The Mathematical Method in Economics

[QuendeltonPG]

In the introduction to their book 'The Theory of Games and Economic Behaviour' von Neumann and Morgenstern consider the arguments against the use of mathematics in economics. One of the reasons they believe that previous applications of mathematics to economics had been unsuccessful was that;

"empirical background of economic science is incomparably smaller than that commanded in physics at the time of the mathematization of that subject was achieved. ... it was backed by several millenia of systematic, scientific, astronomical observation, culminating in an observer or unparalleled calibre, Tycho de Brahe. Nothing of this sort has occurred in economic science. It would have been absurd in physics to expect Kepler and Newton without Tycho,- and there is no reason to hope for an easier development in economics."

The question I would like to put to you all is; In the years since the Theory of Games and Economic Behaviour was publish what successes, if any, do you feel the field of economics has had? Particularly on the level of empirical work at the macro and micro level?

 

[Xenophage]

You need to read Human Action by Ludwig von Mises. The problem with applying mathematics to economic theory is that economics is NOT a hard science.

There is a BIG difference between physics and economics. Economics is bounded only by laws of human behavior, which are nothing like the laws of momentum and gravitation.

 

[loseyourname]

There is nothing at all wrong with applying mathematics to economics. The issue with the accuracy of econometric models is a matter of paring down variables. It's very difficult to work with an equation that has several million independent variables, so we inevitably try to isolate those with the greatest impact using sensitivity analysis and work with only those. The second major problem is that values change and they change quickly. Something like the time preference of consumption, an independent variable that determines interest rates, is a matter of human psychology and can change from minute to minute. It's also impossible to measure, which is arguably the biggest issue and why econometric models are notoriously inaccurate. Mathematics in economics works much better as an analytic tool than as a predictive tool.

It can work fairly well on small scales, though. Take something as simple as non-linear cost-volume-profit analysis from management accounting, which can very accurately give you an idea of optimal production levels by product type over the short run. It breaks down over the long run because, again, you start running into the impact of implicit exogenous variables like the demand for each product, which are themselves determined by a complex mix of economic and psychological factors, but it works very well over the short run and especially when you sell highly differentiated products that don't exhibit a great deal of price elasticity of demand.

 

[Xenophage]

To clarify, yes, mathematics is fine in some analysis, but mostly useless for prediction. This is why mathematical models attempting to predict stock market behavior have never been very accurate.

Economics, in its final and most basic analysis, is a study of human psychology. Value is subjective, and entirely dependent upon individuals. This was Mises' essential thesis and his most profound contribution to the field, and directly contradictory to classical economic theory based on the works of Adam Smith. You'll find a great deal of economic theory, even today, that is based on the fallacy of supposing there is an objective measure for the value of things. You find this fallacy prevalent in Marxian economics.

There is no objective measure to determine the value of anything.

 

[skilgannonau]

To clarify, yes, mathematics is fine in some analysis, but mostly useless for prediction. This is why mathematical models attempting to predict stock market behavior have never been very accurate.

I tend to agree with the sentiment that prediction is a problem in economics but using mathematics to produce models to make predictions is better than nothing. I rather rely on an econometrics model than anecdotal evidence, personal experience, or intuition/gut feeling (which psychology tells us is unreliable) and that is what economics was before the quantification of the economics discipline.

I don’t think the use of mathematics is a problem but how it is used is. A bad argument is a bad argument in words or numbers.

 

[Xenophage]

You can predict long term trends with a general theory of economics and simple logic, but the shorter term your prediction is the more unreliable it will be come. Furthermore, no mathematical model has ever been capable of any degree of accuracy or precision over the short term. Dates and precise values are impossible to predict, and it isn't just a problem *correctly* nailing down variables. It's because there is no objective measurement possible for many of the variables.

You cannot, for instance, predict the price of oil one month from now. The best you could do is guess based on current trends that it will probably be higher than it is currently - but even there you have a high probability of being wrong. This is why day trading is akin to gambling.

You can, however, predict with a very high degree of confidence that if prevailing economic and political trends continue, the average price of oil will rise over the next ten years. This prediction requires no deep mathematical analysis.

