Christian Wolf @ChristianKWolf Twitter profile

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Christian Wolf

@ChristianKWolf

3 years

We just posted a new working paper on LP vs. VAR estimation of macro impulse responses. Comments very welcome, summary below!

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Christian Wolf

@ChristianKWolf

1 year

New paper out on how fiscal deficits are financed, joint with Chen & Marios. Also available here: I'll try to briefly summarize the main idea below.

NBER

@nberpubs

1 year

If Ricardian equivalence fails and output is demand-determined, then fiscal deficits can finance themselves through a mix of output boom and higher inflation, from George-Marios Angeletos, Chen Lian, and @ChristianKWolf

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Christian Wolf

@ChristianKWolf

3 years

Just posted an updated version of my working paper on interest rate cuts & stimulus checks. Three main points on how I think about these two as macro stabilization tools.

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Christian Wolf

@ChristianKWolf

2 years

Very excited to see this paper out in print! As always it was a pleasure to work with Mikkel. Brief summary thread ⬇️

Instrumental Variable Identification of Dynamic Variance Decompositions | Journal of Political...

Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement...

www.journals.uchicago.edu

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Christian Wolf

@ChristianKWolf

3 years

Very happy to see this paper out now, working on it was a lot of fun! Quick summary👇

Econometrica

@ecmaEditors

3 years

Local Projections and Vector Autoregressions share the exact same impulse response estimand. Any identification approach (short-run/long-run/sign restrictions, IVs, etc.) that works with one method can equivalently be implemented with the other method

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Christian Wolf

@ChristianKWolf

2 years

@AlisdairMcKay and I recently posted an updated version of our paper on time-series regressions and macro policy rule counterfactuals. My attempt at a summary 🧵

NBER

@nberpubs

2 years

How to use empirical evidence on policy shocks to predict the effects of changes in systematic policy rules, from @ChristianKWolf and @alisdairmckay

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Christian Wolf

@ChristianKWolf

1 year

I really enjoyed working on this with @AlisdairMcKay , great to see it get published -- also some follow-up work coming soon!

Econometrica

@ecmaEditors

1 year

This paper presents a method for using empirical evidence on the effects of policy shocks to construct counterfactuals following changes in policy rules, without violating the Lucas critique @ChristianKWolf @AlisdairMcKay

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Christian Wolf

@ChristianKWolf

2 years

I recently posted a substantially updated version of my job market paper. Summary 🧵follows.

NBER

@nberpubs

2 years

Cross-sectional analysis often differences out general equilibrium (GE) effects; a look at when and how time series estimates of fiscal spending multipliers can help us learn about the missing GE part, from @ChristianKWolf

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Christian Wolf

@ChristianKWolf

11 months

This year @luigi_bocola and I are organizing the NBER “Methods and Applications for DSGE Models” workshop, to be held in Philadelphia in October. The main theme will be inflation. Please send us your papers, both empirical and theoretical contributions welcome!

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Christian Wolf

@ChristianKWolf

2 years

Really enjoyed presenting my work with @AlisdairMcKay at @nberpubs EFG yesterday. Presentation (with technical hiccup at beginning...) & absolutely fantastic discussion by Valerie Ramey here () and paper here ().

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Christian Wolf

@ChristianKWolf

4 months

Very much looking forward to this!

Eleonora Granziera

@EleGranziera

4 months

You can now submit your application to the latest EABCN Training School: "Empirical Methods for Business Cycle Analysis" by @ChristianKWolf , Manheim, June 10-12 2024

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Christian Wolf

@ChristianKWolf

4 months

Very useful paper on how to study non-linearities in the propagation of macroeconomic shocks and policies!

Pedro Martínez Bruera

@pmbruera

4 months

Very excited to share our new working paper with @tomycaravello . Traditionally, researchers in the applied macroeconomics literature assumed linearity in the DGP, but what if it is nonlinear? Can we learn anything without imposing parametric assumptions? Enter our paper!

