Friday, February 26, 2016

Sanders multiplier magic

The critiques of Gerald Friedman's analysis of the Sanders economic plan  continue. The latest and most detailed and careful so far is by David and Christina Romer.

Bottom line:

  1. The central idea in Friedman's analysis is that taking $1 from Peter to give to Paul raises overall income by 55 cents.  From this, you get multipliers from raising taxes and spending, from higher minimum wages, more unions, and so forth. 
  2. I chuckle a little bit that so many economists who previously liked multipliers now don't like their logical conclusions. 
  3. The Romers charge a serious, elementary arithmetic mistake in treating levels vs. growth rates. If they're right Friedman's whole analysis is just wrong on arithmetic.

The analysis

One might have expected that a sympathetic analysis of the Sanders plan would say, look, this is going to cost us a bit of growth, but the fairness and (claimed) better treatment of disadvantaged people are worth it.

Friedman's having none of that. In his analysis, the Sanders plan will also unleash a burst of growth, claims for which would make a fervent supply-sider like Art Laffer blush.

"The Sanders program... will raise the gross domestic product by 37% and per capita income by 33% in 2026; the growth rate of per capita GDP will increase from 1.7% a year to 4.5% a year." And, apparently, raise the growth rate permanently.

More stunning still are Friedman's claims about employment, shown at left here

and here.


So, where does this spurt of growth come from? The answer is the magic of multipliers.

But it's not just run of the mill fiscal stimulus multipliers.  After all, Friedman also says that the Sanders program would reduce the deficit, and by 2025 turn the Federal Budget to surplus!

How are multipliers so strong?

There seem to be two basic answers. First, Sanders assumes that there is a large multiplier from income transfers.

If the government takes $1 from rich Peter, and gives that $1 to poor Paul, overall income rises 55 cents! The one quote that makes this clearest is
The stimulus from regulator[y] changes is in Table 9. In general, the assumption is that wages have a multiplier of 0.9 compared with a multiplier of 0.35 for profits accruing to high-income persons. A wage increase coming out of profits, therefore, has a multiplier of 0.55.
It's also visible here explaining how a balanced budget still has a multiplier
the average value of the (governent spending) multiplier from 2017-26 is 0.89, falling from 1.25 to 0.87 as the output gap closes 
Other taxes are assumed to reduce effective demand with a multiplier of 0.35
[The] balance of revenue and spending programs will increase employment and economic growth because the spending program has a larger fiscal multiplier than do progressive tax increases. 
So tax $1 and spend $1 raises GDP by 54 cents.

He cites many standard sources for multipliers. He does not give a theory.  The standard story is that poor Paul consumes a lot more of his income, while rich Peter was investing it all in venture capital startups.  Consumption is good, savings is bad, so GDP rises.

From this central assumption, the rest of the magic follows.  Friedman creatively goes far beyond conventional deficit multipliers, to conjure multipliers out of tax increases, raises in the minimum wage, greater unionization, increased social program spending, and so forth. For example
 I assume that the Paycheck Fairness Act will raise women’s wages by 1% relative to men’s, and there will be an increase of 0.2% a year for the next decade.  I assume that 50% of the increased cost goes to higher prices and 50% comes from profits, and these are assumed to lower spending by higher income people with a multiplier of 0.35.
This, I think, is the central case. Admire it for its courage, and creative use of Keynesian arguments. These are the kind of interventions that most economists admit reduce growth, but some argue for on other grounds. But in Keynesian economics, taking money from low marginal propensity to consume people, and giving it to high marginal propensity to consume people raises GDP.


At this point, I stop in a bit of amusement at all the criticism. After all, these are just standard Keynesian arguments. The individual multipliers in Friedman's analysis are all conservative, and cite standard middle-of-the-road sources. The economists now so critical of this analysis, including the Romers, former democratic administration CEA chairs who wrote the open letter from past CEA chairs, and Paul Krugman, have been making big multiplier arguments for years to argue for more spending.  The "new Keynesian" academic literature includes multipliers far above two, so one can point to "science" if you wish. (Gauti Eggertsson, Christiano, Eichenbaum and Rebelo ; a simple example with multipliers as large as you want.)

The Romers are right to emphasize that multipliers only operate where "demand" is slack, and monetary policy doesn't steal the show. But the asterisks about fixed interest rates and output below "capacity" have been overlooked by the mainstream many times before. It's a rare Keynesian economist who ever thinks the economy is operating at full capacity. And Friedman has the former monetary asterisk, and he addresses the latter by claiming a large return to the labor force and increased productivity.

