Ducks and Economics

Assume an auction with a small and finite number of bidders with discrete values on the aggregate demand curve. Imagine this is a pure common values auction (wikipedia definition):

Some would call this a pure common value auction, using the term common values to describe any auction in which (i) bidders have different information and (ii) one bidder’s information would be informative to another bidder about the latter’s valuation for the good.

Imagine bids are public. Bids are consecutive and the bidder with the highest final bid wins the good. To call upon a basic economic definition, declared prices are signals that reveal information about bidder’s demand curves. The other implication of having common values is that valuations are correlated. In the auction, this implies bidders have dynamic valuations; when a bidder places a bid, the other auction participants are able to gain additional information that allows them to readjust their values for the asset and bid accordingly.

Quick note: can we assume risk-neutral participants? I need to return to that question later, but let’s make that assumption for now.

At this point, let’s bring in some numbers. Imagine an auction with 5 bidders, with bidder valuations being initially uniformly distributed from 0-100, inclusive, which means that bidder 1 values the good at 20, bidder 2 value is 40, bidder 3 has value 60, bidder 4 has value 80, and bidder 5 values the good at 100. The minimum bid increment is 1. This means that bidder 5 wins the auction at some price between 81-100. Where precisely depends on the correlation factor. A higher correlation factor means that the final price is closer to 100; a lower factor means that the final price is closer to 81.

Let’s loosen a parameter. Imagine instead of 5 bidders, there are 100. It’s obvious here that allowing dynamic bidding and (highly) correlated values means that the final price is at least 100; depending on the correlation function. Hypothesis: if you allow the correlation function to be an exponential greater than 1 for values contiguous to the high end of the distribution, you get an asset bubble, where increasing bids inflate exponentially (you need at least two bidders to get into a bidding war).

Can this provide a framework to thinking about bubbles like technology and housing? Does this make any sense to anyone else? The next step is to formulate this mathematically.

I just had this thought: Asset bubbles are far more probable and meaningful in large markets than in small markets. If this is true, is it obvious? I have a long set of thoughts to write down but since I’m tired, I’ll return to it in the morning. I get a lot of my intuitions from auction theory.

Nouriel Roubini recommends that Ben Bernanke be retained as chairman of the Fed. As the economist who (perhaps) most accurately forecast the housing bust and subsequent recession, I expect his opinion will carry considerable weight. A quick excerpt:

Mr. Bernanke understands that in the Great Depression, the collapse of the money supply and the lack of monetary stimulus during contractions worsened the country’s economic free fall. This lesson has paid off. Mr. Bernanke’s decision to keep interest rates low and encourage lending has, for now, averted the L-shaped near depression that seemed highly likely after the financial collapse last fall.

And:

To be sure, an endorsement of Mr. Bernanke’s reappointment comes with many caveats. Mr. Bernanke, a Fed governor in the early part of this decade, supported flawed policies when Alan Greenspan pushed the federal funds rate (the policy rate set by the Fed as its main tool of monetary policy) too low for too long and failed to monitor mortgage lending properly, thus creating the housing and credit and mortgage bubbles.

He and the Fed made three major mistakes when the subprime mortgage crisis began. First, he kept arguing that the housing recession would bottom out soon (it has not bottomed out even three years later). Second, he argued that the subprime problem was a contained problem when in reality it was a symptom of the biggest leverage and credit bubble in American history. Third, he argued that the collapse in the housing market would not lead to a recession, even though about one-third of jobs created in the latest economic recovery were directly or indirectly related to housing. Mr. Bernanke’s analysis was mistaken in several other important ways. He argued that monetary policy should not be used to control asset bubbles. He attributed the large United States current account deficits to a savings glut in China and emerging markets, understating the role that excessive fiscal deficits and debt accumulation by American households and the financial system played.

Link here.