What do the VARs mean? Measuring the output effects of monetary policy
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Does the average path of output after a monetary policy surprise measure the surprise's own causal effect, or the further, predictable policy moves that historically followed it? Assume only surprise money matters and standard estimates imply large, hump-shaped output effects taking roughly five years to fade; let anticipated, systematic policy matter even slightly and the same data imply much smaller effects, largely gone within a few quarters. Because one policy regime's data cannot settle which assumption is right, Cochrane argues this identifying choice, not the variable-selection debates the literature usually has, does most of the work in what economists claim to know about monetary policy's real effects.
What this paper finds — and why it matters
Cochrane argues that even once a VAR-based monetary policy shock is “correctly identified” – the focus of the extensive VAR literature on variable selection and shock orthogonalization – a further, purely theoretical identifying assumption is still required before the estimated impulse-response function can be read as the causal effect of that shock: whether anticipated monetary policy actions, not just unanticipated shocks, can themselves affect output. Using both a flexible linear model that weights anticipated and unanticipated money by a parameter lambda, and an explicit Rotemberg-style sticky-price model parameterized by a price-adjustment-cost parameter alpha, Cochrane shows that this single identifying choice moves the estimated output effects of monetary policy at least as much as, and typically more than, the variable-selection and orthogonalization assumptions the VAR literature usually debates. Applying both models to a standard M2 VAR and a federal-funds-rate VAR on 1959-1992 U.S. quarterly data, he finds that if anticipated money is assumed to have no effect on output – the implicit assumption behind treating the impulse-response function itself as the policy-invariant effect of a shock – the estimated output response to a shock not followed by the customary further monetary expansion is large, hump-shaped, and takes roughly five years to die out; but allowing anticipated money to matter even slightly shrinks this same estimated response dramatically, because most of the impulse-response function’s persistence then reflects the systematic further money growth that has historically followed such shocks, not the shock’s own lagged causal effect. The sticky-price model reproduces this result through a different mechanism and adds the counterintuitive finding that assuming stickier prices implies a smaller and shorter estimated output response to an unanticipated shock, since more of the VAR’s observed dynamics are then attributed to slow price adjustment. Cochrane concludes that data from a single policy regime cannot settle which identifying assumption is correct, but that circumstantial considerations – the otherwise-coincidental similarity in shape between the money and output impulse responses, and the alternative’s reliance on ad hoc multi-year delay and propagation mechanisms – favor giving at least some role to anticipated, systematic monetary policy, with direct implications for how VAR evidence is used to argue about the length and size of monetary policy’s real effects.
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Questions & answers
Q1. What is the paper’s central methodological claim, and how does it extend Sargent’s (1976) “observational equivalence” warning?
Cochrane’s claim is that “a further, theoretical, identification is necessary to measure the effects of monetary policy” even after monetary policy shocks have been correctly identified within a VAR (Introduction). He frames this as a direct, quantitative application of Sargent’s (1976) “Observational equivalence” result – which “warns us that many different theories of the effects of monetary policy are in fact consistent with the history of monetary policy as captured by a VAR, even if the shocks are correctly identified” – arguing that this is not merely a decades-old theoretical curiosity but a live, empirically first-order issue: “the sensitivity of the output effect calculations to the anticipated/unanticipated identifying assumption is a strong, quantitative reminder of the methodological warning Sargent (1976) gave more than 20 years ago” (Section 5).
Q2. What are the two baseline VARs (Fig. 1) that motivate the puzzle, and what is “surprising” about their estimated output responses?
An M2-shock VAR and a federal-funds-rate-shock VAR both produce the qualitative pattern “just what Friedman (1968) taught us to expect” – a liquidity effect followed by an inflation effect, temporary rises in consumption and output – but “the magnitudes are a bit surprising”: “output peaks two years after the M2 shock, and takes five years to die out,” with a roughly 0.5% output response to a one-standard-deviation M2 shock (Introduction). Cochrane notes he “selected these specifications in part to minimize the size and length of output responses” and that simpler specifications “produce even larger and more protracted responses” – so these magnitudes are, if anything, conservative relative to the literature.
