Good Fellows -- International Man Of History - Barokong

A new lively Good Fellows discussion video and podcast Direct links here if the above embed codes don't work.
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Jones And Fernández-Villaverde Update - Barokong

Chad Jones and Jesús Fernández-Villaverde have updated their SIR model with social distancing. A part I find very intriguing is that they impute the infection rate and the reproduction rate from death rate data. The infection rate \(I_t\)  is given by \[I_t = \frac1\delta \gamma \left( \fracd_t+2-d_t+1\theta - d_t+1 \right)\] where the greek letters are parameters they estimate by fitting the path of deaths over time, and \(d_t\) is the daily death rate. Though deaths only happen a few weeks after infection, you can reverse the versi dynamics to figure out how many are infected today from how many are dying today. (Well, tomorrow and the day after). They similarly infer today's reproduction rate \(R_0\) from the next three days death rates. Now, there is clearly some inaccuracy here, and I've been pestering them to provide standard errors. There is some noise in daily deaths and once you start double and triple differencing them, the noise is larger. But as I think about behavioral and policy responses, these are the numbers we need. How many people in this state, city, zip code, grocery store, kafe, are infectious right now? 1 in 10? 1 in 100? 1 in 1000? 1 in 10,000? Is the virus spreading or slowly decaying, with reproduction rate below one? Just how careful do we need to be? Is wiping down,  surfaces or spraying luggage with disinfectant remotely cost-effective? Where are hot spots? If we had spent 1/1,000,000 of the $5 trillion the government is spending on random testing, we would know the answer to this question.  We don't. We do have death data. So a measurement with error of the thing we need the most is potentially quite valuable. Reproduction rates seem to stabilize around one, as my little behavioral model suggested. The fraction currently infectious is tiny. Still, half a percent is half a percent. If you run in to 100 people a day you're going to get it in two days. (A commenter corrects my sloppiness here -- "run into" has to have enough close interaction to transfer the virus.) Go look up your location in Table 1 (too big to include) The SF Bay Area only has 0.04% infected! That Whole Foods is pretty safe. But the reproduction rate is still above one. Their dashboard has up to date results for lots of places.
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Reopening The Economy, And Aftermath, Now On Youtube - Barokong

My Bendheim Center talk and discussion with Markus Brunnermeier on all things Covid-19 and economics is now on YouTube, direct link here. I start at 14:08. If you like the paintings behind me and you're getting bored, more gosip here. (Shameless nepotism disclaimer.)
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Reopening The Economy -- And The Aftermath - Barokong

I'm doing a Zoom talk at the Bendheim Center, Princeton, with Markus Brunnermeier, 12:30 Eastern today (Monday May 18) on this, tune in if you're interested. It's mostly based on recent blogs and opeds. Sign up here. I'll post a link to the video when it's over.
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Schmitz On Monopoly - Barokong

Jim Schmitz has released the first salvo in what promises to be a monumental work on monopoly, titledMonopolies Inflict Great Harm on Low- and Middle-Income Americans. (I love titles with answers and no colons.) Today, monopolies inflict great harm on low- and middle-income Americans. One particularly pernicious way they harm them is by sabotaging low-cost products that are substitutes for the monopoly products. I'll argue that the U.S. housing crisis, legal crisis, and oral health crisis facing the low- and middle-income Americans are, in large part, the result of monopolies destroying low-cost alternatives in these industries that the poor would purchase. He promises more to come Legal Services, Residential Construction, Hearing Aids, Eyecare and ...Repair, Pharmaceutals, Credit Cards, Public Education... There is a huge one right there. To Jim the main characteristics of monopoly are A. Monopolies sabotage and destroy markets. They typically destroy substitutes for their products, those that would be purchased by low-income Americans. B. Monopolies also use their weapons to manipulate and sabotage public institutions for their own gains... Unlike worries about big business (or today's FANGs), most monopolies are associations of smaller businesses Monopolies are difficult to detect...they  form power relationships of infinite complexity that are hard to untangle.... From the literature in the 1940s he mentions labor unions and farmers. ..construction (with “concealed protection of monopoly by doctored building and other ordinances”), retail trade (with “so-called ‘fair-trade’ laws which compel businessmen to act as if they were monopolists even if they wish not to”), farming (where farmers enjoy “the pleasures and profits of monopolistic behavior”)...Professional associations,... union- management monopolies. Jim is not just assembling evidence on particular markets. He has a methodological quest, to revive and reinvigorate a tradition from Henry Simons and Thurman Arnold in the first half of the 20th century, and to displace and destroy the conventional paradigm as taught over and over again in textbooks. What we repeat to generations of undergraduates is that a monopoly is a business that has a downward sloping demand curve. It raises its price, or restricts its output, to earn greater profits. One of many troubles with this view is that it's hard to see that much damage. The Harberger triangle is small. In fact, one of the many theorems about standard analysis is that the perfectly price-discriminating monopolist is efficient,  since it produces the same amount as the competitive firm. Dealing with airlines, credit card companies, and college tuition doesn't feel that way. The textbook goes on to say we need anti-trust to reestablish competition. Jim argues that this entirely misses the point. Most monopolies get their restrictions from government in the first place, and their damage lies in sabotaging low-cost competitors and innovation. Why do we tell the same tired story over and over? It's an interesting reflection on intellectual traditions. Much of Jim's analysis is mulut, historical, and empirical. It's so much easier to push the graphs around, and tell the clearest parables over and over. But in doing so, we lose much of the richness of experience that an earlier generation had.
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Markets Work Even In Crisis - Barokong

