L ECTURE 3 The Effects of Monetary Changes: Vector Autoregressions - - PowerPoint PPT Presentation

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L ECTURE 3 The Effects of Monetary Changes: Vector Autoregressions - - PowerPoint PPT Presentation

Sep 17, 2023 247 likes •719 views

Economics 210c/236a Christina Romer Fall 2016 David

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LECTURE 3

The Effects of Monetary Changes: Vector Autoregressions September 7, 2016

Economics 210c/236a Christina Romer Fall 2016 David Romer

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  • I. SOME BACKGROUND ON VARS
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A Two-Variable VAR

Suppose the true model is: where ε1t and ε2t are uncorrelated with one another, with the contemporaneous and lagged values of the right-hand side variables, and over time.

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Rewrite this as:

  • r

where

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This implies where

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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

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Consider where The elements of B and C are not identified.

An Obvious (at Least in Retrospect) Insight

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  • II. CHRISTIANO, EICHENBAUM, AND EVANS, “THE

EFFECTS OF MONETARY POLICY SHOCKS: EVIDENCE

FROM THE FLOW OF FUNDS”

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  • Two variables, one lag:
  • The reduced form is:

Simplified Version of Christiano, Eichenbaum, and Evans

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From: Christiano, Eichenbaum, and Evans

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From: Christiano, Eichenbaum, and Evans

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From: Christiano, Eichenbaum, and Evans

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From: Christiano, Eichenbaum, and Evans

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Two Other Ways of Estimating the Effects of Monetary Policy Shocks under CEE’s Assumptions

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  • 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
  • f 𝑐

ℎ’s.

  • Note: As always, this presumes that the identifying

assumptions are correct!

The Jordà Local Projections Approach

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Other Types of Restrictions to Make VARs Identified

  • Zero restrictions other than ordering assumptions.
  • Long-run restrictions.
  • Imposing coefficient restrictions motivated by

theory.

  • …
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  • III. RUDEBUSCH, “DO MEASURES OF MONETARY POLICY

IN A VAR MAKE SENSE?”

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Key Points

  • The funds rate equation in many VARs is the Fed’s

reaction function, and so can be evaluated using

  • ther 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.

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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.
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From: Rudebusch, “Do Measures of Monetary Policy …?”

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From: Rudebusch, “Do Measures of Monetary Policy …?”

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Concerns about Rudebusch’s Critique of the Funds Rate Equation of VARs as a Fed Reaction Function?

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Rudebusch’s Concerns about the Monetary Policy Shocks from VARs

  • Comparison with surprises relative to expectations

based on financial markets.

  • Comparisons across VARs.
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From: Rudebusch, “Do Measures of Monetary Policy …?”

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From: Rudebusch, “Do Measures of Monetary Policy …?”

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Concerns about Rudebusch’s Critique of the Monetary Policy Shocks from VARs?

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  • IV. ROMER AND ROMER: “A NEW MEASURE OF

MONETARY SHOCKS: DERIVATION AND IMPLICATIONS”

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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
  • utput growth.
  • Take residuals as new measure of monetary policy

shocks.

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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”

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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.
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From: Romer and Romer, “A New Measure of Monetary Shocks”

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Evaluation of the New Measure

  • Key issue – is there useful information used in setting

policy not contained in the Greenbook forecasts?

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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.

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From: Kenneth Kuttner, “Monetary Policy Surprises.”

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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”

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Fitting this Specification into the Earlier Framework

Suppose the true model is: 𝑧𝑢 = 𝑏1𝑧𝑢−1 + 𝑐1𝑗𝑢−1 + 𝜁𝑧𝑢, (1) 𝑗𝑢 = 𝑏2𝑧 𝑢 + 𝑐2𝜌 𝑢 + 𝜁𝑗𝑢, (2) where 𝑧 and 𝜌 are the forecasts as of period t, and εit is uncorrelated with all the

  • ther things on the right-hand side of (1) and (2) (𝑧𝑢−1, 𝑗𝑢−1, 𝑧

𝑢, 𝜌 𝑢, and 𝜁𝑧𝑢). (2) implies: 𝑗𝑢−1 = 𝑏2𝑧 𝑢−1 + 𝑐2𝜌 𝑢−1 + 𝜁𝑗,𝑢−1. Substituting this in to (1) gives us: 𝑧𝑢 = 𝑐1𝜁𝑗,𝑢−1 + 𝜀𝑢, where 𝜀𝑢 = 𝑏1𝑧𝑢−1 + 𝑐1 𝑏2𝑧 𝑢−1 + 𝑐2𝜌 𝑢−1 + 𝜁𝑧𝑢. Under the assumptions of the model, δt is uncorrelated with εi,t-1, and so we can estimate this equation by OLS and recover the effect of i on y (b1).

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From: Romer and Romer, “A New Measure of Monetary Shocks”

Single-Equation Regression for Output

Using the New Measure of Monetary Shocks Using the Change in the Actual Funds Rate

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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

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From: Romer and Romer, “A New Measure of Monetary Shocks”

Single-Equation Regression for Prices Controlling for Commodity Prices

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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.
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VAR Results

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  • 3.5
  • 3.0
  • 2.5
  • 2.0
  • 1.5
  • 1.0
  • 0.5

0.0 0.5 1.0 4 8 12 16 20 24 28 32 36 40 44 48 Percent Months after the Shock

Comparison of VAR Results: Impulse Response Function for Output

Funds Rate Romer and Romer Shock

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  • 6
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  • 4
  • 3
  • 2
  • 1

1 4 8 12 16 20 24 28 32 36 40 44 48 Percent Months after the Shock

Comparison of VAR Results: Impulse Response Function for Prices

Funds Rate Romer and Romer Shock

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  • 1.0
  • 0.5

0.0 0.5 1.0 1.5 2.0 2.5 4 8 12 16 20 24 28 32 36 40 44 48 Percentage Points Months after the Shock

Impulse Response Function

  • f DFF to Shock
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From: Coibion, “Are the Effects of Monetary Policy Shocks Big or Small?”

Solid black line includes the early Volcker period, dashed blue line excludes it.