So if the Fed raises interest rates, how much and how soon will that help inflation? For another project, I went back to Valerie Ramey's classic review. Here is her replication and update of two classic estimates:

The left side tells us what the federal funds rate typically does after the Fed raises it. The right shows the effect of the rate rise on the

*level*of the CPI. Inflation is the slope of the curve. The horizontal axis is quarters. The top panel uses a vector autoregression. The bottom panel uses the Romer and Romer reading of the Fed minutes to isolate a monetary policy shock.

Top pane (VAR): Multiplying by 10, a 2 percentage point rise in the funds rate (blue dash) might lower cumulative inflation by one percentage point in three years (12 quarters), before it runs out of steam. The black line is the most hopeful, but it is essentially the 1980 experience. Still, multiplying by 5, a 2 percentage point rise in the funds rate only lowers inflation half a percent in those first three years (12 quarters), though after 10 years (40 quarters) you get a full percentage point reduction in the price level.

Bottom panel (Narrative): In the black and red lines that include the 1980 shock, a 3% rise in interest rate produces no noticeable decline in inflation for the first three years. 10 years later, the price level is a decent 4 percent lower, but that is 0.4% per year reduction in inflation. The blue lines that exclude 1980 show a plausible longer-lasting shock, but 1% higher interest rate only produces 1% lower price level in 10 years, m 0.1% per year.

The problem is the ephemeral Phillips curve, which I emphasized in my WSJ oped. In the VARs, the Fed is pretty good at inducing a recession. Here are the Romer-Romer shocks' effects on output and unemployment:

It's just that inducing recessions is not particularly effective at lowering inflation.*any*effect on inflation, or even a positive one:

No theory today, just the facts. This is the empirical basis for the idea that the Fed can swiftly stop inflation by raising interest rates. The underlying machinery does the best that 50 years on the topic has been able to do to separate causation from correlation, and to isolate the Fed's actions from other influences on inflation. Perfect, no, but this is what we have.

*Update:*A few Twitter commenters say that we really don't get much out of "normal times" and we have to look to big "regime shifts." 1980 is an example, and the results with and without 1980 are telling. But that is perhaps the point. If so, then it will take a "regime shift" to tame inflation not the usual "tools."

What about the transition channels of the monetary system?

ReplyDeletePerhaps a little bit of policy experimentation might help here, as I suggested here: https://link.medium.com/WsrrEZpdorb

ReplyDeleteThe money stock can never be properly managed by any attempt to control the cost of credit. Interest is the price of credit. The price of money is the reciprocal of the price level.

ReplyDeleteThe distributed lag effect of money flows, the volume and velocity of money have been mathematical constants for > 100 years (not "long and variable").

From the standpoint of monetary authorities, charged with the responsibility of regulating the money supply, none of the current definitions of money make sense. The definitions include numerous items over which the Fed has little or no control (e.g., M2), including many the Fed need not and should not control (currency). The definitions also assume there are numerous degrees of “moneyness”, thus confusing liquidity with money (money is the “yardstick” by which the liquidity of all other assets is measured). The definitions also ignore the fact that some liquid assets (time deposits) have a direct one-to-one, relationship to the volume of demand deposits (DDs), while others affect only the velocity of DDs. The former requires direct regulation; the latter simply is important data for the Fed to use in regulating the money supply.

Salmo,

Delete"Interest is the price of credit."

Interest is the cost of time associated with any non-simultaneous transaction.

If I am willing to give you $25,000 for a car that you are willing to deliver to me today, but only $20,000 for the same car that you are willing to deliver to me two years from now, I am effectively charging interest on the money that I am paying you now for a car delivered two years from now.

Notice that legally, I am not lending you $20,000, and you are not borrowing $20,000. A borrower / lender agreement is one in which a good is given from one party to another with the expectation that the same good (or a fungible equivalent) is delivered at a later date.

You are presuming that interest is strictly limited to borrower / lender agreements. This is not the case.

"If I am willing to give you $25,000 for a car that you are willing to deliver to me today, but only $20,000 for the same car that you are willing to deliver to me two years from now, I am effectively charging interest on the money that I am paying you now for a car delivered two years from now."

DeleteNot quite. Presuming that the vehicle is still worth $25,000 in two years time, and the seller accepts your proposal, the rate of interest is the current market rate, r , while the discount rate, ρ , is adjusted for risk associated with the delivery event two years hence.

The economics fit neatly into Cochrane's macro model. The utility of taking delivery of the vehicle today is U(C(t)); the utility of deferring delivery for T years is βᵀ∙Eₜ{U(C(t + T))}. The discount factor is βᵀ∙Eₜ{U'(C(t + T))}/U(C(t)) = 1/(1+r)ᵀ.

