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Economy

Rethinking production under uncertainty

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Even at my age, I get a little tingle when a paper is finally published. “Rethinking production under uncertainty” is now out at RAPS (free access for a while) and on my website.

The basic idea is simple.

Our standard way of writing production technologies under uncertainty tacks a shock on to an intertemporal technology.  We might write [ y(s) = varepsilon (s) f(k) ] where  (k) is capital invested at time 0, (s) indexes the state of nature (rain or shine) (y(s)) is output in state (s). That production technology does not allow producers to transform output across states at time 1. No matter high the contingent claim pricer for rain vs. shine, the producer can’t make more in the rain state at the expense of making less in the shine state.

This is the production set of a farmer, say, with initial wheat that can be eaten providing (y(0)) or planted to give ( {y(h), y(l)} ) in states ( h, l).

As a result, marginal rates of transformation are not defined, and you can’t write a true production-based asset pricing model, based on marginal rate of transformation = contingent claim price ratio.

So, why don’t we write down technologies that do allow producers to transform output across states as well as dates? Our farmer could plant wheat in a field that does better in rainy weather than shiny weather, for example. (You can feel an aggregation theory coming.)  The result is a smooth production technology,


For most of the paper, I investigate a particular functional form.  In addition to capital (k), the proucder can choose the technology shock (varepsilon) in a convex set, modeled as a CES aggregate over states [ E left[ left( frac{varepsilon}{theta}right)^{1+alpha} right] = sum_s left[ pi(s) left( frac{varepsilon(s)}{theta(s)}right)^{1+alpha} right]  le 1 . ] The second equality just writes out the expectation as a sum over states to make it clearer.

If a firm maximizes profits ( max E [m varepsilon f(k)] ), then, the first order conditions include ( m = lambda varepsilon^alpha/theta^{1+alpha} ) where (lambda) is a Lagrange multiplier. There you have it, production based asset pricing just like ( m = lambda u'(c)).  

The paper has a curious history. I wrote the first draft in 1993. What took so long? Well, I was never happy with the dynamic extension, and only in doing this update did I sit down and figure out a good solution to that issue. The paper now has a nice analogue to time-separable utility, a version of recursive production and an expression that is separately CES over time and states of nature, which might be a useful alternative to recursive utility as well. I also was never happy with ways of identifying the productivity shock ( theta). Frederico Belo made a crucial breakthrough on that front (ssrn, published paper at JME). And I wanted to do empirical work, which never happened.  Around 1993 I was talking to John Campbell about this and related issues at a conference, and we embarked on “by force of habit.” John convinced me (correctly) to focus on preferences first, and we’d add technology later, but then I moved on to other things as well.

I owe a great debt to Wayne Ferson, who happened on the paper and said “why don’t you publish it?,” and got me going, Nick Roussanov and Jeff Pontiff who shepherded it through RAPS, John Campbell for thinking enough of the idea to write it up in his textbook even though I didn’t write it up in mine, and John and especially Frederico Belo for detailed comments.



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Economy

Reclaiming freedom

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We might be seeing a significant political change, with the left reclaiming freedom and anti-statism from the right.

I'm prompted to say this by the Black Lives Matter slogan, "defund the police" which invites us to see the state as an oppressor. As Grace Blakeley recently tweeted:

People know that the state is fucking them over just as much as their boss or landlord – in fact, it’s helping their boss and landlord fuck them over even more…Rather than saying ‘just give more state power to the goodies (us)’ we need to start saying ‘put power where it belongs – in the hands of working people’.

If we read this alongside the disappearance of right-libertarians (some of whom discovered that they like racism and inequality more than small government) and emergence of big government Toryism, we see a big change from a few years ago. Back then, it was the right who called for a smaller state and much of the left that wanted a bigger one. Now it is, if anything, the opposite*.

In one sense this is a return to normality. Historically, advocates of freedom were opponents of the existing order, such as Tom Paine, John Stuart Mill and – yes – Adam Smith**. And, of course, Marxists have long regarded the state as "a committee for managing the common affairs of the whole bourgeoisie" and looked forward to it withering away.

