Friday, May 8, 2020
Thursday, May 7, 2020
Markets work even in crisis
A lovely result of the corona virus outbreak has been how we see stifling aspects of regulations. Right left and center are figuring out that the regulations need reform. Now, the forces for regulatory stagnation are always strong, so the insight may fade with the virus. Still, let us enjoy it while it lasts.
The trouble with regulations is that, unlike "stimulus," the action is all in minute detail not grand sweeping plan.
John Goodman writes in Forbes
The trouble with regulations is that, unlike "stimulus," the action is all in minute detail not grand sweeping plan.
John Goodman writes in Forbes
The Americans for Tax Reform calculates that 397 regulations have been waived in order to fight COVID-19. That count is probably way too low. The federal Food and Drug Administration (FDA) has eliminated so many restrictions it would be hard to count them all. ...
Consider that, up until a few months ago:
· The only tests for the coronavirus that were approved for use in the United States were produced by the Centers for Disease Control (CDC) and half of those tests turned out to be defective.
· It was illegal to produce, sell and distribute ventilators, respirators, and other medical equipment without complicated and burdensome government regulatory permission.
Covid and economics publishing
The pandemic is dramatically illustrating one area in which the epidemiologists are beating the economists about 100-1: publishing. Scientific publications are reviewed and posted in days, contributing in real time to the policy debate.
Economists are writing papers in a similar flurry. They are writing really good, thoughtful, well done papers that are useful to the policy debate. See the NBER website for example, or SSRN. See my last post and previous one for several great examples.
But when will these papers be peer reviewed? Where will they be published?
Economists are writing papers in a similar flurry. They are writing really good, thoughtful, well done papers that are useful to the policy debate. See the NBER website for example, or SSRN. See my last post and previous one for several great examples.
But when will these papers be peer reviewed? Where will they be published?
Monday, May 4, 2020
An SIR model with behavior
Following my last post, the SIR model has been completely and totally wrong. Answers follow from assumptions. It assumes a constant reproduction rate, and the virus peters out when sick people run in to recovered and immune people. That's not what's happening -- people responded by lowering the contact rate, long before we ran in to herd immunity.
I speculated last time about a model in which people respond to the severity of the disease by reducing contacts. Let's do it. (Warning: this post uses MathJax to show equations. It may not work on all devices.)
I modify the SIR model as presented by Chad Jones and JesúsFernández-Villaverde: \begin{align*} \Delta S_{t+1} & =-\beta S_{t}I_{t}/N\\ \Delta I_{t+1} & =\beta S_{t}I_{t}/N-\gamma I_{t}\\ \Delta R_{t+1} & =\gamma I_{t}-\theta R_{t}\\ \Delta D_{t+1} & =\delta\theta R_{t}\\ \Delta C_{t+1} & =(1-\delta)\theta R_{t}% \end{align*} S = susceptible, I = infected (and infectious), R resolving, i.e. sick but not infectious, D = dead, C = recovered and immune, N = population. The lags give the model momentum. Lowering the reproduction rate does not immediately stop the disease. The model uses exponential decays rather than fixed lags to capture timing. \(\beta\) is the number of contacts per day. A susceptible person meets \(\beta\) people per day. \(I/N\) of them are infected, so \(\beta S_{t}I_{t}/N\) become infected each day. We parameterize \(\beta\) in terms of the reproduction rate \(R_{0}\), \[ R_{0}=\beta/\gamma \] The number of infections from one sick person = number of contacts per day times the number of days contacts are infectious (on average).
The standard SIR model uses a constant \(\beta\) and hence a constant \(R_{0}\). The disease grows exponentially, then becomes limited by the declining number of susceptible people in the population. Each infected person runs in to recovered people, not susceptible people. The whole point is, that did not happen. We lowered \(\beta\) instead.
I model the evolution of \(\beta\) behaviorally. First, suppose people reduce their contacts in proportion to the chance of getting the disease. As people see more infectious people around, the danger of getting infected rises. They reduce their contacts proportionally to the number of infectious people. \[ \log(\beta_{t})=\log\beta_{0}-\alpha_I I_{t}/N_{t}. \] This function could also model a policy response.
However, due to the lack of testing we don't really know how many people are infectious at any time. So as a second model, suppose instead people or policy reduce contacts according to the current death rate, \[ \log(\beta_{t})=\log\beta_{0}-\alpha_D \Delta D_{t}/N. \] \(\beta\) is a rate, how many people do you bump in to per day. I use the log because it can't be negative. The log also captures the idea that early declines in \(\beta\) are easy, by eliminating superspreading activities. Later declines in \(\beta\) are more costly.
I use Chad and Jesús numbers, \(\gamma=0.2\) or 5 days of infectiousness on average, \(\theta=0.1\) implying 10 more days on average with the disease before it resolves, \(\delta=0.08\) \((0.8\%)\) death rate. They parameterize and estimate \(\beta\) \(\ \)via \(R_{0}=\beta/\gamma\). I take the original \(R_{0}% =5\), which is typical of their estimates, and implies \(\beta_{0}=\gamma R_{0}=1\). They estimate \(R_{0}^{\ast}=0.5\) so \(\beta^{\ast}=0.1\), which I will use to calibrate \(\alpha\). New York peaked at 90 deaths per million, but we will see the dynamics overshoot. So I'll pick \(\alpha\) in that case so that \(\beta=\beta^{\ast}\) at 50 daily deaths per milllion triggers \(R_{0}% =0.5\), i.e. \(\alpha_D\) solves \[ \log\left( 0.1\right) =\log\left( 1\right) -\alpha_D\times50/10^{6}. \] The death rate is about 1%, so I calibrate the infection model so that \(R_{0}=R_{0}^{\ast}=0.5\) at an infection rate of 5000 per million or 0.5%. \(\alpha_I\) solves \[ \log(0.1)=\log\left( 1\right) -\alpha_I \times 5000 / 10^{6}. \]
Here is my assumed reproduction rate as a function of deaths per million. The red dot is the calibration point: at 50 deaths per day, people and policy will drive the reproduction rate to 0.5. The red dashed line is a much more aggressive response, which I'll investigate later.
The standard SIR model
As background, here is a simulation of the standard SIR model with these numbers, and a constant \(\beta=1\) meaning \(R_0=5\).
I start at day 1 with a single infected person. The virus grows exponentially. The number infected peaks at about half the population. Around day 25 however, herd immunity starts to kick in. The number infected peaks. Sick people (resolving) peaks a bit later. The pandemic goes away almost as quickly as it came and it's over after two months. With \(R_0=5\) everyone gets it and 0.8% or 8000 people die.
This is the nightmare scenario presented to policy makers in February and caused the economic shutdowns. It is completely wrong -- it's not what happened anywhere.
The behavioral SIR model
Here is the simulation of the behavioral SIR model, in which people (or policy) reacts by lowering the contact rate in response to the number infected.
The vertical scale is different. Only about 4000 people get infected here, not 1 million! The pandemic gets going with the same exponential speed (blue line), but now once infections get up to 1000 per million we see the sharp reduction in the reproduction rate (dashed black line).
This is a lot more like what we saw! A rapid rise, to a plateau, with a much more sensible set of numbers. That's the good news. The bad news is that it goes on and on and on. The minute infections decline people slack off just enough to get it going again. Responding to infections, even though there is a lag, produces very stable dynamics.
The reproduction rate asymptotes to \(R_0=1\). This is both the good news and the bad news outlined in my last post. It doesn't get worse with second waves. But it doesn't get better either.
That result not at all related to the calibration. The reproduction rate always asymptotes to one in this model, with a steady number of infections and a steady number of deaths per day, until finally after years and years we get herd immunity and all efforts to reduce contacts are turned off.
Here is the same simulation with the much stronger response, \( alpha\) is raised by a factor of 5 to the red dashed line in my first graph. No, it's not the same graph. Notice the vertical scale. This response is much less tolerant of infections, so the overall rate of infection is much lower. But the path is exactly the same.
Being more forceful does not change the reproduction rate, which still asymptotes to one. We just trundle along with much lower infections and daily death rates.
This comparison makes nice sense of what we see, per the last post. Far different regimes give rise to essentially the same dynamics, but some at much higher and some at much lower levels.
Technology offers some hope. What happens if the costs of reducing \(beta\) become lower over time, so people can slowly become more careful while also letting the economy grow? Widespread individual testing and tracing, for example, are ways of distancing that are less costly. In this case, we steadily move from the second to last graph to the last graph. To model that, I let \( alpha \) vary over time, growing by a factor of 2 from time 0 to time 100,
This accounts for a plateau with a slow tail. The actual reproduction rate still is close to one, but it's just enough below one to gently let the virus decay.
Deaths and information
A big objection: here I keyed behavior to the infection rate -- people are more careful the more infected people are around. But we don't see how many people are infected. We do see deaths.
Here is the simulation when people respond to the death rate rather than the infection rate
Since deaths lag infections by a few weeks, responding to the death rate leads to over controlling. The pandemic quickly gets out of control before deaths crank up, causing the crash in the reproduction rate. Then people really are careful, and the infection declines quickly. As deaths lower though, people ease up, and a second wave happens and so forth.
The positive feedback does eventually control the pandemic. Each wave is smaller. And this model also trends to \( R_0 = 1\) by the same mechanism. It just takes a lot of wiggles to get there.
Information, rational exceptions, and externalitities
The contrast between the first and second graphs gives a quick policy suggestion: good information on how many people are infected in one's local area would be really helpful to avoid waves of infections. If we had just enough random testing to know how many people are infected in our local area, people and officials could follow the top graphs not the bottom graph. It is not expensive. In the model, one can back out the number of people infected from the increase in the number "resolving." The rate of hospital admissions might be a widely publicized number now available that could be a very good guess.
Widespread, available (no protocol, no prescription, just go get it, free market) testing would radically reduce the economic costs of social distancing, and end this fast. (The optimal \(\alpha\) would rise by orders of magnitude. Yes, you point to externality, why should I test myself. But you ignore economic and social demands. If such testing is available, it's really easy for customers to demand you show your test. Paul Romer is right.
Of course now we get to the delicate question of public vs. private incentives. My first model seems like a reasonable guess of how people will behave -- take actions to be careful the greater my chance of getting sick is by going out.
We want, naturally, a dynamic model in which people's actions incorporate an understanding of the dynamics. In that vein, the latter graph seems unduly pessimistic. People are pretty smart and they know that the death rate is high when the danger of going out has passed. Thus, one may well expect them to foresee the dynamics, be careful when the death rate is increasing, and slack off when it is decreasing. More generally, in this deterministic model, you can back out what the state of all the variables is if you observe one of them. Thus, the rational expectations equilibrium of this model if people want to react to the number of infections is the first one, even if they can't see infections. They can back infections out of the death data. That may be too much to hope for, but reality is likely in between.
