Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Thursday, April 7, 2022

What economic model produces the Fed's inflation forecast?

John Cochrane's blog has always been a favorite of mine. It's provocative. It's entertaining. And it invariably leads me to reflect on a variety of notions I have floating around in my head. 

In his latest piece,  he asks an interesting question: How does the Fed come up with its inflation forecast? What sort of model might be embedded in the minds of FOMC members? I like the question and the thought experiment. My comments below should not be construed as criticism. Think of them more as thoughts that come to mind in a conversation. (It's more fun to do this in public than in private.)

John begins with the observation that while the Fed evidently expects inflation to decline as the Fed's policy rate is increased, at no point in the transition dynamic back to 2% inflation is the real rate of interest very high. To quote John (italics in original): the Fed believes inflation will almost entirely disappear all on its own, without the need for any period of high real interest rates. Of course, this is in sharp contrast with the Volcker disinflation, an episode that demonstrated, in the minds of many, how a persistently high real rate of interest was needed to make inflation go down (some push back in this paper here).

John believes that the current inflation was generated in large part by a big fiscal shock in the form of a money transfer (an increased in USTs unsupported by the prospect of higher future taxes). I'm inclined to agree with this view, though surely there other factors playing a role (see here). John asks how this type of shock can be expected to generate a transitory inflation with the real interest rate kept (say) negative throughout the entire transition dynamic. Below, I offer a simple model that rationalizes this expectation. Whether it's the model FOMC members have in their heads, I'm not sure. (Well, I happen to know in the case of two FOMC members, but I won't share this here.)

Formally, I have in mind a simple OLG model (see, here). The model is Non-Ricardian (the supply of government debt is viewed as private wealth). The model's properties are more Old Keynesian than New Keynesian. The model is also consistent with Monetarism, except with the supply of base money replaced with the supply of outside assets (i.e., all government securities--cash, reserves, bills, notes and bonds). 

So, I'm thinking about my model beginning in an hypothetical stationary state. The real economy is growing at some constant rate (say, zero). The supply of outside assets consists of zero interest securities (monetary policy is pegging the nominal interest rate to zero all along the yield curve). This supply of "debt" is also growing at some constant rate. Debt is never repaid--it is rolled over forever. Indeed, the nominal supply of debt is growing forever. New debt is used to finance government spending. The real primary budget deficit is held constant. The government is running a perpetual budget deficit via bond seigniorage; see here. The steady-state inflation rate in this economy is given by the rate of growth of the supply of nominal outside assets. (It is also possible that the inflation rate is determined by shifts in the demand for USTs; see here, for example). The real interest rate (on money) is negative. 

OK, now let's consider a large fiscal shock in the form of a one-time increase in the supply of outside assets (i.e., a helicopter drop of money that is never reversed).  The effect of this shock is to induce a transitory inflation (a permanent increase in the price-level). An increase in the nominal supply of money at a given interest rate at full employment makes the cost of living go up -- it makes the real debt go down. And oh, by the way, the debt-to-GDP ratio is declining thanks in part to inflation:

This is despite the persistent negative real interest rate prevailing in the economy. I mean, what else might one imagine from a one-time injection of money? Is this is what the Fed is thinking? (This is what I'm thinking!) Note: an increase in the interest rate in this model would unleash a disinflationary force, but this would only serve to speed up the transition dynamic. 

As it turns out, this simple story seems consistent with what I take to be John's preferred theory of inflation. The large fiscal shock here is unaccompanied by the prospect of future primary budget surpluses. The effect is to increase the price level (i.e., a temporary inflation). Maybe the Fed has John's FTPL model in mind? 

Neither of these stories line up particularly well with the New Keynesian model, which emphasizes interest rate policy as *the* way inflation is controlled. There are, however, many strange things going on in this model. First, while no explicit attention is paid to fiscal policy, the fiscal regime plays a critical role in determining model dynamics (basic assumption is lump-sum taxes and Ricardian fiscal regime). Second, the Taylor principle that is needed to determine a locally unique rational expectations equilibrium is an off-equilibrium credible threat to basically blow the economy up if individuals do not coordinate on the proposed equilibrium (I learned this from John here.)  By the way, Peter Howitt provides a different (and in my view, a more compelling) explanation for the "Taylor principle" here--published a year before Taylor 1993. Given these shortcomings, why are we even using this model as a benchmark? This is another good question. 

John presumably picks this model because he sees no better alternative for modeling monetary policy via an interest rate rule. If he wants an alternative, he can read my paper above. Or, he can appeal to his own class of models extended to permit a liquidity function for USTs. These models easily accommodate stable inflation at negative real rates of interest. But whether this is how FOMC members organize their thinking, I'm not sure.