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Christian Wolf

@ChristianKWolf

2 years

Original summary thread here: Headline results haven't changed too much, but our confidence in those conclusions has increased further 🙂

NBER

@nberpubs

2 years

Local projections estimate impulse responses with little bias, but high variance. Shrinkage via Bayesian VARs or penalized LPs is thus generally attractive, from Dake Li, Mikkel Plagborg-Møller, and @ChristianKWolf

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Christian Wolf

@ChristianKWolf

3 years

Across all methods, those that offer shrinkage - notably penalized LP (green) and BVARs (dark blue) - are usually the most preferred ones. [Figure: Method that on average performs best, as function of horizon and weight on bias squared.]

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Christian Wolf

@ChristianKWolf

3 years

What does that mean for applied work? For me the main take-away is this: IRF analysis in time series macro is nothing more than a researcher willing to give a structural interpretation to certain linear projections. VARs and LPs are two techniques to estimate those projections.

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Christian Wolf

@ChristianKWolf

2 years

Let me close with a word on my committee: @ben_moll , Mikkel Plagborg-Møller, @glviolante and Mark Watson. I benefited tremendously from their support and guidance, both on this project and the PhD in general. A big thank you goes to them!

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Christian Wolf

@ChristianKWolf

10 months

Submission deadline today!

Christian Wolf

@ChristianKWolf

11 months

This year @luigi_bocola and I are organizing the NBER “Methods and Applications for DSGE Models” workshop, to be held in Philadelphia in October. The main theme will be inflation. Please send us your papers, both empirical and theoretical contributions welcome!

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Christian Wolf

@ChristianKWolf

1 year

How big can this be? The main result of the paper is that, as the gov't pushes the promised financing further into the future, these "self-financing" channels get strong enough to *fully* finance the deficit -- the promised future tax hike turns out to not be necessary in eq'm.

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Christian Wolf

@ChristianKWolf

3 years

Your choice of estimation technique should be dictated by the question of how to "best" (in a loss function sense) estimate those projections, and different DGPs & loss functions will give different answers. We are working on this right now, and should have some results out soon.

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Christian Wolf

@ChristianKWolf

2 years

... a bit counterproductive when the literature talks of monetary or fiscal shocks as if these were 1-dimensional objects. Time paths of instruments (e.g., interest rates or gov't spending) matter a lot — the more time paths we have, the more counterfactuals we can construct.

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Christian Wolf

@ChristianKWolf

3 years

1. There very much is a bias-variance trade-off. Low-order VARs don't accurately describe our DGPs, so LPs generally have lower bias than VAR estimators. This confirms concerns voiced e.g. in the "Identification in Macroeconomics" paper by Nakamura & Steinsson.

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Christian Wolf

@ChristianKWolf

3 years

@ben_moll @1954swilliamson @SergioRebelo6 @EichMartin @GregWKaplan @glviolante @YannKoby We did a bit of work in that direction, didn't go all that far though. I'm also aware of this interesting recent paper with an explicitly modeled financial intermediation problem. @RalphLuet @MortenORavn

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Christian Wolf

@ChristianKWolf

2 years

Final point: I thought the editorial process was great. Previous drafts of the paper weren't the most accessible, but comments from the editor and referees really helped, pushing us to distill the core intuitions in very simple examples (Section 6 and this thread, hopefully 🙂).

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Christian Wolf

@ChristianKWolf

2 years

Thanks for reading! 🙂

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Christian Wolf

@ChristianKWolf

3 years

In previous work we've argued that LPs and VARs *in population* estimate the same IRFs. In any finite sample you face a bias-variance trade-off: VARs extrapolate a couple of short-horizon sample autocovariances, while LPs directly project future outcomes on current covariates.

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Christian Wolf

@ChristianKWolf

2 years

My favorite way to interpret those findings is to say that typical business-cycle models, if calibrated to my pieces of cross-sectional and time-series evidence, would invariably agree with the conclusions of the previous figure.

