Economics 210c/236a Christina Romer Fall 2016 David Romer L ECTURE 3 The Effects of Monetary Changes: Vector Autoregressions September 7, 2016
I. S OME B ACKGROUND ON VAR S
A Two-Variable VAR Suppose the true model is: where ε 1 t and ε 2 t are uncorrelated with one another, with the contemporaneous and lagged values of the right-hand side variables, and over time.
Rewrite this as: or where
This implies where
Extending to K Variables and N Lags The “true model” takes the form: where C is K x K , X is K x 1, B is K x K , and E is K x 1. This leads to: where
An Obvious (at Least in Retrospect) Insight Consider where The elements of B and C are not identified.
II. C HRISTIANO , E ICHENBAUM , AND E VANS , “T HE E FFECTS OF M ONETARY P OLICY S HOCKS : E VIDENCE FROM THE F LOW OF F UNDS ”
Simplified Version of Christiano, Eichenbaum, and Evans Two variables, one lag: • The reduced form is: •
From: Christiano, Eichenbaum, and Evans
From: Christiano, Eichenbaum, and Evans
From: Christiano, Eichenbaum, and Evans
From: Christiano, Eichenbaum, and Evans
Two Other Ways of Estimating the Effects of Monetary Policy Shocks under CEE’s Assumptions
The Jordà Local Projections Approach Suppose that (as in CEE) our assumption is that monetary • policy can respond to output within the period and output does not respond to monetary policy within the period. To see how monetary policy affects output at different • horizons, we can estimate a series of regressions for h = 1, 2, 3, …: The estimated impulse response function is just the sequence • � ℎ ’s. of 𝑐 Note: As always, this presumes that the identifying • assumptions are correct!
Other Types of Restrictions to Make VARs Identified • Zero restrictions other than ordering assumptions. • Long-run restrictions. • Imposing coefficient restrictions motivated by theory. • …
III. R UDEBUSCH , “D O M EASURES OF M ONETARY P OLICY IN A VAR M AKE S ENSE ?”
Key Points • The funds rate equation in many VARs is the Fed’s reaction function, and so can be evaluated using other evidence about Fed behavior. • The residuals from the equation are monetary policy shocks, and so can be evaluated using other evidence about monetary policy shocks.
Rudebusch’s Criticisms of the Funds Rate Equation of VARs as a Fed Reaction Function • Assumed to be stable over time. • “The scope of the information set.” • Use of revised data. • Inclusion of many lags.
From: Rudebusch, “Do Measures of Monetary Policy …?”
From: Rudebusch, “Do Measures of Monetary Policy …?”
Concerns about Rudebusch’s Critique of the Funds Rate Equation of VARs as a Fed Reaction Function?
Rudebusch’s Concerns about the Monetary Policy Shocks from VARs • Comparison with surprises relative to expectations based on financial markets. • Comparisons across VARs.
From: Rudebusch, “Do Measures of Monetary Policy …?”
From: Rudebusch, “Do Measures of Monetary Policy …?”
Concerns about Rudebusch’s Critique of the Monetary Policy Shocks from VARs?
IV. R OMER AND R OMER : “A N EW M EASURE OF M ONETARY S HOCKS : D ERIVATION AND I MPLICATIONS ”
Deriving Our New Measure • Derive the change in the intended funds rate around FOMC meetings using narrative and other sources. • Regress on Federal Reserve forecasts of inflation and output growth. • Take residuals as new measure of monetary policy shocks.
Regression Summarizing Usual Fed Behavior ff is the federal funds rate y is output; π is inflation; u is the unemployment rate ~ over a variable indicates a Greenbook forecast From: Romer and Romer, “A New Measure of Monetary Shocks”
What kinds of thing are in the new shock series? • Unusual movements in funds rate because the Fed was also targeting other measures. • Mistakes based on a bad model of economy. • Change in tastes. • Political factors. • Pursuit of other objectives.