Many Austrian economists predicted correctly the housing market bust that occurred in 2008, some of them many years before it happened, but none of them attempted to nail down a date or place precise values on housing market volatility because they knew such efforts were futile.

 

[Artus]

I think Economics as Weather. Numerical models are useful to explain what's happenning, but we won't be able to predict beyond some weeks. The problem is not Mathematics but our concept or "value", which is subjective because of the individual's perception. Mathematical models must be focused on modelling subjectivity and other issues.

 

[Pyrrhus]

I agree with the poster above. It is better to have some sort of estimate, and qualitative direction rather than nothing to base decisions. Thus, plenty of efforts in economics is being focused on validation of economic models. A classical example is the Solow-Swan Model. Does a steady state really exist?. According to the data, it doesn't!. Thus, several tweaks can be made such as exogenous technological changes, and so on.

 

[Odysseus]

I was convinced that mathematical models would never be predictive in social sciences until I saw this lecture:

http://www.ted.com/talks/nicholas_christakis_how_social_networks_predict_epidemics.html"

I think (like many here) that the variables traditional economic analysts use are not quantifiable. But with the methods mentioned here and the massive amount of data gathering that is possible now with smart phones and the internet, trends propagating within society will be measurable, detectable and predictable. Social science will still be statistical in nature, but it’s methods will be much more powerful.

 

[BWV]

Have seen some papers by Lee Smolin and others applying gauge theories to economics, for example treating arbitrage as curvature on a manifold

http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.4274v1.pdf

don't see how useful this is other than as a metaphor for someone who is already inclined to think about things in terms of differential geometry

Smolin has a point about how neoclassical assumptions of market efficiency, if largely correct, say nothing about the dynamics of how arbitrage opportunities arise and disappear. That said, the experimental economics of Vernon Smith and Charles Platt seem to me a more productive approach than throwing in a bunch of gauge transformations and curvature tensors

 

[Pyrrhus]

You're generalizing, Odysseus. There are quantifiable variables such as price, time, income... And.there are not quantifiable variables such as comfort, stress level, and others. One of the recent advancaments in consumer choice modeling is the Hybrid choice approach. Basically econometrics meets psychometrics. The incorporation of latent variables representing the attitude of consumers in their decisions. This is an example of where economics is heading.

 

[Pyrrhus]

The problem with economic modeling is that of normative vs. Positive approaches. Are we modeling what should the decisions of economic agents should be or what the decisions will be?. More sophisticated models should take this.in consideration, plus also the scale of the model. It is reasonable to think that aggregate choices are formed by diaaggregate events of heterogeneous agents.

 

[Odysseus]

You're correct Pyrrhus, I'm generalizing, but the criticism stands. The majority of my experience in economics comes from macroeconomics (specifically aid economics). To be quite blunt, I think most of it is a load of ****. Macroeconomists find some interesting trends, but their data is so convoluted and patchy that it's impossible to trust it. Their "theory" tries to reduce very complex social phenomena into two or three variables. Most of it amounts to ideologically opposed camps bitching at each other with graphs. I saved this gem from my undergrad days: "Given that these studies fail to substantiate the theoretically predicted contribution of fiscal decentralization to economic growth, the methods used by these studies to investigate the effect of fiscal decentralization may be inappropriate" (I'll dig out a citation if someone really wants to see it).

I'm not trying to say that macroeconomics is not something that can be usefully studied with reason. I am saying that it is not science (yet). I make no comment on microeconomics.

 

[Pyrrhus]

You're correct Pyrrhus, I'm generalizing, but the criticism stands. The majority of my experience in economics comes from macroeconomics (specifically aid economics). To be quite blunt, I think most of it is a load of ****. Macroeconomists find some interesting trends, but their data is so convoluted and patchy that it's impossible to trust it. Their "theory" tries to reduce very complex social phenomena into two or three variables. Most of it amounts to ideologically opposed camps bitching at each other with graphs. I saved this gem from my undergrad days: "Given that these studies fail to substantiate the theoretically predicted contribution of fiscal decentralization to economic growth, the methods used by these studies to investigate the effect of fiscal decentralization may be inappropriate" (I'll dig out a citation if someone really wants to see it).

