L$-USD exchange rate dynamics -- theory vs. observation

Sounds like very good news. I will be able to buy more lindens for less money.

Ah, but that's a double edged sword, isn't it?

Buying L$ for less money means someone is having to *sell* for less money. Which means that to maintain the same USD income (enough to pay tier for example), the seller will have to either sell more product (out of their control and driven by price elasticity) or (more likely) raise prices.

Suddenly, your L$1,000 doesn't buy as much as it used to. Welcome to the wonderful world of inflation!

This is a fundamental balance for international trade -- if the exchange rate is too high, the importer (e.g. you importing entertainment from SL) won't buy as much in local currency (L$) and the exporter's revenues drop. If the exchange rate is too low, then the local currency becomes cheap, and the exporter (e.g. those who make things you find entertaining) will raise prices to compensate for the ease with which she can sell for a reasonable price.

I can say that as the exchange rate dropped, we at GOM saw several of our large sellers turning over significantly larger USD amounts each month, probably due to the decreased USD cost for "importers". The question is, given all these competing forces what is the optimal rate such that revenues are maximized?

Boy, is economics ever interesting!

Doesn't this mode, like any model, require certain externa factors held constant?

In other words the model should only be viewed over a period of time during which the economy was NOT being manimpulated or the mechanics changed significantly.

Hasn't the SL economy undergone some serious changes over the past year that this model does not compensate for?

I would question the statistical validity of the input data and the models ability to compensate for manipulative forces that LL has applied during the past year.

I've just finished a preliminary modelling of the dynamics of the USD-L$ exchange rate over the past year (from November 1, 2004 until GOM closed on October 2, 2005). I'm in the process of writing up the results more formally, but here's the executive overview.

I modelled the evolution of the exchange rate with a Cox-Ingersoll-Ross model. This was chosen because it has some desirable properties that seemed to fit well with observed dynamics. The CIR model requires three parameters -- Long-term average (the exchange rate the market will trend toward), volatility (the amount of randomness in the exchange rate), and mean reversion (the speed with which the rate will trend toward its long-term value).

First of all, the CIR process is mean-reverting, which means it tends toward a long-term average as time passes. I was able to demonstrate that by farming the stipend from premium accounts (and assuming a few things about market price of risk, USD interest rate, etc.), the USD-L$ exchange rate should tend toward approximately $2.88 per block in the long term. This is the value that was used in all simulations.

Secondly, the volatility of the exchange rate depends on the rate itself. As the rate gets smaller, the volatility will decrease. This keeps the exchange rate from becoming negative, and also matches observed market behaviour. A base volatility of 0.5% per day was used in the simulations. Again, this value is consistent with typical intraday movements seen in the market data.

With two of the model's parameters fixed, we were able to tune the mean reversion rate to match observed trends. It is important to note that a single, constant reversion rate was unable to match the market data. This is due to a sudden increase in market liquidity that occured when "partial order filling" was introduced into GOM's trading system. At this point, the mean reversion increased suddenly and significantly, going from a value of ~0.5 to a value of ~2.5 over a timespan of a few days.

Finally, the CIR model was augmented to include jump discontinuities. The jump term is intended to model the effects of Linden Lab actively managing the economy to try to keep the exchange rate near $4/block. Jumps occur at random (Poisson distributed) intervals with an average of two jumps per year. The jump magnitudes have Gaussian distribution with zero mean and a standard deviation proportional to the current exchange rate's distance from Linden Lab's stated target rate of $4.00/block.

Results are summarized in the attached plot. This plot contains the volume-weighted average market exchange rate for the time interval in question, and two simulated exchange rate evolutions. Note that the models are able to faithfully reproduce periodic exchange rate increases (boom periods), sudden rate changes (tweaking of the economy by Linden Lab), and the long term trend downward.

