Macroeconomics 101Methods for Macroeconomic Research

Summer 2010

Instructor: Freddy Cama, WH 222, 646-2126 (Macro dept: 646-3901), email: fcama@imf.org.

Time and Location: T, Th 11:45 - 1:00, San Marcos main building 108.

O¢ ce Hours:Tuesday 10:30 - 11:30Wednesday 12:00 - 1:30Thursday 1:30 - 3:00.

Textbook: F. Canova (2007) �Methods for Applied Macroeconomic Research�.Material: Chapters 3, 4, 5 and 6This course is an applied one for macroeconomic research. The goal of this course is to give tools for

research and adapt the student to the working climate on macroeconomics. The course has 5 lectures andis strongly based on Canova (2007), additionally we are including some relevant papers from prestigiouseconomic and statistical journals; we recommend strongly that students check out these papers for someextensions or details.Grading: There will be daily quizzes and a �nal exam. They will count toward the grade as follows.

Pop Quiz 60%Homeworks 15%Final 25%.

The �nal exam will be on Friday, January 15 between 3:30 p.m to 5:30 p.m.In addition to these exams there will be dialy quizzes which would be graded the same day. they will

consist in basic calculations, matlab (stata) codes or some mathematical proofs. After you learn basictechniques of extracting information at the beginning of the course, you will be ready to have your �rsthomework; indeed after each lecture there will be a homework. These homeworks will barely a¤ect thegrade you receive in the course, but they will be critical for the �nal exam because the exan will cover thehomeworks and theoretical discussions. That is why you need basic mathematical skills to pass the course.Further information about the exam will be provided later.

Description of the Course

The course will be centered around six main topics covering the notion of basic econometrics, extractingcyclical information, Vector Auto Regressive (VAR), Bayesian VAR models, Real Exchange Rate models andcrisis models using limited-dependent-variable econometric speci�cations. The purpose of the �rst chapter( We called this lecture or chapter 0 or basic) is to do a quickly review of basic courses of econometricsthatyou�ve already taken. This lecture will be 2 hours long, therefore we recommend you to be familiar withall the subchapters or prepare some questions related to each topic. The daily quizz will include some easytask usually consisting of basic calculations, matlab (or stata) codes or some mathematical proofs. All theassignments will be done individually and the homeworks will be done in groups of 3 or 4 students. Eachgroup will turn in one write-up.The purpose of written homework in this course is to use the tools we are learning in the course and

develop skills in understanding and communicating results from some particular questions in the �eld ofmacroeconomics. It is not to give you busy work, drill or some . Don�t think of your homework paper as acerti�cate proving that you have done or tried to do the best on the assignment. Think of it as an exercise inlearning and in reporting what you have learned, likewise you could try to put on the paper some discussionsrelated to the below topics, all they are welcome in the research �eld, let�s discuss!. Please be clear on yourstatements because there is a lot of truth in the statement if you can�t explain it, you don�t understand it,and it is true as well that (this is mine) if you learnt it withouth some understanding, pretty sure you willforget it tomorrow, be e¢ cient!. Don�t write to the instructor (who already knows how to do the problems),but explain your solutions to someone who needs help, perhaps a classmate who has been sick. Start at thebeginning and be clear, logical and complete. The ultimate test of what you write is this: can someone learnfrom your paper? Easily? Remember, the reader will see only what you wrote, not what you meant to say.So it must all be there, and be accurate. Make your paper reader friendly. We will talk some about this inclass.The �rst chapter talks about how to deal with the measurement of cycles, we have interesting algorithms

like beveridge and Nelson methodology but it is based on strong assumptions about how the shocks arecorrelated, we need to know what these assumptions are; a purpose of the course is to give to students whatare the advantages and disvantages of the methodologies as well as the limitations. The second chapteris designed for giving you the basic of programming, then use these tools for performing montecarlos andboostrap methods. The third chapter is aimed to know more about the VAR models, we will discussspeci�cations and forecast from these kind of models, likewise we will provide some format for the resultsand extend alternative presentations using bootstrap methods in the impulse response functions. At the endof the chapter we will see some applications using fan chart models and comparing the results with DSGEmodels. The fourth chapter wants to introduce the International-Monetary-Fund methods for assessing thedynamic of real exchange rate in low income countries. Basicly we present three methods: the �rst one basedon disalignments of the current account which would be helpful when we want to know how much the realexchange rate would need to appreciate for closing this current account gap, the second one is realted to theexternal sustainability using a proxy of net foreign assets, the last methodology is the typical one which isknowly used in the macroeconomic research �eld the �fth chapter aims to use crisis models using logit panelmethods; we would have applications using the crisis data from southamerica.The purpose of working in groups is twofold. First, by sharing ideas you will be able to learn from each

other, allowing you to clarify what you get out of the lecture and reading. Second is to get you accustomedto working with other people, a likely situation in your future jobs. The goal for an assignment is to get eachgroup member to understand the entire assignment. Frequently a major part of an assignment will be tosummarize the various components. In order to do this you will need to understand the entire assignment.Therefore you should not divide the problems among your group members, but have each person work oneach part and discuss what you come up with. Again the idea of the course is to give you tools, the durationof the osurse is just a week but we expect you could learn much you can. Good luck!.

