Identifying Monetary Policy Shocks

Level: Graduate | Field: Monetary Economics

1. The identification problem

Policy rates respond to the state of the economy, so the correlation between interest rates and output says little about the causal effect of policy. Write policy as a rule plus a shock, \(i_t=f(\Omega_t)+\varepsilon^m_t\), where \(\Omega_t\) is the central bank's information. The effects of policy are the responses to \(\varepsilon^m_t\), the part of policy not explained by the systematic response. Every identification strategy is a way of isolating \(\varepsilon^m_t\) (Ramey, 2016).

2. Recursive VARs

Christiano, Eichenbaum and Evans (1999) estimate a VAR \(Y_t=c+\sum_{l=1}^pA_lY_{t-l}+u_t\) and assume that output and prices do not respond to the policy shock within the period, while policy may respond to them. With the policy rate ordered last, the shock is the last element of \(S^{-1}u_t\), where \(S\) is the Cholesky factor of \(\Sigma_u\). The approach produces the facts of Lecture 1 — a gradual fall in output with a trough after 1–2 years — but also the price puzzle: prices often rise after a tightening (Sims, 1992). The usual explanation is that the Fed reacts to information about future inflation not in the VAR. Adding commodity prices or Fed forecasts reduces the puzzle.

3. Narrative shocks

Romer and Romer (2004) construct the Fed's intended funds-rate changes at each FOMC meeting from narrative records and regress them on the Greenbook forecasts the Fed was looking at; the residual is a shock purged of the Fed's information. With these shocks, output falls substantially more than in recursive VARs, and prices fall after a delay. Updates extend the series to 2019 (Exercise 14.2 uses Acosta's update). Narrative methods depend on the quality of records and forecasts.

4. High-frequency identification

Monetary-policy surprises can be measured as changes in interest-rate futures in a narrow window (e.g., 30 minutes) around FOMC announcements (Kuttner, 2001; Gürkaynak, Sack and Swanson, 2005). Within the window, nothing else systematically moves rates, so the surprise is plausibly exogenous. Surprises are used as external instruments (proxies) in VARs (Stock and Watson, 2012; Mertens and Ravn, 2013; Gertler and Karadi, 2015). Two problems arise:

• Information effects. A surprise tightening can signal that the Fed sees a stronger economy, so stock prices may rise rather than fall (Nakamura and Steinsson, 2018). Jarociński and Karadi (2020) separate pure policy shocks from information shocks using the sign of the co-movement between interest rates and stock prices.
• Predictability. Surprises are predictable from public data released before the announcement, reflecting the Fed's response to news (Bauer and Swanson, 2023); orthogonalising them yields cleaner shocks.

5. Local projections

Jordà (2005) estimates the impulse response at horizon \(h\) directly:

Local projections do not impose the dynamic restrictions of a VAR, so they are robust to misspecification at long horizons, but they have larger variance. Plagborg-Møller and Wolf (2021) show that LPs and VARs estimate the same population impulse responses with enough lags; the difference is a bias–variance trade-off (Li, Plagborg-Møller and Wolf, 2024). Residuals are serially correlated by construction, so inference uses heteroskedasticity- and autocorrelation-robust standard errors or lag augmentation (Montiel Olea and Plagborg-Møller, 2021).

6. What we know

Across methods, a 100 bp contractionary shock lowers industrial production by roughly 1–5% at the peak after one to two years and eventually lowers the price level, with substantial uncertainty about magnitudes and timing (Ramey, 2016). Estimates based on high-frequency instruments and on narrative shocks tend to find larger output effects than recursive VARs. Monetary shocks explain a modest share of output fluctuations — systematic policy matters more than shocks. Matching these responses is a common way to estimate DSGE models (Christiano, Eichenbaum and Evans, 2005): choose structural parameters to minimise the distance between model and VAR impulse responses.

7. Evidence outside the United States

For small open economies such as Korea, identification must account for the exchange rate and foreign shocks (Kim and Roubini, 2000). Block-exogeneity assumptions for foreign variables and high-frequency surprises from government bond futures around Bank of Korea announcements have been used. For economies with monetary targeting and administered rates, such as Bangladesh before 2023, the policy instrument itself must be chosen carefully.