I'm not trying to say that macroeconomics is not something that can be usefully studied with reason. I am saying that it is not science (yet). I make no comment on microeconomics.

One of the big problems with Macroeconomics. It's that for a while it couldn't be explained under microeconomics. The models of economic growth couldn't relate to the what the typical microeconomic assumptions of agents maximizing utility, and firms maximizing profit, and the measured outcome explained in the macro model should relate this (why?, because the Macro model is explaining an aggregation of smaller economic agents events). In fact, even in the widely used model Solow-Swan, the behavior of consumers is not utility maximizing, only the behavior of the firms is profit maximizing. Thus, the role of the consumers is mostly exogenous, and this is obviously unrealistic. However, it is an improvement in comparison to the Keynesian approach which had no connection to Microeconomics.

In terms of mathematical methods, Economics is improving. New ares such as Network Economics, Computational Economics, and Mechanism Design (Incentive-Compatibility model) has been more successful in explaining economic behavior. A very successful theory is Auction theory (AT) based on Game theory. The FCC spectrum auctions are an example of successful application of AT.

Other good methods are Random Utility Models. These has been used widely since the 1980s to predict demand shares for interesting choice problems such as labor participation, transportation mode choices, and others. These models have even branched out to other areas such as Medicine. The models has all the nice properties of demand models, and thus allow for example the estimation of elasticities.

Note all of these models are still a normative approach. A conjecture of how we think Economic agents should behave, and this calibrated to the data. I think focus has been focusing on studying how the agents actually behave. Another new area in economics is Neruoeconomics, basically Neuroscience trying to explain economic phenomena.

 

[skilgannonau]

I was convinced that mathematical models would never be predictive in social sciences until I saw this lecture:

http://www.ted.com/talks/nicholas_christakis_how_social_networks_predict_epidemics.html"

I think (like many here) that the variables traditional economic analysts use are not quantifiable. But with the methods mentioned here and the massive amount of data gathering that is possible now with smart phones and the internet, trends propagating within society will be measurable, detectable and predictable. Social science will still be statistical in nature, but it’s methods will be much more powerful.

You're correct Pyrrhus, I'm generalizing, but the criticism stands. The majority of my experience in economics comes from macroeconomics (specifically aid economics). To be quite blunt, I think most of it is a load of ****. Macroeconomists find some interesting trends, but their data is so convoluted and patchy that it's impossible to trust it. Their "theory" tries to reduce very complex social phenomena into two or three variables. Most of it amounts to ideologically opposed camps bitching at each other with graphs. I saved this gem from my undergrad days: "Given that these studies fail to substantiate the theoretically predicted contribution of fiscal decentralization to economic growth, the methods used by these studies to investigate the effect of fiscal decentralization may be inappropriate" (I'll dig out a citation if someone really wants to see it).

I'm not trying to say that macroeconomics is not something that can be usefully studied with reason. I am saying that it is not science (yet). I make no comment on microeconomics.

Odysseus the quantities and the data has always been there it’s just been impossible to collect enough of it in a realistic time frame for it to be useful. If economists had access to information about all the quantities and prices in the world in real time of course their ability to come up with more meaningful theories would be multiplied. It’s no surprise with the rise of the internet and falling cost of computing power the associated access to new data as well as being able to collect old data more efficiently is coinciding with new applications (as illustrated by the TED lecture).

But even with the current explosion in amount data and capabilities in using those data it’s still a fraction what is needed. Take for example macroeconomics, if economists had real time data of economic activity by households and firms such as retail spending, investment spending, debt levels, frequency of transactions, etc. etc., they probably could’ve picked up on the housing bubble before it became a bubble, but instead they have to rely on relatively small samples of very few aggregate indicators that are a lot of times months old and rely on theories produced by those data.