Which poses the question: why are things now changing (back)?

One reason is that the left has learned that states are indeed often repressive. I'm thinking here not just of police killings but of the social murder that is austerity and tough benefit sanctions, and the forced deportations of black Britons (something still going on).

Secondly, they've learned that, as Grace says, it is not good enough to "give more state power to the goodies". Yes, New Labour did make significant achievements in tax credits, Sure Start and better funding of schools and the NHS. But many of these have been reversed by the Tories in the subsequent decade. The left cannot pin its hopes merely on winning temporary (and partial) control of the state.

Thirdly, changes within capitalism have changed the state. Of course, capital (pdf) has always wielded power over governments. But there was a time when this was relatively benign. In the post-war war mass production Fordist capitalists needed a mass market and hence an affluent working class. Extractive finance capital, though, doesn't. It needs cheap and plentiful money which fiscal austerity helps provide. General Motors needed a large well-paid working class; Goldman Sachs, not so much. This means there is now more tension between the needs of working people and the function of the state than there used to be.

All of which poses the question. What would anti-statist leftism look like?

Many of you might think the slogan "defund the police" goes too far. No matter: we don't know what's right unless we know what's too much. And what is right – as Elinor Ostrom showed – is that the police should be small and locally accountable. Also, there's a strong case for decriminalizing drugs, in part because it removes a pretext for the police to harass black people.

A high universal basic income would also expand freedom, not just by removing the harsh conditionality of Universal Credit, but also by giving us the freedom to reject exploitative labour or to drop out of the labour market to care for others or to train for better work. As Guy Standing says (pdf), "basic Income’s emancipatory value exceeds its monetary value."

Also, left-libertarianism must empower local communities, and embrace the community wealth-building advocated by Martin O'Neil and Joe Guinan and pioneered by Preston council. In weakening the power of central government, localization mitigates the damage done by Tory austerity. And it also gives local people more republican freedom – the freedom to collectively control more of their own lives.

There's something else, which the Black Lives Matter movement is also highlighting. It's that slavery teaches us something about economics. As Peter Doyle shows in a brilliant paper (pdf), markets produce incentives to undermine others' agency. Although slavery is the most extreme example of this we also see it in everyday capitalist labour markets. As Marx said, when we they start work workers leave behind the realm of equality and freedom and become mere factors of production. Left-libertarianism would put in place institutions to resist this and expand the realm of genuine agency. This would comprise worker coops and more local say over public services.

I say all this not to offer detailed blueprints: Marx was right to be sceptical of these. Instead, the point is that the left can and should pick up the cause of freedom now that the right has abandoned it.

* We mustn't be misled by the right's loud assertion of a right to free speech. What they are really proclaiming is the "right" to spout rubbish without any comeback, which is an altogether different matter.

** If you think the Adam Smith Institute is a representative guide to Smith's thinking, the wallet inspectors would like to meet you.



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Economy

The Surplus Process

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How should we model surpluses and deficits? In finishing up a recent articleand chapter 5 and 6 of a Fiscal Theory of the Price Level update, a bunch of observations coalesced that are worth passing on in blog post form.

Background: The real value of nominal government debt equals the present value of real primary surpluses, [ frac{B_{t-1}}{P_{t}}=b_{t}=E_{t}sum_{j=0}^{infty}beta^{j}s_{t+j}. ] I ‘m going to use one-period nominal debt and a constant discount rate for simplicity. In the fiscal theory of the price level, the (B) and (s) decisions cause inflation (P). In other theories, the Fed is in charge of (P), and (s) adjusts passively. This distinction does not matter for this discussion. This equation and all the issues in this blog post hold in both fiscal and standard theories.

The question is, what is a reasonable time-series process for (left{s_{t}right} ) consistent with the debt valuation formula? Here are surpluses

The blue line is the NIPA surplus/GDP ratio. The red line is my preferred measure of primary surplus/GDP, and the green line is the NIPA primary surplus/GDP.

The surplus process is persistent and strongly procyclical, strongly correlated with the unemployment rate.  (The picture is debt to GDP and surplus to GDP ratios, but the same present value identity holds with small modifications so for a blog post I won’t add extra notation.)