Being careful has an externality, of course, so people following a private optimum of costly but careful behavior vs. getting sick is not necessarily the social optimum. Most economists jump quickly from this observation to calibrated time-varying lockdown policies to try to control \(\beta\). But let us not forget the other side of that coin: The public policy tools are sledgehammers, which do a poor job of controlling interactions \(\beta\) at reasonable economic cost. Really, what we have are at best exhortations to be careful in the details of daily life, plus extremely expensive business shutdowns. As a concrete example, in the model one may be tempted to advocate that officials lie about the number of infected to get people to be more careful than they would be privately. But once a lie is found out, nobody believes anything anymore, and the next step is China. I still think timely and accurate information is better.
To do list
Some more thought on functional form would be useful. Do we have any data or other ways of measuring how people behave?
Obviously a real economic model would derive these behavioral responses from a maximization problem, and consider the tradeoff between more distancing \( \beta\) and economic costs.
Optimal policy may differ most from individual behavior in the dynamics. It is not worth it to an individual to be careful early when there are few sick people around, but policy considers the effect of you getting sick on everyone who gets it from you. Optimal control of \(\beta\) beckons. But to be realistic we must include the fact that public control of \(\beta\) against private wishes will be much less efficient.
On the other papers: Chad and Jesús model social distancing, whether voluntary or by policy, via a deterministic and permanent exponential decay from a state of nature \(\beta_{0}\) to a new lower value \(\beta^{\ast}\) over a period \[ \beta_{t}=\beta_{0}e^{-\lambda t}+\beta^{\ast}(1-e^{-\lambda t}). \] The point here is to realize there is feedback, and both people and policy behavior respond to facts. Their paper fits the data so far beautifully. My goal is to think about what happens next. That \( \beta\) just sits at \(beta^\ast\) as it does in their model, seems unrealistic because people aren't going to keep distancing voluntarily or involuntarily.
Eichenbaum, Rebelo and Trabandt, have an economic model of \(\beta\). People work and shop less when they are more afraid of getting sick. But the tradeoff is not very attractive. Here is their model (solid) vs. the basic SIR model (dash)
In their model all people can do to avoid getting sick is to avoid work or consumption, both of which offer very little protection for great economic cost. So you still see the basic -- and false -- prediction of the SIR model. I think a good direction is to modify their model, calibrating it to data as Chad and Jesús do, which would imply an economically easier reduction in reproduction rate.
Update:
1) Equilibrium social distancing by Flavio Toxvaerd is a simple economic model with endogenous social distancing. It also produces plateaus when people choose to be safer
(Thanks to a tweet from Chryssi Giannitsarou @giannitsarou)
2) Economists vs. epidemiologists has a long history. Economists point out that disease transmission is not a biological constant, but varies with human behavior. And human behavior varies predictably in response to incentives (and information). Many beautiful facts and stories on this point are collected in Tomas Phillipson and Richard Posner's book, Private Choices and Public Health: The AIDS Epidemic in an Economic Perspective. For example, AIDS patients in clinical trials would mix their medicines together. Half of the drug for sure is better than a 50 50 chance of nothing. Thanks to a correspondent for the reminder.
3) A Multi-Risk SIR Model with Optimally Targeted Lockdown by Daron Acemoglu, Victor Chernozhukov Michael Whinston and Ivan Werning just came out. I haven't read it yet, but it is an obvious addition to the stack for people working on epidemiology models with economic incentives. It has diverse populations and transmission mechanisms, which have long struck me as a key insight. We are not all average, and that really matters here.
4) From the comments, a many-authored paper arguing that herd immunity may be much lower. Essentially the super spreaders are more likely to get the disease, so they are more likely to be immune first. "Super spreader" includes people in nursing homes, emergency room technicians, bus drivers, etc., not just jet setting partiers.
5) I missed Macroeconomic Dynamics and Reallocation in an Epidemic by Dirk Krueger Harald Uhlig and Taojun Xie
7) Systematic biases in disease forecasting – The role of behavior change by Ceyhun Eksina Keith Paarpornb Joshua S. Weitzcde
8)...I'm sure more updates will follow.
Code
Here is the Matlab code for my plots
close all
clear all
gam = 0.2;
thet = 0.1;
delt = 0.008;
R0 = 5;
alphaD = (0 - log(0.1))*1E6/50;
alphaI = (0 - log(0.1))*1E4/50;
beta0 = R0*gam;
N = 1E6;
T = 100;
% plot beta
figure
drate = (0:100)'/1E6;
betat = exp(log(beta0) - alphaD*drate);
betat1 = exp(log(beta0) - 5*alphaD*drate);
plot(drate*1E6, betat/gam,'linewidth',2);
hold on
plot(drate*1E6, betat1/gam,'--','linewidth',2);
hold on
plot(50, 0.5, 'o','markerfacecolor','r')
legend('Original','\alpha multiplied by 5','location','best')
xlabel('Daily deaths/million');
ylabel('Reproduction rate R0 = \beta / \gamma')
axis([0 80 0 5]);
print -dpng betafig.png
% standard SIR model
S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;
S(1) = N-1;
I(1) = 1;
for t = 1:T-1;
S(t+1) = S(t) -beta0*S(t)*I(t)/N;
I(t+1) = I(t) + beta0*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);
end;
figure;
plot((1:T)',[S I R 100*D C]/1E6, 'linewidth',2);
legend('Susceptible','Infected','Resolving','100 x Dead','ReCovered','location','best')
xlabel('Days')
ylabel('Millions');
axis([10 70 0 1]);
title('SIR model, constant R0 = 5');
print -dpng std_sir.png
figure;
plot((2:T)',[ I(2:T) -(S(2:T)-S(1:T-1)) 100*(D(2:T)-D(1:T-1))]/1E6, 'linewidth',2);
legend('Infected','New Infections','100 x New Dead','location','best')
xlabel('Days')
ylabel('Millions');
axis([10 70 0 0.6]);
title('SIR model, constant R0 = 5');
print -dpng std_sir_diffs.png
disp('last s i r d');
disp([S(T) I(T) R(T) D(T)]);
% my model, response to infections
S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;
betat = S;
S(1) = N-1;
I(1) = 1;
I(1) = 1;
S1 = S;
I1 = I;
R1 = R;
D1 = D;
C1 = C;
betat1 = betat;
S2 = S;
I2 = I;
R2 = R;
D2 = D;
C2 = C;
betat2 = betat;
for t = 1:T-1;
betat(t) = exp(log(beta0) - alphaI*((I(t))/N));
S(t+1) = S(t) -betat(t)*S(t)*I(t)/N;
I(t+1) = I(t) + betat(t)*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);
betat1(t) = exp(log(beta0) - 5*alphaI*((I1(t))/N));
S1(t+1) = S1(t) -betat1(t)*S1(t)*I1(t)/N;
I1(t+1) = I1(t) + betat1(t)*S1(t)*I1(t)/N - gam*I1(t);
R1(t+1) = R1(t) + gam*I1(t)-thet*R1(t);
D1(t+1) = D1(t) + delt*thet*R1(t);
C1(t+1) = C1(t) + (1-delt)*thet*R1(t);
betat2(t) = exp(log(beta0) - (1+1*t/T)*alphaI*((I2(t))/N));
S2(t+1) = S2(t) -betat2(t)*S2(t)*I2(t)/N;
I2(t+1) = I2(t) + betat2(t)*S2(t)*I2(t)/N - gam*I2(t);
R2(t+1) = R2(t) + gam*I2(t)-thet*R2(t);
D2(t+1) = D2(t) + delt*thet*R2(t);
C2(t+1) = C2(t) + (1-delt)*thet*R2(t);
end;
figure;
%yyaxis left
plot((2:T)',[ I(2:T) 100*(D(2:T)-D(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);
yyaxis right
plot((1:T)',betat/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);
legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')
title('BSIR model, R0 varies with infection rate');
print -dpng std_sir_aI.png
figure;
%yyaxis left
plot((2:T)',[ I1(2:T) 100*(D1(2:T)-D1(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);
yyaxis right
plot((1:T)',betat1/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);
legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')
title('BSIR model, R0 varies with infection rate, higher \alpha');
print -dpng std_sir_aI1.png
figure;
%yyaxis left
plot((2:T)',[ I2(2:T) 100*(D2(2:T)-D2(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);
yyaxis right
plot((1:T)',betat2/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);
legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')
title('BSIR model, R0 varies with infection rate, \alpha increases over time');
print -dpng std_sir_aI2.png
% my model, response to deaths
S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;
betat = S;
S(1) = N-1;
I(1) = 1;
I(1) = 1;
betat(1) = beta0;
for t = 1:T-1;
S(t+1) = S(t) -betat(t)*S(t)*I(t)/N;
I(t+1) = I(t) + betat(t)*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);
betat(t+1) = exp(log(beta0) - alphaD*((D(t+1)-D(t))/N));
end;
figure;
%yyaxis left
plot((2:T)',[ I(2:T) 100*(D(2:T)-D(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 100 0 inf]);
yyaxis right
plot((1:T)',betat/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 100 0 inf]);
legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')
title('BSIR model, R0 varies with death rate');
print -dpng std_sir_aD.png
I speculated last time about a model in which people respond to the severity of the disease by reducing contacts. Let's do it. (Warning: this post uses MathJax to show equations. It may not work on all devices.)
I modify the SIR model as presented by Chad Jones and JesúsFernández-Villaverde: \begin{align*} \Delta S_{t+1} & =-\beta S_{t}I_{t}/N\\ \Delta I_{t+1} & =\beta S_{t}I_{t}/N-\gamma I_{t}\\ \Delta R_{t+1} & =\gamma I_{t}-\theta R_{t}\\ \Delta D_{t+1} & =\delta\theta R_{t}\\ \Delta C_{t+1} & =(1-\delta)\theta R_{t}% \end{align*} S = susceptible, I = infected (and infectious), R resolving, i.e. sick but not infectious, D = dead, C = recovered and immune, N = population. The lags give the model momentum. Lowering the reproduction rate does not immediately stop the disease. The model uses exponential decays rather than fixed lags to capture timing. \(\beta\) is the number of contacts per day. A susceptible person meets \(\beta\) people per day. \(I/N\) of them are infected, so \(\beta S_{t}I_{t}/N\) become infected each day. We parameterize \(\beta\) in terms of the reproduction rate \(R_{0}\), \[ R_{0}=\beta/\gamma \] The number of infections from one sick person = number of contacts per day times the number of days contacts are infectious (on average).
The standard SIR model uses a constant \(\beta\) and hence a constant \(R_{0}\). The disease grows exponentially, then becomes limited by the declining number of susceptible people in the population. Each infected person runs in to recovered people, not susceptible people. The whole point is, that did not happen. We lowered \(\beta\) instead.
I model the evolution of \(\beta\) behaviorally. First, suppose people reduce their contacts in proportion to the chance of getting the disease. As people see more infectious people around, the danger of getting infected rises. They reduce their contacts proportionally to the number of infectious people. \[ \log(\beta_{t})=\log\beta_{0}-\alpha_I I_{t}/N_{t}. \] This function could also model a policy response.
