Ricardian confusions squared

Hang on now, Paul, Mark, Progrowthliberal, and Antonio Fatas. Justin Yifu Lin (pdf) is basically right. He's making an important point. It's similar to one I made a couple of years back.

Sure, a temporary increase in useless government expenditure, even under Ricardian Equivalence, will give a bang for the buck. But it's a totally useless bang. No Keynesian economist would recommend it, even if there were no useful alternatives. And useful government expenditure will not only give a useful bang for the buck, it will give a bigger bang for the buck.

The intuition is simple. Paying unemployed resources to do something totally useless is equivalent to giving them a transfer payment. A transfer payment is equivalent to a tax cut. A tax cut has no effect under Ricardian Equivalence.

[Update: Paul Krugman responds.]

The Ricardian Equivalence Proposition says that a bond-financed increase in government expenditure is equivalent to a tax-financed increase in government expenditure. Because consumption depends only on permanent income and so on the present value of current and future tax liabilities. Assume Ricardian equivalence is true.

Assume, for simplicity, that the marginal propensity to consume out of permanent income is one. Ignore interest rates, exchange rates, and supply-constraints.

A permanent $100 increase in government expenditure will have zero effect on output, if it causes an equal $100 increase in permanent taxes, and so an equal $100 decline in consumption.

A temporary $100 increase in government expenditure will cause output to increase by less than $100, because it causes permanent taxes to increase by less than $100, and so consumption to decline by less than $100.

In the limit, as the $100 increase in government spending becomes purely transitory, we can ignore any offsetting effect of increased present value of taxes on current consumption. So output increases by $100. Just like the balanced budget multiplier in the old Keynesian Cross.

Now assume that the $100 increase in government expenditure is spent on something totally useless, like digging a hole and filling it in again. Which is what Justin Yifu Lin assumed. Does output really increase by $100?

Well, if you count that totally useless hole-digging-and-filling exercise as part of GDP, then yes, GDP does increase. And if you don't, it doesn't. And National Income Accountants can have great fun discussing whether the true value added of a filled hole is any different from the value added of a hole that doesn't exist because it was never dug in the first place. But it's still a totally useless activity. And no reasonable measure of output would include digging a hole and filling it in again for no purpose whatsoever. Its market value is precisely zero.

In terms of useful output, the multiplier of a useless project is precisely zero. And remember, there is no effect of increased consumption from the extra $100 earned by the people digging the hole, because it is exactly offset by the extra $100 present value of taxes. No Keynesian should recommend government expenditure on totally useless projects, under Ricardian Equivalence.

Now suppose the government spends the same $100 to dig a hole, plant a seed in the hole, and fill it in again. And the seed grows into a tree, and the tree produces exactly enough apples to repay the $100 the government borrowed including interest. So the government never needs to raise taxes. And people know this. What's the effect on output?

At a minimum, output increases by $100. And it really is a $100 increase in useful output. Unemployed resources, that would otherwise have produced $0, now produce something worth $100. And since that $100 increase in real wealth causes an additional increase in consumption expenditure, there will be a multiplier effect bigger than one.

Now suppose the government plants a tree at the cost of the same $100, but the tree now yields enough fruit to pay back double what it cost to plant. So the government can actually cut future taxes. You get the same direct effect as before, but real wealth has now increased by $200, which induces an even bigger additional increase in consumption expenditure, and an even bigger multiplier.

That's what Justin Lifu Lin is saying. (OK, that's a reasonable interpretation of what he's saying). He's right. If Ricardian Equivalence is true, then useless government expenditure, even if temporary, even if there are zero other sources of crowding out, will have a multiplier effect on useful output of precisely zero. And useful government expenditure, which requires no increase in present or future taxes, will have a bigger multiplier. And if it's even more useful, and allows a cut in future taxes, or an increase in future disposable income, it will have an even bigger multiplier.

Useful government expenditure doesn't just create a useful bang for the buck; it creates a bigger bang for the buck.

Comments

[anon]

RSJ, Your model is unclear to me, but I'm not quite sure why. ISTM that you can only derive this result by assuming some market imperfection, such as imperfect competition among developers, or perhaps demand externalities.

Suppose that developers rent housing to their tenants and pay a ground rent to the government. Assume that the market for housing is so dispersed that each developer cannot affect the value of surrounding land, so she takes the amount of ground rent as exogenous. Developers near the origin will have to pay high ground rents, but they also anticipate that their tenants will pay more, so their marginal revenue is higher and they build taller structures. Developers farther from the origin know that their tenants will pay lower rents due to distance, so they build shorter and cheaper structures. In either case, ground rent payments are factored into input costs, so, in a sense, developers are deterred from building near the origin. But land is included in input costs already, due to either acquisition or opportunity costs![1] The basic theory of LVT does not posit that land acquisition costs will rise under a land tax: if anything, that can happen as a result of decreasing burden from other taxes which would otherwise bear on land--in which case, the increase in costs is presumably balanced by increasing revenue.

[1] (Or perhaps it isn't, if developers are somehow "tied to the land": but in that case, ground rent payments are irrelevant unless they're so large that developers exit the market.)

[anon]

POWinCA, interesting comment. Yes, reputation and signaling/screening wrt. future employers is important. This explains the growth of unpaid internships and volunteer jobs (at least in the US) during this recession.

You mention uncertainty about future economic conditions as a reason not to commit to large public projects. But "uncertainty" cuts both ways: the safest assumption is for the recession to continue for an extended period. If recovery was expected soon, we would see clear signals of this in financial markets. (This is how we can tell that QE2 has helped somewhat in the U.S.)