Q3. What is the key conceptual distinction Cochrane draws between “the impulse-response function” and “the [causal] effect of a monetary policy shock”?
If only unanticipated money affects output, the estimated money-to-output impulse-response function is itself “policy invariant” – it gives the effect of a shock “in any regime, or no matter what the path of money following the shock.” But if anticipated money can also affect output, “the continued expansion of money that is expected to follow a shock can, when it happens, cause the prolonged expansion of output following the shock,” so that “the effects of a monetary policy shock on output…may be in fact small, short and decaying (rather than hump-shaped)” once the historically typical further policy response is stripped out (Section 1). The raw impulse-response function conflates these two very different objects.
Q4. What are the paper’s two explicit models for parameterizing the anticipated/unanticipated distinction?
The first is a flexible linear model (equation 3), y_t = a(L)[lambdam_t + (1-lambda)(m_t - E_(t-1)m_t)] + b(L)d_t, where lambda in [0,1] governs the fraction of money’s output effect attributed to its anticipated component; lambda = 0 gives the standard Lucas-style unanticipated-money model and lambda = 1 gives a purely mechanistic money-output relation with no expected/unexpected distinction at all* (Section 2.2). The second is a modified Rotemberg (1982, 1994) sticky-price model (equation 10), in which firms set prices one period in advance subject to a quadratic price-adjustment-cost parameter alpha in [0,1]; alpha = 0 again recovers the unanticipated-money limit and alpha = 1 recovers the mechanistic limit, with intermediate alpha generating output effects through the (forward-looking) response of prices rather than an ad hoc lag structure (Section 2.3).
Q5. How does Cochrane identify a*(L) from the VAR’s estimated impulse responses, and what do the two extreme cases (lambda=0, lambda=1) correspond to?
Substituting the VAR’s estimated moving-average representation of money and output into the structural model and matching coefficients (equation 5) shows that at lambda = 0, a(L) = c_ym(L)/c_mm(0) – exactly the standard impulse-response function – while at lambda = 1, a(L) = c_ym(L)/c_mm(L), the dynamic-multiplier object obtained from regressing output on the level of money rather than on the money innovation** (Section 2.2.2, equations 6-7). Cochrane notes that Romer and Romer (1994), who “analyze systematic policy with a view that there is no expected-unexpected distinction,” are implicitly working in exactly this lambda = 1 case, which is why they use a dynamic regression simulation rather than an impulse-response function to measure policy effects.
Q6. What do the M2 VAR results show about how sensitive the estimated output effect is to the anticipated-money parameter lambda?
“The effects of this experiment are the same across identifying assumptions for the first quarter. But then the output effect calculated with the unanticipated-money assumption increases dramatically, and decays back to zero very slowly,” while “the output effect calculated with no anticipated/unanticipated distinction is very small, and reverts to zero after three quarters” (Section 3.1). Strikingly, Cochrane reports that “one only needs to assume that anticipated money matters slightly in order to identify short-lived effects of this monetary intervention” – even lambda = 0.2 “produces a response pattern much closer to the completely anticipated (lambda=1) assumption than to the completely unanticipated (lambda=0) assumption,” meaning the estimated policy-invariant response collapses quickly once any role for anticipated money is admitted.
Q7. What does the sticky-price model add to this result, and what “counterintuitive” finding does Cochrane highlight?
“Notice the counterintuitive result: Assuming stickier prices implies shorter and smaller effects of these monetary interventions than is given by the impulse-response functions” – because a higher price-stickiness parameter alpha lets slow price adjustment, rather than a long structural money-output lag a*(L), account for more of the VAR’s observed persistence, so “the lag polynomial a*(L) becomes much smaller and shorter” as alpha rises (Section 3.2). Cochrane also shows the sticky-price model implies that an anticipated increase in money causes output to decline in advance of the increase itself, since forward-looking price-setters raise prices ahead of the anticipated expansion (Section 3.2, discussing Fig. 5) – a qualitatively different mechanism from, but numerically similar conclusion to, the plain anticipated-money model.
