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The basic problem with economics is mathematical. Economists keep acting like the economy is normally distributed when it is not. For example, the "Black Schole

by JDDunn9 13y ago

The basic problem with economics is mathematical. Economists keep acting like the economy is normally distributed when it is not. For example, the "Black Scholes Model", assumed that the system was normally distributed, differentiable at all points, continuos, etc., which of course was not true. What's worse is that every economist knows this, but they continue to use these faulty formulas because they are afraid of the alternative, chaos. The economy is governed by chaos theory. Just like the weather or earthquakes. Chaotic systems don't have nice little formulas. They are extremely complex, and the slightest miscalculation can produce large changes in outcome. At least with the weather, the core principles are well understood. Scientists can perform experiments on how heat affects pressure and other properties. We can't experiment in economics. The core principles are not well understood. Therefore, economic models are hopelessly lost. Admitting that makes economists look dumb though, so they stick with Calculus and pretend the world is normal.

pfortuny 13y ago
You do not understand stochastic analysis. What Black & Scholes did was to notice that all the randomness can be taken away if all you want to do is * Price a specific type of option under specific conditions. Those conditions DO assume and include randomness. The funny thing is, just like in the physics of heating (which is the same as brownian motion), there are values which are deterministic, despite the intrinsic randomness of the process. Really, it is not that the Black-Scholes model is differentiable (which is not).
- JDDunn9 13y ago
  You missed the whole point. Randomness exists in both normal and chaotic systems. The difference is that in normally distributed systems, randomness can be predicted.
  - pfortuny 13y ago
    No, not at all: what can be predicted can because it is essentially free from that randomness. The fact that it is easy because the distribution is normal has nothing to do with the randomness. Really. You cannot 'predict' randomness in a normal distribution as you cannot in a geometric or uniform.
  - JDDunn9 13y ago
    Yes, you can predict the amount of randomness in a normally distributed system. If you could not, standard deviations would have no meaning, and all branches of statistics built thereon would be false. In chaos theory, the best you can hope for is strange attractors. Unfortunately, economics doesn't even seem to have these.
  - thetwiceler 13y ago
    I think you're just spouting a lot of buzzwords, and you're actually conflating (a) the relevance of chaos theory and (b) criticisms of normal distributions in economics. A major recent criticism is of some economic models which have assumptions to the effect of "returns on this investment will be normally distributed." The criticism is that evidence seems to suggest that returns are not actually normally distributed; rather they have "fat tails," meaning that extreme events are more likely than with a normal distribution. And this error causes economic models to discount the role of these unlikely extreme events. The Black-Scholes model effectively models stock prices as Brownian motion. This boils down to a single assumption: stock prices are the buildup of lots of very small INDEPENDENT random events (with FINITE variance) that occur over short times periods; this leads straight to Brownian motion. Brownian motion is indeed continuous; however, it is nowhere differentiable with probability 1. Because of the assumptions of finite variance and independence, the CLT tells us that returns will be normally distributed. So here, people pretty much agree that it's always these assumptions of independence that cause these models to predict poorly. This is totally different from chaos theory. First of all, chaotic systems are not necessarily complex. Here's a chaotic map with a "nice little formula": f : [0,1) -> [0,1) f(x) = 2*x (mod 1) While this is chaotic, we can understand much about this map. For example, each application produces an entropy of 1 bit (see entropy of dynamical systems...). So this is a map that "produces randomness" in a way. This is philosophically nice, because probability theory itself doesn't at all explain how randomness comes about.
    - JDDunn9 13y ago
      You can create a chaotic map with a simple formula, but those don't appear often in the real world. Give me the formula for the weather, or to predict the next earthquake, or to model turbulence. If the stock market movements were normally distributed, crashes would be extremely rare. Something like 1 every 10,000 years. Virtually all economic models assume something to be true that we know isn't.
      - thetwiceler 13y ago
        Once again, don't confuse predictability with ability to understand a system. We actually have a fairly good understanding of weather dynamics and turbulence - and I can give you the formula for both of these - the Navier-Stokes equation! Not the simplest equation, but something understandable (yes, I know there's a Millenium Prize problem to see if we always get a smooth solution). We do understand how turbulence arises from this. And we understand the weather very well. However, we can't predict the weather, nor can we predict the earthquakes. And as you correctly point out, the reason for this is chaos. The reason is not that we don't understand the underlying processes that govern these dynamics. Rather, the uncertainties in our initial conditions increase exponentially with time (due to chaos) and make long-term predictions unreliable.