Even that view is not so out of the mainstream. For example,  Brad DeLong and Larry Summers wrote an influential Brookings paper arguing for very large fiscal multipliers, with some of the same flavor. There is hysterisis; a multiplier will bring people back to the labor market (as Friedman claims), those people will regain skills, productivity will increase; higher investment will give us better capital and also increase productivity. Demand creates its own supply.

Friedman is apparently just taking the consumption-first, poor-people-spend-more-than-rich-people, undergraduate ISLM analysis, with a bit of Delong-Summers hysterisis, to its logical conclusion. I agree in a way: take those ideas to their logical conclusion and you get silly propositions (old essay on that). Robbing Peter to pay Paul raises income; wasted government spending is good; theft improves the economy, transfers even from thrifty poor to spendthrift rich improve the economy, hurricanes are good for us, social programs, unions, minimum wages raise GDP, and so forth. Well, if the logical conclusions are patently silly, maybe one shouldn't have been making small versions of those arguments all along. Economic Homeopathy is not wisdom. 


But the Romers uncover a deeper puzzle. Even with these assumptions -- government spending multipliers around 0.8, and a transfer multiplier of around 0.55 -- you still don't get the wild increase in growth that Friedman claims. So how does he do it? Their answer: 
We have a conjecture about how Friedman may have incorrectly found such large effects. Suppose one is considering a permanent increase in government spending of 1% of GDP, and suppose one assumes that government spending raises output one-for-one. Then one might be tempted to think that the program would raise output growth each year by a percentage point, and so raise the level of output after a decade by about 10%. In fact, however, in this scenario there is no additional stimulus after the first year. As a result, each year the spending would raise the level of output by 1% relative to what it would have been otherwise, and so the impact on the level of output after a decade would be only 1%.
If this is right, it's absolutely damning. This is a question of arithmetic, not economics. (And I would have to swallow some of my above snark!) 

A clearer (maybe) example: The government spends an extra $1 for one year.  With a 1.0 multiplier GDP goes up $1 that year, period. If the government stops spending next year, GDP goes back to where it was. That's the conventional definition of multiplier, and the one that all Fridman's cited sources have in mind. Per Romers, Friedman misread that calculation and assumed the first $1 of spending raises GDP by $1 forever. In 10 years, you have a multiplier of 10! 

The Romers are cautious, and don't directly make this charge. It's not my job to get into the Hilary vs. Bernie whose-numbers-add-up fight. (At least someone here actually seems to care about numbers and economic plans!) But whether the spreadsheets make this arithmetic mistake or not is an answerable question. I hope to inspire someone with a spreadsheet and a nose for such things to check. This is a great time for a replication exercise! 

(Note: This post has pictures and quotes, which don't translate well when the post is picked up elswhere. If you're not seeing them, come back to the original.)

Update: Joakim Book tries to reproduce the numbers and comes up way short.

Update 2: Justin Wolfers at the New York Times did some old-fashioned journalism: He called up Friedman for a reaction.  The article is great, and clear. Yes, Friedman did the calculation as the Romers allege: An extra dollar of government spending today raises GDP permanently; an extra dollar of permanent government spending raises GDP growth permanently. That is at least not what the cited sources have in mind.


  1. Just as an FYI, the chart you depict appears to be nominal (not real) GDP. Nominal GDP at the beginning of 2015 was about $17.7 trillion. Real GDP at the beginning of 2015 was about $16.2 trillion.

    Currently, the BEA (Bureau of Economic Analysis) utilizes 2009 as it's baseline for calculating "constant dollar" GDP (aka Real GDP).

    Obviously that baseline date has been changed on more than one occasion, so perhaps the first thing the Sanders administration will do is reset the baseline for real GDP to 2016.

  2. Do Keynesian's maintain that multipliers are the same no matter the current state of the economy? My intuition is that it's really a ROI argument. When the economy seizes up the ROI on [some] government intervention is probably larger private industry. As the economy gets healthier that reverses. This implies the "multiplier" depends on that ratio.

    1. Keynesian argument is as follows (as understood by non-economist):
      In normal, growing economy all resources are utilized and any additional project (like government works) has to compete for resources with others on the market, making them more expensive and rising inflation; it is standard assumption of every capitalist economic school that private investors will utilize resources better (more efficiently) than government, so extensive entrance of government in the markets rises inflation and lowers GDP.

