Economics 607 Monetary Theory and Policy

Homework 6

Due Tuesday 3/1

1. Find the first two principle components of the consumption, investment, GDP, labor hours, employment (all in growth rates), and the unemployment rate.

2. Use these to estimate a FAVAR comprised of GDP growth, inflation (use this), the federal funds rate, and the two factors derived from step 1.

3. Show how inflation and labor hours respond to a shock to the federal funds rate. Is there a price puzzle in this model?

Homework 4

1. Use a Johansen test to determine how many co-integrating relationships are there among real income, prices, and the money supply (use GDPC96, JCXFE, and M2SL in FRED and the sample period 1959:1-2010:4). Can real output be excluded from the relationship? Are real money balances stationary? Is velocity stationary?

Homework 3

Homework 3
Winter 2011
Due Tuesday 2/1/2011

1. Use the Shapiro and Watson type model discussed in class to estimate the three variable system involving the federal funds rate, real GDP, and the CPI less food and energy. Impose the restrictions that shocks to GDP and shocks to the CPI have no effect on the federal funds rate in the long-run, and that shocks to the federal funds rate and the CPI have no effect on real GDP  in the long-run. Find the IRFs and VDCs for both the levels and differences representations. (The model is Δff, ΔlnGDP, and ΔlnCPI. The Δff is used simply to illustrate the technique. There are instances of articles in places like the AER where Δff has been used in VAR models in the past, but the level of the ff rate would normally be used today.)

2. Given the system of equations

          R_t = d_R + ∑ [A_RjR_t-j + B_RjΠ_t-j + C_RjY_t-j ]+ U_t

          Π_t = d_Π + ∑ [A_ΠjR_t-j + B_ΠjΠ_t-j + C_ΠjY_t-j ]+ V_t

          Y_t = d_Y + ∑ [A_YjR_t-j + B_YjΠ_t-j + C_YjY_t-j ]+ W_t

where the sum runs from j=1 to j=3, and U, V, and W are white noise errors, and given the definition of the real interest rate

          r_t = R_t - E[Π_t+1 | Ω_t],

where  Ω_t  = all information dated t and earlier and Π_t+1 is the inflation rate between t and t+1, (a) how many restrictions does the hypothesis r_t = λ₀ + λ₁r_t-1 + e_t impose on the model? (b) Derive the restricted set of equations. (c) Suppose the hypothesis is changed to r_t = λ₀ + λ₁r_t-1 + λ₂r_t-2 + e_t. What problems, if any, do you encounter in trying determine the number of restrictions this hypothesis imposes on the unrestricted VAR model?

Homework 2

Economics 607
Monetary Theory and Policy
Winter 2011
Homework 2
Due Tuesday, January 18 likely the 20th

1. Using data on the growth rates of real GDP and M2 (calculate as the difference in logs), estimate a VAR model. To select the lag length, use the AIC criterion to determine the lag length for the money growth and output growth equations individually, then use the maximum of the two estimates as the lag length in the VAR model.

2. Find the lag length using the system approach to the AIC described on pages 210-211 of the User's Guide for version 8.

3.  Collect data on real GDP, M2, the Federal Funds Rate, and the Perrsonal Consumption Index less Food and Energy and convert it into a RATS data set.

4.  Use the data from problem 3 to estimate a four variable two lag VAR model for the growth rate of real GDP, the growth rate of M2, the Federal Funds Rate, and the growth rate of Personal Consumption Index less Food and Energy.   Then graph the IRFs for (a) the response of real output to a money shock, and (b) the response of real output to a shock to the FF rate. (c) What ordering did you use and why did you choose it?

5.  Repeat the previous problem, except calculate the VDCs for (a) the response of real output to a money shock, (b) the response of real output to a shock to the FF rate, (c) the response of money to a shock to real output, and (d) the response of the FF rate to a shock to real output.

6.  Carry the numerical example used in class to calculate IRFs and VDCs out one more step (calculate the values after one more step for both the IRFs and the VDCs).

7.  Are the IRFs and VDCs in problem 4 and 5 robust to changes in the ordering?

Homework 1

Economics 607
Monetary Theory and Policy
Fall 2011
Homework 1
Due Tuesday, January 11

1. Estimate a four lag St. Louis equation using RATS and data from FRED on output, government expenditures, and money (average the monthly money stock data to covert it to quarterly data). Examine three specifications of the model (i) a difference model of output on current and lagged values of government spending and money, (ii) a log-difference model of output on current and lagged values of government spending and money, and (iii) a log-difference model of output on current and lagged values of government spending, money, and lagged values of output. What do the results imply?

2. Duplicate the results shown in equations (4) and (5) and the associated F-tests discussed in the text in Barro's (1976) paper on the reading list (this is the first Barro article we discussed).