However, due to the lack of testing we don't really know how many people are infectious at any time. So as a second model, suppose instead people or policy reduce contacts according to the current death rate, \[ \log(\beta_{t})=\log\beta_{0}-\alpha_D \Delta D_{t}/N. \] \(\beta\) is a rate, how many people do you bump in to per day. I use the log because it can't be negative. The log also captures the idea that early declines in \(\beta\) are easy, by eliminating superspreading activities. Later declines in \(\beta\) are more costly.
I use Chad and Jesús numbers, \(\gamma=0.2\) or 5 days of infectiousness on average, \(\theta=0.1\) implying 10 more days on average with the disease before it resolves, \(\delta=0.08\) \((0.8\%)\) death rate. They parameterize and estimate \(\beta\) \(\ \)via \(R_{0}=\beta/\gamma\). I take the original \(R_{0}% =5\), which is typical of their estimates, and implies \(\beta_{0}=\gamma R_{0}=1\). They estimate \(R_{0}^{\ast}=0.5\) so \(\beta^{\ast}=0.1\), which I will use to calibrate \(\alpha\). New York peaked at 90 deaths per million, but we will see the dynamics overshoot. So I'll pick \(\alpha\) in that case so that \(\beta=\beta^{\ast}\) at 50 daily deaths per milllion triggers \(R_{0}% =0.5\), i.e. \(\alpha_D\) solves \[ \log\left( 0.1\right) =\log\left( 1\right) -\alpha_D\times50/10^{6}. \] The death rate is about 1%, so I calibrate the infection model so that \(R_{0}=R_{0}^{\ast}=0.5\) at an infection rate of 5000 per million or 0.5%. \(\alpha_I\) solves \[ \log(0.1)=\log\left( 1\right) -\alpha_I \times 5000 / 10^{6}. \]
Here is my assumed reproduction rate as a function of deaths per million. The red dot is the calibration point: at 50 deaths per day, people and policy will drive the reproduction rate to 0.5. The red dashed line is a much more aggressive response, which I'll investigate later.
The standard SIR model
As background, here is a simulation of the standard SIR model with these numbers, and a constant \(\beta=1\) meaning \(R_0=5\).
I start at day 1 with a single infected person. The virus grows exponentially. The number infected peaks at about half the population. Around day 25 however, herd immunity starts to kick in. The number infected peaks. Sick people (resolving) peaks a bit later. The pandemic goes away almost as quickly as it came and it's over after two months. With \(R_0=5\) everyone gets it and 0.8% or 8000 people die.
This is the nightmare scenario presented to policy makers in February and caused the economic shutdowns. It is completely wrong -- it's not what happened anywhere.
The behavioral SIR model
Here is the simulation of the behavioral SIR model, in which people (or policy) reacts by lowering the contact rate in response to the number infected.
The vertical scale is different. Only about 4000 people get infected here, not 1 million! The pandemic gets going with the same exponential speed (blue line), but now once infections get up to 1000 per million we see the sharp reduction in the reproduction rate (dashed black line).
This is a lot more like what we saw! A rapid rise, to a plateau, with a much more sensible set of numbers. That's the good news. The bad news is that it goes on and on and on. The minute infections decline people slack off just enough to get it going again. Responding to infections, even though there is a lag, produces very stable dynamics.
The reproduction rate asymptotes to \(R_0=1\). This is both the good news and the bad news outlined in my last post. It doesn't get worse with second waves. But it doesn't get better either.
That result not at all related to the calibration. The reproduction rate always asymptotes to one in this model, with a steady number of infections and a steady number of deaths per day, until finally after years and years we get herd immunity and all efforts to reduce contacts are turned off.
Here is the same simulation with the much stronger response, \( alpha\) is raised by a factor of 5 to the red dashed line in my first graph. No, it's not the same graph. Notice the vertical scale. This response is much less tolerant of infections, so the overall rate of infection is much lower. But the path is exactly the same.
Being more forceful does not change the reproduction rate, which still asymptotes to one. We just trundle along with much lower infections and daily death rates.
This comparison makes nice sense of what we see, per the last post. Far different regimes give rise to essentially the same dynamics, but some at much higher and some at much lower levels.
Technology offers some hope. What happens if the costs of reducing \(beta\) become lower over time, so people can slowly become more careful while also letting the economy grow? Widespread individual testing and tracing, for example, are ways of distancing that are less costly. In this case, we steadily move from the second to last graph to the last graph. To model that, I let \( alpha \) vary over time, growing by a factor of 2 from time 0 to time 100,
This accounts for a plateau with a slow tail. The actual reproduction rate still is close to one, but it's just enough below one to gently let the virus decay.
Deaths and information
A big objection: here I keyed behavior to the infection rate -- people are more careful the more infected people are around. But we don't see how many people are infected. We do see deaths.
Here is the simulation when people respond to the death rate rather than the infection rate
The positive feedback does eventually control the pandemic. Each wave is smaller. And this model also trends to \( R_0 = 1\) by the same mechanism. It just takes a lot of wiggles to get there.
Information, rational exceptions, and externalitities
The contrast between the first and second graphs gives a quick policy suggestion: good information on how many people are infected in one's local area would be really helpful to avoid waves of infections. If we had just enough random testing to know how many people are infected in our local area, people and officials could follow the top graphs not the bottom graph. It is not expensive. In the model, one can back out the number of people infected from the increase in the number "resolving." The rate of hospital admissions might be a widely publicized number now available that could be a very good guess.
Widespread, available (no protocol, no prescription, just go get it, free market) testing would radically reduce the economic costs of social distancing, and end this fast. (The optimal \(\alpha\) would rise by orders of magnitude. Yes, you point to externality, why should I test myself. But you ignore economic and social demands. If such testing is available, it's really easy for customers to demand you show your test. Paul Romer is right.
Of course now we get to the delicate question of public vs. private incentives. My first model seems like a reasonable guess of how people will behave -- take actions to be careful the greater my chance of getting sick is by going out.
We want, naturally, a dynamic model in which people's actions incorporate an understanding of the dynamics. In that vein, the latter graph seems unduly pessimistic. People are pretty smart and they know that the death rate is high when the danger of going out has passed. Thus, one may well expect them to foresee the dynamics, be careful when the death rate is increasing, and slack off when it is decreasing. More generally, in this deterministic model, you can back out what the state of all the variables is if you observe one of them. Thus, the rational expectations equilibrium of this model if people want to react to the number of infections is the first one, even if they can't see infections. They can back infections out of the death data. That may be too much to hope for, but reality is likely in between.
Being careful has an externality, of course, so people following a private optimum of costly but careful behavior vs. getting sick is not necessarily the social optimum. Most economists jump quickly from this observation to calibrated time-varying lockdown policies to try to control \(\beta\). But let us not forget the other side of that coin: The public policy tools are sledgehammers, which do a poor job of controlling interactions \(\beta\) at reasonable economic cost. Really, what we have are at best exhortations to be careful in the details of daily life, plus extremely expensive business shutdowns. As a concrete example, in the model one may be tempted to advocate that officials lie about the number of infected to get people to be more careful than they would be privately. But once a lie is found out, nobody believes anything anymore, and the next step is China. I still think timely and accurate information is better.
To do list
Some more thought on functional form would be useful. Do we have any data or other ways of measuring how people behave?
Obviously a real economic model would derive these behavioral responses from a maximization problem, and consider the tradeoff between more distancing \( \beta\) and economic costs.
Optimal policy may differ most from individual behavior in the dynamics. It is not worth it to an individual to be careful early when there are few sick people around, but policy considers the effect of you getting sick on everyone who gets it from you. Optimal control of \(\beta\) beckons. But to be realistic we must include the fact that public control of \(\beta\) against private wishes will be much less efficient.
On the other papers: Chad and Jesús model social distancing, whether voluntary or by policy, via a deterministic and permanent exponential decay from a state of nature \(\beta_{0}\) to a new lower value \(\beta^{\ast}\) over a period \[ \beta_{t}=\beta_{0}e^{-\lambda t}+\beta^{\ast}(1-e^{-\lambda t}). \] The point here is to realize there is feedback, and both people and policy behavior respond to facts. Their paper fits the data so far beautifully. My goal is to think about what happens next. That \( \beta\) just sits at \(beta^\ast\) as it does in their model, seems unrealistic because people aren't going to keep distancing voluntarily or involuntarily.
Eichenbaum, Rebelo and Trabandt, have an economic model of \(\beta\). People work and shop less when they are more afraid of getting sick. But the tradeoff is not very attractive. Here is their model (solid) vs. the basic SIR model (dash)
Update:
1) Equilibrium social distancing by Flavio Toxvaerd is a simple economic model with endogenous social distancing. It also produces plateaus when people choose to be safer
2) Economists vs. epidemiologists has a long history. Economists point out that disease transmission is not a biological constant, but varies with human behavior. And human behavior varies predictably in response to incentives (and information). Many beautiful facts and stories on this point are collected in Tomas Phillipson and Richard Posner's book, Private Choices and Public Health: The AIDS Epidemic in an Economic Perspective. For example, AIDS patients in clinical trials would mix their medicines together. Half of the drug for sure is better than a 50 50 chance of nothing. Thanks to a correspondent for the reminder.
3) A Multi-Risk SIR Model with Optimally Targeted Lockdown by Daron Acemoglu, Victor Chernozhukov Michael Whinston and Ivan Werning just came out. I haven't read it yet, but it is an obvious addition to the stack for people working on epidemiology models with economic incentives. It has diverse populations and transmission mechanisms, which have long struck me as a key insight. We are not all average, and that really matters here.
4) From the comments, a many-authored paper arguing that herd immunity may be much lower. Essentially the super spreaders are more likely to get the disease, so they are more likely to be immune first. "Super spreader" includes people in nursing homes, emergency room technicians, bus drivers, etc., not just jet setting partiers.
5) I missed Macroeconomic Dynamics and Reallocation in an Epidemic by Dirk Krueger Harald Uhlig and Taojun Xie
...we distinguish goods by their degree to which they can be consumed at home rather than in a social (and thus possibly contagious) context. We demonstrate that, within the model the “Swedish solution” of letting the epidemic play out without government intervention and allowing agents to shift their sectoral behavior on their own can lead to a substantial mitigation of the economic and human costs of the COVID-19 crisis, avoiding more than 80 of the decline in output and of number of deaths within one year, compared to a model in which sectors are assumed to be homogeneous. For different parameter configurations that capture the additional social distancing and hygiene activities individuals might engage in voluntarily, we show that infections may decline entirely on their own, simply due to the individually rational re-allocation of economic activity: the curve not only just flattens, it gets reversed.6) A behavioral SIR model YouTube talk from Lones Smith
7) Systematic biases in disease forecasting – The role of behavior change by Ceyhun Eksina Keith Paarpornb Joshua S. Weitzcde
...during real-world outbreaks, individuals may modify their behavior and take preventative steps to reduce infection risk. ... we evaluate this hypothesis by comparing the dynamics arising from a simple SIR epidemic model with those from a modified SIR model in which individuals reduce contacts as a function of the current or cumulative number of cases.Thanks to Andy Atkeson for the tip. See his A note on the economic impact of coronavirus and Talk at NBER
8)...I'm sure more updates will follow.
