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Components of a Fed rate… Real rate & Inflation response

Below the previous post on Refining a NGDP target for a policy rate rule, there were comments by Reason regarding real growth of output and the effects of inflation. These are the two components of the Fed rate, which seeks to stabilize inflation and promote full-employment output growth.

I thought it would be helpful to post a graph that separates out those two components side by side. The data for the graph comes from my own equations for determining the short-term real rate and the inflation response in the Fed rate. (link) My equations determine the short-term real rate and the inflation response, and then add them together to prescribe a Fed rate.

First here is my equation plotted against the actual Fed rate. The blue line represents my equation to determine the Fed rate.

 ngdp inf tar 6

Now I will separate out the two components of my equation for the Fed rate.

ngdp inf tar 7

The blue line here shows the short-term real rate which reflects real output growth. You can see that it normally plateaued between 2% and 4% since the 1960’s. Normally real output growth was in the 3% range. But since the crisis, we see that real output growth is still below 2%. The economy is sick, unproductive and demand constrained.

The orange line represents the response to inflation so that nominal GDP would return to its price level target. The general pattern shows that the need to control inflation has been going lower. Now we have the reverse where there is a need to liberate inflation.

The complication now is that real output growth is suffering at the same time that inflation pressures are weak.

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Refining a NGDP target for a policy rate rule

This post will lay out a way to incorporate a NGDP target into a policy rate rule, so that the rule steers inflation back to a NGDP target, not to an inflation target.

First, the equation for a NGDP target.

NGDP target, Nt = real rate of output growth, Lr + desired long-run average core inflation target, Ct

Nt = Lr + Ct

Ct = Nt – Lr

For example, if Lr = 1.8% and a Ct of 2.5% is desired, then Nt will be established at 4.3%. Nt is meant to be constant over time. If actual NGDP diverges from Nt, then inflation will need to over-compensate to bring NGDP back to its target over time. When actual core inflation falls below Ct, then, NGDP will fall below target. Then eventually core inflation will have to rise above Ct in order for the NGDP target to return back to its target. In this way, the NGDP target is maintained. For example, if NGDP drops below 4.3%, then NGDP will have to go above 4.3% in the future to compensate the drop. David Beckworth has estimated that maybe 5% would be a good NGDP target, but he recognizes that it may be above or below 5%.

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Public schools

Via Alternet:

New data reveals our public—not private—school system is among the best in the world. In fact, except for the debilitating effects of poverty, our public school system may be the best in the world.

The most recent data from the National Center for Education Statistics (NCES) reveal that the U.S. ranked high, relative to other OECD countries, in reading, math, and science (especially in reading, and in all areas better in 4th grade than in 8th grade). Some U.S. private schools were included, but a separate evaluation was done for Florida, in public schools only, and their results were higher than the U.S. average.
Perhaps most significant in the NCES reading results is that schools with less than 25% free-lunch eligibility scored higher than the average in ALL OTHER COUNTRIES.

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Social Welfare Programs and The Culture of Dependency II

David W. Brown, Amanda E. Kowalski, Ithai Z. Lurie present evidence of long term beneficial effects of Medicaid available in childhood. They consider the expansion of Medicaid and note that increased availability of Medicaid to children is correlated with higher earnings as adults. They note that this means that the Federal Government recouped part of the cost of the Medicaid.

Via Margot Sanger-Katz via Paul Krugman (so I guess my linking adds little).

They can identify the effect because Medicaid expanded at different times in different states. This strategy is the same as that in the study of the long term effects of food stamps.

The empirical result is the same too and it is the opposite of the social safety net is a hammock hypothesis that social welfare spending creates dependency and leads to a culture of poverty. This is another study providing convincing evidence that social welfare spending helps break the cycle of poverty.

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Secular Stagnation, The US Recovery, and Houses

Larry Summers and Brad DeLong have even more than usually stimulating thoughts about secular stagnation and extremely low interest rates. I notice a strong focus on non residential fixed capital investment.

disclaimer: I owe debts I can never repay to both of them, so this post might even be civil.

Summers responds to Marc Andreesen on secular stagnation. The post is rather brilliant (no surprise there). In particular, I very much liked and strongly agree with (the parts I understand) of

the evolution of productivity growth is not essential to the argument about whether equilibrium real interest rates have declined. This decline could have occurred for many other reasons – including increased foreign saving, lower priced capital goods, slower labor force growth, increased demand for safe assets, more burdens on financial intermediation, and lower rates of inflation.