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Christian Wolf

@ChristianKWolf

1 year

The paper itself has lots more on the underlying mechanism, a discussion of generality & limitations, and a connection to the quantitative HANK literature. Thanks for reading!

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Christian Wolf

@ChristianKWolf

3 years

See the figure for a visual representation. It shows the time-0 consumption response to macro-equivalent rate cuts and stimulus checks as a function of household wealth. The key here are the different gradients of "direct" effects - ⬆️ for rates, and ⬇️ for transfers.

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Christian Wolf

@ChristianKWolf

2 years

Starting point: A lot of very creative work in macro recently has managed to find so-called "proxies"/"external IVs" for macro shocks, e.g. high-frequency monetary policy surprises (e.g. @peterkaradi ) or news about oil supply (e.g. @drkaenzig ).

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Christian Wolf

@ChristianKWolf

3 months

@BachmannRudi @ludwigstraub Vielen Dank, @BachmannRudi ! 🙂

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Christian Wolf

@ChristianKWolf

3 years

So what method should you choose? That depends on (a) the shape of the bias-variance frontier (which is a function of the underlying data-generating process) and (b) researcher preferences over bias vs. variance.

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Christian Wolf

@ChristianKWolf

1 year

This boom in turn helps to finance the initial deficit: more output means more tax revenue, and higher inflation erodes the real value of nominal gov't debt. We call this "self-financing" -- the deficit contributes to its own financing via eq'm adjustments in prices/quantities.

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Christian Wolf

@ChristianKWolf

2 years

But sometimes interest centers not on such dynamic causal effects, but on shock *importance* -- say, how important are news about oil supply for macro fluctuations? Our paper works out how much those IVs can tell us about shock importance (= variance decompositions).

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Christian Wolf

@ChristianKWolf

11 months

Call for papers here:

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Christian Wolf

@ChristianKWolf

1 year

Starting point: gov't runs a deficit today (say, sending out stimulus checks) and promises to finance this expenditure a couple of years down the road, through tax hikes. Our Q: how big do these future tax hikes need to be?

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Christian Wolf

@ChristianKWolf

3 years

Viewed in this light, it makes sense to think of LPs and VARs as two points on a bias-variance frontier. Other estimation techniques - penalized LP, Bayesian VARs, VAR model averaging, etc - are other points on that frontier.

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Christian Wolf

@ChristianKWolf

3 years

@nberpubs Thread with more details ⬇️

Christian Wolf

@ChristianKWolf

3 years

Just posted an updated version of my working paper on interest rate cuts & stimulus checks. Three main points on how I think about these two as macro stabilization tools.

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Christian Wolf

@ChristianKWolf

3 years

2. Reducing that bias via direct projection, however, incurs a steep cost in terms of increased sampling variance. As it turns out, only researchers with a very high concern for bias are willing to pay this cost. Two plots help make that point.

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Christian Wolf

@ChristianKWolf

1 year

We study this question in a pretty standard macro model, with two key ingredients: households are non-Ricardian -- so the initial deficit increases demand -- and prices are at least somewhat sticky -- so output is partially demand-determined. The deficit thus leads to a boom.

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Christian Wolf

@ChristianKWolf

3 years

Interest rate policy, on the one hand, gets off the ground at the top: wealthy/intertemporally substituting households respond, while constrained households with little in the way of (liquid) assets simply don't *directly* care about changes in interest rates.

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Christian Wolf

@ChristianKWolf

3 years

The first point is conceptual. In typical business-cycle macro (NK) models, interest rate policy works by re-shuffling (consumer) demand over time. Can stimulus checks do the same? Under Ricardian equivalence the answer is no, as is well-known.

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Christian Wolf

@ChristianKWolf

1 year

@SakiBigio Results apply to both surprise deficit shocks (baseline case) and deficit news shocks (same logic). Permanent shocks outside of the purview of the analysis (since we linearize).