From: Romer and Romer, “A New Measure of Monetary Shocks”
Evaluation of the New Measure • Key issue – is there useful information used in setting policy not contained in the Greenbook forecasts?
Digression: Kuttner’s Alternative Measure of Monetary Shocks • Get a measure of unexpected changes in the federal funds rate by (roughly) comparing the implied change indicated by fed funds futures and the actual change.
From: Kenneth Kuttner, “Monetary Policy Surprises.”
Single-Equation Regression for Output y is the log of industrial production S is the new measure of monetary policy shocks D ’s are monthly dummies From: Romer and Romer, “A New Measure of Monetary Shocks”
Fitting this Specification into the Earlier Framework Suppose the true model is: 𝑧 𝑢 = 𝑏 1 𝑧 𝑢−1 + 𝑐 1 𝑗 𝑢−1 + 𝜁 𝑧𝑢 , (1) 𝑗 𝑢 = 𝑏 2 𝑧 � 𝑢 + 𝑐 2 𝜌 � 𝑢 + 𝜁 𝑗𝑢 , (2) where 𝑧 � and 𝜌 � are the forecasts as of period t , and ε it is uncorrelated with all the other things on the right-hand side of (1) and (2) ( 𝑧 𝑢−1 , 𝑗 𝑢−1 , 𝑧 � 𝑢 , 𝜌 � 𝑢 , and 𝜁 𝑧𝑢 ) . (2) implies: 𝑗 𝑢−1 = 𝑏 2 𝑧 � 𝑢−1 + 𝑐 2 𝜌 � 𝑢−1 + 𝜁 𝑗 , 𝑢−1 . Substituting this in to (1) gives us: 𝑧 𝑢 = 𝑐 1 𝜁 𝑗 , 𝑢−1 + 𝜀 𝑢 , where 𝜀 𝑢 = 𝑏 1 𝑧 𝑢−1 + 𝑐 1 𝑏 2 𝑧 � 𝑢−1 + 𝑐 2 𝜌 � 𝑢−1 + 𝜁 𝑧𝑢 . Under the assumptions of the model, δ t is uncorrelated with ε i,t -1 , and so we can estimate this equation by OLS and recover the effect of i on y ( b 1 ).
Single-Equation Regression for Output Using the New Measure of Monetary Shocks Using the Change in the Actual Funds Rate From: Romer and Romer, “A New Measure of Monetary Shocks”
Single-Equation Regression for Prices Using the New Measure of Monetary Shocks Using the Change in the Actual Funds Rate From: Romer and Romer, “A New Measure of Monetary Shocks”
Single-Equation Regression for Prices Controlling for Commodity Prices From: Romer and Romer, “A New Measure of Monetary Shocks”
VAR Specification • Three variables: log of IP, log of PPI for finished goods, measure of monetary policy (also include commodity prices in one variant). • Monetary policy is assumed to respond to, but not to affect other variables contemporaneously. • We include 3 years of lags, rather than 1 as Christiano, Eichenbaum, and Evans do. • Cumulate shock to be like the level of the funds rate.
VAR Results
Comparison of VAR Results: Impulse Response Function for Output 1.0 0.5 0.0 -0.5 Percent Funds Rate -1.0 -1.5 -2.0 -2.5 Romer and Romer Shock -3.0 -3.5 0 4 8 12 16 20 24 28 32 36 40 44 48 Months after the Shock
Comparison of VAR Results: Impulse Response Function for Prices 1 Funds Rate 0 -1 Percent -2 -3 Romer and Romer Shock -4 -5 -6 0 4 8 12 16 20 24 28 32 36 40 44 48 Months after the Shock
Impulse Response Function of DFF to Shock 2.5 2.0 1.5 Percentage Points 1.0 0.5 0.0 -0.5 -1.0 0 4 8 12 16 20 24 28 32 36 40 44 48 Months after the Shock
Solid black line includes the early Volcker period, dashed blue line excludes it. From: Coibion, “Are the Effects of Monetary Policy Shocks Big or Small?”
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