[Theory] Ricardian Equivalence as an Auction?

Time Magazine

Let's continue with the economic theory.

Maybe I'm a million miles off here, and maybe I'm the only person with a strong enough interest in mechanism design to care, to what extent could Ricardian Equivalence be seen as a specific result of the Revenue Equivalence Theorem?

Flamed Diving

The Economist wrote: »

Let's continue with the economic theory.

Maybe I'm a million miles off here, and maybe I'm the only person with a strong enough interest in mechanism design to care, to what extent could Ricardian Equivalence be seen as a specific result of the Revenue Equivalence Theorem?

I'm not a fan of Ricardian Equivalence, at all. But I never heard of RET, could you flesh it out a bit for me?

Time Magazine

Nor am I a fan of Ricardian Equivalence, but it's still interesting from a theoretical point of view.

The Revenue Equivalence Theorem states that an auctioneer's expected revenue from any type of auction will be the same, obviously under certain assumptions.

There are many types of auctions. Three typical examples are first-price, second-price and all-pay auctions. First-price is what you may expect. You submit a bid in an envelope and if you win you pay your bid. Second-price is slightly different. You submit a bid in an envelope and if your bid is the highest you pay the bid of the second-highest bidder. All-pay auctions are cute. You don't submit a bid; you put your money in an envelope and the winner gets the prize and nobody gets refunded. It sounds ridiculous, but it applies to certain scenarios quite well, such as political lobbying.

The primary assumption in auction theory is that although you do not know the other players' valuations of the prize, you do not the distributions of these valuations. In all auctions you want to win, but you also want some consumer surplus, so you optimise your bid. Roughly speaking, if v is your valuation and b is your bid you seek to maximise:
Expected Utility = (v-b) x prob(b > all other b's)
As your utility depends on all other b's, we're in a Nash game.

It's a rather beautiful result, though I'm sure nesf will disagree with me on that :P, but the utility-optimizing Nash Equilibrium in any auction will result in the same revenue for the seller. The key to this result is that "rational" buyers will change their bids to reflect the institutional settings and optimise their expected utility.

I've had an inclination in my head that Ricardian Equivalence could be a subset of this result. "Rational" citizens will change their behaviour to reflect the institutional settings and optimise their expected utility. Discuss?

See: Myerson (1980) 'Optimal Auctions'; Nobel Prize winner on Mechanism Design.

Thraktor

There are even more interesting results from the RET, such as that even an 'All-Pay' auction (where everyone pays their bid whether they win the auction or not) results in optimal revenue for the seller.

Back to the topic, though, I don't quite see how Ricardian equivalence could be seen as a special case of it. They're both interesting from the point of view of individuals optimising returns from a given mechanism, but in very different circumstances.

Flamed Diving

The Economist wrote: »

Nor am I a fan of Ricardian Equivalence, but it's still interesting from a theoretical point of view.

The Revenue Equivalence Theorem states that an auctioneer's expected revenue from any type of auction will be the same, obviously under certain assumptions.

There are many types of auctions. Three typical examples are first-price, second-price and all-pay auctions. First-price is what you may expect. You submit a bid in an envelope and if you win you pay your bid. Second-price is slightly different. You submit a bid in an envelope and if your bid is the highest you pay the bid of the second-highest bidder. All-pay auctions are cute. You don't submit a bid; you put your money in an envelope and the winner gets the prize and nobody gets refunded. It sounds ridiculous, but it applies to certain scenarios quite well, such as political lobbying.

The primary assumption in auction theory is that although you do not know the other players' valuations of the prize, you do not the distributions of these valuations. In all auctions you want to win, but you also want some consumer surplus, so you optimise your bid. Roughly speaking, if v is your valuation and b is your bid you seek to maximise:
Expected Utility = (v-b) x prob(b > all other b's)
As your utility depends on all other b's, we're in a Nash game.

It's a rather beautiful result, though I'm sure nesf will disagree with me on that :P, but the utility-optimizing Nash Equilibrium in any auction will result in the same revenue for the seller. The key to this result is that "rational" buyers will change their bids to reflect the institutional settings and optimise their expected utility.

I've had an inclination in my head that Ricardian Equivalence could be a subset of this result. "Rational" citizens will change their behaviour to reflect the institutional settings and optimise their expected utility. Discuss?

See: Myerson (1980) 'Optimal Auctions'; Nobel Prize winner on Mechanism Design.

Ok, so irrespective of institutional changes in the auction, every bidder will change their behaviour accordingly thus arriving at the same solution as the previous setting? How, by changing the distribution? By making the object more/less valuable?

Time Magazine

Thraktor wrote: »

There are even more interesting results from the RET, such as that even an 'All-Pay' auction (where everyone pays their bid whether they win the auction or not) results in optimal revenue for the seller.

Emm...

The Economist wrote: »

The Revenue Equivalence Theorem states that an auctioneer's expected revenue from any type of auction will be the same.

and

the utility-optimizing Nash Equilibrium in any auction will result in the same revenue for the seller.

Back to the topic, though, I don't quite see how Ricardian equivalence could be seen as a special case of it. They're both interesting from the point of view of individuals optimising returns from a given mechanism, but in very different circumstances.

In the auction setting, buyers change their bids (the variable they can change in influencing their utility) based on the environment. In a Ricardian world, voters change their consumption (the variable they can change in influencing their utility) based on the environment.

I'm wondering if a generalised framework of the permanent income hypothesis can be implemented in the Revenue Equivalence Theorem. It would have to link time-varying choices (Ricardian equivalnces) to scenario-varying choices (RET). I'm not sure if this is doable. Perhaps the only link is setting u'(.) = 0.

Flamed Diving wrote: »

Ok, so irrespective of institutional changes in the auction, every bidder will change their behaviour accordingly thus arriving at the same solution as the previous setting? How, by changing the distribution? By making the object more/less valuable?

The value of the object is inherent. The bids change depending on the "competition" for an object. If there is a lot of competition, each player's bid goes closer to their valuation which acts as a supremum of their bid. If there's less competition, people can get away with bidding less and increasing their surplus. One primary determinant of this competition is the mechanism. The pretty little result is that expected revenue in any mechanism is the same for the seller. So the expected revenue from an all-pay auction with n bidders will be the same the revenue from a first-price auction. Obviously therefore the winning bid in a first-price will be (roughly - distributions change things) n times bigger than in an all-pay.

Thraktor

The Economist wrote: »

Emm...

Note to self: In future, read posts before replying to them.