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Christian Wolf

@ChristianKWolf

2 years

... the Lucas critique bites in a particular, limited way: through expectational effects. Empirical evidence on the propagation of distinct policy shocks is precisely what you need to deal with these expectational effects. That's the key insight of the paper.

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Christian Wolf

@ChristianKWolf

2 years

Putting everything together, I conclude that deficit-financed stimulus checks give a large (short-lived) boost to consumption, with the overall macro effect (grey) quite close to the initial cross-sectional estimate (green).

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Christian Wolf

@ChristianKWolf

3 years

The main take-away from the formula is that, with realistic MPCs, even relatively moderate checks and thus similarly moderate (and transitory) increases in gov't debt can replicate quite substantial rate cuts.

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Christian Wolf

@ChristianKWolf

2 years

The figure shows an example application, plotting the importance of IV-identified monetary shocks for several macro var's. As you can see, the lower bound is usually the trivial 0. But crucially, for several variables (e.g., inflation), the upper bound can be quite informative.

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Christian Wolf

@ChristianKWolf

2 years

As a result, if you regress macro outcomes on the IV to see how much of the volatility in the macro variables the IV "explains", then you'll get a number that's probably too low. That's attenuation bias -- no problem for relative IRFs, big problem for variance decompositions.

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Christian Wolf

@ChristianKWolf

3 years

This notion of the equivalence of different policy tools is reminiscent of Correia et al. While they view monetary policy as a sequence of price wedges and replicate those via taxes/subsidies, I view monetary policy as a sequence of net excess demands & mimic that via transfers.

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Christian Wolf

@ChristianKWolf

3 years

I give a condition - I call it strong Ricardian non-equivalence - under which time-varying paths of (uniform) transfers and taxes indeed move "demand" just as flexibly as conventional interest rate policy. As it turns out, this condition is generically satisfied in HANK models.

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Christian Wolf

@ChristianKWolf

2 years

Here's where my paper comes in. I ask: Is this approach to aggregating cross-sectional "demand" estimates actually a good idea? When does it work/when does it not? And how exactly should you do it?

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Christian Wolf

@ChristianKWolf

3 years

A bit more formally: Consider applying your favorite SVAR identification scheme. We show that a local projection with judiciously chosen contemporaneous controls will give you the same IRFs. Conversely, for any (linear) LP, we show what kind of SVAR would give you the same IRFs.

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Christian Wolf

@ChristianKWolf

2 years

The figure below shows the results. You get a sequence of policy shocks (right panel), and the procedure spits out some paths for output and inflation (blue dashed). Those don't look particularly close to the true orange counterfactual. What's going on?

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Christian Wolf

@ChristianKWolf

3 years

For the third and final point I zoom in on how interest rate cuts and stimulus checks actually go about stimulating demand in the cross-section of households.

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Christian Wolf

@ChristianKWolf

3 years

VARs and local projections are two of the most popular approaches to impulse response analysis in macro. We ask: What do the population versions of those two techniques (i.e., infinitely many lags on infinitely large samples) estimate? Answer: the same thing!

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Christian Wolf

@ChristianKWolf

2 years

Let me close with an observation & hope for future work. Our paper is still a bit of "theory ahead of measurement". Our theory reveals that having empirical evidence on distinct types of policy shocks (e.g., transitory rate changes vs. forward guidance) is extremely useful.

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Christian Wolf

@ChristianKWolf

4 years

@yfatihkarahan @MartinBeraja @arpitrage Draft with all the details will be ready in a couple of weeks, but the slides get the gist of it. In addition to policy implications, they also contain analytical characterizations that go beyond what's currently in the paper. I'll make sure to pass on the draft once we're done.

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Christian Wolf

@ChristianKWolf

2 years

Then scaling your cross-sectionally identified demand impulse by estimates of aggregate fiscal multipliers should give you something close to a true macro effect. This is the basic approach followed in much policy practice (e.g., by the CBO).