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 rincian 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. ·     It was also illegal to produce, sell and distribute personal protective equipment such as masks, gowns, gloves, etc. ·     Medicare actually dictated how many beds a hospital could have and no one could create additional beds anywhere without government permission. ·     In most cases it was illegal for a doctors to practice across state lines – consulting with patients in states where they had not been licensed to practice. ·     It was illegal for employers and insurers to waive the deductibles and copayments for coronavirus detection and treatment for the 26 million families with Health Savings Accounts (HSAs). ·     Medicare refused to pay for doctor consultations by means of phone, email, or Skype – except under special circumstances. ·     Medicare refused to pay for direct primary care services (concierge care) that would give patients 24/7 access to a physician, including contact by phone, email, and video at nights and on weekends. ·     It was illegal for employers to put money into an HSA so that employees could choose their own direct primary care physician. . And it was illegal to use employer money to buy individually owned insurance that employees could take with them when they moved to another job or exited the labor market. These barriers to sensible virus responses are largely gone for now. Will there be another ratchet effect, holding these responses in place after the COVID scare is gone? Let’s hope so. On the other hand, Jerry Brown noticed that planning and zoning rules were hindering recovery from wildfires and rebuilding after earthquakes, and rescinded all sorts of rules. Construction happened fast. Once. That wisdom did not stick. The ill effects of price controls, even in a crisis, especially for items whose price is objectively pretty low, is another one of those issues like free trade where economists and laypeople look at each other with jaws hanging in disbelief. Actually, it is a life-changing proposition -- counterintuitive to common sense, and clear as a bell when you understand it. It's a great conversion moment. Demand curves do slope down, and supply curves do slope up. Russ Roberts writes beautifully on price controls and face masks: What usually happens when masks are in short supply is that prices start to rise as buyers compete for the masks that are still available. The higher price encourages the manufacturer to add a night shift. Hire more workers. Work the existing shifts more intensely. If prices rise enough, companies that make other things may find it profitable to start making masks. Russ doesn't quite emphasize enough that it's more expensive to ramp up mask production quickly. So charging double the normal price doesn't even mean "profit," a rent that can be taxed away without distortion. The higher prices encourage hospitals that don’t need masks — the ones in Wyoming, say — to not hoard them, leaving them free to go to New York. Buyers of masks pay a premium, but there are a lot more to go around. Demand curves slope down, people are more careful to allocate expensive goods. It seems cruel, heartless, and immoral to make hospitals pay more for masks just when they are most desperately needed to save lives. But the alternative, a world where prices do not rise when life and death are on the line, is cruel and heartless, too. I add, masks are 50 cents on a wajar day. We are spending and losing a trillion dollars a month on the coronavirus. Haggling over who has to pay for masks is like complaining about the price of chewing gum at a $1,000 a night resort. If you hold prices down artificially when masks are in high demand, you destroy the financial incentive to make more masks. You also destroy any incentive to create excess capacity or stockpiles for a future pandemic. This is really an important point. Price controls are said to discourage "hoarders." But in fact it is exactly "hoarders" that we want! This message needs to be multiplied by about a million and sent to the Federal Reserve. Their actions have destroyed the incentive to keep some cash around, some ekstraequity on the balance sheet, and the ability to sweep in and buy at "fire sales." Ironically, perhaps, this seems to be happening in China, where over 3000 companies, including FoxConn and a Chinese automaker added mask making to their production lines at the beginning of the year. But it doesn’t seem to be happening very much in the United States. Why? Markets are failing in America because we’re not letting them work. It’s not a market failure. It’s a policy failure... U.S. distributors can’t pass higher prices through to hospitals in the midst of the crisis, for fear of being accused of profiteering. .. Most states have laws against “price gouging.” In California, for example, a state of emergency was declared on March 4, 2020 which limits price increases to 10% with violators subject to a year in prison and a fine up to $10,000 and other financial consequences. As for any masks in private stockpiles, forget about it. An auctioneer in Houston, Texas, offered 750,000 masks for bids. The state attorney general sued him for price gouging. The masks are in limbo. From the Department of Justice press release on April 2, 2020: “If you are amassing critical medical equipment for the purpose of selling it at exorbitant prices, you can expect a knock at your door,” said Attorney General William P. Barr. “The Department of Justice’s COVID-19 Hoarding and Price Gouging Task Force is working tirelessly around the clock with all our law enforcement partners to ensure that bad actors cannot illicitly profit from the COVID-19 pandemic facing our nation.” This sounds good but it comes at a cost — government has destroyed the opportunities to make profits by increasing the supply of masks. ... 3M, the largest manufacturer of N95 respirators in the U.S., says that it has doubled production in the last two months to about 100 million per month with plans to double that number in the next 12 months. Double in 12 months ? This will be over long before that. That’s great, but I wonder if they could get there quicker if they could charge more for masks. 3M has been under attack from President Trump for selling some of their masks to Canada and they’ve been under attack from 20 attorneys general demanding that 3M police the price distributors charge for their masks. Incentives matter. Pride or fear or kindness will motivate you. But so does money. And because responding with urgency is usually expensive, money makes it easier to indulge your kindness. Bottom line: Prices allocate resources and transfer incomes. Governments control prices to transfer incomes, putting up with the bad allocation of resources. Cheap items that are critically needed in a pandemic are exactly the items where allocating resources takes full precedents over transferring incomes -- especially between branches of a government spending trillions of dollars.
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Romer: If Virus Tests Were Like Sodas; A Modest Extension - Barokong

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: 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 persoalan: 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 duduk perkara 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.
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Economics Of Lockdowns Video - Barokong

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.
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An Sir Versi With Behavior - Barokong

Following my last post, the SIR versi 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 versi 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 versi as presented by Chad Jones and JesúsFernández-Villaverde: \beginalign* \Delta S_t+1 & =-\beta S_tI_t/N\\ \Delta I_t+1 & =\beta S_tI_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% \endalign* 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 versi saat-saat. Lowering the reproduction rate does not immediately stop the disease. The versi 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 \(\beta S_tI_t/N\) 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 versi 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 versi, 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 versi 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 versi 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 versi 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 versi, 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 versi, 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 versi 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 versi 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 versi 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 perorangan 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 versi 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 \[ \beta_t=\beta_0e^-\lambda t+\beta^\ast(1-e^-\lambda t). \] 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 versi, seems unrealistic because people aren't going to keep distancing voluntarily or involuntarily. Eichenbaum, Rebelo and Trabandt,  have an economic versi 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 versi (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 versi 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 missedMacroeconomic 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 versi 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 versi 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 versi with those from a modified SIR versi in which individuals reduce contacts as a function of the current or cumulative number of cases. Thanks to Andy Atkeson for the tip. See hisA 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 versi, 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 versi, 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 versi,  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 versi, R0 varies with death rate'); print -dpng std_sir_aD.png
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Heckman Haiku - Barokong

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. 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, " The current research in the field is shoddy. It has gained traction because it appeals to the negative image of American society held by leading opinion makers like the New York Times and the Atlantic. In truth, the evidence based on the IRS data is deeply flawed and has been incorrectly analyzed. ... The same can be said of the academics who write about the growth of the Top 1%. Careful studies show much less growth in disparity than what is picked up in the popular press and by populist politicians. Economists thrill to "shoddy",  one-big-star-disparages-other-big-stars inside baseball. But the fact is true -- inequality statistics are horrendously badly calculated, and are often used and abused even in academic circles to push a political jadwal. A new “wisdom” has emerged: large samples more than compensate for faulty or missing data. The wisdom of this crowd is that sample size trumps careful data analysis. Again roman-a-clef if you care to know who he is talking about. And they might answer that identification is hard in small samples too, and that they acknowledge the limits of what one can infer from well estimated correlations, so  "wisdom" is a bit of straw man. A precisely estimated correlation is also an interesting stylized fact. But putting aside inside baseball, it is an important point for everyone to remember in the big-data age. I attended Jim's econometrics PhD class when I was an assistant professor at Chicago. He started with this: What are the three most important issues in Econometrics? 1) Identification 2) Identification 3) Identification.
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Good Fellows And Grumpy Podcast - Barokong