In any case, John picks an off-the-shelf NK model and assumes that it adequately captures what is in the mind of many FOMC members. Let's see what he does next (Modeling the Fed). 

He writes: "The Fed clearly believes that once a shock is over, inflation stops, even if the Fed does not do much to nominal interest rates. This is the "Fisherian" property. It is not the property of traditional models. In those models, once inflation starts, it will spiral out of control unless the Fed promptly raises interest rates." [I think he meant "threatens to raise interest rates.]

Comment 1: I'm not sure what he means by a "Fisherian" property. (Note: the Fisher equation holds in the OLG model I cited above--though the real rate of interest is not generally fixed in those settings.) 

Comment 2: Conventional models? I presume he means Woodford's basic NK model. It seems likely to me, however, that FOMC members may have other "conventional" models in their heads -- like the Old Keynesian model or the Old Monetarist model--both of which continue to be taught as standard fare in undergraduate curricula.  

OK, so John considers a very basic IS-PC model and considers two alternative hypotheses for how inflation expectations are determined. The first hypothesis is a simple adaptive rule (see also Howitt's work above). The second hypothesis is perfect foresight (rational expectations) -- which, by the way, implicitly embeds knowledge of the Ricardian fiscal regime. 

Under the adaptive expectations model, inflation explodes. Under the rational expectations hypothesis, inflation largely follows the Fed's actual forecast. Maybe this is what the Fed is thinking? The Fed has rational expectations? 

Except that I'm not really sure what this means. John does give us a further hint though. He goes on to say "Not only is the Fed rational expectations, neo-Fisherian, it seems to believe that prices are surprisingly flexible!" 

Right. So the Neo-Fisherian hypothesis is that to get a permanently lower rate of inflation, the Fed must (at least eventually) lower its policy rate (and vice versa to raise the rate of inflation). I've questioned this hypothesis in the past (see here). But what's going on here now? Is John suggesting that the FOMC is made up of closet Neo-Fisherians? Steve Williamson would no doubt be pleasantly surprised. 

John writes: "The proposition that once the shock is over inflation will go away on its own may not seem so radical. Put that way, I think it does capture what's on the Fed's mind. But it comes inextricably with the very uncomfortable Fisherian implication. If inflation converges to interest rates on its own, then higher interest rates eventually raise inflation, and vice-versa." 

No, I'm afraid the conclusion that inflation is transitory (even with negative real rates) is NOT inextricably linked to the Neo-Fisherian proposition. It is only inextricably linked this way in a class of economic models that: [1] are pretty bad; and [2] highly unlikely to be in the heads of most FOMC members. 

Saturday, January 29, 2022

The Inflation Blame Game

Inflation is back together with a new season of America's favorite sport: zero-contact, finger-pointing. I thought I'd sit back and share a few thoughts with you on the subject on this cold Saturday afternoon. Use the comments section below to let me know what you think.

In one corner, I see some pundits somehow wanting to blame the 2021 inflation on workers. Workers are somehow forcing their improved bargaining positions on employers, raising the costs of production, with some or all of these costs passed on to consumers. Then, as workers see their real wages erode, the cycle begins anew begetting the dreaded "wage-price spiral." Those pesky workers. 

There's no doubt something to the idea that wage demands can lead to higher prices (and why shouldn't workers want cost-of-living adjustments?) But what is the evidence that this behavior was the impulse behind the 2021 inflation? 

While it's difficult to tell just by eye-balling the data, I think it's reasonable (under this hypothesis) to see wage growth precede (or at least be coincident with) inflation. Unfortunately (for this hypothesis), this is not what we see in the data. In the diagram below, use the Atlanta Fed's Wage Growth Tracker to construct nominal wage inflation for the bottom (green) and top (yellow) wage quintiles. This is plotted against CPI inflation (blue). 

Another problem for this hypothesis is that wage inflation is moving in the wrong direction for the top three wage quintiles over the Covid era. What we see here is a clear acceleration in the rate of inflation, followed by modest acceleration in wage inflation for the bottom quintile and a deceleration in wage inflation for the top quintile. In 2021, real wages across all quintiles declined (according to this data). So much for increased worker bargaining power. [Note: it is quite likely that net income for the bottom one or two quintiles increased, thanks to government transfers.] 

On the other side of the political spectrum, we see pundits and politicians blaming the 2021 inflation on "corporate greed." Framing the issue in terms of "corporate greed" is not especially helpful, in my humble opinion. The substantive part of this claim is that large firms were somehow able to leverage their pricing power in 2021 into higher profit margins and record corporate profits. There is, in fact, some evidence in support of this. The diagram below plots profit margins for firms in the Compustat database. Profit margin below is computed on an after tax basis (net income divided by sales). The data is divided between large and not-large firms. Large firms are those in the top 10% of sales volume.