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Christian Wolf

@ChristianKWolf

2 years

The attached figures do exactly that, with more and more shocks. As you can see, the blue dashed lines converge to the orange truth. The key is what you see on the right: while Sims-Zha relies on one shock repeated over time, our result uses many shocks, *all at date 0*.

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Christian Wolf

@ChristianKWolf

2 years

Those micro regressions however don't give you aggregate causal effects, simply because they miss GE feedback like price changes or Keynesian multipliers -- things that affect all of the micro units.

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Christian Wolf

@ChristianKWolf

2 years

Long story short, the paper derives the upper bound & shows by example that it can be quite tight in applications (see next tweet). We also have a code suite available that implements all of our routines:

GitHub - mikkelpm/svma_iv: Inference in SVMA models identified by external instruments/proxies

Inference in SVMA models identified by external instruments/proxies - mikkelpm/svma_iv

github.com

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Christian Wolf

@ChristianKWolf

3 years

The equivalent transfer policy generates the opposite pattern: now well-insured Ricardian households don't care (Ricardian equivalence), while consumption of the asset-poor responds a lot.

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Christian Wolf

@ChristianKWolf

2 years

With such an IV, it's quite easy to get *relative* impulse responses -- say, how much does output respond to a monetary policy shock that moves nominal rates by 100bp. Just regress output and interest rates on the IV and compute ratios to scale as you want.

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Christian Wolf

@ChristianKWolf

2 years

The econometric identification challenge is pretty much just standard measurement error. For example, you may think that measured high-frequency monetary policy surprises only capture a subset of all monetary policy shocks.

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Christian Wolf

@ChristianKWolf

3 years

@EmilVerner @MSchularick Thanks! I'd be reluctant to extend our particular conclusions to panel settings, just because - with a large cross-sectional dimension - the nature of the bias-variance trade-off may well be very different. I.e., you may not need as much shrinkage to arrive at something precise.

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Christian Wolf

@ChristianKWolf

1 year

@BachmannRudi @ggargiulo3 @JonSteinsson Nope, quite unrelated. Dynamic/modern versions of the Haavelmo balanced-budget multiplier are in Woodford (2011, AEJ:M) or the IKC paper of Auclert-Rognlie-Straub.

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Christian Wolf

@ChristianKWolf

2 years

Of course that's conditional on certain "standard" models. In the paper I go through a list of plausible model extensions that could break the result. The main message is that, with those extensions, simple aggregation using fiscal multipliers tends to miss some GE crowding-out.

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Christian Wolf

@ChristianKWolf

3 years

The second point is a characterization of the stimulus check policy that replicates a given rate cut. In the paper I give a formula characterizing this mapping. Crucially, this formula depends only on a small number of empirically measurable "sufficient statistics".

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Christian Wolf

@ChristianKWolf

3 years

Our paper is essentially an exercise in trying to figure out what (a) looks like in typical U.S. macro time series. This then for example allows us to back out the implied researcher preferences (b) necessary to justify the use of one estimation method over the other.

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Christian Wolf

@ChristianKWolf

3 years

In a bivariate choice of LP vs. VAR, only researchers with a weight on squared bias >4x that on variance would prefer to run the LP. [Figure: Share of DGPs for which LP is preferred to VAR, as function of horizon and weight on squared bias (= 1 - weight on variance).]

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Christian Wolf

@ChristianKWolf

2 years

Suppose you have somehow estimated the aggregate effects of changes in gov't purchases (i.e., a fiscal spending multiplier). Suppose also that changes in gov't purchases and changes in private demand propagate similarly in GE, as e.g. predicted by the simple Keynesian cross.

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Christian Wolf

@ChristianKWolf

2 years

The intuitions above use static variances and covariances. Our upper bound simply refines this by in fact looking at the entire autocovariance function. [Though technically the proof turns out to work most neatly by writing everything in terms of spectral densities.]

