



Part I This is the second part of the Advanced Macro sequence. It will be both about learning technical tools and about applying them. We will set up a pretty general CE model with infinite horizon, heterogenous firms and consumers. We will prove the First Welfare Theorem and discuss the Second Welfare Theorem for this environment. Then we will show how to simplify the model to the deterministic one sector growth model (aggregation). In the next part of the course, we will extend the model to account for the 2 most important features of current economies: long run growth (briefly as already done in macro 1) and business cycle fluctuations. In the next part of the course, we will be interested in the government's role in the economy and the optimal fiscal policies. We will set up the classic Ramsey linear taxation problem and derive the celebrated ChamleyJudd result, which states that optimal taxes on capital are zero in the long run. Finally, we will discuss recent developments in the literature. Part II This course will focus on general equilibrium models of economic growth. The course will start with neoclassical growth models and continue with recent models which try to explain longrun growth endogenously. The course will follow with some empirical evidence on growth models. The course will also cover the basic fiscal policies introduced in the neoclassical growth model. Using a basic monetary model fiscal and monetary theories will be briefly presented.
As a main textbook for Parts I to III and V we will use Barro and SalaiMartin’s Economic Growth [BS] and additionally Aghion and Howitt’s The Economics of Growth [AH]. For Part IV we will use Ljungquist and Sargent’s Recursive Macroeconomic Theory [LS]. Last update: Papariga Anna, Mgr. (24.01.2022)



Part I · Lecture notes: 1. Jones, Larry (2010): Lecture Notes, available on the course website and Larry Jones's website. I will base most of my lectures on these notes. It is a good idea to print them out in advance, skim trough them and bring them to class. I am grateful to Larry for letting me use them. · Books and papers: 1. Chari, Kehoe (1999): Optimal fiscal and monetary policy, in Handbook of Macroeconomics 2. Judd, Kenneth L. (1998): Numerical Methods in Economics. 3. Ljungqvist, Lars and Thomas J. Sargent (2004): Recursive Macroeconomic Theory, MIT Press, Cambridge/London. 4. MasCollel, Whinston and Green (1995): Microeconomic Analysis. 5. Stokey, Nancy L., Robert E. Lucas with Edward C. Prescott (1989): Recursive Methods in Economic Dynamics, Harvard University Press, Cambridge/London. Additional readings are given at each topic. Part II · [BS] Barro, Robert and Xavier SalaiMartin (2004) Economic Growth (Second Edition). McGrawHill · [AH] Aghion, Philippe and Peter W. Howitt (2009) The Economics of Growth. The MIT Press · [LS] Ljungquist, Lars and Thomas J. Sargent (2018) Recursive Macroeconomic Theory (Fourth Edition).
Last update: Papariga Anna, Mgr. (24.01.2022)



Part I Grading of this part of the course will be based on problem sets (25% of the grade) and a midterm exam (75% of the grade). The problem set will be graded, returned to you and discussed in a TA session organized by the TA. You are allowed (and I strongly encourage you) to work on them in groups up to 3 people. You will submit one solution for the whole group. Ideally, you should submit your problem sets typed in LaTex (e.g. WinEdt) or Scientific Word. It is a useful skill to learn in any case. Unreadable solutions will not be accepted. Part II Grades will be based on student’s performance final exam and homeworks set weekly. There will also The grading schemes is the following: Part II Full course (Part I and Part II) Final exam 70% 35% Problem sets and class participation 30% 15% Last update: Papariga Anna, Mgr. (24.01.2022)