In summary, these results indicate that the exchange rate moves inexorably downward toward its long-term target of $2.88/block. This downward trend was accelerated by the increased market liquidity introduced by the addition of partial order filling into GOM. Significant intervention is required if Linden Lab wants to keep the exchange rate at $4.00/block. This will need to take the form of a reduced stipend or increased premium account fees (back-of-the-envelope calculations indicate an average stipend of ~L$360 per week or an annually-billed premium account cost of ~$100 should stabilize the exchange rate), or a revision of the target exchange rate to ~$2.88/block.


Comments are highly encouraged.

I've looked at this... and wondered (in a positive way).

While theory can always be matched to past performance, and 'wrong' models thrown out... would you consider projecting your model of the $L forward to March 2006 please, and speculate upon its accuracy?

Of course there is no way you could know when 'major' changes outside of the model occur, but I would love to see the baseline prediction.

Forecasting is the proof of theory.

fools' errand, the 'mean' the market is seeking is no where near 2.88, thats a magical fantasy made up number.

The market was crippled under GOM because they actively promoted a 'pulldown' system where the market essentially was unrecoverable... thanks to their encouragement of bulk traders, and monkeying with block sizes etc, and a rather disasterous 'partial block' transfer, they created out of nowhere a market trend that amazingly enough, was far more profitable to *THEM* than to anyone else (since they took comission on whole blocks not as a direct percent, the lower the block value the bigger their cut)

Since this kind of market directly hurts the viability of SL content creators to pay their generally rather large tier (and LL's bills) LL stepped foreward and essentially shut GOM down with a far better and more convenient system.

One thing people seem to forget here is that the more convenient the system is to small purchasers, the more you will see a slow upward trend as overall 'buy' volume increases... the less convenient the system is to small purchasers, the more you will see a slow downward trend as overall buy volume decreases.

One need only look at Hank Ramos' brief system which essentially 'sold out' of lindens faster than he was willing to purchase them, and was selling in general 50-75 cents *ABOVE* the gom market rate... his system was just *SO* much more convenient for small buyers that the price difference was almost a non issue as far as demand went

I saw the topic and decided to write.
I didnt read any of above posts. Because i dont know english well.
But i know economy&business very well.
It is for sure $L is dying with highest inflation in the world.
Two immediate movemont MUST be done to save balance:
1-> Do not make real $ auctions. Make them all $L. So people will buy $L first. To buy lands. I know Anshe Chung will hate this idea. And lindens will also not like. Because they will not earn directly from usd dollars. But they will earn from $Ls while selling them(to lindens:do not use extra $L to sell. Only sell what u get.).But sl is like a country. It has its own dynamics. And no country in world sell lands using outside money. It kills economy.
2-> Do not give 500/ week to premium accounts. Make it 250/week.(this is not necessary at all if u do first one.)
3-> Remove basic accounts. And make trial accounts. After a month people must buy premium. This will create foreign currency.And it is the medicine of inflation. And will also kill "alt" inflation.
4-> Dont afraid creating a real economy in sl. if u do these steps. sl will save you and players both. Because it has strong dynamics. Like foreign currency income. And a dynamic stuff selling economy.
Kazanture Aleixandre

You cant use any common economy model or theory to explain SL economy.
SL economy has over 400% cumulative yearly inflation according to today's data.
Yes u can try to model it. IMF has done in Argentina. And ofcourse didnt work. You need immediate solutions.
Sell lands(islands and auctions) using $L not usd. This is the ONLY solution. And find 2 good economists for linden lab.

In summary, these results indicate that the exchange rate moves inexorably downward toward its long-term target of $2.88/block. This downward trend was accelerated by the increased market liquidity introduced by the addition of partial order filling into GOM. Significant intervention is required if Linden Lab wants to keep the exchange rate at $4.00/block. This will need to take the form of a reduced stipend or increased premium account fees (back-of-the-envelope calculations indicate an average stipend of ~L$360 per week or an annually-billed premium account cost of ~$100 should stabilize the exchange rate), or a revision of the target exchange rate to ~$2.88/block.

so where are we?

In summary, these results indicate that the exchange rate moves inexorably downward toward its long-term target of $2.88/block.

btw
52 weeks x l$500 / $72 = l$361/$1