Niall Ferguson, H.R. McMaster and I did another "good fellows" discussion here And the latest Grumpy Economist podcast Update: To readers having trouble,  you did figure out to click the link above, not the picture, right? I haven't figured out how to launch the podcast directly from this blog. You have to go to the link on the hoover website. Thanks for your persistence. John
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Weisbach Advice - Barokong

Mike Weisbach is writing an excellentbook of advice, A Field Guide to Economics: A Young Scholar’s Introduction to Research, Publishing, and Professional Development. As a good scholar he is circulating the manuscript. It's really half advice and half a meditation on how the profession works and how it should work. There is a lot of good advice, and a lot of good questions. I'll highlight a few things I disagree with, but don't take that as criticism of the project, rather an invitation to read and think about the issues yourself. Mike advises throughout that you have to spend time explaining why your research is important. I don't have the experience of reading papers that I understand easily but that under-sell their importance. My experience is the exact opposite. I am nearly always lost halfway through any seminar, and notice we seldom get to the actual contribution before 1:00. Bloviation about how something is important before I know what it is annoys me. I struggle with most papers to figure out what it is the authors have actually done, usually explained badly or not at all in the introduction. So I offer contrary advice: don't bury the lede. Tell us what you have done, first and foremost. in the simplest possible terms. Then we can figure out why it's important, how it contributes to a literature, and so on. I noted quite a few famous -- even Nobel-Prize winning -- papers in which the authors had no idea why it was important. Mike counters with a few examples from corporate finance that really needed some effort. It's a worthy discussion. I've also noticed it's a cultural thing -- corporate finance seems to want a long discussion of why it's important before we know what it is, asset pricing and macro seem a bit more the other way. Though, perhaps I'm getting old, but the tendency to puff up papers seems to be increasing. Here too, perhaps I am confusing positive and normative advice. I wish people wrote more transparent papers. But Mike is trying to tell you how to get ahead in the profession, and lots of people do that very well by writing papers that I find hard to read! I encouraged Mike to have a longer discussion of what not to do. Much writing and self-improvement consists of editing, recognizing simple mistakes and fixing them. "Write clearly" is hard to follow. "Don't tell us why it's important before we know what it is" is easier to follow. I think the next draft will have more of that. Mike start well with "how to pick a topic." He encourages young researchers to pick a research program. It is important to emerge with a acara, a merk name, a set of ideas that you are known for. But by his own admission that's not how Mike worked. It's certainly not how I have worked. Every time I sit down to write what I think will be a Nobel-prize winning masterpiece it falls flat. When I think I'm going to make a clever point and move on, it results in a well-cited paper and a program. Mike encourages you to ask big questions. I think questions are a dime a dozen. Research topics are about a hunch of an answer.  Unraveling DNA did not happen by researchers asking "how can we cure cancer." It happened from a fascination with X-ray crystallography. Modern physics -- Galileo, Newton -- was not born from "how do we start an industrial revolution and cure world poverty?" It started by trying to explain the motion of the stars. Here's a good question for topic selection. Should you address politically controversial issues? Should you follow the topic of the day? COVID-19 papers are being produced at amazing speed, just as financial crisis papers were for 10 years. There is an interesting tradeoff of salience vs. permanence. But it is also a fact, emphasized by Mike, that research advances are produced collaboratively, by a group of people working on similar topics, and that much success is measured by influence, by others following in your footsteps. The lone sage answering a question from a mountaintop tends to be unproductive and ignored. Mike's general career advice is also a bit how to be like Mike -- a successful tenured academic at a strong university with an active and well respected post-tenure portfolio of academic research. His examples tend to be our academic superstars. Here my advice was more positive and less normative. There are lots of careers doing research, and many paths to success. Applied research in think tanks, government, central banks, NGOs, is an important and valuable social contribution even if it doesn't get published in Econometrica. The career paths of Larry Summers, Thomas Piketty, Paul Krugman, Ben Bernanke, are as worthy of study as those of Gene Fama and  Bob Lucas. How to avoid the post-tenure slump many people experience who focus on academic publication is worthy of study too. But these are small notes, and I hope they encourage you to read Mike's book and think for yourself what advice is good for younger scholars, or for you if you are one. The main advice I usually give is "don't listen to old people like me, you figure it out." Especially on topics, none of my heroes did what the old people of their generation told them to do!
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Real Time Labor Market Survey - Barokong

Alex Blick and Adam Blandin are putting together a real-time labor market survey. Labor market statistics for the United States are collected once a month and published with a three week delay. .... Currently, the most recent statistics refer to the week of March 8- 14; new statistics will not be available until May 8... This project aims to provide data on labor market conditions every other week, and to publish results the same week, thereby reducing the information lag. We do so via an online labor market survey of a sample representative of the US working age population. Our core survey closely follows the CPS, which allows us to construct estimates consistent with theirs. The first wave of our survey covers the week of March 29-April 4. Our findings reveal un- precedented changes in the US labor market since the most recent CPS data were collected: 1. The employment rate decreased from 72.7% to 60.7%, implying 24 million jobs lost. 2. The unemployment rate increased from 4.5% to 20.2%. 3. Hours worked per working age adult declined 25% from the second week of March.  Half of this decline is due to lower hours per employed as opposed to lower employment. 4. Over 60% of work hours were from home, compared with roughly 10% in 2017-2018. 5. Those who still have their jobs are working fewer hours; 21% report a decline in earnings. 6. Declines were most pronounced for workers who were female, older, and less educated. Bottom line, even worse than you thought. Well, if we shut down the economy, we shut down the economy.
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Mr Admiration - Barokong

24 hours of Marginal Revolution: April 16 1:23 PM Covid-19Fast Grants update April 16 12:15 PM. The vital daily links, including 2. An alternating lockdown strategy. 3. Vox on the Watney Stapp Mercatus mask plan. 4. Derek Lowe on vaccine prospects. 5. Will coronavirus change the proper CPI bundle? 6. “This paper argues that daily ‘universal random testing’, as recently proposed by Paul Romer, is not likely to be an effective tool for reducing the spread of Covid-19... Link here. 7. Why is Detroit worse than Baltimore?  And is there also a Brazilian heterogeneity? (limited information, however) 8. JPMorgan reopening plan, involves building herd immunity among the young. ... 9. How well did Italy do lowering R0 through lockdown? [Very important -- models predict much swifter end than were are seeing] 11. Ongoing chart of Covid-19 deaths in Sweden, also accounting for reporting delays. 12. Who is this helping? (NYT): “Amazon said Wednesday that it would temporarily halt its operations in France after a court ruled the company had failed to adequately protect warehouse workers against the threat of the coronavirus and that it must restrict deliveries to only food, hygiene and medical products until it addressed the issue.”  April 16 7:28 AMWhen Will The Riots Begin? Protests against lockdowns have begun. Crucial. April 16 7:26 AMPPE Shortages and the Failure to Increase Prices. Vital. Anti-price gouging rules are inhibiting supply. An interesting new mechanism: usually people won't pay for stuff until it's delivered. But if you have to ramp up production 10x, you don't have working capital to buy supplies. higher prices provide working capital. There is a rising supply curve everywhere. April 16 2:59 AM (!) One reason why food intended for restaurants is not reallocated to supermarkets We've been puzzling about that here. Why are farmers throwing away food? At our dinner table the answer was obvious -- some regulation is getting in the way. But which one? Food labeling is an obvious one. You can't just sell, you know, food, in a food store. "I’ll say it again: America’s regulatory state is failing us." April 16 12:22 AM Supply curves slope up round 1. Why you get more tests if you agree to pay higher prices. (As I've written a few times, ponder that we are spending a trillion dollars a month on stimulus yet worrying about "price gouging" and haggling over $40 tests and $1 face masks.) I can't keep up! I can barely read this fast.
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How Soon Does It End? - Barokong

