The Intuition behind Wallace Neutrality, Attempt 3

Ok, if I might make another attempt to explain the elusive intuition behind Neil Wallace's model, and why Wallace neutrality doesn't work in the real world. The issue recently re-arose in the econoblogosphere. I have two earlier attempts that I think are interesting and show some good intuitions. Here's try three:

Please consider this:

With Miller Modigliani (MM), if the firm borrows more, it increases the overall debt level of its shareholders. Since we're assuming at the start that everyone's a perfect optimizer, with perfect expertise, public information, etc., and since we're assuming we start at equilibrium, then everyone is already at their optimal debt level, that they want to stay at.

So, when the firm borrows more, the shareholders just borrow less, enough less so that their overall debt level remains unchanged.

In MM, it's a partial equilibrium model, in that the interest rate is taken as given, exogenous, to use the term of the biz; the people in the model can't change it. But even if it weren't, the total demand for debt in the debt market doesn't change, because it all comes down to the fundamental demanders: the people. The firm is just an intermediary for them. The firm demands more debt? Well, they just demand less by an equal amount. Total demand in the market as a whole remains the same, and thus so would the market interest rate, even if this were a global equilibrium model.

So, now we go to Wallace's 1981 AER paper, “A Modigliani-Miller theorem for open-market operations”. You look at it, and it's a wall of very terse math. I have the dreaded ABD in finance. But at least I took all the courses and passed all the written exams, plus a whole lot of study on top of that. I think I'm pretty good at decoding the intuition behind math. And I spent about 50 hours on this two years ago, a giant amount for me. Still, I would love to have two months uninterrupted to just study this paper. Ah, a man can dream… Some want to pet turtles in the Galapagos when they retire, some want to get jiggy with Wallace…

Oh, oh, ok, wake up. Anyway, I think I got, nonetheless, a substantial amount of intuition out, and I would venture this:

In Wallace's model, the government is like a big MM firm. And the citizens are shareholders of the government. When the government does the Wallace version of a QE, it basically is like it borrows more money (really lends, but let's look at the converse for now). That would make its citizens overall debt level higher than they like, so they want to borrow less by an equal amount to stay at their optimal overall debt level. The total demand for debt in the market remains unchanged. Government demand goes up by X, and private demand goes down by X, so the interest rate remains the same.

In Wallace, all people are perfectly expert, with perfect public information, can do all analysis and information gathering and digesting instantly, at zero cost, and are perfect rational optimizers. They start the model in equilibrium with their optimal level of debt, and if the government, that they're "shareholders" in, borrows more, then they just instantly borrow less by an equal amount. So, interest rates don't change.

More specifically, in Wallace there is a single consumption good. I called it C's. People save some of their C's for period two of their two period lives. The government's "QE" is to print dollars and exchange them for C's, which it will store for one period. Then it will sell all of those C's back again out into the market for dollars – with 100% certainty. That's their plan, everyone knows it, and they're going to stick to it.

The people own the government. They're its shareholders; they get dividends in the form of government transfer payments, so when this government "firm" saves more C's, by selling newly printed dollars to get C's, and puts them into storage, then the people's overall savings goes up – up above their optimum that they had settled on in equilibrium.

So they sell C's out of their private stores in an equal quantity to compensate. The total demand overall for the market to save C's for the future does not change, and so the interest rate doesn't either. And that's the thinking; that's why it works in Wallace's model. That's why you can prove no change when you do the math in this model.

But why wouldn't this work in the real world?

Well, first off, people are far from perfectly expert (especially in the super complex modern world), with perfect public information that they can gather, digest, and analyze at zero time, effort, or money cost. This should be like, duh, but then you hear some of the things some freshwater economists imply, and you're stunned. Partly to sell their ideology, partly to make the models they're top experts in more valued, partly, perhaps, just detached from reality from selling, and smelling, their own B.S. for so long. But for whatever reasons, obviously the vast majority of people are far from this.

So, when the government "firm" starts to lend a lot more, almost no one thinks, MM style, or Wallace style, I want to start selling some of my bonds to compensate in equal measure as I see them doing that. And so total lending in the market does, in fact, go up, and market interest rates drop. People just don't react that way. And it won't be nearly enough if a savvy minority do. They won't control enough money to drive us to Wallace neutrality.

It's like in Miller and Modigliani's model if the firms start borrowing a lot more, but the shareholders are mostly not really paying attention, and/or don't know well the implications, so, for the most part, they don't want to borrow any less to compensate. In that case, aggregate demand for borrowing would not remain unchanged. The aggregate demand curve for borrowing would, in fact, shift out, and the interest rate would rise.

Other issues: In the real world there are a lot more different kinds of financial assets than just money, and borrowing and lending the single consumption good risk-free, like in Wallace's model. So, if the government does a QE in just some types of assets, people, even if they are perfect at optimizing, won't be able to funge their portfolios to relieve completely price pressure on those assets. Markets are not complete, and far from it, so that you could construct a synthetic for any asset. I talk about this in an earlier post on Wallace neutrality when I ask what if the government did a QE where they printed up a dollars and used it to purchase 100 million ounces of gold.

Next, Miller-Modigliani irrelevance doesn't hold if investors face different borrowing costs and liquidity constraints than the firm. Likewise, Wallace irrelevance will not hold if individuals and firms face different borrowing costs and liquidity constraints than the federal government. Do they? 

Finally, Wallace's model assumes that with 100% certainty the central bank will completely reverse the QE one period later, and everyone knows this. All of the C's purchased with the newly printed dollars will be sold back. In the real world, investors cannot be completely certain a QE will be 100% reversed in the future.

From UCLA economist Roger Farmer:

A wealth of evidence shows not just that quantitative easing matters, but also that qualitative easing matters. (see for example Krishnamurthy and Vissing-Jorgensen, Hamilton and Wu, Gagnon et al). In other words, QE works in practice but not in theory. Perhaps its time to jettison the theory.