Impulse responses
 

What we did

  1. Data and VAR

    Nine U.S. aggregates from FRED, 1965Q3–1995Q3, in a VAR(4) in levels estimated by OLS.

  2. Identification

    The paper’s timing assumption: output, consumption, prices, investment, wages and productivity do not respond to the policy shock within the quarter.

  3. Responses

    Impulse responses with 68% and 95% bootstrap bands, the variance decomposition, and a point-by-point comparison with the paper’s Figure 1 and Table 1.

  4. Robustness

    Commodity prices in the Fed’s information set, and VARs with 2, 4 and 6 lags.

What we found

A short-lived cut in the funds rate produces a delayed, hump-shaped and persistent rise in real activity, while inflation responds only slowly.

+0.54%
Peak of GDP six quarters after an expansionary shock (paper: +0.5% after five); the funds rate is back to baseline after about six quarters.
−0.26 → −0.12
Initial dip in inflation, the price puzzle, without and with commodity prices; the paper has −0.12.
36% / 38%
Share of the variance of GDP explained by policy shocks at two years, ours and the paper’s.

Inflation turns positive after about a year and a half and peaks after three years (+0.15 points, paper +0.2). The results hold with 2 and 6 lags, and with commodity prices the price puzzle shrinks to the paper’s size while the rest of the picture is unchanged.

DifferencesConsumption responds more than in the paper (+0.50% against +0.2%), investment dips in the first quarter before rising, and the shock is larger (−85bp against −65bp). Today’s chain-weighted FRED data differ from the 2005 vintage precisely in how consumption and investment are deflated.