By this measure, profit margins seem remarkably stationary over long periods of time. There is some evidence of a modest secular increase in margins c. 2003. Large firms have higher margins. But the part I want to focus on here is near the end of the sample. Profit margins for 90% of firms seem close to their historical average. We see some evidence that profit margins for the top 10% of firms increased in 2021. But this increase peaked in Q3 and then declined back to historical norms in Q4. While the spike in profit-margins likely contributed to inflation, it hardly seems like a smoking gun. And the Q4 reversion to the mean suggests that "corporate greed" is not likely to be a source of inflationary pressure in 2022. 

Well, if workers and firms are not to blame, then who or what is left? There's the C-19 shock itself, of course, along with the effects it has had on the global supply chain. But the 19 in C-19 refers to the year 2019 (and 2020). We're talking about 2022 here. Sure, the supply chain issues are still with us. But at most, I think they account for a substantial change in relative prices (goods becoming more expensive than services) and an increase in the cost-of-living (an increase in the price-level--not a persistent increase in the rate of growth of the price-level). 

While the factors above no doubt contributed in some way to the 2021 inflation dynamic, let's face it--the size and persistence of the inflation was mainly policy-induced. The smoking gun here seems to be the sequence of the C-19 fiscal transfers. As we know, this had the unusual and remarkable effect of increasing personal disposable income throughout most of the pandemic. The Fed also had a role to play here because it accommodated the fiscal stimulus (normally, one might have expected a degree of monetary policy tightening to partially off-set the inflationary impulse of fiscal stimulus). Below I plot retail sales (actual vs trend) and the timing of the fiscal actions. 

I used retail sales here (I think I got this from Jason Furman), but the picture looks qualitatively similar using PCE (the path of nominal PCE went above trend in 2021 and not earlier in the way retail sales did). Just eye-balling the data above, I'd say the CARES Act was a major success (especially under the circumstances). The subsequent two programs might have been scaled back a bit and/or targeted in a more efficient manner. And, knowing what we know now, the Fed could have started its tightening cycle in 2021. 

Having said this, I wouldn't go so far as to say these were flagrant policy mistakes--given the circumstances. If there was a policy mistake, it was in not having a well-defined state-contingent policy beforehand equipped to deal with a global pandemic. Not having that plan in place beforehand, I think monetary and fiscal policy reacted reasonably well.

Policymaking in real-time is hard. And policy, whether formulated beforehand or not, must necessarily balance risks. There was a risk of undershooting the support directed to households. We saw this during the foreclosure crisis a decade ago. And there was a risk of overdoing it in some manner. Keep in mind that it was not clear when the legislation was passed how 2021 would unfold. Similarly, for the Fed--perhaps still feeling the sting of having moved too soon and too fast in the past, hopeful that inflation would decline later in the year--delayed its tightening cycle to 2022. It wasn't perfect. But taken together, the economic policy responses had their intended effect of redistributing income to those who suffered disproportionate economic harm during the pandemic. 

Finally, what does all this mean for inflation going forward? Well, as I suggested above, I don't think we have to worry about a wage-price spiral (the fiscal policy I think is necessary to support such a phenomenon is not likely to be present). Profit margins appear to be declining (reverting to their long-run averages). The money transfers associated with the last fiscal package are gone for 2022. No big spending bills seem likely to pass in 2022. For better or worse, we're talking a considerable amount of "fiscal drag" here (although, some have pointed to how flush state government coffers are at the moment). Hopefully (fingers crossed), supply-chain problems will continue to be solved. If so, then all of this points to disinflation (a decline in the rate of inflation) going forward. Some recent promising signs as well: [1] month-over-month CPI inflation has declined for two consecutive months (November and December); and [2] the ECI (employment cost index) decelerated in Q4 of 2021. (These numbers are notoriously volatile, so don't put too much stock in the direction. But still, it's better than seeing them go the other way.)

Some caveats are in order, of course. In December 2020, I suggested we prepare for a "temporary" burst of inflation in 2021. While this came to pass, the level of inflation surprised me (to be fair, I hadn't incorporated the ARP in my assessment, but even if I had, I think I still would have been surprised). Moreover, I was also surprised by the persistence of inflation--I thought it would decelerate more rapidly (even given the ARP). This just serves to remind me how bad I am at forecasting. Someone recently mentioned a great quote by Rudi Dornbusch: "In economics, things take longer to happen than you think they will, and then they happen faster you thought they could." I can relate to this. 