Something like an AR(1) quickly springs to mind, [ s_{t+1}=rho_{s}s_{t}+varepsilon_{t+1}. ] The main point of this blog post is that this is a terrible, though common, specification.

Write a general MA process, [ s_{t}=a(L)varepsilon_{t}. ] The question is, what’s a reasonable (a(L)?) To that end, look at the innovation version of the present value equation, [ frac{B_{t-1}}{P_{t-1}}Delta E_{t}left( frac{P_{t-1}}{P_{t}}right) =Delta E_{t}sum_{j=0}^{infty}beta^{j}s_{t+j}=sum_{j=0}^{infty}beta ^{j}a_{j}varepsilon_{t}=a(beta)varepsilon_{t}% ] where [ Delta E_{t}=E_{t}-E_{t-1}. ] The weighted some of moving average coefficients (a(beta)) controls the relationship between unexpected inflation and surplus shocks. If (a(beta)) is large, then small surplus shocks correspond to a lot of inflation and vice versa. For the AR(1), (a(beta)=1/(1-rho_{s}beta)approx 2.) Unexpected inflation is twice as volatile as unexpected surplus/deficits.

(a(beta)) captures how much of a deficit is repaid. Consider (a(beta)=0). Since (a_{0}=1), this means that the moving average is s-shaped. For any (a(beta)lt 1), the moving average coefficients must eventually change sign. (a(beta)=0) is the case that all debts are repaid. If (varepsilon_{t}=-1), then eventually surpluses rise to pay off the initial debt, and there is no change to the discounted sum of surpluses. Your debt obeys (a(beta)=0) if you do not default. If you borrow money to buy a house, you have deficits today, but then a string of positive surpluses which pay off the debt with interest.

The MA(1) is a good simple example, [ s_{t}=varepsilon_{t}+thetavarepsilon_{t-1}% ] Here (a(beta)=1+thetabeta). For (a(beta)=0), you need (theta=-beta ^{-1}=-R). The debt -(varepsilon_{t}) is repaid with interest (R).

Let’s look at an estimate. I ran a VAR of surplus and value of debt (v), and I also ran an AR(1).

Here are the response functions to a deficit shock:

The blue solid line with (s=-0.31) comes from a larger VAR, not shown here. The dashed line comes from the two variable VAR, and the line with triangles comes from the AR(1).

The VAR (dashed line) shows a slight s shape. The moving average coefficients gently turn positive. But when you add it up, those overshootings bring us back to (a(beta)=0.26) despite 5 years of negative responses. (I use (beta=1)). The AR(1) version without debt has (a(beta)=2.21), a factor of 10 larger!

Clearly, whether you include debt in a VAR and find a slightly overshooting moving average, or leave debt out of the VAR and find something like an AR(1) makes a major difference. Which is right? Just as obviously, looking at (R^2)   and t-statistics of the one-step ahead regressions is not going to sort this out.

I now get to the point.

Here are 7 related observations that I think collectively push us to the view that (a(beta)) should be a quite small number. The observations use this very simple model with one period debt and a constant discount rate, but the size and magnitude of the puzzles are so strong that even I don’t think time-varying discount rates can overturn them. If so, well, all the more power to the time-varying discount rate! Again, these observations hold equally for active or passive fiscal policy. This is not about FTPL, at least directly.

1) The correlation of deficits and inflation. Reminder, [ frac{B_{t-1}}{P_{t-1}}Delta E_{t}left( frac{P_{t-1}}{P_{t}}right) =a(beta)varepsilon_{t}. ] If we have an AR(1), (a(beta)=1/(1-rho_{s}beta)approx2), and with (sigma(varepsilon)approx5%) in my little VAR, the AR(1) produces 10% inflation in response to a 1 standard deviation deficit shock. We should see 10% unanticipated inflation in recessions! We see if anything slightly less inflation in recessions, and little correlation of inflation with deficits overall. (a(beta)) near zero solves that puzzle.