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Chapters

The course will be centered around several main topics covering the extraction of cyclical information,sampling methods, VAR models, real Exchange Rate disalignments and contagious models.

Chapter 0: (Macro) econometrics

1. Ordinary Least Squares [12]; [20]

1.1 Gauss Theorem

1.2 Inference

1.3 Prediction

2. Maximum Likelihood [12]; [20]

2.1 Cramer-Rao lower bound

2.2 Inference

2.3 Application

3. Data features

3.1 Heterocedasticity,

3.2 Autocorrelation

3.3 Multicolinearity

4. Generalized Least Squares

4.1 E¢ cient Estimation

4.2 Autocorrelation, consequences for OLS

4.3 heterocedasticity, consequences for OLS

4.4 Inference

5. Non-Linear Least Squares

5.1 Numerical methods

5.2 Starting values and convergence criteria

5.3 Applications

6. Limited Dependet Variable

6.1 Linear probability model

6.2 Preferences, choice and modeling

6.3 Functional forms

6.4 Estimation

6.5 Inference

7. Panel Data

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Chapter 1: Extracting, Filling and Measuring Cyclical Information

1. Statistical Decompositions, de�nitions [8, Ch3]

1.1 Traditional methods1.1.1 Polynomics functions1.1.2 First di¤erences

1.2 Beveridge-Nelson (BN) decomposition [4]; [27]; [22]; [28]1.2.1 Univariate �lter [26]1.2.2 Multivariate �lter1.2.3 Caveats

1.3 Unobservable Components (UC) decompositions [19]1.4 Regime shifting decomposition

2. Hybrid Decompositions [8]; [13]

2.1 The Hodrick and Prescott (HP) Filter [16]2.1.1 Univariate �lter2.1.2 Multivariate �lter

2.2 Exponential smoothing (ES) �lter2.3 Moving average (MA) and non-linear �lters [30]2.4 Band Pass (BP) �lters; Baxter & King [3]

3. Economic Decompositions [8]

3.1 Blanchard and Quah (BQ) Decomposition [5]3.2 King, Plosser Stock and Watson (KPSW) Decomposition [29]3.3 Time Aggregation, Cycles and Spectral Analysis [15, Ch6]; [8, Ch1]3.4 Persistence and Cycles3.5 Collecting Cyclical Information [7]

4. Classical Economics

4.1 Output Gap and measuring cyclical information [25]; [24]4.1.1 Production function4.1.2 Multivariate methodology with non-observed components

5. Interpolation and curve �tting [32, Ch3]

5.1 Linear interpolation5.2 Lagrange Polynomial5.3 Newton Polynomial5.4 Chebychev polynomial5.5 Curve �tting5.6 Fourier tranformations

6. Denton�s interpolation method [11]; [9]; [1, Ch6]

7. Chow and Lin�s interpolation method [10]

8. Other methods

8.1 De Jong8.2 Casas et. al.8.3 Litterman�s method [23]

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Chapter 2: Simulation Methods

1. Pseudo random numbers

2. Montecarlo experiments

3. Boostrapp

3.1 Block Bootstrapp

3.2 Stationary Block bootstrapp [2]

4. Applications

4.1 Impulse responses

4.2 Growth and terms-of-trade shocks

Chapter 3: VAR and BVAR models

1. The Wold Theorem

2. Testing the speci�cation

3. Moments and parameter estimation

4. Reporting VAR results [8, Ch4]; [30]

4.1 Impulse responses

4.2 Asymtoptic con�dence intervals

4.3 Boostrap con�dence intervals

5. Identi�cation

6. Forecasting [15, Ch4]

6.1 Principles of forecasting

7. Asymetrics VARs

8. Fan Charts models using VAR and BVAR

8.1 Public debt

8.2 In�ationary Expectations

9. Validating DSGE models with VARs

Chapter 4: Relative Prices and Disalignments

1. Introduction and review of literature [17] [31]

1.1 Real Exchange Rate models, the theory

1.2 Real Exchange Rate models, the empirics

2. Macroeconomics Balance Approach [18, Ch2]

1.1 Theoretical background and de�nitions

1.2 Estimations results

1.3 Current Account Norms

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1.4 Exchange Rate assessments

3. Equilibrium Real Exchange Rate Approach [18, Ch3]

1.1 Theoretical background and de�nitions

1.2 Panel Unit Roots

1.3 Estimations results

1.4 Equilibrium Real Exchange Rate

1.5 Exchange Rate assessments

4. External Sustainability [18, Ch4]

1.1 Theoretical background

1.2 Choosing a benchmark level for Net Foreign Assets

1.3 An Application Using 2004 NFA as the Benchmark Level

1.4 Current Account, Net Foreign Assets and Exchange Rate Adjustment

5. Fiscal e¤ect and Real Exchange Rate

5.1 Dutch disease

5.2 Salter-Swan e¤ect

5.3 Applications: The chilean case

Chapter 5: Crisis and contagious models

1. Some theory [2]; [6]; [21]

1.1 Firts generation models

1.2 Second generation models

1.3 Third generation models

2. Crisis models [14]

2.1 Speci�cation

2.2 Inference

2.3 Applications

References

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[2] M. Agosin. Corea y taiwan en la crisis �nanciera. french-Davids Ed. Previniendo Crisis Financierasen Economias Emergentes Exitosas (2001).