      In demand crisis, lots of resources are under-utilized (easiest thing to imagine hundreds of construction companies without anything to do). When government starts projects, it competes with noone, but utilizes free resources. This has several advantages: first, in demand crises money is cheap, government can increase deficit at very low cost - US 10y bond is below 2%, 30y is below 3%, UK 50y bond is around 2% - if inflation returns to 2%, and GDP rises some 3% nominal annually, these are extremely favorable numbers. Second, it mitigates the worst of the crisis - less people are unemployed, more resources are consumed... More companies can stay in business and crisis ends earlier. Therefore multiplier: every $ that government spends keeps one company and its workers in business, they order resources, consume goods... they otherwise wouldn't have, keeping other people and companies in business and so on.

      As crisis ends, private capital employs more resources, and further government projects start again to compete with private capital, so government should start getting out of the markets, to "standard" level.

      Problem that Keynesians have with Friedman's analysis is that they believe that US would recover long before it hits Friedman's targets and in normal economy there is no multiplier (it's same if funding comes from government or private sources). Actually, it's always the same whether funding comes from government or private sources, but during crisis there are not enough private sources.

      There is no question of ROI in standard sense - Keynesian multiplier and "helicopter money" theory (that is, any type of stimulus) comes into play only in crises where there is insufficient private funding, so government must make up the rest, nobody says that government can invest better than private companies.

  3. "The Sanders program... will raise the gross domestic product by 37% and per capita income by 33% in 2026; the growth rate of per capita GDP will increase from 1.7% a year to 4.5% a year."

    Just to put this projection in perspective, since 2000 real GDP per capita has grown at just under 1% per year. During the Reagan and Clinton years, it was around 2.6%.

  4. What is the explanation for the rapid expansion of the US economy during WWII?

    1. Taking the slack out of a huge output gap left over from the depression.

    2. There wasn't one from the consumers perspective

  5. Though I prefer FICA tax cuts and plenty of QE to the Sanders plan (in my plan the Fed funnels Treasuries into the Social Security and Medicare budgets to make up for lost tax revenues), I will say this: there have been conservative economists recently who have posited that 4% annual growth in GDP is possible even while maintaining a $1 trillion a year "natural security" budget (DoD, DHS, VA, black budget, and prorated debt) and extensive rural subsidies.

    Frankly, I admire such optimism.

    So Sanders is only a little more optimistic on his plans than the 4%'ers.

    To my despair, the ideologues of both sides ignore ubiquitous property zoning, the parasitic effect of national security spending, or how tight money appears to suffocate the economy more than hold down inflation.

    And how did the U.S. GDP expand by 8.5% real in 1965? Was it low inflation? Balanced budgets? Tight money? The 20% expansion on real GDP in four years after the 1975-6 recession?

    Yes, there should be war on structural impediments. I doubt we will see much done on property zoning, rural subsidies and the national security tax-eater anytime soon.

    So we have to live with structural impediments. Given the reality on the ground, what are the best macroeconomic policies?

    1. This comment has been removed by the author.

    2. "And how did the U.S. GDP expand by 8.5% real in 1965? Was it low inflation? Balanced budgets? Tight money?"

      Well, CPI inflation was under 2% that year and the deficit was just 0.2% of GDP. It was also right after a major tax cut. For that cycle as a whole, the economy did grow at a historically strong rate, but it still didn't reach the type of growth Friedman is projecting.

      "The 20% expansion on real GDP in four years after the 1975-6 recession?"

      This is bit of cherry picking isn't it? There was a deep recession in the mid-70's, followed by a few years of high growth, followed by two sharp back-to-back recessions in the early 80's. Looking at that entire period, the numbers don't look great at all.

      Also, you realize defense spending was a much larger share of the total budget and of GDP during those earlier years you referenced, right?

    3. I can't figure out how these comments are supposed to work. I meant this as a comment rather than a reply. Oh well...

      When economists contemplate the end of the Great Depression they think of charts and graphs that are mostly irrelevant. What actually happened was the New Deal and the government took over the system during WWII: wage and price controls, 8.5 million drafted into the Army, government expenditures 40% of GDP, a top tax rate of 94%, and rationing as private debt fell from 141% to 67% of GDP. The income share of the bottom 90% increased over 20% during the war and didn’t fall until the 1980s. Social insurance came to be; government’s share of GDP more than doubled, and the financial system was strictly regulated after the war.