2) Inflation volatility. The AR(1) likewise predicts that unexpected inflation has about 10% volatility. Unexpected inflation has about 1% volatility. This observation on its own suggests (a(beta)) no larger than 0.2.

3) Bond return volatility and cyclical correlation. The one-year treasury bill is (so far) completely safe in nominal terms. Thus the volatility and cyclical correlation of unexpected inflation is also the volatility and cyclical correlation of real treasury bill returns. The AR(1) predicts that one-year bonds have a standard deviation of returns around 10%, and they lose in recessions, when the AR(1) predicts a big inflation. In fact one-year treasury bills have no more than 1% standard deviation, and do better in recessions.

4) Mean bond returns. In the AR(1) model, bonds have a stock-like volatility and move procyclically. They should have a stock-like mean return and risk premium. In fact, bonds have low volatility and have if anything a negative cyclical beta so yield if anything less than the risk free rate. A small  (a(beta)) generates low bond mean returns as well.

Jiang, Lustig, Van Nieuwerburgh and Xiaolan recently raised this puzzle, using a VAR estimate of the surplus process that generates a high (a(beta)). Looking at the valuation formula [ frac{B_{t-1}}{P_{t}}=E_{t}sum_{j=0}^{infty}beta^{j}s_{t+j}, ] since surpluses are procyclical, volatile, and serially correlated like dividends, shouldn’t surpluses generate a stock-like mean return? But surpluses are crucially different from dividends because debt is not equity. A low surplus (s_{t}) raises  our estimate of subsequent surpluses (s_{t+j}). If we separate out
 [b_{t}=s_{t}+E_{t}sum_{j=1}^{infty}beta^{j}s_{t+j}=s_{t}+beta E_{t}b_{t+1}  ] a decline in the “cashflow” (s_{t}) raises the “price” term (b_{t+1}), so the overall return is risk free. Bad cashflow news lowers stock pries, so both cashflow and price terms move in the same direction. In sum a small (a(beta)lt 1) resolves the Jiang et. al. puzzle. (Disclosure, I wrote them about this months ago, so this view is not a surprise. They disagree.)

5) Surpluses and debt. Looking at that last equation, with a positively correlated surplus process (a(beta)>1), as in the AR(1), a surplus today leads to  larger value of the debt tomorrow. A deficit today leads to lower value of the debt tomorrow. The data scream the opposite pattern. Higher deficits raise the value of debt, higher surpluses pay down that debt. Cumby_Canzoneri_Diba (AER 2001) pointed this out 20 years ago and how it indicates an s-shaped surplus process.  An (a(beta)lt 1) solves their puzzle as well. (They viewed (a(beta)lt 1) as inconsistent with fiscal theory which is not the case.)

6) Financing deficits. With (a(beta)geq1), the government finances all of each deficit by inflating away outstanding debt, and more. With (a(beta)=0), the government finances deficits by selling debt. This statement just adds up what’s missing from the last one. If a deficit leads to lower value of the subsequent debt, how did the government finance the deficit? It has to be by inflating away outstanding debt. To see this, look again at inflation, which I write [ frac{B_{t-1}}{P_{t-1}}Delta E_{t}left( frac{P_{t-1}}{P_{t}}right) =Delta E_{t}s_{t}+Delta E_{t}sum_{j=1}^{infty}beta^{j}s_{t+j}=Delta E_{t}s_{t}+Delta E_{t}beta b_{t+1}=1+left[ a(beta)-1right] varepsilon_{t}. ] If (Delta E_{t}s_{t}=varepsilon_{t}) is negative — a deficit — where does that come from? With (a(beta)>1), the second term is also negative. So the deficit, and more, comes from a big inflation on the left hand side, inflating away outstanding debt. If (a(beta)=0), there is no inflation, and the second term on the right side is positive — the deficit is financed by selling additional debt. The data scream this pattern as well.

7) And, perhaps most of all, when the government sells debt, it raises revenue by so doing. How is that possible? Only if investors think that higher surpluses will eventually pay off that debt. Investors think the surplus process is s-shaped.