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Christian Wolf

@ChristianKWolf

2 years

@BachmannRudi Nebenbei, für den Link Makro Shocks => (Teile von) strukturellen Modellen: Schöne Alternative zu standardmäßiger single-equation estimation.

Identifying Modern Macro Equations with Old Shocks*

Abstract. Despite decades of research, the consistent estimation of structural forward-looking macroeconomic equations remains a formidable empirical chall

academic.oup.com

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Christian Wolf

@ChristianKWolf

3 years

@EmilVerner @MSchularick That being said, the conceptual point remains: There will still be a trade-off and different methods again trace out a frontier. It would be super interesting to do a version of what we're doing here for a "canonical" (?) DGP tailored to panel settings. Maybe for future work :)

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Christian Wolf

@ChristianKWolf

2 years

To go from cross-sectional spending estimates to macro counterfactuals, pretty much all the information you need is contained in fiscal multipliers -- a "sufficient statistics" type result consistent with the basic Keynesian cross intuition.

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Christian Wolf

@ChristianKWolf

2 years

A standard approach is to build a fully-specified model that matches empirical evidence on policy shocks, and then trust this model as a laboratory for policy counterfactuals. The obvious appeal is robustness to the Lucas critique; the obvious concern is model mis-specification.

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Christian Wolf

@ChristianKWolf

2 years

We claim that you can get at this *without* knowledge of the structural equations of the model. Rather, the only thing you need are the effects of *shocks* to the prevailing monetary rule — that is, the monetary policy shocks that SVARs/local projections promise to give you.

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Christian Wolf

@ChristianKWolf

2 years

@BachmannRudi Im Prinzip kannst du auch Spektren schätzen und dann deine Identifikationsannahmen auf das Spektrum setzen -- wird dir (in population) die gleichen Antworten geben. Gleiches gilt für local projections.

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Christian Wolf

@ChristianKWolf

2 years

We discuss in detail when this logic applies/when it fails, and then turn this theory of identification into an actually implementable empirical method. We also present several empirical applications.

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Christian Wolf

@ChristianKWolf

2 years

But this suggests a fix: identify more policy shocks! (e.g., both transitory as well as persistent shocks to interest rates = forward guidance). Intuitively, with more policy shocks, you can enforce the counterfactual rule not just ex post *but also in ex ante expectation*.

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Christian Wolf

@ChristianKWolf

2 years

@BachmannRudi Deswegen fange ich in meinem Unterricht mit einem SVMA an -- jedes linearisierte Makro Modell gibt dir ein solches SVMA. Die lecture notes hier fassen meine Sicht auf das Identifikationsproblem in diesem Rahmen zusammen:

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Christian Wolf

@ChristianKWolf

3 years

@mickey_gb @_LukasFreund_ Super closely related - exactly the same objective (finding equivalent policies), just the proof strategy is a bit different.

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Christian Wolf

@ChristianKWolf

3 years

@AlisdairMcKay 👀

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Christian Wolf

@ChristianKWolf

2 years

The theoretical results in my paper say that, to aggregate these estimates, the "right kind" of fiscal multiplier is one for a similarly transitory, deficit-financed uptick in gov't spending. I estimate that, and find a multiplier around (or slightly below) 1.

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Christian Wolf

@ChristianKWolf

2 years

@BachmannRudi Aber warum sollten wir genauso viele Schocks wie observables haben? n Schocks sind genug um jede möglichen zweiten Momente zu generieren, aber n + X shocks können das genauso gut. Nur dann wird das Identifikationsproblem sehr viel härter.

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Christian Wolf

@ChristianKWolf

2 years

The upshot is that, when aggregating via fiscal multipliers, you get something that's usually best interpreted as an *upper bound*. I however also give some conditions under which this upper bound is likely to be tight (= close to the truth).