      The economic system that emerged from the New Deal and WWII was not the system that led us into the 1930s. It was a system of higher taxes, more government, strict regulation, and less inequality. This was what pulled us out of the Great Depression and into the economic prosperity that followed WWII, not the magical workings of free markets or the monetary and fiscal policies of Keynesian economics. And neither free markets nor monetary or fiscal policies are going to get us out of the Great Recession we face today or allow us to avoid another worldwide catastrophe comparable to WWII.

      Policies that do not reduce the trade deficit and concentration of income will simply prop up a failed system that makes the rich richer and poor poorer as the federal debt grows.

      It is essential that we use the legislative, tax, and spending powers of the government to reduce the trade deficit, expand government services, and increase the economic and political power of those at the bottom to achieve full employment through a more equitable, efficient, and productive distribution of income if we are to deal effectively with the fundamental problems we face today.

    4. I disagree with you, but it is true that during the postwar era 1945-1975 the US economy expanded rapidly, per capita income soared, labor unions were huge, transportation and communications and finance were heavily regulated and the top tax rate was 90%. And there was little international trade.

      And the economy was boom boom boom boom boom boom boom.

      Now we hear from macroeconomists how important it is to keep inflation below 2 percent or even below 1 percent or exactly at zero percent (as measured) or maybe even below zero.

    5. It kind of makes me wonder where and why you disagree with me?

  6. Zack-- it may be defense spending was a larger a fraction of GDP, and it certainly was during World War II, when US GDP doubled in five years.

    However, if you look at national security spending today, and include DoD, DHS, VA, black budget, and prorated interest on debt, you come to about $1 trillion dollars.

    That $1 trillion is financed by income and capital gains taxes, which of course are disincentives on productive behavior.

    There was also a 20% spurt in GDP in the 1980s after a recession.

    I suspect the US economy is similarly underutilized today, and much more globalized, and with the right policies we could enjoy another 20% spurt in real GDP.

    Anyway, John Cochrane recently suggested we could enjoy 4% real growth GDP permanently.

    I say go for it, with both barrels.

    1. I certainly won't argue that there isn't wasteful spending in the defense budget or that it couldn't be decreased. I just having a hard time seeing how it can be blamed for our increased deficits compared to the past.

      "There was also a 20% spurt in GDP in the 1980s after a recession.

      I suspect the US economy is similarly underutilized today, and much more globalized, and with the right policies we could enjoy another 20% spurt in real GDP."

      No disagreement from me here. I believe growth averaged somewhere in the 4% range during those long 80's and 90's expansions. That wasn't so long ago. At the very least, I'm sure we can do better than the weak growth we've been getting for the last decade or so.

  7. Jamie Galbraith's refutation of the Romer Analysis here.

    1. Not at the link you sent. The Romers charge a mistake of arithmetic, not a debate bout models: That Friedman took one dollar of spending and multiplied that to one dollar more GDP forever, not one dollar more GDP for one year. Nothing I could find in the link you sent has anything to do with that central charge. If it's there and I missed it, please send the appropriate quote.

    2. Do you think that Mr. Galbraith's refutation is correct?

    3. As I said, nothing in the link even addresses let alone refutes the central charge, that Friedman just made an arithmetic mistake. He cited sources that say if the government spends a dollar this year, GDP goes up 80 cents this year, to project that GDP goes up 80 cents forever, and possibly keeps growing. That's the core of the Romer's charge, and nothing I know of in the Galbraith quotes had anything to do with it. Nor could it, as the quote predates Friedman's analysis, let alone Romers.

      If there is another Galbraith refutation, send it along.

      I wish somebody here would get out a spreadsheet, reproduce Friedman's numbers and for once and for all tell us how he got there.

    4. Jamie Galbraith's original defense noted how real GDP grew at 5.4% per year from 1983 to 1985. Of course he forgot to mention that the GDP gap was over 8% and potential output was growing at 3% per year.

      I was impressed with your take down of Friedman's multiplier mistakes. Of course the real problem is that Friedman completely fails to model the supply-side as do his defenders.


      I think he accepted it's "not standard" but how he sees the world and "may be a mistake". Not sure how those two are consistent ...

  8. It is at least odd that Christina Romer claimed about the same strength of multiplier as Friedman when she was part of the government, as Chair or prospective Chair of the CEA. Maybe the math and model changed according to who was paying her.