I will discuss why I like Summers’s list of possible causes of secular stagnation after the jump, but here I just note that it is appropriately long. A model adicted economist would look at one possible explanation and assume away all the others. In fact the point (if any) of this post is to add another explanation — lower demand for housing. I note that the second and third explanations focus on non-residential fixed capital investment.

This passage also clearly focuses on non-residential investment

Marc and I agree that we are headed into a period of soft real interest rates, where there will be more money available than great deals. This may, as he suggests, not be all bad; as it will make it easier for risky ideas to get funded.

Brad too doesn’t mention houses. For example, here is his first concern about problems with low interest rates

safe interest rates expected to be very low for a long time artificially boost the value of long-duration assets–so capital is misallocated and we wind up with a capital structure that has in it too many long-duration relatively-safe projects that make at best very small contributions to societal well-being.

Emphasis mine and he doesn’t mean housing project.

Yet the latest bubble was in housing and the components of aggregate demand which have been strangely low during the long disappointing phase of the recovery (which phase might be over by now) were G and residential investment.

Standard macroeconomic models don’t include a housing sector. Compared to most economists DeLong and Summers are not at all model addicted. Yet even they ignore housing when discussing investment in general and long run growth and such.

I can think of two more explanations. First lower population growth causes much lower housing investment — houses last a long time so a whole lot of gross housing investment is expanding the housing stock not replacing depreciated and torn down houses. So far, I can see why houses factories and office parks are lumped together — the issues are basically the same.

Second and again, maybe there has been either bubbles or extremely low real interest rates since the productivity slowdown (starting 1973). That is maybe the housing bubble has lasted for decades and the generally recognised housing bubble post 2000 was just more extreme. People have long believed that houses are good investments because the relative price of housing trends up. Shiller has long argued that they have been mistaken. If he is right, demand has been high because of irrational expectations of price appreciation for a very long time. The argument that, during bubbles, asset prices must shoot up and become clearly crazy so the bubble can’t last is based on the standard assumption that investors know the full history of prices. This is true of stocks but definitely not true of houses. Again if Shiller is right, the current low forecast of house price appreciation and current low demand for housing might be the new normal.

Finally US housing demand has included the demand for huger and huger houses. The trend will slow if the desire for more and more floor space is satiated. This is an issue related to preferences and quite different from any discussed by DeLong or Summers.

There is a similar issue related to consumption and savings. The suspicion that inequality leads to secular stagnation is based on the idea that the super rich are satiated — that they can’t possibly consume a large fraction of their huge incomes basically because they don’t have the time. Standard assumptions about utility functions are made so that there can be unbounded growth at a constant rate with a contstant balanced growth real interest rate. It is perfectly possible to write a model in which growth stops because consumers are satiated.

Finally, back to housing

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What might a NGDP inflation target look like in a policy rule?

A nominal GDP target makes sense. If inflation runs below target for a while, it makes sense for inflation to run over target in the future in order to achieve the desired long run growth to inflation.

So how might a policy rule to determine the Fed rate be modified for a NGDP target?

A policy rule has this essential structure…

Policy rule rate = short term real rate + inflation target + 1.5*(core inflation – inflation target)

So if core inflation runs over target, the policy rule rate rises to move inflation back down to target. As well, if core inflation runs below target, the policy rule rate drops to move inflation back up to target.

However, in nominal GDP targeting, the idea is to move inflation beyond the desired long run inflation target in order to compensate for the time being off target. So for example, if core inflation runs below target, the inflation target in the policy rule would be raised to guide inflation to a higher level above the target.

Thus the inflation target in the policy rule would have to be adjusted to allow core inflation to average to its long run target. The adjusted inflation target could look like this…

Adjusted inflation target = long-run inflation target + (long-run inflation target – average core inflation over previous time period)

Let’s put this equation to a graph. I plot core inflation (blue) over time going through periods over a 2% target, followed by periods under the target.

ngdp inf tar 1a

The orange line gives the adjusted inflation target through time averaging all the previous core inflation from time 0. So as core inflation is averaged over longer and longer time periods, the adjusted inflation target for NGDP targeting stabilizes near 2%. The grey line is the adjusted inflation target if core inflation is averaged after it ran below target. That line too will stabilize near 2% through time.

Whether the adjusted inflation target is measured from time 0 or time 4, it will stabilize near the constant inflation target currently used in policy rules. So is there really a need for adjusting the inflation target?

