Monetary Policy Rules Based on Real-Time Data

Questions & answers

Q1. What question motivates this paper, and why does it matter for how economists study monetary policy?

Orphanides asks how large the informational problem is when Taylor-type interest rate rules are evaluated or estimated using the data actually available to policymakers in real time, rather than the ex post revised data conventionally used in the literature — and whether policy reaction functions estimated on revised data give an accurate description of historical policy. As he puts it, “even if policy rules can be designed optimally in a hypothetical problem that abstracts from informational difficulties, it is necessary to assess the magnitude of informational problems when such rules are implemented in practice” (Introduction, p. 964). The stakes are high: he argues that “estimated policy reaction functions obtained using the ex post revised data yield misleading descriptions of historical policy,” so that “identification of monetary policy shocks under such circumstances becomes a haphazard enterprise” (Section IV, p. 983).

Q2. How does Orphanides construct the real-time data set, and how different is it from the revised data economists usually use?

The real-time series come from Federal Reserve Greenbook staff forecasts prepared for each FOMC meeting between 1987:1 and 1992:4 (extended to 1993:4, i.e., 24 and 28 quarterly observations respectively, for the forward-looking IV specifications) — specifically the within-quarter Greenbook estimate of current inflation (a four-quarter moving average of GDP deflator growth, π_{t|t}) and the within-quarter output gap using the staff’s Q* concept of potential output (y_{t|t}). These are compared against revised vintages from 1993:1 and 1994:4 (the “final” vintage as of publication), each evaluated under both Taylor’s original linear-trend output-gap concept and the Federal Reserve staff’s Q* concept of potential output. The differences are large: the real-time output gap averages -1.25% versus -0.23% for the 1994:4 revised series, a gap the paper calls “dramatic” (Table 1, Figure 2, pp. 967-968), while real-time and revised inflation means are closer (3.46% vs. 3.76%).

Q3. How do the actual federal funds rate and the Taylor rule’s prescriptions compare once the vintage of data is taken into account?

Table 2 reports the gap between the actual funds rate and the standard Taylor rule prescription (r=2%, π=2%, coefficients 1.5 on the inflation gap and 0.5 on the output gap) separately for each data vintage and for each of the two output-gap concepts used in the paper — Taylor’s original linear-trend concept (denoted R^T) and the Federal Reserve staff’s Q* concept (denoted R) — and the sign and size of the gap depend on both. With real-time (t|t) data the Fed looks substantially too tight relative to the rule: 96 basis points under the linear-trend concept and 123 basis points under the Q*-concept (both significant at the 1% level). With the 1993:1 revised vintage the gap is a statistically insignificant -2 basis points under the linear-trend concept but 40 basis points too tight under the Q*-concept (significant at 1%). With the 1994:4 revised vintage the sign flips under the linear-trend concept, where the Fed looks about 20 basis points too easy (significant only at the 10% level), while the Q*-concept still shows the Fed about 27 basis points too tight (significant at 5%)** (Table 2, pp. 971-972). The standard deviation of the real-time-versus-revised discrepancy is 0.58 percentage points, and the maximum discrepancy approaches 200 basis points at some points in the sample (Figure 3, p. 971).

Q4. How much do the real-time estimates get revised over time, and are those revisions “news” or “noise”?

Revisions grow substantially over the year following a Greenbook forecast — the output-gap revision standard deviation rises from 0.66 after one quarter to 1.02 after four quarters, inflation from 0.23 to 0.44, and the cumulative effect on the implied Taylor rule from 0.46 to 0.67 (Table 3, p. 976), driven largely by cumulative rebenchmarking of potential-output estimates (Section II.B, p. 975). Testing two polar characterizations of the revision process — a “news” hypothesis (revisions uncorrelated with the real-time estimate, as in rational forecasting) versus a “noise” hypothesis (revisions uncorrelated with the final data, as in classical measurement error) — Orphanides finds correlations of revisions with real-time estimates of -0.44 (inflation) and -0.62 (output gap), versus -0.31 with final data for both, and concludes “for the most part the data revisions in this sample represent noise” (p. 977, citing Mankiw and Shapiro 1986). A footnote adds that revisions to the level of potential output are themselves serially correlated (first-order correlation 0.4), reflecting the nonstationary way Q* estimates get updated (p. 977, fn. 11).