See Williamson, S., "Asset Pricing", Sept. 2020: https://drive.google.com/file/d/1gelOJSOM5kmbhWBx29x3n_JZY4kZm1mx/view

The expectation is conditional on the future state -- the forward delivery date. In effect, the discount takes into consideration both the current cost of money, r , and the chance event of delivery T periods forward.

Economic theory neatly explains the difference and how it relates to the observed subjective discount rates applied to a game of chance (e.g., the future delivery of a commodity). r is the risk-free rate of interest, e.g., 13-week T-bill discount rate.

S. Trutta's observation stands.

"Presuming that the vehicle is still worth $25,000 in two years time, and the seller accepts your proposal, the rate of interest is the current market rate, r, while the discount rate, ρ, is adjusted for risk associated with the delivery event two years hence."

DeleteThe rate of interest r already incorporates the risk associated with the delivery event two years hence.

"r is the risk-free rate of interest, e.g., 13-week T-bill discount rate"

Ultimately there is no such thing as a risk-free rate of interest since none of us are going to live forever. If I buy a 13 week T-bill today and die two weeks from now, was that investment risk free?

As I expect you know, the only certainties in life are death and taxes. The T-bill will be settled at maturity and the proceeds paid to your estate. I had similar situation arise when my passed away suddenly and unexpectedly during 2020. Her investment portfolio included $50,000 (face value) Treasury bills maturing at maturities ranging from 2 weeks after her death to 6 months after death. The estate rec'd full value $50,000. I thought that you might perhaps challenge Steve Williamson's asset pricing algorithm. It differs from the run-of-the-mill net present value formula that my engineering class was taught in the 1970s, and, in truth, I've never seen it applied in practice in any industrial project evaluation during Capex budgeting in the states or SE Asia when I was active as an executive officer or a consulting executive.

Delete"The T-bill will be settled at maturity and the proceeds paid to your estate."

DeletePresuming that there is an estate, the transfer will not be taxed, and the owner of said T-Bills is investing with an eye towards transferring those assets to a beneficiary.

All three of your "conditions" are met: (1) an estate is created at the time death, (2) the transfer is not taxed, (3) the beneficiaries receive the residue of the estate after creditors have been paid.

Delete"All three of your conditions are met: (1) an estate is created at the time death, (2) the transfer is not taxed, (3) the beneficiaries receive the residue of the estate after creditors have been paid."

DeleteIn your example ($50,000 portfolio), perhaps.

In the general case:

(1) The owner of the securities may not have any living heirs

(2) The owner of the securities may have total assets that exceed the tax free limit on inheritance

(3) The owner of the securities may not want to give his living heirs anything at time of death

My point was and still is, the notion of a "risk free" rate of interest is effectively meaningless.

Heirs are one class of beneficiary. In the absence of heirs, and a Will naming beneficiaries that are not heirs, the beneficiary of the residual estate is the State government. The incurrence of an income tax liability does not negate or derogate the payment of asset value and income to the estate upon death of the annuitant. "Risk-free asset" is not conditional on the three conditions you have chosen to stipulate.

DeleteYour last sentence expresses a personal opinion. In practice, esp. in financial economic modeling studies, the "risk-free asset" is typically taken to be the 13-week Treasury bill ("T-bill"). You will find this usage in option pricing formulas, stock and bond portfolio pricing models, and in the valuation of going-concern businesses, and in capital asset investment decision-making models. Occasionally, the zero-Beta asset is substituted for the U.S. T-bill as the risk-free asset. In that instance, the risk of the asset is fully diversifiable and, accordingly, the specific risk is not priced in.

For the U.S. T-bill to be deemed not to be a "risk-free asset", the U.S. economy would have to be in deep peril with no expectation of the government being capable of redeeming its obligations to creditors. You'd have to have a major disaster or a broad irredeemable defeat in a military conflict or war to find the country in such a position.

But, of course, "risk-free" pertains to the return of principal, typ. "nominal" dollars, and it does not include the loss of purchasing power through the effects of money supply inflation, such as we have at present or which we had during Paul Volker's term as chairman of the Federal Reserve Bank. To that extent, the term "risk-free" is a conditional statement subject to the context in which it is used.

"To that extent, the term risk-free is a conditional statement subject to the context in which it is used."

DeleteAgreed. I find that economists use the term in a loosey-goosey sense without clarifying the specific risks they are ignoring.

In a U.S. context, the risk is the probability of an event of default or dishonor of the debt by the U.S. Department of the Treasury. The probability of the event occurring increases whenever the Congress's statutory borrowing limit is approached. When the statutory borrowing limit is well above the actual face value of the total federal debt issued and outstanding, the U.S. Treasury is able to redeem the debt on the due date by payment of nominal dollars (the numeraire), and the debt is considered "risk-free" in that sense. Whatever else it is, you can always use a dollar to pay your tax liabilities and debts private and public (the "legal tender" declaration). Typically, the "risk-free" asset is not a variable of interest in an economic problem or theory (e.g., modern portfolio theory, CAPM, the weighted average cost of capital when used to determine the discount rate in a present value calculation, or option pricing algorithms). And, it's not just economists who follow that practice, but engineers also, and managers of investment portfolios, etc.

