97(3), pp. 543-61. Woodford, Michael. “Revolution and Evolution in Twentieth-Century Macroeconomics.” Unpublished Manuscript, 1999 Woodford, Michael. “Convergence in Macroeconomics: Elements of the New Synthesis.” American Economic Journal: Macroeconomics, January 2009, 1(1), pp. 267-79. Great Depressions of the Twentieth Century: Of course, all good science is a combination of inductive and deductive methods, a constant interchange between data and theory. It simply cannot be asserted that either one or the other comes “first” as a matter of principle. Data Sources: An Introduction Conference Board and Groningen Growth and Development Centre. Total Economy Database. November, 2007 (http://www.conference-board.org/economics/) Heston, Alan; Summers, Robert and Aten, Bettina. Penn World Table Version 6.2. Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, September 2006. Organization for Economic Cooperation and Development (OECD). The OECD STAN database. Paris: OECD, 2005. World Bank Group, WDI Online, http://devdata.worldbank.org/dataonline/ Readings “Economic Growth and Economic Development: The Questions”, Acemoglu, Chapter 1 Bernanke, Ben S., and Gurkaynak, Refet. “Is Growth Exogenous? Taking Mankiw, Romer and Weil Seriously.” In Ben S. Bernanke and Kenneth S. Rogoff eds., NBER Macroeconomics Annual, Cambridge, MA: MIT Press, 2001, Caselli, Francesco. “Accounting for Cross-Country Income Differences.” In Philippe Aghion and Steven Durlauf eds., Handbook of Economic Growth, Elsevier Press, 2005, pp. 679-741. Hall, Robert E. and Jones, Charles I. “Why Do Some Countries Produce So Much More Output per Worker than Others?” Quarterly Journal of Economics, February 1999, 114(1), pp. 83-116. Hulten, Charles R. and Isaksson, Anders. “Why Development Levels Differ: The Sources of Differential Economic Growth in a Panel of High and Low Income Countries.” NBER Working Paper Series, No: 13469, October 2007. Klenow, Peter J., and Rodríguez-Clare, Andrés. “Economic Growth: A Review Essay.” Journal of Monetary Economics, December 1997, 40(3), pp. 597-617. Klenow, Peter J., and Rodríguez-Clare, Andrés. “The Neoclassical Revival in Growth Economics: Has It Gone Too Far?” In Ben S. Bernanke and Julio Rotemberg eds., NBER Macroeconomics Annual, Cambridge, MA: MIT Press, 1997, pp. 73-102. IV. MATLAB LINKS Beginning Scientific Computing with Matlab Example 1: system_linear Example 2: example_1 playing functions Matlab_intro.m: Run this code for getting started….. Matlab tutorials Getting Started with Matlab Matlab Summary and Tutorial Matlab Tutorial Information If you want to read more about numerical methods, and in particular if you need algorithms to implement some method, you will find much useful material in the Numerical Recipes For very detailed instructions on specific features and toolboxes, see the documentation available in the Help menu as well as online on the Mathworks website MATLAB Manual from Mathworks. MATLAB Codes from Mathworks. An interactive An Introductory Guide to MATLAB by Dr. Ian Cavers, Department of Computer Science, University of British Columbia. A Practical Introduction to Matlab by Mark S. Gockenbach at the Department of Mathematical Sciences, Michigan Technological University. V. NUMERICAL ALGORITHMS Description of the codes: PDF Matlab Codes for Introduction to Matlab EX1.m EX2.m EX4.m EX7.m EX7_2.m myfun2.m myfun2_2.m quad_roots.m Matlab Codes: Download the following codes into a same directory bisection.m exbisection.m falseposition.m exfalseposition.m fixedpoint.m newtonsimple.m simpleGS.m solving_newton.m example.m Discrete Time Solow Model Description of the Model Solution: PDF Matlab Code: Solow.m Solving the Deterministic Growth Model: Secant Description of the Model Solution and the codes: PDF Matlab Codes: Main605.m Main Code: Run this code. Explanations are written. transition605.m secant605.m Extended Path Method Description of the Model Solution and the codes: PDF Matlab Code: MainPath.m Path.m VI. Dynamic Programming under Certainty and Stochastic Models To analyze dynamic equilibrium models, we must first be able to characterize solutions to dynamic optimization problems since the behavior of agents in these models will be determined by the solutions to such problems. We will consider a technique for solving dynamic optimization problems that fall into a particular class called stationary discounted dynamic programming problems. “Markov Chains”, Ljungqvist and Sargent, Chapter 2
“Markov Processes”, Stokey and Lucas, Chapter 8
Markov Chains Lecture Notes: PDF Flodén, Martin. “A Note on the Accuracy of Markov-Chain Approximations to Highly Persistent AR (1) Processes.” Economics Letters, June 2008, 99(3), pp. 516-520. Matlab code Tauchen, George. “Finite State Markov-Chain Approximations to Univariate and Vector Autoregressions.” Economics Letters, 1986, 20(2), pp. 177-181. Tauchen, George and Hussey, Robert. “Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models.” Econometrica, March 1991, 59(2), pp. 371-396. Simulation of AR (1) Process: Code Example 1: Code function Example 2: Code Tauchen (1986): Paper Matlab Code “Stochastic Dynamic Programming”, Acemoglu, Chapter 16 “Stochastic Growth Models”, Acemoglu, Chapter 17 “Sequential Problems”, Ljungqvist and Sargent, Chapter 3.1