Code
Here is the Matlab code for my plots
close all
clear all
gam = 0.2;
thet = 0.1;
delt = 0.008;
R0 = 5;
alphaD = (0 - log(0.1))*1E6/50;
alphaI = (0 - log(0.1))*1E4/50;
beta0 = R0*gam;
N = 1E6;
T = 100;
% plot beta
figure
drate = (0:100)'/1E6;
betat = exp(log(beta0) - alphaD*drate);
betat1 = exp(log(beta0) - 5*alphaD*drate);
plot(drate*1E6, betat/gam,'linewidth',2);
hold on
plot(drate*1E6, betat1/gam,'--','linewidth',2);
hold on
plot(50, 0.5, 'o','markerfacecolor','r')
legend('Original','\alpha multiplied by 5','location','best')
xlabel('Daily deaths/million');
ylabel('Reproduction rate R0 = \beta / \gamma')
axis([0 80 0 5]);
print -dpng betafig.png
% standard SIR model
S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;
S(1) = N-1;
I(1) = 1;
for t = 1:T-1;
S(t+1) = S(t) -beta0*S(t)*I(t)/N;
I(t+1) = I(t) + beta0*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);
end;
figure;
plot((1:T)',[S I R 100*D C]/1E6, 'linewidth',2);
legend('Susceptible','Infected','Resolving','100 x Dead','ReCovered','location','best')
xlabel('Days')
ylabel('Millions');
axis([10 70 0 1]);
title('SIR model, constant R0 = 5');
print -dpng std_sir.png
figure;
plot((2:T)',[ I(2:T) -(S(2:T)-S(1:T-1)) 100*(D(2:T)-D(1:T-1))]/1E6, 'linewidth',2);
legend('Infected','New Infections','100 x New Dead','location','best')
xlabel('Days')
ylabel('Millions');
axis([10 70 0 0.6]);
title('SIR model, constant R0 = 5');
print -dpng std_sir_diffs.png
disp('last s i r d');
disp([S(T) I(T) R(T) D(T)]);
% my model, response to infections
S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;
betat = S;
S(1) = N-1;
I(1) = 1;
I(1) = 1;
S1 = S;
I1 = I;
R1 = R;
D1 = D;
C1 = C;
betat1 = betat;
S2 = S;
I2 = I;
R2 = R;
D2 = D;
C2 = C;
betat2 = betat;
for t = 1:T-1;
betat(t) = exp(log(beta0) - alphaI*((I(t))/N));
S(t+1) = S(t) -betat(t)*S(t)*I(t)/N;
I(t+1) = I(t) + betat(t)*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);
betat1(t) = exp(log(beta0) - 5*alphaI*((I1(t))/N));
S1(t+1) = S1(t) -betat1(t)*S1(t)*I1(t)/N;
I1(t+1) = I1(t) + betat1(t)*S1(t)*I1(t)/N - gam*I1(t);
R1(t+1) = R1(t) + gam*I1(t)-thet*R1(t);
D1(t+1) = D1(t) + delt*thet*R1(t);
C1(t+1) = C1(t) + (1-delt)*thet*R1(t);
betat2(t) = exp(log(beta0) - (1+1*t/T)*alphaI*((I2(t))/N));
S2(t+1) = S2(t) -betat2(t)*S2(t)*I2(t)/N;
I2(t+1) = I2(t) + betat2(t)*S2(t)*I2(t)/N - gam*I2(t);
R2(t+1) = R2(t) + gam*I2(t)-thet*R2(t);
D2(t+1) = D2(t) + delt*thet*R2(t);
C2(t+1) = C2(t) + (1-delt)*thet*R2(t);
end;
figure;
%yyaxis left
plot((2:T)',[ I(2:T) 100*(D(2:T)-D(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);
yyaxis right
plot((1:T)',betat/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);
legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')
title('BSIR model, R0 varies with infection rate');
print -dpng std_sir_aI.png
figure;
%yyaxis left
plot((2:T)',[ I1(2:T) 100*(D1(2:T)-D1(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);
yyaxis right
plot((1:T)',betat1/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);
legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')
title('BSIR model, R0 varies with infection rate, higher \alpha');
print -dpng std_sir_aI1.png
figure;
%yyaxis left
plot((2:T)',[ I2(2:T) 100*(D2(2:T)-D2(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);
yyaxis right
plot((1:T)',betat2/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);
legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')
title('BSIR model, R0 varies with infection rate, \alpha increases over time');
print -dpng std_sir_aI2.png
% my model, response to deaths
S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;
betat = S;
S(1) = N-1;
I(1) = 1;
I(1) = 1;
betat(1) = beta0;
for t = 1:T-1;
S(t+1) = S(t) -betat(t)*S(t)*I(t)/N;
I(t+1) = I(t) + betat(t)*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);
betat(t+1) = exp(log(beta0) - alphaD*((D(t+1)-D(t))/N));
end;
figure;
%yyaxis left
plot((2:T)',[ I(2:T) 100*(D(2:T)-D(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 100 0 inf]);
yyaxis right
plot((1:T)',betat/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 100 0 inf]);
legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')
title('BSIR model, R0 varies with death rate');
print -dpng std_sir_aD.png
Dumb reopening might just work
A smart reopening, with well worked out protocols at work, and a robust competent test and trace public health response to stamp out the embers, seems unlikely. Technology to save us -- vaccine, cure, cheap daily test, scaled up and implemented -- seems unlikely in the next few months. We seem fated to a dumb reopening. Conventional wisdom says we will then get a massive second wave in the fall, followed by a larger shutdown.
Spread in last week's tidbits and a bit of modeling over the weekend, I see hope that this dumb reopening might just work, including the steady and slowly declining new set of cases we are seeing right now.
In February and early March, the models predicted exponential growth, massive infections, hospitalizations, and deaths, with most everyone getting the virus in a matter of months, and then the virus to quickly pass. The models were disastrously -- or, better, miraculously -- wrong. New cases plateaued quickly and then slowly declined. In many parts of the country, hospitals have plenty of extra space.
Conventional wisdom holds this great good fortune is because of the lockdown. But, that wisdom warns, the minute the economy reopens, it all starts again absent the above public health or a vaccine. Conventional wisdom thus says, do not extrapolate the current trends.
The tidbits of news that give me hope, below, are that the plateau came far sooner than expected, it is lasting far longer than expected, and the shape seems quite similar across many regimes.
I hazard here a guess of why this is occurring: 1) The models do not take account that the reproduction rate R0, how many people each infected person gives it to, is immensely influenced by human behavior. And, said humans, read the news. 2) The average reproduction rate heavily influenced by super-spreading activities. The average is composed of a large majority of activities that give it to less than one other person, and a small minority of activities -- singing in choirs, beer pong at ski resorts, big loud indoor wedding parties -- that super-spread it.
Add up 1) and 2). When people hear there is a disease about, they quickly stop super-spreading activities, all on their own, because they don't want to get sick. Shutdowns only marginally affect this process. We saw, for example, massive declines in travel and restaurants long before shutdowns were announced. This action quickly and rather easily reduces the average reproduction rate to something like 5 to something below 2.
Then, as people hear news of how bad it is in their area, they adjust more. If people hear it's not so bad, they adjust less. If the virus is on the upswing, they social distance more. Do you walk or take the bus? Do you eat at a social distanced restaurant or take out? There are hundreds of little behaviors each of us take that push the reproduction rate around.
You can see a self-regulating state here, where the number of new cases sits at a steady plateau for a long time. You can easily see a self-regulation that drives the system to R0=1, or to a steady number of new cases.
That's not great news. There will still be a steady flow of new cases per week, just enough to scare people. But as people slowly start to adopt common sense and ignore silly shutdowns, and as people start to adopt common sense and avoid even permitted dangerous activities, the economy can recover a good deal. All we need is good information.
Spread in last week's tidbits and a bit of modeling over the weekend, I see hope that this dumb reopening might just work, including the steady and slowly declining new set of cases we are seeing right now.
The Theme
Conventional wisdom holds this great good fortune is because of the lockdown. But, that wisdom warns, the minute the economy reopens, it all starts again absent the above public health or a vaccine. Conventional wisdom thus says, do not extrapolate the current trends.
The tidbits of news that give me hope, below, are that the plateau came far sooner than expected, it is lasting far longer than expected, and the shape seems quite similar across many regimes.
I hazard here a guess of why this is occurring: 1) The models do not take account that the reproduction rate R0, how many people each infected person gives it to, is immensely influenced by human behavior. And, said humans, read the news. 2) The average reproduction rate heavily influenced by super-spreading activities. The average is composed of a large majority of activities that give it to less than one other person, and a small minority of activities -- singing in choirs, beer pong at ski resorts, big loud indoor wedding parties -- that super-spread it.
Add up 1) and 2). When people hear there is a disease about, they quickly stop super-spreading activities, all on their own, because they don't want to get sick. Shutdowns only marginally affect this process. We saw, for example, massive declines in travel and restaurants long before shutdowns were announced. This action quickly and rather easily reduces the average reproduction rate to something like 5 to something below 2.
Then, as people hear news of how bad it is in their area, they adjust more. If people hear it's not so bad, they adjust less. If the virus is on the upswing, they social distance more. Do you walk or take the bus? Do you eat at a social distanced restaurant or take out? There are hundreds of little behaviors each of us take that push the reproduction rate around.
You can see a self-regulating state here, where the number of new cases sits at a steady plateau for a long time. You can easily see a self-regulation that drives the system to R0=1, or to a steady number of new cases.
That's not great news. There will still be a steady flow of new cases per week, just enough to scare people. But as people slowly start to adopt common sense and ignore silly shutdowns, and as people start to adopt common sense and avoid even permitted dangerous activities, the economy can recover a good deal. All we need is good information.
Now in detail.
Friday, May 1, 2020
Romer: if virus tests were like sodas; a modest extension
Paul Romer has a lovely post, If virus tests were like sodas. (HT Marginal Revolution.) Go enjoy the whole thing. It's short. A few excerpts and a suggested addition:
Let me offer a suggestion. Allow people and businesses to pay the labs whatever the labs want to charge and buy the tests themselves. Require only that they report the test result to the CDC's national database.
Lots of people and businesses will happily pay cash for a test. Spitting in a cup and sending it in -- or putting it in an Abbot Labs machine for instant results -- cannot possibly hurt anyone. There is no reason such tests should not be sold, unregulated, on the free market, like pregnancy tests.
Sure, label the test with the best estimate of its false positive and negative rate, and the same long legal boilerplate disclaimers that go on a lawnmower you buy from Home Depot.