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Christian Wolf

@ChristianKWolf

1 year

@cmatthes_econ Thanks! The writing improved a lot through the editorial process. Best not to look at the early drafts 😬

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Christian Wolf

@ChristianKWolf

2 years

@BachmannRudi Wenn du mit einem n-variable VAR anfängst, dann denkst du auch sehr natürlich in strukturellen Modellen mit n Schocks. Sobald du so viele Schocks wie Variablen hast hält Invertibilität sehr häufig (und "recoverability" hält immer, e.g. siehe p.2182 hier: ).

Instrumental Variable Identification of Dynamic Variance Decompositions | Journal of Political...

Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement...

www.journals.uchicago.edu

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Christian Wolf

@ChristianKWolf

3 years

With finitely many - say, p - lags in both VARs and LPs, the equivalence holds up to IRF horizon p (roughly speaking, in a sense made precise in the paper). It's thus not surprising that, in empirical practice, LPs and VARs are often close at short horizons.

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Christian Wolf

@ChristianKWolf

2 years

Let me illustrate the basic idea with a thought experiment. To fix ideas let's suppose that the true data-generating process was some standard quantitative business cycle model, say Smets-Wouters (2007). You now want to know how, in this particular economy, ...

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Christian Wolf

@ChristianKWolf

2 years

Unfortunately it's hard to find such variation. One response is to look at cross-sectional data, e.g. exploiting differences in *when* people got checks. Loosely speaking, such cross-sectional analysis can tell you by how much the checks stimulated "demand".

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Christian Wolf

@ChristianKWolf

4 years

@_LukasFreund_ @AndresFreundPol @MartinBeraja However long COVID restrictions will be in place -- our argument is simply that the recovery will be slower than in a hypothetical alternative scenario where you had those restrictions not on services, but on durables consumption.

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Christian Wolf

@ChristianKWolf

1 year

@SakiBigio Finally, with partially sticky prices and nominal gov't debt, the cumulative fiscal multiplier gets strictly smaller in both cases, with some of the financing coming through inflation instead.

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Christian Wolf

@ChristianKWolf

2 years

Then monetary policy shocks can't possibly account for much of the overall movements in inflation. Why? If they did, then they would account for more than the *entire* overall variation in interest rates, which can't be true.

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Christian Wolf

@ChristianKWolf

2 years

By the same token, suppose interest rates and inflation were positively correlated in data, but are moved in opposite directions by the monetary IV. Then again monetary shocks couldn't account for much of the overall variation in the data, as they give the "wrong" co-movement.

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Christian Wolf

@ChristianKWolf

2 years

In the paper we revisit a classical question: Can we use the long empirical literature that studies the propagation of policy *shocks* to learn about the likely effects of changes in systematic policy *rules*? (say, predicting the effects of switching to nominal GDP targeting)

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Christian Wolf

@ChristianKWolf

2 years

We want to instead see how far you can get without committing to a particular model. Our main result is that — under some assumptions of course, but assumptions that fall short of assuming a specific model — you *can* say something without running afoul of the Lucas critique.

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Christian Wolf

@ChristianKWolf

2 years

My point of departure is a "quantitative" macro model (think: NK-DSGE/HANK). I give conditions under which evidence on the "right kind" of fiscal multiplier (more on this below) is really all you need to transform cross-sectional spending estimates into macro causal effects.

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Christian Wolf

@ChristianKWolf

2 years

The existing empirical evidence is already rich enough for us to construct *some* counterfactuals (see our applications), but of course knowing the effects of even more shocks would mean we could construct even richer counterfactuals. In light of this I think it's ...

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Christian Wolf

@ChristianKWolf

2 years

The fact that direct regression gives you a *lower bound* on shock importance is thus pretty much immediate. Our main contribution is to work out the *upper bound*. But why should there be an interesting/non-trivial upper bound? Let me try to give intuition through examples.

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Christian Wolf

@ChristianKWolf

2 years

Say you have an IV for monetary policy shocks, and let's say also that you observe two macro variables, inflation and interest rates. Suppose both of them have the same overall variance, but an innovation to your monetary policy IV moves interest rates much more than inflation.

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