Inflation may turn out to be more persistent that I am suggesting. But how might this happen, given the disinflationary forces I cited above? One reason may have to do with the tremendous increase in outside assets the private sector has been compelled to absorb--the increase in the national debt has manifested itself as an increase in private sector wealth. Jason Furman sees this as "excess saving." The question going forward is whether the private sector will be compelled to spend this (nominal) wealth (it already has done so, as my chart above shows) or continue to save (not spend) it? It is possible that this "pent up demand" will be spent over a prolonged period of time. The effect of this would be to keep inflation elevated higher than it would otherwise be (serving to reduce real nominal wealth). How long this might take, I have no idea. But even so, it seems clear that the effect cannot persist indefinitely. At some point the debt-to-GDP ratio will decline to its equilibrium position (D/Y has already started to decline; see here). 

Another reason why inflation forecasts should be discounted is that it's very difficult to forecast future contingencies. What might happen, for example, if Russia invades the Ukraine this year? Events like these will create disruptions and there's not much monetary and fiscal policy can do about them. But whatever happens, I think the long-run fiscal position of the U.S. will remain anchored (Americans will demand this). And remember, the Fed is bound by its Congressional mandates to keep inflation "low and stable." The Fed's record on inflation since the Volcker years has been pretty good. I'm betting that the record will be equally good over the next 10 years.


PS. I see some people out there strongly asserting it is a "fact" that fiscal policy did not cause the 2021 inflation (see here, for example). The reason, evidently, is because inflation is a global phenomenon. There's something to this, of course. After all, C-19 is a global pandemic. But this reasoning nevertheless seems faulty to me. First, the USD is the global reserve currency. It's quite possible that the U.S. exported some of its inflation to the world (much in the way it did in the 1970s). Second, many other countries (like Canada, for example) adopted similar fiscal policies. Those countries with less expansive fiscal policies also displayed lower inflation, as far as I know. Rather than deflect the blame, we should own it here. Fiscal policy had a lot of positive effects too (e.g., lowering child poverty). The challenge, as always, is to develop ways to calibrate these policies in a more effective manner. 

Some Thoughts on the Fed's CBDC Report

Economists within the Federal Reserve System have been musing about central bank digital currency for a while now. For example, yours truly provided a few thoughts on the possibility way back in 2015 (see here) and most recently here. But the views of individual Fed researchers are simply our own personal views. What people are really interested in is an official view--namely the view of the Board of Governors of the Federal Reserve. At long last, their report is now available here). 

The report makes it clear that the Fed has no immediate plans to issue a CBDC. The main purpose of the report is to provide some background information, discuss the potential costs and benefits of a CBDC, and solicit feedback from the general public. It is a very nice educational piece. There was nothing really new in it for people who have been following the discussion over the past few years, but there was one thing I found interesting (and potentially important). The interesting part, I think, has to do with their definition of CBDC:

For the purpose of this paper,  a CBDC is defined as a digital liability of the Federal Reserve that is widely available to the general public.
I used bold font to highlight the important part in the passage above. Most of the digital money Americans use today consists of dollar credits in transaction accounts that reside in the broader bank sector (which includes non-banks providing digital payment services). This form of digital money is technically a liability of private sector agencies, not the government. Is this an important distinction to make? I'm not sure--I suppose it depends on what one thinks is important. 

For one thing, the Board's adopted definition appears to rule out the "wholesale CBDC" proposal that some have advocated for (including myself). Wholesale CBDC (also referred to as "synthetic CBDC" or "sCBDC") is essentially a narrow-banking proposal (which has a long history in the banking policy debate). 

In my writings, I contrasted "wholesale CBDC" with "retail CBDC," the latter of which I interpreted as a product that is both a liability of the Federal Reserve and a payment service managed by the Federal Reserve. I thought this latter property was a bad idea--the Fed should probably not get involved with the challenges of retail banking. I missed the possibility of separating the legal status of digital money from the agencies responsible for managing digital money accounts. As George Selgin explains well here, the Board's definition of CBDC means a privately-intermediated liability of the Federal Reserve (George calls this iCBDC to distinguish it from sCBDC). 

Speaking for myself, I'd be happy with either an sCBDC or an iCBDC (assuming they are properly designed). My main concern was over the prospect of a government agency operating a large retail business. Both sCBDC and iCBDC are intermediated products--we can let the private sector manage the day-to-day operations of processing payments. George, however, believes that sCBDC should be preferred to iCBDC for reasons that he spells out here (I'm not sure I share his concerns).

My own view is that the distinction between sCBDC and iCBDC will be of interest mainly to lawyers and regulators (John Kiff points me to this IMF report). From an economic perspective, the two products appear to be very close--if not perfect--substitutes (again, assuming their design is optimized). The practical difference between a Federal Reserve liability and a private liability fully-insured by the government seems almost non-existent to me. But I'm willing to be persuaded otherwise.