Who gets it first? Well, those willing to pay the most. This is not a capitalist inequality outrage, this is a good idea. GDP and employment are cratering. The people and businesses who get most economic value out of testing should get them first. And, by doing so, they fund the immense expense of test development and rapid ramp up for the rest of us. And, of course, the higher the price, the more quickly competitors will ramp up and drop prices. We'll all get tests faster if those who "can afford it" pay through the nose to get it first.
Imagine a world in which the only way to get a soda is to get your doctor to write a prescription. It costs $20 per can. Your insurance company pays. ...
Because they have to keep total costs from running out of control, insurance companies, health care providers, and government regulators have cobbled together a system that limits access to soda. One part of this system is an expensive regulatory process...
The only people who can get sodas are those already under the care of the health care system. They are not thirsty, but the insurance company covers the cost, so whatever.
People who are thirsty start going to the hospital just to get soda. Doctors comply with their requests for a prescription. Soda producers try to increase output, but soon run into “bottlenecks.” One vendor with an approved soda delivery system that packages a straw with a can finds that its supplier of straws can not keep up with the increased demand. This soda company explains to its unhappy customers that it has FDA approval only for a product that includes a straw from its traditional supplier. The soda company says that it is applying to the FDA for an Emergency Use Authorization (EUA) that gives it permission to bundle a can with a straw from a different vendor. As it waits, it keeps repeating its excuse: “There is a straw bottleneck!”...
In their experiments with drinking from the can, these same university researchers realize soda is just flavored sugar water and that they could produce millions of sodas per day at a price well under $1 per can. The researchers publicize their findings. Policy wonks urge them to get going: “Produce the sodas that a thirsty nation needs.” But these do not say anything about who will pay for all these additional sodas. The researchers are good sports, but they are not idiots. They produce some token batches of soda and go back to writing papers.
... wonks conclude that even an economic system as big, as powerful, and as innovative as the one we have established in the United States cannot rise to the challenge of producing millions of sodas per day. They settle for a stretch goal of offering one soda per month to each family.Comment: The policy wonks as usual left out the problem: big, powerful, innovated, and regulated to death.
The facts:
Researchers affiliated with Rutgers University did discover that you do not need a swab to do an RT-PCR test for the SARS-CoV-2 virus. They even went to the trouble to get an EUA to conduct tests on saliva samples.
No one has proposed a way to pay the researchers at Rutgers, or their peers in comparable laboratories located throughout the United States, for the tests they could supply. For now, they do them because they are good sports.
The US economy produces 350 million 12 oz cans worth of soda each day.
Soda producers do not need to get regulatory approval each time they innovate around some hurdle or bottleneck.I'm not sure soda is so lightly regulated, but we'll leave that.
Lessons
If we want to use this nation’s massive capacity – much of which, by the way, is now sitting idle – to produce tens of millions of virus tests per day, there is a way to do it:
Decide what a test should do.
As long as labs provide tests that do what a test is supposed to do, let them worry about the details.
Do not appeal to charity; be prepared to pay these labs twice as much as we spend on soda.On the last point, the usually clear Paul ran out of steam. Who should be prepared to pay the labs? The same insurance companies and government purchasers where the whole problem started?
Let me offer a suggestion. Allow people and businesses to pay the labs whatever the labs want to charge and buy the tests themselves. Require only that they report the test result to the CDC's national database.
Lots of people and businesses will happily pay cash for a test. Spitting in a cup and sending it in -- or putting it in an Abbot Labs machine for instant results -- cannot possibly hurt anyone. There is no reason such tests should not be sold, unregulated, on the free market, like pregnancy tests.
Sure, label the test with the best estimate of its false positive and negative rate, and the same long legal boilerplate disclaimers that go on a lawnmower you buy from Home Depot.
Who gets it first? Well, those willing to pay the most. This is not a capitalist inequality outrage, this is a good idea. GDP and employment are cratering. The people and businesses who get most economic value out of testing should get them first. And, by doing so, they fund the immense expense of test development and rapid ramp up for the rest of us. And, of course, the higher the price, the more quickly competitors will ramp up and drop prices. We'll all get tests faster if those who "can afford it" pay through the nose to get it first.
Weekly Podcasts
The grumpy economist, on the university finances post and related issues. I found the embed code! The original is here.
Good fellows conversation Direct link here. On reopening, and strategic issues.
Good fellows conversation Direct link here. On reopening, and strategic issues.
Thursday, April 30, 2020
Ready to reopen?
I've been on the "reopen fast but smart" bandwagon for weeks. The reopening is coming. Are we ready? I'm afraid not. I remain on the "plan ahead" bandwagon, which means not lots of ideas from bloggers but lots of implemented plans of action for local public health bureacracies. Two items in today's news.
Coronavirus Testing Capacity Is Going Unused
Testing meant, for example, widespread random testing, or at least testing of volunteers, so we could find out where the virus is. Just how many people in Palo Alto have the virus, right now? With 1000 roughly random tests we could find out. Nobody is doing that.
We remain, I think, sorely lacking in the public health infrastructure that must take over from blanket shutdowns. California just issued a revised list of what businesses can open. Apparently that's all we know how to do.
Food plants turned out to be a super spreader. ( Kris Maher, Jacob Bunge and Alexandra Berzon in WSJ) The larger point here: About 40% of the economy is still open as "essential." Well, as we get ready to reopen safely the rest of the economy, one would think that the "essential" parts would be rapidly implementing the open with distance protocols that the rest will follow. No. It's pretty much business as usual. The same cropped up in the Amazon and Instacard delivery strikes.
If the "essential" businesses are still not operating with reasonable protocols, just how can the rest reopen?
It's not zero. I read with pleasure the quite sensible list of actions that our county required of the local hardware store, including posting said list on the front window where I could see compliance. (Waiting with the dog while my wife bought TP.) But one would expect the essential part of the economy to be really zooming along with safety protocols if the 'inessential' part is ready to reopen.
That does not mean reopen. The economic carnage is everywhere, and people will not stand to watch their livelihoods disappear, while virus trackers in many counties remain with stable small numbers. But watch out for the second wave.
We Still Don’t Know How the Coronavirus Is Killing Us is a great essay by David Wallace-Wells. While we're spending $2 trillion or more, and printing $5 trillion or more, it is really striking that our government is not spending massive amounts on research, including just collecting data. Sure, bottlenecks and waste abound here too, but the amount just not known is striking.
For example, I attended a great presentation by Stanford's Jay Bhattachrya on his random sample testing in Santa Clara County, which found a surprisingly large number of asymptomatic cases. Yes, I've read the controversy. Some other day. But, in a $2 trillion dollar budget why are lonely heroes like Jay doing random testing on a shoestring?
Coronavirus Testing Capacity Is Going Unused
Many commercial and academic laboratories in the U.S. are processing coronavirus diagnostic tests far below their capacity, leaving tools crucial to slowing the virus’s spread unused.
Lab executives and public-health officials say that in some cases, the labs are getting far fewer orders for tests than they could conduct.For weeks, everyone has been saying "test test test," and bemoaning the lack of testing capacity. Well, now we have testing capacity. What's going wrong? Well, our public health officials don't have (and did not, in the last month, develop) concrete ready to implement testing protocols in place. You still get a test if you ask for one, which mainly is if you think you have symptoms and can get through the guidelines that still restrict testing. These guidelines are not developed with public health in mind.
Testing meant, for example, widespread random testing, or at least testing of volunteers, so we could find out where the virus is. Just how many people in Palo Alto have the virus, right now? With 1000 roughly random tests we could find out. Nobody is doing that.
We remain, I think, sorely lacking in the public health infrastructure that must take over from blanket shutdowns. California just issued a revised list of what businesses can open. Apparently that's all we know how to do.
Food plants turned out to be a super spreader. ( Kris Maher, Jacob Bunge and Alexandra Berzon in WSJ) The larger point here: About 40% of the economy is still open as "essential." Well, as we get ready to reopen safely the rest of the economy, one would think that the "essential" parts would be rapidly implementing the open with distance protocols that the rest will follow. No. It's pretty much business as usual. The same cropped up in the Amazon and Instacard delivery strikes.
If the "essential" businesses are still not operating with reasonable protocols, just how can the rest reopen?
It's not zero. I read with pleasure the quite sensible list of actions that our county required of the local hardware store, including posting said list on the front window where I could see compliance. (Waiting with the dog while my wife bought TP.) But one would expect the essential part of the economy to be really zooming along with safety protocols if the 'inessential' part is ready to reopen.
That does not mean reopen. The economic carnage is everywhere, and people will not stand to watch their livelihoods disappear, while virus trackers in many counties remain with stable small numbers. But watch out for the second wave.
We Still Don’t Know How the Coronavirus Is Killing Us is a great essay by David Wallace-Wells. While we're spending $2 trillion or more, and printing $5 trillion or more, it is really striking that our government is not spending massive amounts on research, including just collecting data. Sure, bottlenecks and waste abound here too, but the amount just not known is striking.
For example, I attended a great presentation by Stanford's Jay Bhattachrya on his random sample testing in Santa Clara County, which found a surprisingly large number of asymptomatic cases. Yes, I've read the controversy. Some other day. But, in a $2 trillion dollar budget why are lonely heroes like Jay doing random testing on a shoestring?
Wednesday, April 29, 2020
The fire in Treasurys
Just where was the fire that caused the Federal Reserve to buy $1.3 trillion of treasury debt in a month -- financing all treasury sales and then some? I've been puzzling about this question in a few posts, most recently here. Commenter "unknown" impolitely but usefully points me to a nice paper by Andreas Schrimpf, Hyun Song Shin and Vladyslav Sushko that explains some market mechanics. I am still not persuaded that these gyrations motivate or justify the Fed buying these or more trillions of debt, but there is an interesting story here.
Treasury yields
Their first graph shows stock prices and bond yields. As risk and risk aversion rose, as they always do in bad times, stock prices fell and bond prices rose, with yields falling.
Trouble starts on 9 March when "the market experienced a snapback in yields" Look hard at the graph. The blue line rises a bit while the red line continues to fall.
OK, but still -- is it a disaster that the US treasury, that had been borrowing happily at 1.8% in January, must borrow at 0.8-1.2% in March? Is it such a disaster that the Fed must buy all new issues of debt?
"Arbitrage" redux
What caused the "snapback?" here is where the paper gets interesting. Basically a bunch of hedge funds replayed an age-old strategy and got caught. Plus ça change. They bought treasury bonds and simultaneously sold them in futures markets. Since treasury bonds are great collateral they can lever up a small price difference to make a lot with little investment.
But even arbitrage opportunities are not risk free.** Prices that are slightly off can get further off before they eventually converge. And then the hedge funds need to post margin, which they don't have. So, they follow the mother of all financial fallacies -- risk management that consists of selling positions on the way down, trying to synthesize a put option with a stop loss order. But selling to who? Everyone else is doing the same thing, markets get illiquid in times of stress (no, they've never done that before), so the price difference widens even more.