All of these phenomena are tied together.  You can’t fix one without the others. If you want to fix the mean government bond return by, say, alluding to a liquidity premium for government bonds, you still have a model that predicts tremendously volatile and procyclical bond returns, volatile and countercyclical inflation, deficits financed by inflating away debt, and deficits that lead to lower values of subsequent debt.

So, I think the VAR gives the right sort of estimate. You can quibble with any estimate, but the overall view of the world required for any estimate that produces a large (a(beta)) seems so thoroughly counterfactual it’s beyond rescue. The US has persuaded investors, so far, that when it issues debt it will mostly repay that debt and not inflate it all away.

Yes, a moving average that overshoots is a little unusual. But that’s what we should expect from debt. Borrow today, pay back tomorrow. Finding the opposite, something like the AR(1), would be truly amazing. And in retrospect, amazing that so many papers (including my own) write this down. Well, clarity only comes in hindsight after a lot of hard work and puzzles.

In more general settings (a(beta)) above zero gives a little bit of inflation from fiscal shocks, but there are also time-varying discount rates and long term debt in the present value formula. I leave all that to the book and papers.

(Jiang et al say they tried it with debt in the VAR and claim it doesn’t make much difference.  But their response functions with debt in the VAR, at left,  show even more overshooting than in my example, so I don’t see how they avoid all the predictions of a small (a(beta)), including a low bond premium.)

A lot of literature on fiscal theory and fiscal sustainability, including my own past papers, used AR(1) or similar surplus processes that don’t allow (a(beta)) near zero. I think a lot of the puzzles that literature encountered comes out of this auxiliary specification. Nothing in fiscal theory prohibits a surplus process with (a(beta)=0) and certainly not (0 lt a(beta)lt 1).

Update

Jiang et al. also claim that it is impossible for any government with a unit root in GDP to issue risk free debt. The hidden assumption is easy to root out. Consider the permanent income model, [ c_t = rk_t + r beta sum beta^j y_{t+j}] Consumption is cointegrated with income and the value of debt. Similarly, we would normally write the surplus process [ s_t = alpha b_t + gamma y_t. ] responding to both debt and GDP. If surplus is only cointegrated with GDP, one imposes ( alpha = 0), which amounts to assuming that governments do not repay debts. The surplus should be cointegrated with GDP and with the value of debt.  Governments with unit roots in GDP can indeed promise to repay their debts.



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Economy

"The Market Was Made for Man, Not Man for the Market": Time to Ramp Up Direct Cash Payments

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The need for large redirections of financial flows to avoid large increase in poverty during this coronavirus plague is large. The need for substantial top-ups to spending flows in view of the large jump in savings rates triggered by the arrival of coronavirus is large. The U.S. government continues to be able to borrow at unbelievable terms—terms so unbelievable that, when the accounting is done correctly, a larger national debt is not a drag on the funds the government has available for its other missions but rather a source of current cash flow.

(Why? Because in real population-adjusted terms, people are not charging the government interest on its debt but are instead paying the government to keep their money safe, but that is a discussion for another time.)

Moreover, a plan to have the government top off spending flows by whatever large amount is necessary to immediately return to full employment is moderately conservative, and the only effective way to give American businesses their proper chance to adjust and survive the coronavirus plague. It is, as John Maynard Keynes wrote back in 1936:

moderately conservative… [to] enlarge… the functions of government… [to include] the task of adjusting to one another the propensity to consume and the inducement to invest…. [It is] the condition of the successful functioning of individual [entrepreneurial] initiative. For if effective demand is deficient, not only is the public scandal of wasted resources intolerable, but the individual enterpriser who seeks to bring these resources into action is operating with the odds loaded against him. The game of hazard which he plays is furnished with many zeros, so that the players as a whole will lose if they have the energy and hope to deal all the cards…. [Success then requires] courage and initiative… supplemented by exceptional skill or unusual good fortune. But if effective demand is adequate, average skill and average good fortune will be enough… [thus] preserving [both] efficiency and freedom…

Our financial flows and property orders are a societal accounting system to guide and manage our collective societal division of labor. If dotting the i’s and crossing the t’s in this societal accounting system produces mass unemployment, the right response is to adjust it to produce full employment and then reconcile the accounting entries, not to watch employment fall and then sit around with our thumbs up our butts wondering what to do.