How soon does it end? This is a big question which models can help us with. Jesús Fernández-Villaverde and Chad Jones are working on estimating and simulating a epidemiological (SIRD) model of Covid-19. The numbers are based entirely on numbers of deaths, which eliminates much data uncertainty. It includes an initial spreading rate (R0), and the introduction of public policies that lower that rate. One may object to economists treading in these waters but economists (especially of such great talent) are really good at fitting models to data. Here is how the versi fits New York daily deaths per million. The three lines reflect three different possibilities for the death rate, 0.1%, 0.3% and 0.5% of infected people. You can see how the three death rates fit about the same up to now (the other parameters get reoptimized), but differ on the forecast for the future. The cumulative death rates under the three assumptions are quite different, about 800, 1200 or 1500 per million. But what struck me is how close the peaks are -- no matter what parameters you pick, the peak is between April 11 and April 20. By mid-May things are well under control, and it's over by June. This is a really hopeful simulation for our big V U or L discussion. The key input to seeing it over is indeed, "bending the curve," or the peak in sight.  Here is Italy, Italy is clearly past the peak, no matter what parameters you use, and will be over in a month. Here is another insightful plot, for New York The lines are forecast based on data made 1,2, 3, 4, out to 7 days ago (red). The time of the peak is pretty well known. But here is California: California is at a much lower level -- note the vertical scale. 2 deaths per million not 50 in NY. But we don't have that signature of exponential growth, growth slowing and then a peak. So the progression of the forecast rom red to tan (extraordinary good news) is very sensitive to the data from the last 7 days, and you can see it's a bit noisy. In all these simulations, the big unknown is the total death rate. The speed of the event is still in months. On current data, New York ends up with 21% ever infected, and California with 1% ever infected, and total deaths 0.3% of that. But the infection always comes and goes in a matter of two months. This seems like great news for the V, U, L, debate. Back to work in June. There is a big assumption here. Jesús and Chad assume there is an initial reproduction rate, and policy intervenes to bring that down to a lower level. For New York, those are 4.9 and 0.9. (How many people each sick person infects.) For California, 4.0 and 1.0. They then assume that the new lower reproduction rate stays put. If "reopening" in California means going back to a 4.0 reproduction rate, in a population that 99% of people still are uninfected, we just start right back again. So where is a rosy economic scenario that this is over by June and the economy can get going again? Absent a vaccine, it depends on public health being able to take over form blanket shutdowns, to keep R0 below one in a population with very few (but not zero) cases. If we just reopen there will be a second wave, or an endless half open economy. Public health -- lots of testing, tracing, isolating -- allows you to keep R0 low when there are relatively few cases without shutting down the economy. So I think Jesús and Chad's simulations offer great hope that the economic calamity can end quickly if the public health infrastructure is in place to do what it so massively failed to do in January. (The slide deck and paper will be up soon on Chad and Jesús websites. I saw it at our Monday zoom lunch pelatihan. Thanks to Chad and Jesús  for sharing the slides.)
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Rajan On Piketty - Barokong