    The proponents of the stimulus predicted an effect which didn’t happen, namely 3.7 MM new jobs.
    === ===
    [edited] In sharp contrast, Christina Romer, Chair of President Obama’s Council of Economic Advisers in 2009, argued that a multiplier of 1.6 should be used in estimating the new jobs that would be created by the stimulus program. This sharp difference between Barro’s [ multiplier = 1] and Romer’s multiplier estimates translated into an enormous disparity of 3.7 million new jobs, the number which Romer notoriously claimed would be generated by the stimulus package by the end of 2010.
    === ===
    === ===
    [edited] Team Obama has released its analysis of fiscal stimulus, coauthored by CEA Chair-designate Christina Romer and Vice President-elect adviser Jared Bernstein. If you go to the penultimate page, you can find the fiscal policy mutlipliers they assume. For government purchases, their multiplier is 1.57; for taxes, 0.99.
    === ===

    Obama and our government is Keynesian to the core, even under Republicans. Keynes is the high priest of “tax and spend”, which is why politicians love him so.

  9. Dear John, more than a month ago, I sent an email to my colleagues criticizing Friedman's analysis of the costs and benefits of Sanders' single-payer plan (used by the Sanders campaign) and accusing Friedman of bad economics. Specifically, his analysis on how the proposed increase in the payroll tax will impact household finances ignores the role of the elasticity of labor supply relative to that of demand in determining tax incidence, and fails to discuss how the inelasticity of the supply of health care will affect the price/quality of care (and yes, I did forward a link to your paper on what to do after the ACA). I am sure many of my colleagues dismissed my comments as coming from a market fundamentalist (which I am not, but I am the most skeptical in my department when it comes to Keynesian ideas). So thank you for this post, as I feel somewhat vindicated. I see a pattern by Friedman, and it is not a good one.

  10. Didn't Bob Lucas describe this analysis via multipliers best, as "shlock economics"? Why are we still taking any of this seriously?

    1. "We" don't (if by we you mean the economics profession net of a lunatic fringe). The public, and the legions of politicians whose job is not to be right but to be convincing, take seriously anything that confirms their previously-determined "truths".

  11. Three points. 1, Friedman uses CBO projections as a baseline. But when was even a single CBO projection not way above later outcomes? I think never. So, baseline already biased. 2, what are we fussing about here? If we are talking about alternative realities, using CBO methods, let CBO do the computations. Bernie is still in the Senate, he can get them to do it. 3, why is that Bernie's beloved social democratic countries in northern Europe always do better, wealth- and employment-speaking, when they move back from unaffordable socialist pie-in-the-sky policies? Why does reality and actual experience not cloud any Keynesian projection, ever?

  12. I remember Friedman, he said something really smart: There is no such thing as a free lunch. ... oh, wait, maybe that was another Friedman ... never mind, it's still really smart. But apparently it doesn't apply to Bernie-economics when viewed through a New Keynesian looking glass. Score MIT 1, Old School UChicago 0. Pity, that.

  13. Do you support the Trump Campaign? Does their arithmetic add up?

  14. Do you think conservative claims about the output and employment effects of tax reductions and regulatory easing are any more plausible than Keynesian multipliers?

  15. "Consumption is good, savings is bad, so GDP rises."

    No. Consumption is counted in GDP, saving is not, so GDP rises.

    1. Except that savings = investment, and investment is in GDP, so GDP rises no matter what!

    2. #1 (Anonymous argument)
      Saving = Investment
      Investment is counted in GDP.
      Therefore Saving is counted in GDP.

      #2 (No one's argument)
      The number of human shadows = the number of people standing in the light.
      People standing in the light are counted in the population.
      Therefore human shadows are counted in the population.

      I do not accept either argument.

  16. This topic would be less controversial if economists shared a framework to think about fiscal multipliers and income flows.

    I have developed such a method that separates the government and the private sector. It is vizualized by a matrix.

    My analysis makes the assumptions about how the private sector reacts to stimulus explicit, as well as what happens in case the government runs a balanced budget.
    It points out the importance of choosing the baseline scenario (=without fiscal stimulus) to calculate the multiplier:

    To relate it to your blog post, these are the assumptions of the people you cite:

    -DeLong & Summers assume that in the absence of stimulus, private sector spending will be low for a very long time
    -Friedman assumes that private sector spending is constant, unless government applies stimulus, in which case private spending increases (and remains at that level permanently, also when stimulus is stopped)


Comments are welcome. Keep it short, polite, and on topic.

Thanks to a few abusers I am now moderating comments. I welcome thoughtful disagreement. I will block comments with insulting or abusive language. I'm also blocking totally inane comments. Try to make some sense. I am much more likely to allow critical comments if you have the honesty and courage to use your real name.