“Stochastic Control Problems”, Ljungqvist and Sargent, Chapter 3.2
“Practical Dynamic Programming”, Ljungqvist and Sargent, Chapter 4
“Dynamic Programming under Certainty”, Stokey and Lucas, Chapter 4
“Applications of Dynamic Programming under Certainty”, Stokey and Lucas, Chapter 5
“Stochastic Dynamic Programming”, Stokey and Lucas, Chapter 9
“Applications of Stochastic Dynamic Programming”, Stokey and Lucas, Chapter 10
Consumption and Utility Grids Code Discrete Value Function Iteration: Code Dynamic Programming – Numerical Solution poweru.m cobb.m growth.m Matlab Code for Deterministic Dynamic Programming Matlab Code for Stochastic Dynamic Programming VII. COMPETITIVE EQUILIBRIUM The fundamental concept that markets are interrelated and therefore the equilibrium of the economy is characterized by simultaneous equality of supply and demand on all markets is due to Walras (1874). The concept as further developed and expounded by Pareto (1896, 1909). The case that equilibrium exists was made plausible by showing that the number of equations equaled the number of unknowns. The optimality of the competitive equilibrium was argued by both Walras and Pareto. General equilibrium theory describes the equilibrium and disequilibrium arising from the interaction of all economic agents in all markets. The principal objective of general equilibrium (GE) theory is to study the allocation of resources via system of markets. If all activity in an economy could be viewed as taking place in a single period then it would perhaps be reasonable to assume that markets are complete; that is, there is a market and associated price for each good. This is the environment of the classical theory resource allocations which finds its most elegant synthesis in the Arrow-Debreu theory. Classical GE theory as synthesized by Arrow-Debreu has the property of being theoretically the most elegant part of the economic theory. It is elegant, because within the context of a precisely formulated set of hypotheses it leads to a clear and simple explanation of how an idealized system of markets allocates resources and achieves what amounts to a best possible solution to the problem of resource allocation. GE crystallizes a classical tradition in economic theory that has its origin in Adam Smith’s theory of the invisible hand, by which a competitive system with market prices coordinates the otherwise independent activities of consumers and producers acting purely in their self-interest. “Pareto Optima and Competitive Equilibria”, Stokey and Lucas, Chapter 15
“Applications of Equilibrium Theory”, Stokey and Lucas, Chapter 16
“Recursive (Partial) Equilibrium”, Ljungqvist and Sargent, Chapter 7
“Equilibrium with Complete Markets”, Ljungqvist and Sargent, Chapter 8
“Recursive Competitive Equilibrium”, Ljungqvist and Sargent, Chapter 12
“Recursive Methods for Computing Equilibria in Business Cycle Models”, Hansen and Prescott
VIII. REAL BUSINESS CYCLE MODELS The real business cycle (RBC) approach to macroeconomic fluctuations seeks to explain the main stylized facts of the business cycle by building stochastic artificial economy models in which economic equilibria are the outcomes of the interaction of rational agents who solve explicit intertemporal maximization problems. The first generation of RBC models typically specified a closed economy with a single production sector and in which shocks to aggregate production function were the only type of random disturbance. These simple models were consistent with many aspects of the cyclical behavior of industrialized economies. More recently, researchers have focused their attention on two major discrepancies between the properties of simple RBC models and the U.S. data, both of which are related to the labor market. First, total hours worked are much more volatile compared to average labor productivity in the data than in the simple RBC models. Second, simple RBC models predict a high correlation between hours worked and average labor productivity which is absent from the data. These two stylized facts of the labor market constitute a puzzle which RBC models have had trouble solving. Various modifications have been proposed to the baseline RBC model in order to generate predictions which are more compatible with the data. As illustrated in a unified framework by Hansen and Wright (1992), RBC models can be made to generate a higher volatility of hours either by introducing preferences that are nonseparable between leisure in different time periods as in Kydland and Prescott (1982) or by introducing indivisibilities in the labor-leisure tradeoff as in Hansen (1985) and Rogerson (1988). “Economic Growth and Business Cycles”, Cooley and Prescott
“Real Business Cycles”, Ellen R. McGrattan (The note has been prepared for The New Palgrave Dictionary of Economics, 2nd edition)
Ellen R. McGrattan (1994) A Progress Report on Business Cycle Models. Federal Reserve Bank of Minneapolis.