Syllabus for Winter 2011

Monetary Theory and Policy
Course: Economics 607
Professor: Mark Thoma
Office/Hours: PLC 471 on T/Th from 1:30-2:30 p.m.
Phone/Email: (541) 346-4673, mthoma@uoregon.edu
Web Page: http://economistsview.typepad.com/economics607monetary/

Tests and Grading: There will be a midterm and a final.  The midterm will be given on Thursday, February 3^rd.  The final will be given on Tuesday, March 15^th at 1:oo p.m.  No make-up exams will be given.  The midterm is worth 35% and the final is worth 45%.  The remaining 20% will come from the class presentation and the homework assignments.  Grades will be assigned according to your relative standing in the class.

Homework: Problem sets will be assigned periodically.  These will be worth 15%.

Class Presentation:  In this assignment, choose a fairly recent paper covering monetary issues (theory or policy), and present it to the class. This is worth 5% of your grade. I will talk more about this during lecture. (Note: Ph.D. students only; optional for M.A. students, homework counts 20% if M.A. students choose not to do the presentation).

Course Outline: [Tentative]

Topic	Reference
The St. Louis Equation	*Carlson, Keith Does the St. Louis Equation Now Believe in Fiscal Policy?, FRB St. Louis
New Classical Tests	*Barro, R.J.  "Unanticipated Money Growth and Unemployment in the United States, 1977, AER. *Barro, R.J.  "Unanticipated Money, Output, and the Price Level in the United States"  1978, JPE. *Mishkin, F.S. 1982.  "Does Anticipated Monetary Policy Matter?  An Econometric Investigation"  JPE  90:22-51. Mishkin, F.S. 1983.  A Rational Expectations Approach to Macroeconomics.  Chicago:  University of Chicago Press for the NBER. Hoffman, D.H. and Schlagenhauf, D.E.  1982.  "An Econometric Investigation of the Monetary Neutrality and Rationality Propositions from and International Perspective,"  RESTAT  pp. 562-571.
Granger Causality	Granger, C.W.J. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods" 1969, Econometrica. *Sims, C.A. "Money, Income, and Causality" 1972, AER. *Sims, C.A. "Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered" , AER.
Levels versus Differences	*Stock and Watson 1987. "Interpreting the Evidence on Money-Income Causality" NBER Discussion Paper No. 2228. *Friedman, Benjamin M. and Kuttner, Kenneth N., "Another Look at the Evidence on Money-Income Causality," Working Paper #90-17, Federal Reserve Bank of Chicago, October, 1990 Krol and Ohanion, "The Impact of Stochastic and Deterministic Trends on Money-Income Causality: A Multi-Country Investigation," Journal of Econometrics 45 (September, 1990), 291-308
Rolling Regression Techniques	*Thoma, Mark Subsample Instability in Money‑Income Causality, 1994 , Journal of Econometrics
Is the Real Interest Rate Exogenous?	*Litterman, R.L. and Weiss, L. 1985. "Money, Real Interest Rates and Output: A Reinterpretation of U.S. Postwar Data," Econometrica 53: 129-155.
Structural VARS and Co-integration	*Friedman, Benjamin M. and Kuttner, Kenneth N., "Money, Income, Prices, and Interest Rates," American Economic Review (volume 82, no. 3), June 1992, 472-492. *Bernanke, Ben S. and Blinder, Alan S., "The Federal Funds Rate and the Channels of Monetary Transmission," American Economic Review (volume 82, no. 4), September 1992, 901-921. *Blanchard, Olivier and Quah, Danny, "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, September 1989, 655-673. *Shapiro, Mathew D. and Watson, Mark W., "Sources of Business Cycle Fluctuations," in Stanley Fischer, ed., NBER Macroeconomics Annual, Cambridge: MIT Press, 1988, 111-148. McCandless, George T. and Weber, Warren E. Some Monetary Facts, 1995, FRB Minneapolis
Bootstrapping	Class notes
ARCH Models	*Engle, R.F. "Estimates of the Variance of U.S. Inflation Based upon the ARCH Model," JMCB, August, 1983.
Narrative Measures of Monetary Policy and Case Studies	*Romer and Romer, Does Monetary Policy Matter? A New Test in the Spirit of Friedman and Schwartz, 1990, NBER Macroeconomics Annual Sargent The Ends of Four Big Inflations, 1986, FRB Minneapolis.
Factor Models	*Bernanke, Boivin, Eliasz, Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach.
Other Papers	*Jordi Galí and Luca Gambetti, On the Sources of the Great Moderation. *Jean Boivin and Marc P. Giannoni, Has Monetary Policy Become More Effective?. *Richard Clarida, Jordi Gali, Mark Gertler, Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory. John Taylor, An Historical Analysis of Monetary Policy Rules. Judd and Rudebusch, Taylor's Rule and the Fed: 1970-1997, FRBSF, 1998. *Athanasios Orphanides, Monetary Policy Rules, Macroeconomic Stability, and Inflation: A View from the Trenches, JMCB, April 2004. Woodford, Michael, The Simple Analytics of the Government Spending Multiplier, June 2010.