D = readtable('us_monthly.csv');
k = D.year >= 1965 & D.year <= 2007;
Y = [100 * log(D.indpro(k)) 100 * log(D.cpi(k)) D.ffr(k)];
p = 12;
% TODO: X = [1, Y(t-1), ..., Y(t-p)]; B = X \ Y(p+1:end,:); Sigma; chol; companion-form IRFs

D = readtable('us_monthly.csv');
k = D.year >= 1965 & D.year <= 2007;
Y = [100 * log(D.indpro(k)) 100 * log(D.cpi(k)) D.ffr(k)];
p = 12; [T, n] = size(Y);
X = ones(T - p, 1); for l = 1:p, X = [X Y(p+1-l:T-l, :)]; end
B = X \ Y(p+1:end, :); U = Y(p+1:end, :) - X * B; Sigma = U' * U / (T - p - size(X, 2));
S = chol(Sigma)';                                   % lower triangular: IP, CPI, FFR
shock = S(:, 3) * 0.25 / S(3, 3);                   % 25 bp funds-rate shock
H = 49; IR = zeros(n, H); Acomp = [B(2:end, :)'; eye(n * (p - 1)) zeros(n * (p - 1), n)];
s = [shock; zeros(n * (p - 1), 1)];
for h = 1:H, IR(:, h) = s(1:n); s = Acomp * s; end
fprintf('months after shock   %s\n', sprintf('%7d', [0 6 12 24 36 48]));
lab = {'industrial prod.', 'CPI             ', 'funds rate      '};
for v = 1:3, fprintf('%s     %s\n', lab{v}, sprintf('%7.3f', IR(v, [0 6 12 24 36 48] + 1))); end

months after shock         0      6     12     24     36     48
industrial prod.       0.000 -0.072 -0.188 -0.252 -0.247 -0.214
CPI                    0.000  0.066  0.078  0.085  0.068  0.040
funds rate             0.250  0.172  0.100  0.071  0.039  0.021

D = readtable('us_monthly.csv'); S = readtable('mp_shocks_monthly.csv');
% TODO: align on year/month; build lags of dy and RR; loop over h with ols_nw(lhs, X, h+1)

D = readtable('us_monthly.csv'); S = readtable('mp_shocks_monthly.csv');
key = @(y, m) 12 * y + m;
[~, ia, ib] = intersect(key(D.year, D.month), key(S.year, S.month));
yr = D.year(ia); rr = S.rr(ib); T = numel(yr);
L = @(v, j) [NaN(j, 1); v(1:end-j)];
hs = [0 6 12 24 36 48]; lab = {'industrial prod.', 'CPI             '};
fprintf('months after shock   %s\n', sprintf('%7d', hs));
for v = 1:2
  if v == 1, y = 100 * log(D.indpro(ia)); else, y = 100 * log(D.cpi(ia)); end
  dy = [NaN; diff(y)];
  ctrl = []; for j = 1:12, ctrl = [ctrl L(dy, j) L(rr, j)]; end
  b = zeros(size(hs)); se = b;
  for m = 1:numel(hs)
    h = hs(m); lhs = NaN(T, 1); lhs(1:T-h) = y(1+h:T) - L(y, 1)(1:T-h);
    X = [ones(T, 1) rr ctrl];
    k = yr >= 1970 & yr <= 2007 & all(~isnan([lhs X]), 2);
    [bb, ss] = ols_nw(lhs(k), X(k, :), h + 1); b(m) = bb(2); se(m) = ss(2);
  end
  fprintf('%s     %s\n', lab{v}, sprintf('%7.2f', b));
  fprintf('   (s.e.)            %s\n', sprintf('%7.2f', se));
end

months after shock         0      6     12     24     36     48
industrial prod.        0.34   0.29  -0.89  -2.10  -1.65  -1.49
   (s.e.)               0.14   0.39   0.75   1.20   1.27   1.59
CPI                     0.06   0.47   0.58   0.49  -0.85  -2.51
   (s.e.)               0.03   0.11   0.22   0.42   0.62   0.87