Treasury yields
Their first graph shows stock prices and bond yields. As risk and risk aversion rose, as they always do in bad times, stock prices fell and bond prices rose, with yields falling.
Trouble starts on 9 March when "the market experienced a snapback in yields" Look hard at the graph. The blue line rises a bit while the red line continues to fall.
OK, but still -- is it a disaster that the US treasury, that had been borrowing happily at 1.8% in January, must borrow at 0.8-1.2% in March? Is it such a disaster that the Fed must buy all new issues of debt?
"Arbitrage" redux
What caused the "snapback?" here is where the paper gets interesting. Basically a bunch of hedge funds replayed an age-old strategy and got caught. Plus ça change. They bought treasury bonds and simultaneously sold them in futures markets. Since treasury bonds are great collateral they can lever up a small price difference to make a lot with little investment.
But even arbitrage opportunities are not risk free.** Prices that are slightly off can get further off before they eventually converge. And then the hedge funds need to post margin, which they don't have. So, they follow the mother of all financial fallacies -- risk management that consists of selling positions on the way down, trying to synthesize a put option with a stop loss order. But selling to who? Everyone else is doing the same thing, markets get illiquid in times of stress (no, they've never done that before), so the price difference widens even more.
Tuesday, April 28, 2020
University finances
Colleges and universities are being badly hit by the Covid-19 virus. The spring and summer were pretty bad. If, as likely, it extends into the fall things will be much worse. The tragedy of all this, for large private colleges, is that our administrations apparently learned nothing from 2009, and set themselves up for exactly the same (if not worse) financial crisis.
The exposure
It's hard to think of a business model more susceptible to pandemics. Students come to universities from all over the country, and all over the world. Many US colleges are highly dependent on full-tuition revenue from overseas, especially China. College education was a big export industry for the US, which travel and visa restrictions are likely to kill.
Many state schools depend on people paying full tuition from out of state. Lots of people are not likely to want to pay for online classes, and they certainly don't want to pay more quarters of room and board while living at home in another state. (This might be good for some flexible state schools or community colleges that can let people pick up some transferable credits).
Classes are really not the problem. Undergraduates barely go to classes anyway, and, as reviewed in previous super-spreader posts, we have not seen classrooms as a site of such events. It seems like if people don't talk loudly, they don't spread the virus. The main problem is that the college experience in most of the US centers on a loosely supervised alcohol-fueled bacchanalia. As Stanford's president put it delicately in a recent email to faculty and staff,
The exposure
It's hard to think of a business model more susceptible to pandemics. Students come to universities from all over the country, and all over the world. Many US colleges are highly dependent on full-tuition revenue from overseas, especially China. College education was a big export industry for the US, which travel and visa restrictions are likely to kill.
Many state schools depend on people paying full tuition from out of state. Lots of people are not likely to want to pay for online classes, and they certainly don't want to pay more quarters of room and board while living at home in another state. (This might be good for some flexible state schools or community colleges that can let people pick up some transferable credits).
Classes are really not the problem. Undergraduates barely go to classes anyway, and, as reviewed in previous super-spreader posts, we have not seen classrooms as a site of such events. It seems like if people don't talk loudly, they don't spread the virus. The main problem is that the college experience in most of the US centers on a loosely supervised alcohol-fueled bacchanalia. As Stanford's president put it delicately in a recent email to faculty and staff,
A key challenge is the highly communal nature of our undergraduate living, dining and learning settings, which are not conducive to the physical distancing that has been a key means of controlling the pandemic...
How to spread Covid-19? Nursing home. Aircraft Carrier. Cruise Ship. Jail. College dorm or fraternity.
Saturday, April 25, 2020
Economics of lockdowns video
Cato took some comments I made in a recent event and produced it into a nice short video, 8 minute overview of where I am, or was last week, on the economics of lockdowns. I clearly need to work on the visuals.
Friday, April 24, 2020
Heckman Haiku
Jim Heckman's interview with Gonazlo Schwartz at the Archbridge Institute is making the rounds of economists. I admire it for how much the interviewer and Heckman pack in so little space, so pithy, well expressed, and so happy to trounce on today's pieties. (As blog readers will have noticed, short does not come easily to me.) It's hard to summarize a Haiku -- go read the whole thing. But I'll try.
On "current academic and policy discussion on income mobility and inequality, "
Gonzalo Schwarz: Many commentators have said that it is not possible to achieve the American Dream any more in the United States. Do you think the American Dream is alive and well?
Dr. James Heckman: Ask any immigrant. They are grateful for the chances that America has given them. Many came with nothing. They live in decent neighborhoods and their families have better lives than they could have before coming here. Their children go to college and integrate into American society. The progress of African Americans over the past century is staggering. Many have shaken off the legacies of poverty and discrimination....Social mobility:
G: ...what do you think are the main barriers to income or social mobility?...
H: The main barriers to developing effective policies for income and social mobility is fear of honest engagement in the changes in the American family and the consequences it has wrought. It is politically incorrect to express the truth and go to the source of problems.... Powerful censorship is at play across the entire society....The family is the source of life and growth. Families build values, encourage (or discourage) their children in school and out. Families — far more than schools — create or inhibit life opportunities. A huge body of evidence shows the powerful role of families in shaping the lives of their children. Dysfunctional families produce dysfunctional children. Schools can only partially compensate for the damage done to the children by dysfunctional families.He is right on the fact, how blissfully it is ignored by those wishing more "policies" to address inequality and other social programs, and censorship against those who say it.
On "current academic and policy discussion on income mobility and inequality, "
Ban parties not business
A while ago, I started getting messages that my computer was running out of memory. I put off doing anything about it -- cleaning up a decade's worth of files did not sound like a fun task. But eventually I took a look, sorted files by size, and came to a lovely discovery. There were a few large files -- some video attachment to an email someone sent me three years ago, stuff like that. After I deleted 10 or 20 of these, all of a sudden there was lots of space! The rest of my computer remains a Marie Kondo nightmare.
Every distribution has fat tails. And if you need to do something about it, spend all your time on the tail events and don't bother with the small stuff.
That lesson, of course applies to stopping the spread of the corona virus. Stopping the negligible possibility that a hiker passes it to another hiker out on a (now closed) trail in the Santa Cruz mountains is beyond pointless. Stopping the tiny probability that a worker passes it to another worker in a thoughtfully structured high value business is equally pointless, and vastly more costly.
What do we know about the fat tail? Not as much as we should. Jonathan Kay's lovely Quillette essay on super spreader events covers a lot. (HT Marginal Revolution).
Jonathan points out that our scientists still don't reallhy know whether Covid-19 is spread primarily by large "ballistic" droplets, small persistent aerosol droplets, or contact with surfaces where droplets have landed. They don't know what kind of activities lead to spread. He investigated super spreader events to try to figure out. Jonathan put together all the information he could find on known Covid-19 super spreader events. He found 54, with details on 38. A bit more data collection and research effort on this crucial question would seem worthwhile.
I have a different goal -- what are the activities that we can reduce with greatest effect on the disease, and least economic cost, and within the everyday more apparent limitations of our political and government apparatus?
Like others (see Arnold Kling for example) I'm starting to despair of a way out. We will not have a vaccine for a long time, and kill the economy till the vaccine comes is not an option. Bend the curve, followed by vigorous test, trace and isolate would be possible, but I doubt the US, has the institutional capacity or political will for trace and isolate once we eventually get test to work. I cannot imagine our authorities imposing life in Wuhan (another MR HT). Paul Romer has articulately advocated a big push for widespread testing, notably by relaxing regulations (university labs not allowed to conduct tests, for example). Paul notes correctly that it's worth spending hundreds of billions of dollars on testing to save trillions of dollars of economic and fiscal damage. If we could test everyone every day, and get most of the positives to stay home, the virus would quickly peter out. But I'm dubious our government is capable of even this. Let it rip, argue many others, and wait for herd immunity. But I don't think our governments can do that either, as Boris Johnson found out.
Our governments can, however, come up with lists of banned activities. So let those lists have just a little more common sense. Let the lists of banned activities 1) focus on the tail of super spreader events 2) consider the economic damage vs. public health benefit.
The bottom line I get from Jonathan: It looks like the biggest transmission danger is large droplets exchanged by people talking loudly in large gatherings, in closed quarters, and where many different people interact. Yes, it may be transmitted in other ways, but this is the fat tail, and start with the fat tail. The even greater news: practically no GDP is lost if you ban the super spreading activities on his list.
However the rhetoric needs to change. Right now the calls are for "relax social distancing." This is exactly wrong. Keep social distancing, but relax economic prohibitions. The challenge is that our regulatory state finds it much easier to shut down business -- at tremendous economic cost -- than birthday parties.
Epidemiologists know about fat tails “20% of the individuals within any given population are thought to contribute at least 80% to the transmission potential” of previous infectious diseases.
Also from here (again HT Marginal Revolution)
Jonathan's events:
Every distribution has fat tails. And if you need to do something about it, spend all your time on the tail events and don't bother with the small stuff.
That lesson, of course applies to stopping the spread of the corona virus. Stopping the negligible possibility that a hiker passes it to another hiker out on a (now closed) trail in the Santa Cruz mountains is beyond pointless. Stopping the tiny probability that a worker passes it to another worker in a thoughtfully structured high value business is equally pointless, and vastly more costly.
What do we know about the fat tail? Not as much as we should. Jonathan Kay's lovely Quillette essay on super spreader events covers a lot. (HT Marginal Revolution).
Jonathan points out that our scientists still don't reallhy know whether Covid-19 is spread primarily by large "ballistic" droplets, small persistent aerosol droplets, or contact with surfaces where droplets have landed. They don't know what kind of activities lead to spread. He investigated super spreader events to try to figure out. Jonathan put together all the information he could find on known Covid-19 super spreader events. He found 54, with details on 38. A bit more data collection and research effort on this crucial question would seem worthwhile.
I have a different goal -- what are the activities that we can reduce with greatest effect on the disease, and least economic cost, and within the everyday more apparent limitations of our political and government apparatus?
Like others (see Arnold Kling for example) I'm starting to despair of a way out. We will not have a vaccine for a long time, and kill the economy till the vaccine comes is not an option. Bend the curve, followed by vigorous test, trace and isolate would be possible, but I doubt the US, has the institutional capacity or political will for trace and isolate once we eventually get test to work. I cannot imagine our authorities imposing life in Wuhan (another MR HT). Paul Romer has articulately advocated a big push for widespread testing, notably by relaxing regulations (university labs not allowed to conduct tests, for example). Paul notes correctly that it's worth spending hundreds of billions of dollars on testing to save trillions of dollars of economic and fiscal damage. If we could test everyone every day, and get most of the positives to stay home, the virus would quickly peter out. But I'm dubious our government is capable of even this. Let it rip, argue many others, and wait for herd immunity. But I don't think our governments can do that either, as Boris Johnson found out.
