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.

Multipliers

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.

Snark

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. 

Arithmetic 

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.