DeleteGiven the very high correlation between the Fed balance sheet and S&P500 performance, how powerful of a tool is balance sheet reduction, by comparison? What could we expect from shrinking from $9t to $8t?

ReplyDeleteNice try with your regime shift proposal

ReplyDelete"Big Regime shifts." Inflation vs. Stock Market Returns

ReplyDeletePosted October 24, 2021 by Ben Carlson. I used his data from the highest years of inflation with corresponding S&P 500 returns to run an OLS. I regressed returns on inflation. To wit. S&P returns = 7.17 + .256 Inflation. Rho was very low. .04 and R^2 was.006. Slope not significantly different than horizontal. Average return was 9.45% Vol 17.5%. Orderly markets? Average inflation was 8.75% with SDEV of 2.76. Maybe the markets are better managers of inflation than the Federal Reserve. The data were a small sample of 17 data points.

The Fed CAN use an interest rate tool to reduce inflation as long as those interest rate changes can be made independently of fiscal policy.

ReplyDeleteSee:

https://musingsandrumblings.blogspot.com/2019/09/the-case-for-equity-sold-by-u.html

The Fed doesn't control interest rates. It controls its own overnight lending rate and that's about it. It can add to and subtract from reserves, which it has done so the last 15 years, adding an incomprehensible $8 trillion in reserves, enough to support $72 trillion in new loans, assuming a 10% reserve. This has a great effect on interest rates. But eventually the party must come to an end. Interest rates have an international flavor. The nations that deluge reserves, sharply lowering domestic interest rates, must ultimately pay the price when market conditions turn. And have they turned. Japan is suffering. And so shall many others.

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteI follow the Fraser Institute of Canada. I enjoy the perspective on the US. I thought of you as I read this article: Fiscal Costs of Debt-Financed Government Spending.

ReplyDeletehttps://www.fraserinstitute.org/studies/fiscal-costs-of-debt-financed-government-spending?utm_source=Facebook-and-Twitter&utm_campaign=Fiscal-Costs-of-Debt-Financed-Government-Spending&utm_medium=Social&utm_content=Learn_More&utm_term=531

Great post. This post sheds some much needed light on a very basic issue. There is a widely held view that somehow the Fed can "steer the ship" of the US economy. Unfortunately, the data and facts point to the opposite. One would think that surely the Fed can impact inflation as inflation is a monetary phenomenon but, alas, the data show otherwise. People should consider this evidence when they trot out the notion that the Fed can impact the real economy. If they can't move the needle on inflation then the case for doing so with the real economy is exceptionally weak. As an aside, I agree with the point about 1980. We effectively had an explosive monetary/fiscal expansion and the Fed could decide to "undo it" but unless they go as extreme on the backside as they did on the frontside then elevated inflation is here to stay (in levels at least).

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteHi Professor Cochrane,

ReplyDeleteWhen I use Ramey's original code and data to estimate the Christiano et al. (1999) VAR over 1959m1-2007m12, I find that a 0.4 percentage point increase in Fed funds rate causes only a 0.2 percent drop in price level over four years (48 months). The magnitude seems small to me.

Next, using the Romer and Romer shocks over 1969m1-2007m12 in the 'Coibion VAR', I find a 0.25 percentage point shock to Fed funds rate causes a 0.4 percent drop in price level over 48 months. Bigger than the above, but still seems small.

Last, using Romer and Romer shocks in local projections over the same period, I find a 1 percentage point shock to Fed funds rate causes price level to drop by about 2 percent in 48 months. The magnitude is similar to the above.

Overall, I am surprised by the small magnitude. I am also surprised that monetary policy has such persistent impact, given monetary neutrality.

Thank you.

Eric

Point estimates are surprisingly weak. As to persistent, they are also statistically weak. Including all the specification fishing to try to get a negative sign (the price puzzle conundrum) do we even really know the sign? The small size of shocks is a problem, and trying to make them exogenous to everything is a bigger problem. Finding shocks that are taken in response to other things, but not inflation concerns, might help.

DeleteProf. Cochrane: Trying to relate the sensitivity of CPI to changes in the fund funds path from the VAR charts and you commentary. I've read your write-up as applying two different sensitivities (10, and 5) to the CPI values (e.g. "Multiplying by 10 ... might lower cumulative inflation by one percentage point ... multiplying by 5 lowers inflation half a percent). I don't understand the use of the multipliers. Looking at the plots, I interpreted this as an initial 200bp shock (blue line) produced a forward reduction of 100bps by quarter 20. Thank you.

ReplyDelete