People often ask what I think of Piketty. I have to admit: I haven't read his books (or pretended to). Life is short, and it's 1,000 pages. But Raghu Rajan has, and writes a splendid and well writtenreview at the FT.  Bottom line, the choir is singing: as a call for nations to enact massive redistribution programmes to reduce inequality, this latest work will persuade few outside his devoted following. What's wrong? Piketty describes social systems through the ages — such as slavery, feudalism, colonialism and caste — collectively as “inequality regimes”. No surprises, then, about what he thinks is their key attribute. In each case, he uses historical sources to map the distribution of incomes and wealth and show how the situation today parallels those earlier abhorrent episodes. The obvious implication: if we are not disturbed by what is going on around us, we should be. If our level of inequality is the same as slavery, feudalism, colonialism, and caste, then we are no better or different. That's an astonishing statement, though common on the left. Unlike Marx, Piketty does not seem to believe the structure of society — the ownership of property, and the economic shares of different groups — is strongly influenced by the technology of production. Marx argued the plough gave us the feudal manor and the steam engine gave us the capitalist mill. Piketty claims instead that the nature of property rights and their distribution is largely driven by the prevailing ideology, a vague term that seems to imply a kind of public brainwashing. Raghu has also read Marx. As economists even the choice of ideas can be analyzed by its utility: the reason for the emphasis here is clear. If inequality stems primarily from ideology, all the reformer has to do is to change the prevailing ideology. Piketty's program: Piketty wants steeply progressive taxes on income, wealth, carbon emissions and, if anyone has somehow managed to hold on to any wealth after all that, on bequests. (I love that little clause in the middle. Great sentence Raghu!) The economic vision is interesting. Piketty does not have the government run the whole economy: Small and medium-sized businesses have an important role to play, he argues. He prefers “temporary ownership” by which successful businesspeople will not accumulate wealth but will see it taxed away, giving others the chance to succeed. This strikes me very much as a French academic's view of running a business. It takes no skill, risk taking, hard work or entrepreneurial spirit. One does it as one becomes a middle manager in the French Railway system. The central conceit of Piketty's earlier work, that all wealth is first stolen and then passed on through generations at r>g has already been well analyzed and destroyed. No, Julius Cesar's descendants do not own all today's wealth. Ragu says it well. Piketty’s assumption in this and his previous book is that today’s rich are largely the idle rich....most top earners in the US today are the self-made “working rich”, such as lawyers, doctors and car dealers, deriving their income from their skills rather than their physical or financial capital. This matters, as If today’s rich work, the sky-high taxes Piketty wants could have serious adverse effects on effort, gross domestic product and tax revenues. I might have chosen a more forceful verb than "serious adverse effects. " And the real issue is tomorrow's rich. Who will found and start great companies in the future just to suffer confiscatory wealth taxation? Also, one virtue of the entrepreneurial rich retaining control over their wealth is that they have already shown an ability to put resources to good use — which is why they are wealthy. How costly would it be to hand over their wealth to a bevy of untried entrepreneurs? Temporary ownership may be very detrimental to society’s productivity. Another superb logical inconsistency: in the “glorious” high-tax years (1950-1979) that Piketty favours, the personal income tax collected in the US averaged 7.6 per cent of GDP, while in the supposedly lower-tax 1980-2018 period he disfavours, it averaged a higher 7.9 per cent. Piketty believes tax loopholes can be eliminated today through international agreement and better information. Yet, if loopholes were rampant then, it undermines his argument that high progressive taxes are consistent with strong growth. If nobody actually paid those taxes in the glorious years between 1950 and 1979, we never actually ran the high-tax experiment. Piketty's vision is as much political and ideological as economic. Raghu points out interesting contradictions here too: while he claims he wants greater democratic participation, he pushes grand elite-devised centralised schemes that suggest a tin ear to the protest movements that have roiled the world it is unclear what would offer a countervailing balance to an overpowerful state when so many are dependent on it for endowments or minimum support, and there are few independent private players of any size. there is a fundamental contradiction in Piketty’s alluring vision of participatory socialism — the pretence that a dose of democracy and a dollop of egalitarianism can be picked off a hidangan. He admits that more coercion will be needed to achieve this in Europe — a European superstate, where no country will have veto power, and common fiscal rules will be imposed on all countries (all the better to tax the rich). Yes, it ostensibly will be democratic but also centralised, with the tyranny of the majority deemed a virtue. Most people will have little sense of control over their futures. It was this very view of Europe that many in Britain rejected with the Brexit vote. Raghu closes Inequality is a real problem today, but it is the inequality of opportunity, of access to capabilities, of place, not just of incomes and wealth. Higher spending and thus taxes may be necessary, not to punish the rich but to help the left-behind find new opportunity. This requires fresh policies not discredited old ones. . I think Raghu is as usual trying to be too nice and admit something to find common ground. Is higher spending actually beneficial to helping the left-out find new opportunity? How are subsidies working out in, say India?  Might we not mention getting out of the way first -- the barriers imposed by teachers unions, the battle against charter schools, the criminal justice system, zoning and similar barriers to housing near jobs, social program disincentives, and the effect of various programs on chaotic family lives? Read and learn from the vast amount of scholarship on display in this book. But look sceptically at its solutions What is the point of reading and learning from "vast scholarship" if it is wrong, and visibly assembled with an elephant's thumb on the scale? I measure scholarship by quality not by weight.  Or is Raghu just once again being polite?  In any case Raghu persuaded me of many things, but not to follow his last piece of advice and read 1,000 pages. But go read the whole review and see for yourself.  Or maybe the book. We may all have time on our hands in the next month or so. **** Update. This excursion clarified things a lot for me. It's not really about wealth, it's about property rights. Are they the foundation of prosperity and growth, the central vital incentive for people to work, accumulate, invent, maintain and improve land, buildings and business? Or are they the evil engine of inequality? You can tell which side I'm on. Even my dog understands property rights. Try to take away that bone.
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A Better Wealth And Taxes - Barokong

CATO has put out a much-improved version of my "Wealth and Taxes" series on wealth inequality and the wealth tax. Html here and pdf here. Many thanks to Chris Edwards and the CATO staff for editing and formatting it, and getting it out in this nice format. ******** Alan Reynolds wrote with interesting comments. Among others, the $18+ trillion now invested in retirement, education and health savings accounts has gradually made middle-income investment income more and more invisible in tax returns as time moved on.   Exemption of $500,000 of capital gains on home sales further reduced the IRS-reported capital income of all but the top 1%. ...the Saez-Zucman methodology is sure to show the rich having a larger and larger share of taxable income from capital, and therefore of wealth based on that taxable income, because income from the savings of middle-income taxpayers has become increasingly unreported. Bottom line: Because tax laws exempted a rising share of investment income (and residential capital gains) of the bottom 95%, the visible portion left showing for the top 1% must appear as a rising share (of a meaningless total). I still like my 2006 WSJ title: "The Top 1% of WHAT?"  Pre-tax, pre-transfer income reported on individual income tax returns was never meaningful, and capital income on those tax returns is incomparable over time.
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Grumpy Podcast - Barokong

We're trying a Grumpy Economist Podcast. The first one talks about my series on wealth inequality and wealth tax. I can't stand listening to myself, as think I always sound dumb and regret all the things I could have said better, so I haven't listened. But I hope it sounds better to the rest of you and provides a useful new grumpy outlet. Thanks to Scott Immergut and Troy Senik who do all the work.
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Health Policy Wonks And The Preservation Of Human Capital - Barokong