Our governments can, however, come up with lists of banned activities. So let those lists have just a little more common sense. Let the lists of banned activities 1) focus on the tail of super spreader events 2) consider the economic damage vs. public health benefit.
The bottom line I get from Jonathan: It looks like the biggest transmission danger is large droplets exchanged by people talking loudly in large gatherings, in closed quarters, and where many different people interact. Yes, it may be transmitted in other ways, but this is the fat tail, and start with the fat tail. The even greater news: practically no GDP is lost if you ban the super spreading activities on his list.
However the rhetoric needs to change. Right now the calls are for "relax social distancing." This is exactly wrong. Keep social distancing, but relax economic prohibitions. The challenge is that our regulatory state finds it much easier to shut down business -- at tremendous economic cost -- than birthday parties.
Epidemiologists know about fat tails “20% of the individuals within any given population are thought to contribute at least 80% to the transmission potential” of previous infectious diseases.
Also from here (again HT Marginal Revolution)
We identified only a single outbreak in an outdoor environment, which involved two cases. Conclusions: All identified outbreaks of three or more cases occurred in an indoor environment, which confirms that sharing indoor space is a major SARS-CoV-2 infection risk.An added observation: Fat tails of superspreader events helps to explain why the virus seems to spread quickly in some places and not in others. 2,4, 8, 16, 32, 64, actually takes a while to get to 10,000. 2, 124, 256 from an early super spread event gets you there much faster.
Jonathan's events:
Many of the early SSEs, in fact, centered on weddings, birthday parties, and other events.The joy of life, but nearly zero GDP.
Thursday, April 23, 2020
Treasury Liquidity
So just what was the "disruption" in the Treasury market that so spooked the Fed, that now the Fed is buying more than the Treasury is selling?
A commenter on my last post on corporate bonds points to Treasury Market Liquidity during the COVID-19 Crisis by Michael Fleming and Francisco Ruela at the NY Fed, April 17 .
Michael and Francisco nicely show us the facts. They make no editorial comment at all, except perhaps in the figure titles, so my questions about just how big a problem this is are not directed at them.
Bid-ask spreads widened, to financial crisis levels (when the Fed did not, by the way, intervene.) The plot is hard to read in the far right end in order to compare to 2008. (Suggestion to the authors: focus on the last three months so we can see what was happening, not on the comparison to 2008.) As far as I can make it out, the 5 year spread widened form 0.25 /32 to about 0.4 /32; the 10 year from 0.5 to 1.0 and the 30-year from 1 to 5.
If I read the caption correctly, each of these numbers is 1/32 of one percent of par, 0.03%, so the 5 year spread went from 0.008% to 0.012% and even the 30 year went from 0.03% to 0.16%.
The "order book depth, measured as the average quantity of securities available for sale or purchase at the best bid and offer prices" (my emphasis) declined. There is usually a lot more for sale if you're willing to pay more.
The difficulty of trading includes not just the bid ask spread, but a guesstimate of how much you will depress prices if you sell $100 million in a huge hurry. This price impact went up. But, it is measured as "slope coefficients from ...regressions of one-minute price changes on one-minute net order flow." How bad is it to wait a whole minute to sell $100 million? Also, most traders use fairly complex strategies to minimize price impact. And there is lots to complain about in this measure of price impact. (I prefer autocorrelation measures -- how much did the price bounce back.)
And the absolute value looks to a layperson remarkably small. 7/32 = 0.22%, two tenths of a percent, on the 5 year bond. OK, 0.75% on a 30 year bond which is almost real money. But 30 year bonds are pretty volatile anyway as we'll see in a moment.
Price volatility jumped, especially (actually almost entirely) for the 30 year bond. The 30 year bond was experiencing 70% annualized volatility, which is 4.4% per day. That puts some of these spread and price impact measures into context. They are orders of magnitude smaller than the daily price volatility.
This is not unique to the Treasury market. Stock price volatility went through the roof too by the way. Here's the VIX, peaking at 80. The Fed has not yet seen fit to buy stocks, and let us hope it does not do so.
Throughout all these numbers, the steady march from 1, 5, 10, to 30 year bonds is instructive. Longer bonds are more volatile always. "Liquidity" is usually confined to the shorter maturities.
Trading volume was high too. Again you have to squint to see it.
A trillion dollars a week is a lot of buying and selling. What's "disruptive" or dysfunctional about that? This isn't Costco, whose trading volume in toilet paper went to zero after it sold out.
To me, there is a sense of utterly normal in all of this. Supply curves slope up, of everything, including "liquidity."
Obviously, we hit a period of huge uncertainty, divergence of opinion, and liquidity needs. The fundamental, rational, normal, functional, whatever you want to call it, price will be quite volatile, as was the stock price. The fundamental, rational, normal, whatever you want to call it desire to trade will rise as well.
So how does a market react when there is a large increase in the volatility of prices and demand for trading. Well, supply curves slope up -- that demand is accommodated but at a higher price.
Dealers who buy and have to hold securities in inventory for a day or two are more exposed to risk when prices are more volatile, so they buy less other things constant. Bid ask spreads and price impact rise to give them a higher profit, commensurate with that risk. In a time of volatility, there is more asymmetric information, so dealers charge a higher bid-ask spread. This may sound like less of a problem for Treasuries, but there is short term information about future order flows and future Federal reserve actions and even interest rates given the huge macro uncertainty. And the price volatility may be both a sign of trading demand and an inducement to it. If you can spot the direction, there is a lot more money to be made.
Supply and demand. If trading volume goes up while spreads and price impact are rising, the shock is to the demand for trading. If trading volume went down while spreads and price impact rose, the shock is to the supply of trading services. This event sure looks like a shock to demand, accommodated pretty well by dealers. (I wrote a paper a long time ago called "stocks as money," documenting a similar case of demand for trading)
Where is the evidence that something is wrong with supply, that there is also a shift in the supply curve?
Michael and Francisco wryly note the same point:
Even if "intermediation" were the problem, why is buying up the whole supply the answer, not both buying and selling, to reduce bid-ask spreads?
The Fed announced:
"because of (big financial gobbledygook which you wouldn't understand anyway so it doesn't matter if it makes any sense) we're going to buy a trillion dollars of treasurys?"
Finally, if absolute liquidity in Treasury markets is so important, if the ability to transact at 0.01% or less loss, in minutes, is a crucial social problem, then why not talk about some fundamental reforms to those markets?
There is a tendency throughout economics to write, "here is my policy," then "here are the problems that motivate my policy." But if you look at the problems, a lot of other policies would solve them better. Economics is too often answers in search of questions.
So, bottom line, I'm still looking for evidence. I'm willing to give the Fed the benefit of the doubt. All the people I know at the Fed are smart and well-intentioned looking at a lot more data than I am. Just what is it that motivates buying a trillion dollars of treasury debt, and more trillions to come?
A commenter on my last post on corporate bonds points to Treasury Market Liquidity during the COVID-19 Crisis by Michael Fleming and Francisco Ruela at the NY Fed, April 17 .
Michael and Francisco nicely show us the facts. They make no editorial comment at all, except perhaps in the figure titles, so my questions about just how big a problem this is are not directed at them.
If I read the caption correctly, each of these numbers is 1/32 of one percent of par, 0.03%, so the 5 year spread went from 0.008% to 0.012% and even the 30 year went from 0.03% to 0.16%.
The "order book depth, measured as the average quantity of securities available for sale or purchase at the best bid and offer prices" (my emphasis) declined. There is usually a lot more for sale if you're willing to pay more.
The difficulty of trading includes not just the bid ask spread, but a guesstimate of how much you will depress prices if you sell $100 million in a huge hurry. This price impact went up. But, it is measured as "slope coefficients from ...regressions of one-minute price changes on one-minute net order flow." How bad is it to wait a whole minute to sell $100 million? Also, most traders use fairly complex strategies to minimize price impact. And there is lots to complain about in this measure of price impact. (I prefer autocorrelation measures -- how much did the price bounce back.)
And the absolute value looks to a layperson remarkably small. 7/32 = 0.22%, two tenths of a percent, on the 5 year bond. OK, 0.75% on a 30 year bond which is almost real money. But 30 year bonds are pretty volatile anyway as we'll see in a moment.
This is not unique to the Treasury market. Stock price volatility went through the roof too by the way. Here's the VIX, peaking at 80. The Fed has not yet seen fit to buy stocks, and let us hope it does not do so.
Throughout all these numbers, the steady march from 1, 5, 10, to 30 year bonds is instructive. Longer bonds are more volatile always. "Liquidity" is usually confined to the shorter maturities.
Trading volume was high too. Again you have to squint to see it.
... daily trading volume in the market overall reached a record high for the week ending March 4, averaging over $1 trillion, roughly twice its post-crisis averageWhat does it all add up to?
A trillion dollars a week is a lot of buying and selling. What's "disruptive" or dysfunctional about that? This isn't Costco, whose trading volume in toilet paper went to zero after it sold out.
To me, there is a sense of utterly normal in all of this. Supply curves slope up, of everything, including "liquidity."
Obviously, we hit a period of huge uncertainty, divergence of opinion, and liquidity needs. The fundamental, rational, normal, functional, whatever you want to call it, price will be quite volatile, as was the stock price. The fundamental, rational, normal, whatever you want to call it desire to trade will rise as well.
So how does a market react when there is a large increase in the volatility of prices and demand for trading. Well, supply curves slope up -- that demand is accommodated but at a higher price.
Dealers who buy and have to hold securities in inventory for a day or two are more exposed to risk when prices are more volatile, so they buy less other things constant. Bid ask spreads and price impact rise to give them a higher profit, commensurate with that risk. In a time of volatility, there is more asymmetric information, so dealers charge a higher bid-ask spread. This may sound like less of a problem for Treasuries, but there is short term information about future order flows and future Federal reserve actions and even interest rates given the huge macro uncertainty. And the price volatility may be both a sign of trading demand and an inducement to it. If you can spot the direction, there is a lot more money to be made.
Supply and demand. If trading volume goes up while spreads and price impact are rising, the shock is to the demand for trading. If trading volume went down while spreads and price impact rose, the shock is to the supply of trading services. This event sure looks like a shock to demand, accommodated pretty well by dealers. (I wrote a paper a long time ago called "stocks as money," documenting a similar case of demand for trading)
Where is the evidence that something is wrong with supply, that there is also a shift in the supply curve?
Michael and Francisco wryly note the same point:
High trading volume amid high illiquidity is common in the Treasury market, and was also observed during the market turmoil around the near-failure of Long-Term Capital Management (see this paper) and during the 2007-09 financial crisis (see this paper). Periods of high uncertainty are associated with high volatility and illiquidity but also high trading demand.also
Not surprisingly, volatility caused market makers to widen their bid-ask spreads and post less depth at any given price, and the price impact of trades to increase, illustrating the well-known relationship between volatility and liquidity.So just where is the fire here? Where is the screaming hole in financial markets that justifies the Fed buying $1.3 trillion treasury securities in a month?