Hodrick, Robert J. and Prescott, Edward C. “Postwar U.S. Business Cycles: An Empirical Investigation.” Journal of Money, Credit and Banking, February 1997, 29(1), pp. 1-16. Prescott, Edward C. “Theory Ahead of Business-Cycle Measurement.” Carnegie-Rochester Conference Series on Public Policy, Autumn 1986, 25, pp. 11-44. Rebelo, Sergio. “Real Business Cycle Models: Past, Present and Future.” Scandinavian Journal of Economics, June 2005, 107(2), pp. 217-238. Williamson, Stephen D. “Real Business Cycle Research Comes of Age: A Review of Essay.” Journal of Monetary Economics, August 1996, 38(1), pp. 161-170. HP Filter Example: from Harald Uhlig Instruction: Download all files and store them in a folder . Open MATLAB and change to the previously created folder. Type in "Run_hp.m" to get the desired plots. Type in "edit Run_hp.m" and "edit HP_filter_fun.m" and make sure that you understand the code. Now, try to import data from a .txt file using the Data Import Wizard of MATLAB. In addition, try to replicate the results with your own code. HP Filter: Derivation Notes on Derivations and Examples: PDF Example: Dataset1 HPfilter.m HPfilter example.m IX. OLG MODELS Competitive equilibria in economies of overlapping generations are different from competitive equilibria in economies that extend over finitely many periods, finite economies for short. These differences concern the properties of competitive equilibria, such as existence, optimality and determinacy or local uniqueness; and the phenomena compatible with competitive equilibria, such as net aggregate debt or fiat money with a positive price. Ever since the introduction of the model of overlapping generations by Allais (1947) and Samuelson (1958), economic theories have striven to isolate the reasons for the differences between this model and the definitive model of a finite economy elaborated by Arrow (1951), Debreu (1951, 1970) and Arrow and Debreu (1954). The OLG model of Allais and Samuelson retains the methodological assumptions of agent optimization and market clearing from the Arrow-Debreu model, yet its equilibrium set has different properties: Pareto inefficiency, indeterminacy, positive valuation of money, and a golden rule equilibrium in which the rate of interest is equal to population growth (independent of impatience). The OLG model is used to analyze bubbles, social security, demographic effects on stock returns, the foundations of monetary theory, Keynesian vs. real business cycle macro models, and classical vs. neoclassical disputes. “Overlapping Generations Models”, Ljungqvist and Sargent, Chapter 9
Geanakoplos, John. “Overlapping Generations Models of General Equilibrium.” Cowles Foundation Discussion Paper No: 1663, Yale University, May 2008
“Intertemporal General Equilibrium Models”, Timothy J. Kehoe
“Growth with Overlapping Generations”, Acemoglu, Chapter 9 X. HETEROGENEOUS AGENTS MODELS There are many questions in economics for which heterogeneous-agent dynamic models have to be used to provide answers. Examples of these questions where the desired answer is quantitative are as follows: · What changes in the distribution of wealth will occur if the tax system is changed from progressive to proportional? · What increases in taxation are needed to maintain the current level of US social security benefits under current population patterns? · What type of policy changes can be expected from changes in constitutions? All these questions require models where the households that populate are not identical. With respect to the first question, note that the key property of progressivity of the tax system is that different households face different tax rates. For the second question, the age distribution of the population determines the amounts collected and paid by the administrators of social security. Finally, the determinants of policy should be affected by the relations between different groups of households that do not have the same preferences over policies. Computation of equilibria in these models is usually substantially more difficult than in standard representative agent models, as equilibrium laws of motion become functions not only of aggregate variables, but also of the distribution of these variables across different types of agents. Solving for the laws of motion of such distributions is a nontrivial task. General Surveys Heathcote, Jonathan; Storesletten, Kjetil and Violante, Giovanni L. “Quantitative Macroeconomics with Heterogeneous Households.” Annual Review of Economics, 2009, 1, pp. 