Austin Frakt at theNew York Times covered an interestingsurvey of health economists, revealing their interesting support for the status quo  Mike Cannon at CATO hasan interesting tweet storm in reaction, andTyler Cowen at Marginal Revolution also comments. My diagnosis comes at the end. Those whose human capital is knowledge of the current rules, and whose employment derives from the agencies who run the current system, are unlikely to challenge the status quo. Frakt: Imagine if American health policy were established by the consensus of health economists. What would the system look like? Health economists .. strongly reject repeal [of the ACA], with 89 percent opposing the idea. Really, is this miserable status quo the best that thousands of professional health economists can dream up? Various ideas to cut costs in Medicare and Medicaid have been proposed in recent years. Health economists generally oppose those changes. A related idea for Medicare is to convert it to a voucher-based acara. This would establish a set amount the government would pay for your coverage so that you could shop for a health plan. Most health economists (61 percent) also oppose this idea Commenting Frakt notes, It may surprise some that economists, who normally prefer market-based approaches to government programs, are so supportive of Medicare’s current structure. “Though they recognize the value of free markets, economists also believe that market failures are harmful,” the poll’s conductors told me. “In some cases, such as health insurance for the elderly, many economists think that society does best when government provides services directly.” I may be getting jaded, but it seems no longer true that economists normally prefer market-based approaches to government programs. Especially in health. My pretty uniform experience talking to health economists is that even they say "well, the free market might be fine for apples and oranges, but health is too important to be left to the free market."  What follows is often an amazingly patronizing view of the idiocy of the average health consumer, who requires the paternalistic guidance of, well, an army of health policy economists to tell them what to do. Still, that a large majority of PhD economists prefer the government to run  a health insurance and health care system rather than just pay for one,  allowing thereby healthy competition, is still pretty astounding. That judgement seems far beyond the central point of health economics and deep in to public choice. Sadly, public choice is not a standard part of any PhD program, so most economists still rattle off the party line, there is a market failure in here somewhere so the government has to run things to provide the social optimum. Seventy-seven percent of health economists do not believe work requirements should be part of Medicaid. This is another interesting judgement, rather outside health economics. I have an acquaintance, single and able, who chooses not to work and to be an artist instead, producing art that few will pay much for. They have medicaid. It's awful. I have others who work pretty much just to have the health insurance. There are the people who spend eight hours a day stuffing our orders into boxes at Amazon, or checking out our groceries at Whole Foods, to get a bit of cash and somewhat better health insurance.  It's a lot less fun than being an unpaid artist. It would be nice if nobody had to do these unpleasant tasks and everyone could be an artist. Can we be such a society? That's an interesting question, at the eternal struggle between incentives and compassion that defines good economics. And a politically charged one. You can tell where the politics of health economists lie. Still, there are rays of common sense and good economics among the health economists ..only 14 percent of [health economists]favor the current tax treatment of employer-sponsored health insurance. But they’re just about the only group that feels that way. Also Health economists overwhelmingly (93 percent of them) say that if employers were to spend less on health insurance, wages and other benefits would increase. As blog readers know, I'm a fan of guaranteed renewable or health status insurance in place of the ban on rating for pre-existing conditions. How is this faring? ..insurers cannot raise premiums for pre-existing conditions. Health economists appear to agree with this, with 80 percent saying premiums should not be higher for those with “genetic defects” (the poll’s wording)... But nearly 70 percent of health economists are comfortable charging people more if they engage in unhealthy behaviors that lead to higher health costs. The A.C.A. allows marketplace plans to do just that based on smoking. Sadly, the survey does not really get to the issue.  Genetic defects are about the hardest part of a health status scheme -- they requires that parent's health status insurance covers their children's genetic defects. Even I would consider government topping up heath status accounts or vouchering guaranteed renewable insurance for genetic defects. I wish we had a clearer question, health status or guaranteed renewability vs. community rating (all pay the same price) plus mandate (you have to buy health insurance, even if wildly overpriced for you.) Frakt's bottom line If health economists were in charge of the health system, not a lot would change, with some notable exceptions. Medicaid would not have work requirements (which would be unpopular among conservatives in some states), and taxes would go up for Medicare and for employer-based health insurance (which would make it unpopular among just about everybody). Frakt may be jumping to conclusions here. The survey did not ask about taxes, and one might suspect a majority of health economists answering the survey might think it can all be paid for by taxing "the rich" only. ********* Cannon gets right to the point. “If health economists were in charge of the health system, not a lot would change,” which tells you just about all you need to know about most health economists in the United States Health economists seem to have a lot of attachment to the status quo, which is pretty much universally reviled by everyone else. Why? Cannon's diagnosis there is a mountainous structural ideological-bias dilema in #HealthPolicy. The health policy professions skew left, because federal and state health policy skew left; thus the set of individuals who select into these professions skews toward those whose ideas concern *how* government should allocate resources/regulate rather than *whether* it should. Since the majority and the elites within these professions skew left, it is harder both to attract free-market advocates to the professions and for free-market advocates to advance within the professions. Cannon has a point. Free market analysis has a tough time getting jobs, publishing papers, getting grants, getting tenure. Health policy is a lot like the humanities. But I see it slightly differently. As economists, let us look first not at ideology, but at interest. Economist capture can be independent of political ideology. To be a health economist today, you need to learn a lot about the details of the ACA, medicare and medicaid rules, health insurance regulations, and so on. If we throw all this out and start over, as any good free marketer will tell you to do -- and as a good Sanderista, single-payer will also tell you to do -- all that human capital is thrown out. You will be as relevant as the economists who studied how soviet communism worked, in 1991. You will be as relevant as a typewriter repairman when word processors take over. Health economics is an immense industry now, much of it financed by soft money, either NIH and other government grants or private grants, funneled through an explosion of health policy "centers," not standard tenure track departments. Many health economists depend for their jobs on getting grants from government agencies that promulgate the current system to study the current system and improve it. Or, viewed more cynically, the government agencies that run the current system pay economists to support the current system. Viewed either way, good luck at getting a 3 year grant, with salary support, to study "how a voucher could replace medicare," or "how health-status insurance could obviate the need for the ACA" or "eliminate cross-subsidies with tax-supported charity care, and leave the rest of us to the free market." The average health economist surveyed -- the average member of the American society of health economists --  is not a professor of economics at Harvard or Stanford. He or she is a grant-supported researcher at a health policy center, or directly employed by a federal government agency. From a quick bit of googling, Stanford has a centerhere, a health research division in the medical school here, a health research and policy department of the medical school here, and health economics researchers at Hoover, business school, law school, SIEPR, and doubtless more.   Frakt lists his first affiliation as  "director of the Partnered Evidence-Based Policy Resource Center at the V.A. Boston Healthcare System." Cannon, a lone free-marketer, is at CATO and knows this world well. My view is thus less ideological but perhaps more deep-rooted than Cannon's. In support, note that it is a general phenomenon, not unique to health economics. Why do the majority of bank regulation economists largely support the general structure of the Dodd Frank act, wanting only to fiddle with regulations on the edges, and heaven forbid even thinking about replacing the whole mess with narrow deposits and equity financed banking? Why do the majority of monetary economists support the institutional structure of the Federal Reserve, mostly supporting the actions of the top ("why does QE work?" Not "does QE work?"), fiddling with interest rate rules, and those who even think about really mendasar changes in structure in the sidelines? (Note there the large fraction of monetary economists employed directly by the Federal Reserve, its member banks, BIS, IMF, ECB, etc.) There is nothing necessarily pernicious here. Researchers at the Fed can write pretty much anything they like. But the institutional rewards for "policy relevant" research, research that helps those at the top to manage their day to day affairs, are obviously there. Why do antitrust or securities regulation economists sound pretty much like the health economists here, with only a few outsiders arguing that the efforts are pointless rabbit warrens? Self-interest, for people to preserve hard-won human capital, and for institutions to support research that keeps them going, is a powerful explanatory force. Even if individuals do not respond to this incentive, and are all pure in their pursuit of ideas, selection is a powerful explanatory force. Economics is a good way to explain economics!
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New Paper: Fiscal Theory Of Monetary Policy - Barokong