I'd also argue that--concerns about structural change notwithstanding--employing skilled construction workers in "shovel-ready" public projects would be beneficial. Since these are viable projects which ought to be implemented anyway at some time in the future, it makes sense to step in and do it now when resources are cheaper. The only problem is borrowing constraints, which are starting to bite in the EU, and are increasingly a problem in the US as well due to political realities. "Deficits don't matter" has not worked well there.

[K]

"Now if you levy a tax on the land value, then landlords can lessen the burden of this tax by investing more in land farther out and less in land closer to the oasis."

This is not right. The developer is indifferent to
a) buying the land at its market value and paying interest on a bank loan (or equivalently: foregoing interest on the money used to buy the land); and
b) buying the land for nothing and paying the land tax on the site value.

You are missing the fact that land tax makes the cost of buying land go down. A full land tax reduces the land value to zero. So the developers don't respond with "arbitrage". They don't respond at all! *No behaviour* changes in the least when you put a tax on land.

Vimothy: "Sorry to interject, but, does the supply of land really change with prices?"

The answer is unequivocally no. The only point that matters is that the supply of any given piece of land can't change with its price, unlike almost any other capital good. Put a tax on IBM stock, and IBM will reduce the supply and move to other sources of funding. That's why you could impose different, random tax rates on every piece of land in the world and the optimal use of each piece of land would be totally unchanged compared to the untaxed world. Literally no distortion even if applied badly.

Jacques: There's plenty of fraud and evasion in the current tax system. I contend that a land tax would be significantly less subject to malfeasance. We could take it up (if Nick doesn't mind), but I suppose we have wandered quite far from the topic of the post (though we have had quite a lot of "Ricardian confusion" :-).

As far as indigenous people go, I think you have to raise the issue of who is the community that should receive the proceeds of a land tax. If a group has strong ties to a piece of land maybe a society wants to recognize that fact. Personally, I'm wary of collective rights, but land tax, at least from an efficiency perspective, is orthogonal to the decisions of a democracy as to how to distribute the proceeds.

[RSJ]

Vimothy,

The price of land, even if there were no location specific benefit adjustment, would not be zero.

There is always a MRT between land and structure, because you can buy a bigger lot, or you can build a taller unit, delivering the same total housing services. Land is a factor of production like anything else.

In the absence of any location specific benefits, so that all land is identical and there are many landlords competing to develop it and rent it out in a competitive rental market, they would compete to buy land (from each other) and sell land (to each other), up until the relative price of land in terms of structure is the MRT between land and structure.

That would be true whether the total land was fixed or not.

And in that case, the proportion of land value to total value would be fixed by the MRT as well.

If you levy a tax on land of t*r*land value, where r is the bond rate, then the price of land in terms of structure changes from MRT(L,S) to 1/(1+t) *MRT(L,S).

It declines, but never to *zero*, regardless of the tax. Each time you ratchet up the tax, the price of land would fall so that the total tax payment + interest payment is equal to the original interest payment.

With that change, the landlord is indifferent between selling bonds and buying land for MRT(L,S) and then paying the bond rate, r each period that he produces a housing service, or buying the land for 1/(1+t) *MRT(L,S) and then paying both the bond rate on his investment and the tax.

And in that case, the production decision is unchanged -- the landlord supplies the exact same amount of housing service for the same price as before.

But when all land is *not* identical, the situation changes and you can have the effects I described.

[vimothy]

This is a theoretical argument. I thought that there might be some easy empirical way to resolve this, but okay. RSJ aren't you describing the price elasticity of demand for inputs from producers of housing services, not elasticity of supply of owners of those inputs (land in this case)? Producers face a marginal rate of technical substitution in terms of their ability to substitute between inputs, but how does this imply that suppliers (i.e. owners) of land can vary supply with price?

[Vamsee Kanchi]

Greetings,

I am a Communications Officer at the World Bank and co-editor of 'Let's Talk Development,' a blog hosted by Justin Yifu Lin. I wanted to inform you that Justin Lin has written a new post on Ricardian equivalence, which can be found here - http://blogs.worldbank.org/developmenttalk/underutilization-of-capacity-and-ricardian-equivalence

thanks,
Vamsee.

[RSJ]

Vimothy,

"RSJ aren't you describing the price elasticity of demand for inputs from producers of housing services, not elasticity of supply of owners of those inputs (land in this case)? Producers face a marginal rate of technical substitution in terms of their ability to substitute between inputs, but how does this imply that suppliers (i.e. owners) of land can vary supply with price?"

OK, land is not produced. The quantity of land is fixed. So if a landlord wants to increase his land usage, another landlord has to decrease his usage. The first landlord must buy the land from the second. It doesn't really matter whether the landlord is renting land from a land-landlord, still the landlord desiring to increase his utilization must outbid the current user, whether by offering to pay a higher rent, or by offering to buy the land outright. As the rent will be just the bond rate on the purchase price, you can take either view.

That means the price of land in terms of structure is going to be determined by the landlord's cost of parting with it, which is the amount of additional structure that the landlord would need to deploy in order to obtain the same revenue.

[Henrik Jensen]

Dear Nick:

Interesting post. I haven't read all the comments, so maybe my comments on RE and fiscal stimulus on my own blog is outdated. I collected them in a recent blog post here:

http://blog.hjeconomics.dk/2011/03/21/temporary-and-permanent-ricardian-confusion-going-comfortably-numb/

Kindest regards, Henrik
University of Copenhagen