Part I 1. Introduction (~3 lectures).
· What is macroeconomics? What is a macroeconomic model? HP filtering. A general infinite horizon economy with consumers and firms. Competitive equilibrium. What does the model omit? Slides. Readings: Jones, part 1. · Competitive equilibrium continued. (skip as already covered: Firms' problem as a sequence of static problems. CRS and the zero profit result. Feasibility. Pareto efficiency.) First Welfare Theorem (with proof) and Second Welfare Theorem (without proof). Readings: Jones, part 1, SLP, MasCollel, Whinston and Green (1995). · Simplifying the model: Aggregation. CRS and simplifying the firms' side. Simplifying the consumers' side: (i) identical consumers, (ii) homothetic utility. The social planner's problem. The (stationary deterministic) one sector growth model. Readings: Jones, part 1, SLP, MasCollel, Whinston and Green (1995).
2. Extending the stationary, deterministic one sector growth model (~2 lectures).
· (Briefly) dynamics in the deterministic one sector growth model (SLP, chapter 6). Identifying two problems with the stationary one sector growth model: no growth and no fluctuations. Skip (covered by Veronika and Marek), but feel free to go over in the notes: Adding growth to the one sector growth model. Exogenous growth. One sector growth model with exogenous growth and dynamic programming (rewriting the problem into one with no growth, included in Jones, part 1.). Endogenous growth  the Ak model, the A(k; h) model. Readings: Jones, part 3. · Adding fluctuations to the one sector growth model, i.e. the stochastic one sector growth model. An example stochastic growth model with a closed form solution, i.e. the stochastic Ak model. The role of uncertainty in growth. Relationship of this model to portfolio problems: homothetic utility and linear budget constraint and the MertonSamuelson Theorem. Readings: Jones, part 4.
3. Fiscal policies in the growth model. (~46 lectures). Readings: Jones, part 2.
· Adding government. Tax distortive competitive equilibrium. Ricardian equivalence. Welfare theorems revisited. Pareto optimality of lump sum taxes. Tax structures equivalent to lump sum taxes. Readings: LS, chapter 10, LS, chapter 11. · Solving for the TDCE. The nonarbitrage condition revisited. The transversality condition. · Steady state. Comparative statics of k and c wrt taxes in steady state. Equivalence between various tax structures. Redundancy of consumption and investment taxes. · The Ramsey problem. Setting up the Ramsey problem. The primal vs. the duial approach. The implementability condition. Rewriting the Ramsey problem as a one sector growth model. Steady state. The ChamleyJudd result: 0. Readings: LS, chapter 15. · Long run behavior of the optimal tax on labor. Robustness of the ChamleyJudd result  government BC clearing period by period. When does the ChamleyJudd result break down? Readings: ChariKehoe Handbook Chapter, Jones, Manuelli, Rossi (JET, 1997), Lansing (1999), Straub and Werning (AER), Chari, Nicolini and Teles (JME), Benhabib, Szoke (AEJ: Macro). Part II I. Introduction · Dynamic Optimization in Continuous Time ([BS] Appendix A.3) · Stylized Facts on Economic Growth ([BS] Ch. 0 and [AH] Ch. 1) II. Neoclassical Growth Models · Basic SolowSwan Model ([BS] Ch. 1) · Ramsey Model ([BS] Ch. 2) · Overlapping Generations Model ([BS] Ch. 3) · FiniteLife Model ([BS] Ch. 3) · The OpenEconomy Ramsey Model ([BS] Ch. 3) III. Endogenous Growth Models · AK Growth Models (OneSector Models of Endogenous Growth) ([BS] Ch. 4) o OneSector Model With Physical and Human Capital o Model With LearningByDoing and Knowledge Spillovers o Public Services and Endogenous Growth · TwoSector Models of Endogenous Growth ([BS] Ch. 5) o Extended OneSector Model With Physical and Human Capital o Lucas Growth Model · Endogenous Technological Change o Model With Expanding Variety of Products ([BS] Ch. 6) o Schumpeterian Model of Quality Ladders ([BS] Ch. 7) o Diffusion of Technology ([BS] Ch. 8) IV. Fiscal and Monetary Policy in Growth Model · Fiscal Policy in Neoclassical Growth Model ([LS] Ch. 11) · FiscalMonetary Theories of Inflation ([LS] Ch. 24) V. Empirical Evidence on the Neoclassical Growth Model · Growth Accounting ([BS] Ch. 10) · Convergence and Growth Regressions ([BS] Ch. 11 and Ch. 12) Last update: Papariga Anna, Mgr. (24.01.2022)