A second new paper: "A fiscal theory of monetary policy with partially repaid long-term debt." By "fiscal theory of monetary policy" I mean a model with standard DSGE ingredients, including inertemporal optimization and market clearing, monetary policy described by interest rate targets, price or other frictions, but closed by fiscal theory, "active" fiscal policy rather than "active" monetary policy. I aim to build a standard simple but somewhat realistic model of this sort, a parallel to the three equation textbook model that has been part of the new-Keynesian tool kit since the 1990s. I keep the model as simple and standard as possible, so the effect of the innovations one the fiscal side are clearer. Two parts of the specification are central. First, long-term debt allows the model to produce a negative response of inflation to interest rates. Long-term debt also allows a fiscal shock to result in a protracted inflation, which slowly devalues long term bonds, rather than a price level jump. Second, and most important, the paper writes down a process for fiscal surpluses in which today's deficits are partially repaid by tomorrow's surpluses. Look quickly at the surplus response functions in my last post. When the government runs a deficit, it reliably runs subsequent surpluses that partially repay some of the accumulated debt. The surplus is not an AR(1)! It has an s-shaped response function. So if you want a realistic fiscal theory model, you need a surplus with an s-shaped response function, but you need to keep "active" fiscal policy. This combination is the central innovation of the paper. Active and passive As a quick reminder for new readers, here's what active and passive mean. Take a really simple model with flexible prices, one period debt, a constant zero real rate, and an interest rate target. The economic model boils down to just $$ i_t = E_t \pi_t+1 $$ $$ \Delta E_t+1 \pi_t+1 = \Delta E_t+1 \sum_j=0^\infty \rho^j s_t+1+j. $$ \(i\) is the nominal interest rate,  \(\pi\) is inflation, \(s\) is real primary surplus, and the linearization is is derived in my last post. Unexpected inflation or deflation changes the value government debt, which must equal the present value of surpluses. The central bank, by setting the interest rate target, determines expected inflation. But unexpected inflation is not then determined. If fiscal policy is "active" the second equation and the revision to expected surpluses determines unexpected inflation. If fiscal policy is "passive" meaning that the surplus process reacts to unexpected inflation so that the second equation hold for any value of unexpected inflation, then we need another model equation, "active" monetary policy, to determine unexpected inflation. My goal is to create a model like this, but with sticky prices and output and real interest rate variation, with an empirically sensible specification of surplus (fiscal) policy, that is nonetheless "active" and so closes out the model, determining unexpected inflation. AR(1) puzzles So far, many fiscal theory puzzles have come from assuming an AR(1) or similar positively autocorrelated surplus process. An s-shaped surplus process solves the puzzles -- and, conversely, the puzzles provide many different pieces of evidence that the AR(1) is a terrible assumption. Puzzle 1. Deficits and inflation. An AR(1) surplus predicts that deficits come with substantial inflation. By and large we see the opposite sign, less inflation with deficits in a recession and vice versa, and little reliable correlation. An s-shaped surplus process solves the puzzle. I'll illustrate with a constant interest rate, short term debt version of the model. The simple FTPL is$$ \fracB_t-1P_t = E_t \sum_j=0^\infty \beta^j s_t+j = \frac11-\beta\rho_s s_t$$ where \(B\) is nominal debt, \(P\) is price level and \(s\) is real primary surplus and the last term uses an AR(1). Manipulating, $$ \fracB_t-1P_t-1 \Delta E_t \left( \fracP_t-1P_t \right) = \Delta E_t \sum_j=0^\infty \beta^j s_t+j=\frac11-\beta\rho_s\varepsilon_s,t$$ where \(\Delta E_t \equiv E_t - E_t-1\).  A positive shock to surpluses is a negative shock to inflation, and a deficit means inflation. Since \(1/(1-\beta\rho_s)>1\) inflation is also very volatile. How can we cure this puzzle? Well, the key assumption is that a shock to surpluses today raises forecasts of surpluses in the future -- all the \(s_t+j\) terms are positive. Suppose that the surplus process looks like the graphs in my last post -- in that case that a deficit today (negative \(s_t\)) implies a long string of positive future \(s_t+j\) terms that bring the sum back, perhaps all the way to zero. If the sum of future surpluses is a small number, this force for deficits with inflation can be overwhelmed by other forces. Puzzle 2: Damningly, the AR(1) or other positively autocorrelated surplus predicts that a higher surplus today raises  the value of the debt tomorrow, just as a higher dividend today leads to a higher stock price. A higher surplus forecasts higher future surpluses, and the value of the debt is the present value of subsequent surpluses.  Yet higher surpluses in the data unequivocally pay down the value of the debt, and deficits result in more debt, as pointed out by Canzoneri, Cumby and Diba. A surplus process with an s-shaped moving average solves the puzzle.  A higher surplus today corresponds to a decrease in present value of subsequent surpluses, and hence a decline in the value of debt. Puzzle 3:  With AR(1) or positively autocorrelated surpluses, all deficits are paid for by devaluing outstanding debt via inflation (or default), and none are paid for by selling new debt. Running a deficit involves selling less  real debt.  With an s-shaped moving average, deficits are financed by borrowing. Bond buyers will only hand over resources to finance today's deficits if they are convinced that the bonds will be paid off by future surpluses, essentially proving that bond buyers think the surplus process is s-shaped. Puzzle 4: Models with positively autocorrelated surpluses predict that the risk and hence expected return of government bonds should be huge. The s-shaped surplus process solves this puzzle, allowing even risk free government debt. Since all deficits are paid by unexpectedly inflating away bonds, since \(1/(1-\beta \rho_s)\) is a large number, the AR(1) predicts lots of inflation and hence lots of volatility in real ex-post bond returns. As above the inflation and negative bond returns come in recessions, so that volatility should generate a large risk premium. Equivalently, looking at the present value formula, the surplus is volatile and procyclical, like dividends. So bond returns should be volatile and procyclical, like stocks, and carry an equity premium. Actual government bond returns are quiet (low volatility), countercyclical (they do well in recessions) and carry a very low mean. Jiang, Lustig, Van Nieuwerburgh, and  Xiaolan point out this puzzle. An s-shaped surplus process resolves the puzzle. When the ``dividend,'' surplus, falls, the ``price,'' present value of subsequent surpluses, rises. The overall return need not  move at all, nor offer a positive compensation for risk.  Stock dividends don't follow an s-shaped process. Government deficits and surpluses do. The standard specification of fiscal policy is $$s_t = \gamma v_t + u_s,t$$$$u_s,t=\rho_s u_s,t-1 + \varepsilon_s,t$$ where \(v\) is the real value of the debt.  