Let’s apply this equation to core inflation data since 1967. In the following graph, the line represents the inflation target that you would use now depending on how far back you averaged core inflation. For example, if you averaged core inflation back to 1987, you would need an adjusted inflation target of 1.3% in your current policy rule, instead of the constant 2.0% being used.

ngdp inf tar 2a

If you averaged core inflation back to the end of 2008, you would use an adjusted inflation target of 2.3%, which is already close to the 2.0% inflation target being used. If you averaged back to the 1960’s, you would use an adjusted target of -0.2%. So there is a big difference depending on how far back you average core inflation. Your adjusted inflation target for the policy rule may be above or below your desired long-run target.

The graph above assumes a long-run inflation target of 2.0% for NGDP targeting. What if you desired a LR inflation target of 3.0%?

ngdp inf tar 3a

Even though you have raised your inflation target by 1%, the adjusted inflation target for the policy rule rises by 2.0%. The 1987 target rose from 1.3% to 3.3%. The end of 2008 target rose from 2.3% to 4.3%.

Now what if your long-run inflation target were 4% as Paul Krugman has suggested, and then used the adjusted inflation target for NGDP targeting? The adjusted inflation target rises by 4%. For example, the end of 2008 adjusted target rose to 6.3% from 2.3%.

ngdp inf tar 4a

Let’s put some numbers into the policy rule for NGDP targeting assuming a short term real rate of 0% and a current core inflation of 1.7%. Let’s average core inflation back to the end of 2008. What Fed rate would the policy rule prescribe for us?

Policy rule rate (2% LR inflation target, 2.3% adjusted target) = 0% + 2.3% + 1.5*(1.7% – 2.3%) = 1.4%

Policy rule rate (3% LR inflation target, 4.3% adjusted target) = 0% + 4.3% + 1.5*(1.7% – 4.3%) = 0.4%

Policy rule rate (4% LR inflation target, 6.3% adjusted target) = 0% + 6.3% + 1.5*(1.7% – 6.3%) = -0.6%

So if you want a LR inflation target at or above 3.5% for your NGDP targeting, you would keep the Fed rate at its zero lower bound because the policy rule is giving a Fed rate below 0%. However, if you wanted a LR inflation target below 3.5% for your NGDP targeting, you would want the Fed rate above the ZLB. (assuming a short term real rate of 0%).

So NGDP targeting could be a good idea for balancing inflation to its LR target over time, but the method seems open to a lot of discretion. How far back do we average core inflation? What should the LR inflation target be? And in that range of discretion, the policy rule would give a wide range of options. Is it any wonder that discretionary monetary policy is dominant now?

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Which Party Is Better for the Economy? by state

Guest post by Nathan Salminen (is a lawyer and an amateur economic and political researcher. Nathan has been politically active for many years, including working for the Senate Committee on the Judiciary as a law clerk. Nathan currently practices law in New York and runs Politics that work.)

Dan here…this is the second part to a series of three.

Comparing results between red and blue states

We have 50 different states, each with its own set of policies. In many cases, states have adhered to a generally consistent approach to policy for decades or even a century or more, so the condition the states are in is a strong indicator of the effects those policies have. This presents a great opportunity to evaluate the impacts of those policies by comparing the economies of the states.

The most straight-forward way to see whether the economy is performing better in red states or blue states is simply to look at the per-person median household income. The differences in that regard are stark:

median income by state

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The economics of stuff, or secular stagnation and cast iron frying pans

Dan here…When in Fort Lauderdale, FL to visit a son and his girlfriend this Christmas, I ran into the phenomenon of ‘lots of stuff’ as they furnished their new apartment. Both real estate turnover and ‘used furniture’ were thriving industries, I assume partly from the turnover of ‘snowbirds’ and younger folk offering services to this older population. (update:typos corrected)

Frances Woolley at Worthwhile Canadian Initiative points us to another look at this idea of the economics of stuff…

This post could have been called, “Secular Stagnation and Cast-Iron Frying Pans”. Secular stagnation is sometimes thought to be caused by an imbalance between savings and business investment. The economics of stuff explains secular stagnation in terms of household investment, that is, investment in consumer durables.

Buying cast-iron frying pans is a form of investment – one that pays dividends for decades in the form of excellent grilled cheese sandwiches. But I already own three cast-iron frying pans – I’m not planning on buying any more for the foreseeable future.