After all, the market was made for man, not man for the market—wasn’t it?:

 

Olugbenga Ajilore,​ Mark Blyth,​ J. Bradford DeLong,​ Susan Dynarski,​ Jason Furman,​ Indivar Dutta-Gupta,​ Teresa Ghilarducci,​ Robert Gordon, ​Samuel Hammond, Darrick Hamilton,​ Damon Jones, ​Elaine Maag, Ioana Marinescu,​ Manuel Pastor,​ Robert Pollin,​ Claudia Sahm, & al.: Open Letter from economists on Automatic Triggers for Cash Stimulus Payments https://www.economicsecurityproject.org/wp-content/uploads/2020/07/emp_economists_letter.pdf: We urge policymakers to use all the tools at their disposal to avoid further preventable harm to people and the economy, including​ ​recurring direct stimulus payments, lasting until the economy recovers. The widespread uncertainty created by the COVID-19 pandemic and recession calls for a multifaceted response​ ​that includes automatic, ongoing programs and policies including more direct cash payments to families; extended and enhanced unemployment benefits; substantial aid to state and local governments; stronger SNAP benefits; robust child care funding and more. These programs and policies will hasten the economic recovery far more effectively if they stay in place until economic conditions warrant their phaseout. ​Direct cash payments are an essential tool that will boost economic security, drive consumer spending, hasten the recovery, and promote certainty at all levels of government and the economy–for as long as necessary…

The economic pain is widespread and the need for immediate, bold action is clear. ​The pain from this crisis is undeniable. The unemployment rate is already ​dwarfing​ peak levels from the Great Recession, with ​higher levels​ of unemployment for Black and Latinx workers; GDP is expected to shrink by ​11 percent​ during the second quarter of this year; and ​27 million​ Americans have likely lost their health insurance along with their jobs. Much is still unknown, but it is clear at this point this recession will require significant and sustained stimulus policies that are responsive to the health of the economy. We agree with economists from ​across​ the ​political spectrum​ that concerns about debt and deficit should not get in the way​ of taking appropriately strong measures to stem the downturn now.

Regular, lasting direct stimulus payments will boost consumer spending, driving the economic recovery and shortening the recession. ​Right now, most Americans are just trying to keep their heads above water. The first round of economic impact payments were a lifeline that helped some get by for a few weeks—​early research​ shows that people are spending the stimulus checks quickly and on essentials—but the worst is not over. Consumer spending accounts for about two-thirds of GDP, so reviving the economy will require sustained efforts to strengthen it. Even after businesses start to re-open and jobs begin to come back, there will be ​significant economic fallout​, and demand will continue to lag if people don’t have money to spend. Regular direct stimulus payments tied to economic indicators will help families stay afloat and drive economic activity.

Automatic stabilizers ensure relief for as long as it is needed, promoting a strong recovery and efficient government. ​Many economists believe our response to the Great Recession was ​too small​ and ​too brief​, slowing the recovery and causing preventable harm particularly to low-income people. Cash assistance is an important element of economic aid, injecting resources through direct stimulus payments and ​refundable tax credits​ into low- and middle-income households that need help and are ​likely​ to spend it. That will start a chain reaction to boost local businesses and increase economic activity. Continuing recurring payments until there is reliable evidence of an economic recovery—such as low and declining unemployment—will promote certainty for all sectors of the economy and for state and local governments and federal agencies.
With many unknowns, it is critical to enact policies that will help promote a robust, sustained, racially equitable recovery and will stay in place until Americans are back on their feet.

.#coronavirus #equitablegrowth #highlighted #macro #publichealth #2020-07-07
html: https://www.bradford-delong.com/2020/07/the-market-was-made-for-man-not-man-for-the-market-time-to-ramp-up-direct-cash-payments.html
edit: https://www.typepad.com/site/blogs/6a00e551f08003883400e551f080068834/post/6a00e551f0800388340263e9550b9f200b/edit



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