Q5. What happens when a backward-looking policy reaction function is estimated on real-time versus revised data — and why does the result look “disturbing”?

Estimating f_t = ρf_{t-1} + (1-ρ)(a_0 + a_π π_t + a_y y_t) + η_t over 1987:1-1992:4, the inflation-response coefficient a_π is about 1.5-1.6 with revised 1994:4 data (with or without partial adjustment) but only 0.79 with real-time data and no smoothing, collapsing to about 0.10 (statistically indistinguishable from zero) once partial adjustment is allowed for (Table 4, p. 978). Orphanides calls this “a disturbing result” and notes that taken at face value it “would suggest … that monetary policy over the estimation period might have led to an unstable inflation process,” but he judges the “more likely explanation” to be that the contemporaneous specification is simply misspecified — actual policy responds to forecasts, not current-quarter data (p. 978).

Q6. Does allowing the reaction function to be forward-looking resolve the puzzle, and at what horizon?

Re-estimating the reaction function with forecasts i quarters ahead (instrumented with four lags each of the funds rate, inflation, and the output gap, over the extended 1987:1-1993:4 sample) shows that with real-time data the inflation coefficient only reaches a plausible value — 1.64 (standard error 0.22) — at the four-quarter-ahead horizon; contemporaneous and backward-looking real-time specifications give implausibly low or even negative coefficients (-0.49 and -3.35, respectively) (Table 6, pp. 979-980). Orphanides links the three-to-four-quarter horizon to the “‘six to twelve months or even longer’ horizon that Chairman Greenspan identified as critical for monetary policy decisions” in 1997 Senate testimony (p. 980). Mechanically, he shows the estimated coefficients at short horizons are convolutions of the true (forward-looking) reaction coefficients and the projection coefficients mapping current data onto future forecasts — which is why a_π rises steadily from strongly negative to plausibly positive as the assumed horizon lengthens, “reflect[ing] the forecasting structure, not changes in true policy responsiveness” (p. 982). With partial-adjustment terms included, both the four-quarter-ahead and the contemporaneous real-time rules track the actual funds rate closely over 1987-1993 despite their very different structural coefficients (Figure 7, p. 981).

Q7. What does the correctly specified real-time rule imply about the equilibrium real interest rate?

From the four-quarter-ahead real-time reaction function, the steady-state relationship r = a_0 + (a_π - 1)π implies an equilibrium real rate of 1.8% if the inflation target is 0%, or 3.1% if the target is 2% — which Orphanides calls “reasonable estimates of the equilibrium real interest rate.”** By contrast, the misspecified shorter-horizon (contemporaneous or backward-looking) reaction functions yield “considerably higher and quite misleading estimates,” because their coefficients confound the true policy response with the projection coefficients discussed in Q6 (p. 983).

Q8. What are the main scope conditions and limitations that qualify these findings?

The results rest on a small sample (24 observations for the main 1987:1-1992:4 analysis, 28 for the forward-looking IV specifications extending to 1993:4), which the paper explicitly flags as limiting statistical precision throughout, and on Greenbook forecasts as the real-time proxy for policymakers’ information — forecasts that “may not represent the views of the FOMC” and are conditioned on a specific assumed policy path (p. 979, fn. 14, citing Romer and Romer 1996). The measurement error in the real-time output gap is not classical: revisions to the level of Q* are systematically and partly forecastable, violating standard assumptions (p. 977, fn. 11). The sample covers the Greenspan-era “Great Moderation” and entirely predates the zero lower bound; Orphanides suggests the same real-time measurement problems would likely be even more severe in earlier periods such as the 1970s. Results are reported as robust to substituting the 1993:1 revised vintage for the 1994:4 vintage (detailed in a companion 1997 FRB working paper, p. 978, fn. 12), and standard errors throughout use a Newey-West heteroskedasticity- and serial-correlation-consistent estimator.