l ecture 3

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

Economics 210c/236a Christina Romer Fall 2018 David


  1. Economics 210c/236a Christina Romer Fall 2018 David Romer L ECTURE 3 The Effects of Monetary Changes: Statistical Identification September 5, 2018

  2. I. S OME B ACKGROUND ON VAR S

  3. A Two-Variable VAR Suppose the true model is: where Ξ΅ 1 t and Ξ΅ 2 t are uncorrelated with one another, with the contemporaneous and lagged values of the right-hand side variables, and over time.

  4. Rewrite this as: or where

  5. This implies where The assumptions of the model imply that the elements of 𝑉 𝑒 are uncorrelated with π‘Œ π‘’βˆ’1 . We can therefore estimate the elements of 𝛲 by estimating each equation of π‘Œ 𝑒 = π›²π‘Œ π‘’βˆ’1 + 𝑉 𝑒 by OLS.

  6. Extending to K Variables and N Lags The β€œtrue 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

  7. An Obvious (at Least in Retrospect) Insight Consider where The elements of B and C are not identified. Thus, to make progress we need to make additional assumptions.

  8. II. C HRISTIANO , E ICHENBAUM , AND E VANS : β€œT HE E FFECTS OF M ONETARY P OLICY S HOCKS : E VIDENCE FROM THE F LOW OF F UNDS ”

  9. Timing Assumptions The most common approach to identifying assumptions in β€’ VARs is to impose zero restrictions that give the matrix of contemporaneous effects, C , a recursive structure. Specifically, one chooses an ordering of the variables, 1, 2, …, β€’ n , and assumes that variable 1 is not affected by any of the other variables within the period and potentially affects all the others within the period; variable 2 is not affected by any variables other than variable 1 within the period and potentially affects all the others except variable 1; …; variable n is potentially affected by all the other variables within the period and does not affect any of the others. Such assumptions are known as timing or ordering β€’ assumptions, or Cholesky identification .

  10. Simplified Version of Christiano, Eichenbaum, and Evans Two variables, one lag: β€’ The reduced form is: β€’

  11. From: Christiano, Eichenbaum, and Evans

  12. From: Christiano, Eichenbaum, and Evans

  13. From: Christiano, Eichenbaum, and Evans

  14. From: Christiano, Eichenbaum, and Evans

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

  16. Other Types of Restrictions to Make VARs Identified β€’ Zero restrictions other than ordering assumptions. β€’ Long-run restrictions. β€’ Imposing coefficient restrictions motivated by theory. β€’ …

  17. III. R OMER AND R OMER : β€œA N EW M EASURE OF M ONETARY S HOCKS : D ERIVATION AND I MPLICATIONS ”

  18. Deriving Our New Measure β€’ Derive the change in the intended funds rate around FOMC meetings using narrative and other sources. β€’ Regress on Federal Reserve forecasts of inflation and output growth. β€’ Take residuals as new measure of monetary policy shocks.

  19. Regression Summarizing Usual Fed Behavior ff is the federal funds rate y is output; Ο€ is inflation; u is the unemployment rate ~ over a variable indicates a Greenbook forecast From: Romer and Romer, β€œA New Measure of Monetary Shocks”

  20. What kinds of thing are in the new shock series? β€’ Unusual movements in funds rate because the Fed was also targeting other measures. β€’ Mistakes based on a bad model of economy. β€’ Change in tastes. β€’ Political factors. β€’ Pursuit of other objectives.

  21. Miller Burns Volcker From: Romer and Romer, β€œA New Measure of Monetary Shocks”

  22. Evaluation of the New Measure β€’ Key issue – is there useful information used in setting policy not contained in the Greenbook forecasts?

  23. Digression: Kuttner’s Alternative Measure of Monetary Shocks β€’ 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.

  24. From: Kenneth Kuttner, β€œMonetary Policy Surprises.”

  25. 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, β€œA New Measure of Monetary Shocks”

  26. Fitting this Specification into the Earlier Framework Suppose the true model is: 𝑧 𝑒 = 𝑏 1 𝑧 π‘’βˆ’1 + 𝑐 1 𝑗 π‘’βˆ’1 + 𝜁 𝑧𝑒 , (1) 𝑗 𝑒 = 𝑏 2 𝑧 οΏ½ 𝑒 + 𝑐 2 𝜌 οΏ½ 𝑒 + 𝜁 𝑗𝑒 , (2) where 𝑧 οΏ½ and 𝜌 οΏ½ are the forecasts as of period t , and Ξ΅ it is uncorrelated with all the other things on the right-hand side of (1) and (2) ( 𝑧 π‘’βˆ’1 , 𝑗 π‘’βˆ’1 , 𝑧 οΏ½ 𝑒 , 𝜌 οΏ½ 𝑒 , and 𝜁 𝑧𝑒 ) . (2) implies: 𝑗 π‘’βˆ’1 = 𝑏 2 𝑧 οΏ½ π‘’βˆ’1 + 𝑐 2 𝜌 οΏ½ π‘’βˆ’1 + 𝜁 𝑗 , π‘’βˆ’1 . Substituting this in to (1) gives us: 𝑧 𝑒 = 𝑐 1 𝜁 𝑗 , π‘’βˆ’1 + πœ€ 𝑒 , where πœ€ 𝑒 = 𝑏 1 𝑧 π‘’βˆ’1 + 𝑐 1 𝑏 2 𝑧 οΏ½ π‘’βˆ’1 + 𝑐 2 𝜌 οΏ½ π‘’βˆ’1 + 𝜁 𝑧𝑒 . Under the assumptions of the model, Ξ΄ t is uncorrelated with Ξ΅ i,t -1 , and so we can estimate this equation by OLS and recover the effect of i on y ( b 1 ).