Even if "intermediation" were the problem, why is buying up the whole supply the answer, not both buying and selling, to reduce bid-ask spreads?
The Fed announced:
To support the smooth functioning of markets for Treasury securities and agency mortgage-backed securities that are central to the flow of credit to households and businesses, over coming months the Committee will increase its holdings of Treasury securities by at least $500 billion and its holdings of agency mortgage-backed securities by at least $200 billion.How does buying it all up promote the "smooth functioning" of markets? Is there anything more than
"because of (big financial gobbledygook which you wouldn't understand anyway so it doesn't matter if it makes any sense) we're going to buy a trillion dollars of treasurys?"
Finally, if absolute liquidity in Treasury markets is so important, if the ability to transact at 0.01% or less loss, in minutes, is a crucial social problem, then why not talk about some fundamental reforms to those markets?
As described in this post, roughly half of Treasury securities trading occurs through interdealer brokers (IDBs), in which dealers and other professional traders transact with one another, and roughly half between dealers and clients. Our focus is on the IDB market, and on the electronic IDB market in particular, which accounts for about 87 percent of IDB trading.Wider trading would make a lot of sense. Federal debt is carved up into 250 different securities or more. As I argued here, if you want them liquid, rearranging federal debt to only a few securities would make each one more liquid. If "balance sheet space," i.e. inadequate equity financing and regulatory risk-taking constraints, are stopping those with expertise in market making from making more markets, why in heaven's name after 12 years of Dodd-Frank act, capital requirements, essays on equity-financed banking, Volker rule and the rest, don't broker dealers have enough equity capital to let them trade through the covid-19 virus on top of a new cholera pandemic and a war? "Constrained balance sheets" are not a fact of nature, they are the product of 12 years of regulatory failure.
There is a tendency throughout economics to write, "here is my policy," then "here are the problems that motivate my policy." But if you look at the problems, a lot of other policies would solve them better. Economics is too often answers in search of questions.
So, bottom line, I'm still looking for evidence. I'm willing to give the Fed the benefit of the doubt. All the people I know at the Fed are smart and well-intentioned looking at a lot more data than I am. Just what is it that motivates buying a trillion dollars of treasury debt, and more trillions to come?
Wednesday, April 22, 2020
GoodFellows: Cold War 2
The latest GoodFellows, on just how much we need to ramp up Cold War 2 against China.
Since it was two against one, and I didn't get a response in, I'll add one unfair late hit. In discussing Huawei, and whether Chinese state planning would allow them "economic dominance" in the next decades, my colleagues jumped to the charge that Huawei equipment would include nasty backdoors that the Chinese government would use to spy on us.
I think here they confused "economic competition" with security competition. The topic was whether state planning could give a nation "economic domination" of anything important. The reply that we need to worry about security implications does not answer the question.
The charge I think has also been overstated. Huawei has every interest to assure people its equipment does not have back doors, and my impression is they convinced the UK pretty well on that. Moreover, the US government is explicit in its desire that Apple and other US companies give the NSA back doors. I would welcome more knowledgeable commentary on this issue before next week.
Bond liquidity
When the Fed stepped in, were corporate bonds "illiquid," the market "dysfunctional," or were the prices just low, as they should be in advance of a Great Recession with larger bankruptcy risk? Did the Fed "liquefy" the market, "intermediate," grease the wheels, or is it just buying, and propping up prices so that bondholders can dump bonds on the Fed before things get really bad?
I asked for evidence on bond market liquidity in my last post on the topic, "Bailout redux," and Pierre-Olivier Weill passed on a paper he has recently written with Mahyar Kargar, Benjamin Lester, David Lindsay, Shuo Liu, and Diego Zúñiga, Corporate Bond Liquidity During the COVID-19 Crisis.
Here is their estimate of roundtrip trading costs -- if you buy and then sell, how much do you lose in bid ask spread. Feb 19 is the stock market peak. March 18 is the day after the Fed announced it would lend money to broker-dealers and take bonds such as these as collateral. March 23 the Fed announced it would buy corporate bonds on the secondary market, and buy directly from companies issuing new corporate bonds.
I asked for evidence on bond market liquidity in my last post on the topic, "Bailout redux," and Pierre-Olivier Weill passed on a paper he has recently written with Mahyar Kargar, Benjamin Lester, David Lindsay, Shuo Liu, and Diego Zúñiga, Corporate Bond Liquidity During the COVID-19 Crisis.
We were prepared
A lovely compilation from Judge Glock. Some excerpts
six months before the current outbreak, Congress passed the Pandemic and All-Hazards Preparedness and Advancing Innovation Act of 2019, which offered funds and planning authority for just such a crisis as we now face.[2] This act was a reauthorization and an extension of half a dozen similar acts passed over the previous two decades, which acts were themselves extended in countless congressional spending bills, all of which resulted in countless plans....
Pervasive Pandemic Preparedness Planning
After the avian influenza scare of 2005, Congress did the thing it does best, demand that somebody else come up with a plan. With the help of some of the best known names is Congress, Congress passed the Pandemic Preparedness and Response Act in December of the following year.[3] The act ordered the administration to convene a Pandemic Influenza Preparedness Policy Coordinating Committee, with most of the Cabinet in attendance, to write a plan for a biological catastrophe.[4] The result was, first, a White House Homeland Security Council National Strategy for Pandemic Influenza, followed the next year by National Strategy for Pandemic Influenza Implementation Plan. The latter plan contained 233 pages of nebulous suggestions, such as recommending that, in a crisis, the government should be “providing anticipatory guidance and dispelling unrealistic expectations about the delivery of health and medical care.”[5] These general plans in turn birthed numerous individual departments plan, such as the Department of Defense Implementation Plan for Pandemic Influenza.[6] To supplement these federal plans, the Preparedness Act, and its subsequent iterations, also mandated that states create their own Pandemic Preparedness Plans, which have to be submitted regularly to the Centers for Disease Control and Prevention for approval. These plans total thousands of pages.[7]
Mitigating moral hazard -- unemployment edition
As Kurt Huffman, restaurant owner, writes vividly in the WSJ, concerns that unemployment insurance paying more than wages might induce people to stay home even when jobs are available are not just scare stories told by heartless free-market economists.
Lars Ljungqvist and Tom Sargent long ago pondered the question why Sweden, with an apparently quite generous unemployment insurance program had so much less unemployment than, say, France. The answer, as I recall, is that Sweden had a bit of stick with the carrot: if you got offered a job, you had to take it or lose unemployment insurance.
It's in Ljungqvist, Lars and Thomas J. Sargent. ”How Sweden’s Unemployment Became More Like Europe’s” in Reforming the Welfare State: Recovery and Beyond in Sweden, eds., Richard B. Freeman, Birgitta Swedenborg and Robert Topel. Chicago: University of Chicago Press, 2010, one of many great papers Lars and Tom wrote on unemployment insurance. I don't have a link to an online version. p. 191:
...we realized that we needed to hire back some of our staff to help with the demand. That proved harder than we expected.
We started making the calls last week, just as our furloughed employees began receiving weekly Federal Pandemic Unemployment Compensation checks of $600 under the Cares Act. When we asked our employees to come back, almost all said, “No thanks.” If they return to work, they’ll have to take a pay cut.
This has had the perverse effect of making it impossible for us to hire enough people even for our limited takeout and delivery business at a time of rapidly rising unemployment...it will persist at least until July 31, when the unemployment bonus expires. ...
The Trump administration is talking about setting a timeline for when the country can “open for business.” For my business, Congress has already locked down that date. We plan to open our dining rooms on Aug. 1, once the government stops paying people $15 an hour, on top of standard unemployment compensation, to stay home.Hint to Mr. Huffman: I would not bet too much that this deadline is not extended.
Lars Ljungqvist and Tom Sargent long ago pondered the question why Sweden, with an apparently quite generous unemployment insurance program had so much less unemployment than, say, France. The answer, as I recall, is that Sweden had a bit of stick with the carrot: if you got offered a job, you had to take it or lose unemployment insurance.
It's in Ljungqvist, Lars and Thomas J. Sargent. ”How Sweden’s Unemployment Became More Like Europe’s” in Reforming the Welfare State: Recovery and Beyond in Sweden, eds., Richard B. Freeman, Birgitta Swedenborg and Robert Topel. Chicago: University of Chicago Press, 2010, one of many great papers Lars and Tom wrote on unemployment insurance. I don't have a link to an online version. p. 191:
"The Swedish government was exceptional among European countries in intervening in workers' search processes by monitoring them to make sure they accepted job offers that the government deemed to be acceptable. "A similar idea might make sense to get the US going again. Our unemployment insurance has been extended from those fired to those furloughed. Surely if your employer says "we need you back now," the extra Federal unemployment insurance that pushes wages above replacement for furloughed workers can cease.
Tuesday, April 21, 2020
Forbearance
Peter Wallison has a worthy OpEd in the WSJ, "Forbearance." Continuing my earlier thoughts on the financial response here and here, I don't think he goes far enough.
Let me tell a little story. Andy runs a restaurant. To run the restaurant, and live, he has a mortgage, he rents the restaurant space, and he borrowed money to buy to buy the equipment. Bob is retired. While he was working he lent Andy the money to buy the house and the restaurant equipment, and he owns the building. He lives off the income from these investments.
The virus comes and Andy has no income. He has enough savings to buy food for a while, and other current expenses. But he can't pay rent, mortgage, and debt payments. This is the central problem our government faces right now.
One answer: The federal government prints money and lends it to Andy so he can keep paying Bob. You can see a major problem here. Andy has no income. Eventually the restaurant may reopen, but then from the same profit stream Andy has to keep paying Bob and also pay back the loan that kept things going in the lockdown. Hmm.
Let me tell a little story. Andy runs a restaurant. To run the restaurant, and live, he has a mortgage, he rents the restaurant space, and he borrowed money to buy to buy the equipment. Bob is retired. While he was working he lent Andy the money to buy the house and the restaurant equipment, and he owns the building. He lives off the income from these investments.
The virus comes and Andy has no income. He has enough savings to buy food for a while, and other current expenses. But he can't pay rent, mortgage, and debt payments. This is the central problem our government faces right now.
One answer: The federal government prints money and lends it to Andy so he can keep paying Bob. You can see a major problem here. Andy has no income. Eventually the restaurant may reopen, but then from the same profit stream Andy has to keep paying Bob and also pay back the loan that kept things going in the lockdown. Hmm.
Monday, April 20, 2020
Tidbits of wisdom
From my Hoover colleague Niall Ferguson
It is not just that Trump bungled his response to the crisis (though he certainly did). Much more troubling is the realisation that the parts of the federal government that are responsible for handling a crisis like this – supposedly, the genuine experts — bungled it too.
The United States Department of Health and Human Services is a mansion with many houses, but the ones that were charged with pandemic preparedness appear to have failed abjectly: not only the Centers for Disease Control and Prevention, but also the Food and Drug Administration and the Public Health Service, as well as the National Disaster Medical System.
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