by JDDunn9 13y ago

pfortuny 13y ago

You do not understand stochastic analysis. What Black & Scholes did was to notice that all the randomness can be taken away if all you want to do is * Price a specific type of option under specific conditions. Those conditions DO assume and include randomness. The funny thing is, just like in the physics of heating (which is the same as brownian motion), there are values which are deterministic, despite the intrinsic randomness of the process. Really, it is not that the Black-Scholes model is differentiable (which is not).

JDDunn9 13y ago
You missed the whole point. Randomness exists in both normal and chaotic systems. The difference is that in normally distributed systems, randomness can be predicted.
- pfortuny 13y ago
  No, not at all: what can be predicted can because it is essentially free from that randomness. The fact that it is easy because the distribution is normal has nothing to do with the randomness. Really. You cannot 'predict' randomness in a normal distribution as you cannot in a geometric or uniform.
- JDDunn9 13y ago
  Yes, you can predict the amount of randomness in a normally distributed system. If you could not, standard deviations would have no meaning, and all branches of statistics built thereon would be false. In chaos theory, the best you can hope for is strange attractors. Unfortunately, economics doesn't even seem to have these.
- thetwiceler 13y ago
  I think you're just spouting a lot of buzzwords, and you're actually conflating (a) the relevance of chaos theory and (b) criticisms of normal distributions in economics. A major recent criticism is of some economic models which have assumptions to the effect of "returns on this investment will be normally distributed." The criticism is that evidence seems to suggest that returns are not actually normally distributed; rather they have "fat tails," meaning that extreme events are more likely than with a normal distribution. And this error causes economic models to discount the role of these unlikely extreme events. The Black-Scholes model effectively models stock prices as Brownian motion. This boils down to a single assumption: stock prices are the buildup of lots of very small INDEPENDENT random events (with FINITE variance) that occur over short times periods; this leads straight to Brownian motion. Brownian motion is indeed continuous; however, it is nowhere differentiable with probability 1. Because of the assumptions of finite variance and independence, the CLT tells us that returns will be normally distributed. So here, people pretty much agree that it's always these assumptions of independence that cause these models to predict poorly. This is totally different from chaos theory. First of all, chaotic systems are not necessarily complex. Here's a chaotic map with a "nice little formula": f : [0,1) -> [0,1) f(x) = 2*x (mod 1) While this is chaotic, we can understand much about this map. For example, each application produces an entropy of 1 bit (see entropy of dynamical systems...). So this is a map that "produces randomness" in a way. This is philosophically nice, because probability theory itself doesn't at all explain how randomness comes about.
  - JDDunn9 13y ago
    You can create a chaotic map with a simple formula, but those don't appear often in the real world. Give me the formula for the weather, or to predict the next earthquake, or to model turbulence. If the stock market movements were normally distributed, crashes would be extremely rare. Something like 1 every 10,000 years. Virtually all economic models assume something to be true that we know isn't.
    - thetwiceler 13y ago
      Once again, don't confuse predictability with ability to understand a system. We actually have a fairly good understanding of weather dynamics and turbulence - and I can give you the formula for both of these - the Navier-Stokes equation! Not the simplest equation, but something understandable (yes, I know there's a Millenium Prize problem to see if we always get a smooth solution). We do understand how turbulence arises from this. And we understand the weather very well. However, we can't predict the weather, nor can we predict the earthquakes. And as you correctly point out, the reason for this is chaos. The reason is not that we don't understand the underlying processes that govern these dynamics. Rather, the uncertainties in our initial conditions increase exponentially with time (due to chaos) and make long-term predictions unreliable.