The economics of stuff suggests secular stagnation is due to deficient population growth, as well as population aging. It doesn’t matter how many old people there are, as long as the population is growing, young people will come along who will need to buy stuff. But if there is no net population growth – or if the number of old people exceeds the number of young people – the young no longer need to buy stuff. They can get all the cast-iron frying pans (and furniture and wine glasses and vinyl LPs) they need from old people. Who are happy to get rid of it.

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To Mark Cuban on Student Loans: Grab some Bench, “Rookie”

Guest Post by Alan Collinge

Group Founder Alan Collinge has written numerous articles, and editorials on the topic, and also published The Student Loan Scam in 2009. He was selected as one of seven “Financial Heroes” by CNN/Money Magazine in December 2008.

There has been a disturbing coalescence of papers, positions, and proposals coming from Stanford graduates, academics, and Silicon Valley tycoons regarding student loans recently. All of these have, unfortunately failed to address the relevant economic dynamics governing the lending system, and their proposed solutions either completely neglect the $1.3 Trillion dollar problem at hand, or even defend the Public Policies that gave rise to it. Whether by chance, design, or otherwise, these proposals, collectively, are badly distracting the public discourse, and perpetuating a problem that is simply false.

It started with a paper by G. Marcus Cole, Stanford professor, who argues that because student loans are unsecured, there should be no bankruptcy protections for them. Coles is quoted in the Stanford Law School News:

“…With dischargeable loans, the risk that lenders would not receive the money they originally lent would increase. Cole added that investors wouldn’t see the sense in lending to students anymore.”

Cole completely fails to acknowledge that both private banks and the federal government administer unsecured loans, many of which are very profitable (for instance, the credit card industry). invisible hand Cole also fails to acknowledge that in the absence of bankruptcy protections, a lending system has come about where every element in the chain, up to and including the federal government makes more money on defaulted loans than loans that remain in good stead! This is a defining hallmark of a predatory lending system, and Adam Smith himself would agree is an unfair, intolerable, and unacceptable lending relationship. Would Cole argue similarly that medical debt, credit cards, and other unsecured credit be non-dischargeable?

Cole also completely fails to acknowledge that in the run-up to the 2005 bankruptcy bill- which stripped bankruptcy from private loans- the lenders promised they’d lend to needier students , but this has never happened. What the lenders DID do was begin requiring creditworthy cosigners for virtually all private loans, and now use this to extort vast sums from parents and grandparents under the threat of losing their savings, retirement, real property, etc. That Cole, or any economist would attempt to defend such a blatantly dirty trick and all the havoc it has wrought on so many families is, frankly, unconscionable.

The second attempt to address the student debt problem comes from Mr. Peter Thiel, Stanford Grad, Paypal Founder, and Manhattan Dandy who is essentially using the $1 Trillion student loan crisis as a stepping-stone by arguing that kids-particularly disadvantaged; inner-city kids- should forgo college and instead pursue entrepreneurship. Never mind that Mr. Thiel would never have snagged the success he now enjoys were it not for his Palo Alto pedigree. Never mind that a recent job-posting for Thiels investment company was very clear that only well credentialed with applicants with advanced degrees would be considered for employment. Never mind that this is typically horrible advice for young people who aren’t knowledgeable, skilled, and passionate about a potentially marketable product or service- particularly kids who weren’t lucky enough to be born into the kind of wealth and resources that Mr. Thiel was born.

Most recently, Mr. Mark Cuban, Dotcom Billionaire, Dallas Mavericks owner, television celebrity, and yes- Stanford alum, has calledfor a 10% reduction in lending limits to undergrads. Cuban, like the others, completely fails to acknowledge the root causes of the out-of-control inflationary spiral the student loan system is now on. As such, his solution does absolutely nothing to cure the root causes of the problem, does nothing to address the massive injustices and harms now being inflicted on the citizenry- many of them Dallas Mavericks fans, and only perpetuates the true “shark tank” mentality that has overtaken this industry, and the big-government behemoth that oversees it (scroll down the link to get the punch line).

While these men don’t necessarily represent the prevailing attitudes of the “Stanford Crowd”, I’d say their comments reveal stunning ignorance of the problem(at best), or an agenda to perpetuate/exacerbate a predatory lending system that has inflicted massive harms on tens of millions of citizens, and is poised to wreak a far greater havoc imminently. This reflects poorly on the university. I hope very much that the economics faculty there will have the courage to step up and inform the discussion up there.

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