319-354. Computation of Stationary Distributions Heer and Maussner, Chapter 5 Aiyagari, S. Rao. “Uninsured Idiosyncratic Risk and Aggregate Saving.” Quarterly Journal of Economics, August 1994, 109(3), pp. 659-84. Huggett, Mark. “The Risk-Free Rate in Heterogeneous-Agent Incomplete-Insurance Economies.” Journal of Economic Dynamics and Control, September-November 1993, 17(5-6), pp. 953-69. Dynamics of the Distribution Function Heer and Maussner, Chapter 6 Krusell, Per and Smith, Anthony A., Jr. “Income and Wealth Heterogeneity in the Macroeconomy.” Journal of Political Economy, October 1998, 106(5), pp. 867-96. Ríos-Rull, José-Víctor. “Computation of Equilibria in Heterogeneous-Agent Models.” In Ramon Marimon and Andrew Scott eds., Computational Methods for the Study of Dynamic Economies, Oxford University Press, 1999, pp. 238-264. XI. CHANGES IN THE STRUCTURE OF WAGES AND MODELS OF TECHNOLOGY Wage and income inequality have increased considerably in the U.S. over the past 25 years. This makes an analysis of changes in the wage structure interesting in its own right. Moreover, changes in the wage structure also imply changing labor market prices of different types of skills. Therefore, studying changes in the wage structure will be informative about the changes in the demand for different types of skills and technological developments. Finally, changes in the wage structure will also lead to different incentives for human capital investments, which we might want to understand. Recent technological advances and a widening of the wage structure have led many to conclude that technology and human capital are relative complements. Over the past 60 years, the U.S. relative supply of skills has increased, but: a) there has also been an increase in the college premium, and b) this increase accelerated in the late 1960s, and the skill premium increased very rapidly beginning in the late 1970s. Acemoglu, Daron. “Why Do New Technologies Complement Skills? Directed Technical Change and Wage Inequality.” Quarterly Journal of Economics, November 1998, 113(4), pp. 1055-89. Acemoglu, Daron. “Directed Technical Change.” Review of Economic Studies, October 2002, 69(4), pp. 781-809 Acemoglu, Daron. “Patterns of Skill Premia.” Review of Economic Studies, April 2003, 70(2), pp. 199-230. Acemoglu, Daron and Shimer, Robert. “Wage and Technology Dispersion.” Review of Economic Studies, October 2000, 67(4), pp. 585-607. He, Hui and Liu, Zheng. “Investment-Specific Technological Change, Skill Accumulation, and Wage Inequality.” Review of Economic Dynamics, April 2008, 11(2), pp. 314-34. Krusell, Per; Ohanian, Lee E.; Rios-Rull, Jose-Victor and Violante, Giovanni L. “Capital-Skill Complementarity and Inequality: A Macroeconomic Analysis.” Econometrica, September 2000, 68(5), pp. 1029-53. XII. UNEMPLOYMENT, LABOR MARKET FLUCTUATIONS, SEARCH AND MATCHING In the 1970s, European unemployment started increasing. It increased further in the 1980s, to reach a plateau in the 1990s. It is still high today, although the average unemployment rate hides a high degree of heterogeneity across countries. The unemployment rate in the U.S. fluctuates around six percent, and is strongly countercyclical, sometimes with large fluctuations. Vacancies (measured either as help-wanted ads in the United States, or as job openings in other countries) are even more strongly procyclical, so that vacancy-unemployment ratio is procyclical. Short-run fluctuations in vacancies and unemployment correspond to a Beveridge curve, with a downward sloping relationship Ljungqvist and Sargent, Chapter 6, 26 Ljungqvist, Lars and Sargent, Thomas “Understanding European Unemployment with a Representative Family Model.” Journal of Monetary Economics, November 2007, 54(8), pp. 2180-2204. Ljungqvist, Lars and Sargent, Thomas “Understanding European Unemployment with Matching and Search-Island Models.” Journal of Monetary Economics, November 2007, 54(8), pp. 2139-79. Mortensen, Dale T. and Pissarides, Christopher A. “Technological Progress, Job Creation, and Job Destruction.” Review of Economic Dynamics, October 1998, 1(4), pp. 733-53. Nickell, Stephen. “Unemployment and Labor Market Rigidities: European versus North America.” Journal of Economic Perspectives, Summer 1997, 11(3), pp. 55-74. Pissarides, Christopher A. Equilibrium Unemployment Theory. Cambridge, MA: MIT Press, 2000. Rogerson, Richard; Shimer, Robert and Wright, Randall. “Search-Theoretic Models of the Labor Market: A Survey.” Journal of Economic Literature, December 2005, 43(4), pp. 959-88. |