  27. Single-Equation Regression for Output Using the New Measure of Monetary Shocks Using the Change in the Actual Funds Rate From: Romer and Romer, β€œA New Measure of Monetary Shocks”

  28. Single-Equation Regression for Prices Using the New Measure of Monetary Shocks Using the Change in the Actual Funds Rate From: Romer and Romer, β€œA New Measure of Monetary Shocks”

  29. VAR Specification β€’ Three variables: log of IP, log of PPI for finished goods, measure of monetary policy. β€’ Monetary policy is assumed to respond to, but not to affect other variables contemporaneously. β€’ We include 3 years of lags, rather than 1 as Christiano, Eichenbaum, and Evans do. β€’ Cumulate shock to be like the level of the funds rate.

  30. VAR Results

  31. Comparison of VAR Results: Impulse Response Function for Output 1.0 0.5 0.0 -0.5 Funds Rate Percent -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

  32. 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

  33. 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

  34. Solid black line includes the early Volcker period, dashed blue line excludes it. From: Coibion, β€œAre the Effects of Monetary Policy Shocks Big or Small?”

  35. IV. G ERTLER AND K ARADI : β€œM ONETARY P OLICY S URPRISES , C REDIT C OSTS , AND E CONOMIC A CTIVITY ”

  36. Key Features of Gertler and Karadi’s Approach β€’ A different strategy for trying to isolate useful identifying variation in monetary policy: surprise changes in measures of monetary policy around the times of FOMC decisions. β€’ An IV approach to VARs: β€œexternal instruments.”

  37. Surprise Changes in Measures of Monetary Policy around the Times of FOMC Decisions β€’ The idea that changes in financial market variables in a very short window around an FOMC announcement are almost entirely responses to the announcement seems very reasonable. β€’ Concerns? β€’ Potentially leaves out a lot of useful variation. β€’ Is a surprise change in monetary policy necessarily the same as a pure monetary policy shock?

  38. Background on External Instruments: A NaΓ―ve Approach to IV Suppose we want to estimate β€’ 𝐿 𝑧 𝑒 = οΏ½ 𝑐 𝑙 𝑗 π‘’βˆ’π‘™ + 𝑓 𝑒 , 𝑙=0 and that we have a variable z t that we think is correlated with i t and uncorrelated with the e ’s. It might be tempting to estimate the equation by IV, with β€’ instrument list z t , z t βˆ’1 , …, z t βˆ’ K . Concerns: β€’ We think i t βˆ’ k is affected by z t βˆ’ k and not the other z ’s. So, at β€’ the very least, this approach creates a lot of inefficiency. Conjecture: This approach could magnify the bias caused β€’ by small misspecification. How do we extend this to a VAR? β€’

  39. External Instruments in a Simple 2-Variable Modelβ€”Set-Up Suppose the true model is: β€’ 𝑧 𝑒 = πœ„π‘— 𝑒 + 𝑐 11 𝑧 π‘’βˆ’1 + 𝑐 12 𝑗 π‘’βˆ’1 + 𝜁 𝑧𝑒 , 𝑗 𝑒 = 𝛿𝑧 𝑒 + 𝑐 21 𝑧 π‘’βˆ’1 + 𝑐 22 𝑗 π‘’βˆ’1 + 𝜁 𝑗𝑒 . The reduced form is: β€’ π‘Œ 𝑒 = π›²π‘Œ π‘’βˆ’1 + 𝑉 𝑒 , (where: π‘Œ 𝑒 ≑ 𝑧 𝑒 1 βˆ’πœ„ , 𝐢 ≑ 𝑐 11 𝑐 12 𝑗 𝑒 , Ξ  ≑ C -1 B, ≑ 𝑐 22 , βˆ’π›Ώ 1 𝑐 21 U t ≑ C -1 E t , 𝐹 𝑒 ≑ 𝜁 𝑧𝑒 𝜁 𝑗𝑒 ).

  40. External Instruments in a Simple 2-Variable Modelβ€” Using an Instrument β€’ Suppose we have a variable z t that is correlated with 𝜁 𝑗𝑒 and not systematically correlated with 𝜁 𝑧𝑒 . β€’ Let 𝑣 𝑧𝑒 and 𝑣 𝑗𝑒 be the two elements of U t β€”that is, the reduced form innovations in y and i . β€’ One can show that 𝑣 𝑧𝑒 can be written in the form: 𝑣 𝑧𝑒 = πœ„π‘£ 𝑗𝑒 + 𝜁 𝑧𝑒 . β€’ So, a regression of 𝑣 𝑧𝑒 on 𝑣 𝑗𝑒 , using z t as an instrument allows us to estimate πœ„ .

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