[3] M. Baxter and R. G. King. Measuring business cycles. approximate band-pass �lters for economictime series, nber working paper series n 5022. The review of Economics and Statistics 75(2), 235-243(1995).

[4] S. Beveridge and C. R. Nelson. A new approach to the decomposition of economic time series intopermanent and transitory components with particular attention to measurement of the business cycle.Journal of Monetary Economics 7 151-174 (1981).

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[5] O. Blanchard and D. Quah. The dynamic e¤ect of aggregate demand and supply disturbances.American Economic Review 79 655-673 (1989).

[6] G. Calvo. Crises in emerging market economies. national Bureau of Economic Research working paper11305 (2005).

[7] F. Canova. Detrending and business cycle facts. journal of Monetary Economics 41 475-540 (1998).

[8] F. Canova. �Methods for Applied Macroeconomic Research�. (2007).

[9] P. Cholette and N. Chhab. Converting aggregates of weekly data into monthly values. AppliedStatistics Vol 40, N 3, pp 411-22 (1991).

[10] G. Chow and A.-L. Lin. Best linear unbiased interpolation, distribution and extrapolation of timeseries by related series. Review of Economics and Statistics 53, 372-375 (1971).

[11] F. Denton. Adjustment of monthly or quarterly series to annual totals: An approach based onquadratic minimization. Journal of the American statistical Association (1971).

[12] W. Greene. �Analisis Econometrico�. Prentice Hall (1999).

[13] A. Guay and P. St-Amant. Do the hodrick-prescott and baxter-king �lters provide a good approxi-mation of business cycles. Working paper N 53 (1997).

[14] A. I. Guillermo Calvo and L.-F. Mejia. Systemic sudden stops: The relevance of balance-sheete¤ects and �nancial integration. national Bureau of Economic Research (2008).

[15] J. D. Hamilton. �Time Series Analysis�. Princeton University Press; Princeton, New Jersey (1994).

[16] R. Hodrick and E. Prescott. Post-war us business cycles: An empirical investigation. Journal ofMoney Banking of Credit (1997).

[17] P. Isard. Equilibrium exchange rate: Assessment methodologies. Working Papers (2007).

[18] J. D. O. A. P. Jaewoo Lee, Gian Maria Milessi-Ferreti and L. A. Ricci. Exchange rateassessments: Cger methodologies. Occassional Paper IMF N 261 (2008).

[19] C. N. James C. Morley and E. Zivot. Why are the beveridge-nelson and unobserved-componentsdecompositions of gdp so di¤erent? The review of Economics and Statistics 75(2), 235-243 (2002).

[20] J. Johnston and J. Dinardo. �Econometric Methods�. McGraw-Hill (1997).

[21] G. kaminsky and C. Reinhart. The twin crises: The causes of banking and balance of paymentsproblems. American Economic Review (1999).

[22] E. Z. Kum Hwa Oh and D. Creal. The relationship between the beveridge-nelson decomposition andunobserved components models with correlated shocks. Washington University working paper (2007).

[23] R. Litterman. A random walk, markov model for the distribution of time series. Federal reserve Bankof Minneapolis Research Department Sta¤ Report 84 (1983).

[24] G. LLosa and S. Miller. Estimacion multivariada de la brecha producto in�acionaria: Aplicacionpara el caso peruano 1992-2003. Estudios Economicos Banco Central de Reserva del Peru (2003).

[25] S. Miller. Metodos alternativos para la estimacion del pbi potencial: Una aplicacion para el caso deperu. Estudiso Economicos Banco Central de Reserva del Peru (2003).

[26] J. C. Morley. A state-space approach to calculating the beveridge-nelson decomposition. EconomicLetters 75, 123-127 (2002).

[27] J. C. Morley. The two interpretations of the beveridge-nelson decomposition. Departament of Eco-nomics Washington University (2009).

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[28] C. R. Nelson. the beveridge-nelson decomposition in restrospect and prospect. Washington Universityworking paper (2006).

[29] C. S. R. King, C. Plosser and M. Watson. Stochastic trends and economic �uctuations. AmericanEconomic Review 81 819-840 (1991).

[30] Stata. �Time-Series Reference Manual�. Stata Press (2009).

[31] A. P. Thierry Tressel, Lone Engbo Christiansen and L. A. Ricci. External balance in lowincome countries. Working Papers (2009).

[32] T.-S. C. Won Y. Yang, Wenwu Cao and J. Morris. �Applied Numerical Methods Using Matlab�.Wiley-Interscience A John Wiley Sons INC Publication (2005).

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