If we set \(\gamma=0\) then we have all the AR(1) puzzles. If we set \(\gamma>0\) then we have an s-shaped response, in fact the response of the discounted sum of future surpluses is zero. But then fiscal policy is passive. It has seemed we are stuck, and the puzzles tell us fiscal policy must be passive. But wait, who said the \(u\) process has to be an AR(1)? By abandoning that auxiliary assumption, I create a model with \(\gamma=0\) and active fiscal policy that also solves the puzzles and fits the s-shaped estimates of the surplus process. A regression of model data will show \(\gamma>0\) though that is a mis specified regression and the true \(\gamma=0\). The model OK, hold your breath. Here is the model. If this is too much in one bite, read the paper which builds up to the model bit by bit. (The whole point of this blog post is to get you to read the paper after all!) Here we'll just sit down to the main course without appetizers. \beginalign x_t  &  = E_tx_t+1-\sigma(i_t-E_t\pi_t+1)\labelIS\\ \pi_t  &  =\beta E_t\pi_t+1+\kappa x_t \labelNK\\ i_t   & =\theta_i\pi\pi_t+\theta_ixx_t+u_i,t\labelnm4\\ s_t  &  =\theta_s\pi\pi_t+\theta_sxx_t+\alpha v_t^\ast+u_s,t% \labelnm5\\ \eta v_t+1^\ast  &  =v_t^\ast+i_t-E_t\pi_t+1-s_t+1% \labelnm6\\ \rho v_t+1  &  =v_t+r_t+1^n-\pi_t+1-s_t+1\labelnm7\\ E_tr_t+1^n  &  =i_t\labelnm8\\ r_t+1^n  &  =\omega q_t+1-q_t\labelnm9\\ u_i,t+1  &  =\rho_iu_i,t+\varepsilon_i,t+1\labelnm10\\ u_s,t+1  &  =\rho_su_s,t+\varepsilon_s,t+1. \labelnm11% \endalign The first two equations are the standard intertemporal substitution (IS) and forward-looking Phillips curve. The third equation is a standard interest rate policy rule. The surplus \(s\) equation also starts with a policy rule. Surpluses rise with output, a very strong correlation in the data, and potentially also with inflation. Now for the fun part: Surpluses respond to the state variable \(v^\ast\) but not to the value of debt itself, so fiscal policy remains active. The state variable \(v^\ast\) accumulates past deficits, and responds to change in expected return of government bonds,  but crucially it does not respond to ex-post returns induced by unexpected inflation. The actual value of debt \(v\) follows a similar process, but it does respond to ex-post returns induced by unexpected inflation. One way to think of the  difference between \(v^\ast\) and \(v\) is that the government makes a distinction: It will respond with greater surpluses to higher debts that come from its own borrowing and higher real interest rates. But it will not respond with greater surpluses to a higher real value of debt that comes from an unexpected, unintended, or multiple-equilibrium inflation. The key to "active" fiscal policy is only the last point -- an "active" fiscal policy can respond to any other source of debt variation. The paper goes on (and on) to argue that this is quite sensible and a good reading of many institutions and historical episodes. Including 2008. Why was there not deflation? Because if there was a huge deflation, as standard Keynesian models (new and old) predicted, then the real value of debt would have had to soar. Had a big deflation occurred in 2008, as feared, would Congress really have "passively" raised taxes and slashed spending in order to fund an unexpected and, surely it would be argued, undeserved windfall payment to fat-cat Wall Street bankers and the Chinese central bank? Without that action the deflation cannot happen. Similarly, take a look at Jacobson, Leeper and Preston's marvelous analysis of 1933, when the US again refused to validate a deflation. You can also think of \(v^\ast\) as just a latent variable that represents an s-shaped moving average in vector AR(1) form, of course. The parameter \(\eta\) adjusts how much debt gets repaid. If \(\eta=\rho\) then all debt is repaid, the right end of the s pays off the initial deficits completely, and the response of \(\sum s_t+j\) to a shock is zero. We want to allow for some fiscal inflation, however -- fiscal policy responds to a shock by partially inflating away existing debt, and partially by borrowing and promising future surpluses. \(\eta>\rho\) allows that. \(\eta \rightarrow \infty\) recovers a pure AR(1) surplus shock. The \(v\) equation is the evolution of the real value of government debt in linearized form.  \(r^n\) is the nominal ex-post return on the government bond portfolio, so includes long-term debt. The \(r^n\) equation is the expectations hypothesis. We need a bond pricing formula, and I kept it simple along with everything else not fiscal. The \(r^n\) equation is the return on the government bond portfolio in terms of its price \(q\). The last equations are AR(1) shocks to monetary and fiscal policy. Responses Here are the responses to a fiscal policy shock, a unit \(\varepsilon_s,1\) with no movement \(\varepsilon_i,1\) and thus no movement in the monetary policy disturbance \(u_i\). Monetary policy may still react via inflation and output. I picked parameters to make the plots look pretty, see the paper. This first response has no policy rules -- the \(\theta\) terms are turned off -- so you can see how the versi behaves. The surplus does have an s shaped response, not an AR(1). But it would be darn hard to tell from the AR(1) disturbance \(u^s\). Similarly, the state variable \(v^\ast\) and actual debt \(v\) are similar. The surplus will seem to respond to \(v\) and policy will seem passive if you're not really careful. The initial deficits lead to a rise in debt, which is then slowly paid down by a small string of surpluses. The fiscal shock leads to a AR(1) pattern of inflation, and as a consequence of the standard Phillips curve an output expansion. With no policy response, interest rates stay put. Now, let's add a monetary and fiscal policy response. The rise in inflation and output provokes a rise in interest rate. And the initial inflation devalues long term bonds \(r^n\). Together, monetary policy and long term debt substantially reduce the inflationary impact of the fiscal shock and draw it out.  The larger output also gives rise to  larger surpluses, which reduces the size of the fiscal shock to begin with. Big points: 1) Fiscal theory does not just imply big price level jumps in response to fiscal shocks. Fiscal theory rather naturally here leads to a very long and drawn out inflation in response to a fiscal shock. 2) Endogenous monetary and fiscal policy responses also draw out and buffer the response to a fiscal shock. Here is the response to a monetary policy shock \(\varepsilon_m,1\) holding constant the fiscal policy shock \(\varepsilon_s,1\), with no policy rule responses \(\theta=0\). The interest rate and its shock follow an AR(1). Output and inflation decline persistently. Whether true or not in the data, this is the sort of response that is the Holy Grail of monetary theory. At least the versi can produce this result. Surpluses are not constant, because they react to the rise in value of debt that comes from higher real interest rates, represented by the difference between the interest rate and inflation lines. Bond returns follow the expectations hypothesis, mirroring the interest rate with a one period lag, except in the first period. A rise in interest rates leads to a big ex-post decline in bond prices. Last and most of all, here is the response to monetary policy with policy rules in place. The interest rate no longer follows its shock. Lower output and inflation bring down the actual interest rate. The monetary policy induced recession now has a deficit too, as the surplus responds to lower output and inflation. Inflation and output still decline in response to the monetary policy shock. There is a lot more going on here. Real interest rate variation leads to discount rate effects, for example. But I what to whet your appetite to read the paper. The goal: a really simple baseline fiscal theory of monetary policy model that produces reasonable responses to fiscal and monetary policy. We have drawn out inflation in response to fiscal shocks, not a price level jump; we have lower inflation and output in response to monetary policy not instant Fisherism; and all the AR(1) puzzles are solved. It seems a good place to start. And, for today, to stop. (Note: this post uses Mathjax to display equations, which is not working perfectly.)
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