Q8. How does the analysis extend to a federal-funds-rate VAR, and what pattern does it show?
Using a federal funds VAR that follows Christiano, Eichenbaum and Evans (1996) in ordering the funds rate last and including a commodity price index (to avoid the “price puzzle” in which contractionary shocks spuriously appear to raise prices), Cochrane finds “the anticipated-money effects of the shock peak in three quarters, while the unanticipated-money effects peak in 7 quarters and then die off slowly” (Section 3.3) – the same qualitative pattern as the M2 VAR, confirming the result is not specific to a monetary aggregate. He does not extend the sticky-price model to this VAR, noting it is “unclear how to apply that model to something other than an actual money aggregate.”
Q9. Which identifying assumption does Cochrane ultimately favor, and what are the stakes for debates over Fed policy lags?
Cochrane cannot prove either assumption correct from a single regime’s data, but offers two considerations that “suggest (but of course cannot prove)” some role for anticipated money: first, under the pure unanticipated-money view, “the striking similarity of the output and money responses is a pure and unlikely coincidence, since the output response would be the same for any money response”; second, that view “requires that one construct a theory of the long delayed and hump-shaped response, or swallow these dynamics as an ad-hoc patch,” whereas anticipated-money views generate short, largely contemporaneous effects “of the sort generated by most current monetary theories” (Section 4.1). He shows this choice has direct policy stakes: two common claims in Fed debates – that a funds-rate rise causes output declines peaking 1.5-2 years later, and that it “does not matter” that most funds-rate changes are part of a slow, predictable tightening – rest on opposite identifying assumptions and “are inconsistent,” since only surprise funds-rate movements can generate the long delayed effect, while anticipated, gradual tightenings, if they have any effect, only have the short, small effect implied by the anticipated-money model (Section 4.3).
Key terms in this paper
Definitions below follow the paper's own usage.
- The theoretical (anticipated/unanticipated) identification problem
- Cochrane's point, building on Sargent's (1976) "observational equivalence" warning, that correctly identifying a monetary policy shock inside a VAR (choosing variables, ordering, and orthogonalization) is not sufficient to read the resulting impulse-response function as "the effects of monetary policy": a further assumption about whether anticipated monetary actions can themselves affect output is needed, and "the data (from one regime) cannot tell us" which assumption is correct (Sections 1, 4.1).
- Anticipated/unanticipated money model (lambda)
- the paper's flexible linear model (equation 3), y_t = a*(L)[lambda*m_t + (1-lambda)(m_t - E_(t-1)[m_t])] + b*(L)d_t, in which the parameter lambda in [0,1] specifies what fraction of money's effect on output comes from its anticipated versus unanticipated component; lambda = 0 recovers the standard Lucas-style unanticipated-money model, and lambda = 1 recovers a purely mechanistic money-output relationship with no expected/unexpected distinction (Section 2.2).
- Sticky-price identification (alpha)
- a modification of Rotemberg's (1982, 1994) sticky-price model (equation 10) in which firms set prices one period in advance subject to a quadratic price-adjustment cost, parameterized by a stickiness parameter alpha in [0,1]; alpha = 0 again recovers the pure unanticipated-money (impulse-response) model and alpha = 1 recovers the fully mechanistic model, with intermediate alpha implying that output responds to money through the (forward-looking) response of prices rather than through an ad hoc distributed lag (Section 2.3).
- Policy-invariant output response
- the quantity a*(L) that Cochrane argues should in principle be invariant to the systematic component of monetary policy -- the true causal effect on output of a monetary shock "no matter what the path of money following the shock" -- as opposed to the raw impulse-response function, which conflates the shock's own effect with the effect of whatever further, historically typical policy actions the VAR's estimated money-money dynamics say usually follow it (Introduction, Section 2.1).