As Pyrrhus mentioned there has been a massive effort in microeconomicising of macroeconomics because of the Lucas critique (which basically attacked the old models for not taking into account changing behaviour at the individual level) but these new models are still poor caricatures of reality. The old models were based on aggregate indicators because that was the easiest thing to do but that meant these models were exposed them to changes in individual behaviour. Micro-based macro models are meant to address this but the fact remains they have to be ‘representative’ in order to be usable. If economists had access to accurate and real time aggregate data of individual behaviour I’m sure their ability to come up with better micro-based macro models would also improve. So yes I agree macro is relatively speaking bullsh*t but it’s (better than what we had in earlier times and it’s) not from lack of trying.

I think it’s every economists wet dream of having access to a database of all the quantities and prices in the world in real time but the reality is there is data constraint (like in much all quantitative disciplines) and inevitably that dictates the quality of theories.

 

[BWV]

Take for example macroeconomics, if economists had real time data of economic activity by households and firms such as retail spending, investment spending, debt levels, frequency of transactions, etc. etc., they probably could’ve picked up on the housing bubble before it became a bubble, but instead they have to rely on relatively small samples of very few aggregate indicators that are a lot of times months old and rely on theories produced by those data.

I doubt even that, first there are about 10 billion SKUs traded in the US economy, let's say you consolidate them to a billion (i.e. collapse different sizes of toothpaste tubes, etc). An optimization routine on utility preferences, using complex, nonlinear utility functions, updated in real time is likely intractable even if you cold collect all the relevant information (which is impossible)

Have not seen an analysis of markets in regards to their computing power, but I think it would dwarf anything other than an extremely massive quantum computer

the other problem is that, of course, the forecasters and analysts cannot be kept outside the system. Any communication of their information or forecasts would change the potential outcomes

 

[Pyrrhus]

One of my favorite quotes of all time is by the late Dr. Gordon F. Newell. Paraphrasing, he said that the art of modeling consists of identifying the relevant factors of the system, and throw the irrelevant factors to the trash, and to hope that the relevant factors are those we can understand. This should be kept in mind when we look at any type of mathematical model, even for economic models or physics models.

 

[BWV]

The winning traders don't use complex methods at all, they use common sense. What I'm saying is that mathematics isn't needed at all to analyze financial markets, the information needed to do it is mostly qualitative in nature. Real estate bubble? Winning traders knew real estate would be in trouble much time before it happened, you can be sure of that. Stock market bear market? Same thing. Recent stock market crash? Same... It's not like they knew how far the move would go, but they knew it would be in trouble.

So who are these traders? Sounds like magical thinking to me

 

[BWV]

I've said too much It's magical thinking alright, that's what they want you to think...

ah its a secret then, at least until you spend a few hundred bucks at the seminar and buy the secret trading kit and decoder ring

pardon me for requesting some substantiation for a rather extraordinary claim, this is after all a science forum

 

[Odysseus]

I understand that the lack of data constitutes the biggest hurtle in coming up with good models of economic behavior. I'm sure most of you did not watch the original lecture I posted (don't worry, I don't click on many links in forums either), but that guy is trying to identify ways to collect "better" data on social phenomena. Meaning that he's attempting to identify the best places to look when searching for an impending social trend. And he's had, if he's being honest with us, some serious success with his method.

I see that as the future: parsing the data for what's important. Certainly an economist doesn't need to know all the prices all the time to do scientific work. He needs reliable and objective measurements.

For those who are saying that macroeconomics will be microtized. How do the new models plan to cope with things like politics? Which is decidedly non micro and is a significant determinant of macroeconomic variables.

 

[Pyrrhus]

I understand that the lack of data constitutes the biggest hurtle in coming up with good models of economic behavior. I'm sure most of you did not watch the original lecture I posted (don't worry, I don't click on many links in forums either), but that guy is trying to identify ways to collect "better" data on social phenomena. Meaning that he's attempting to identify the best places to look when searching for an impending social trend. And he's had, if he's being honest with us, some serious success with his method.

I see that as the future: parsing the data for what's important. Certainly an economist doesn't need to know all the prices all the time to do scientific work. He needs reliable and objective measurements.

For those who are saying that macroeconomics will be microtized. How do the new models plan to cope with things like politics? Which is decidedly non micro and is a significant determinant of macroeconomic variables.

Another problem with social science that economics encounters is that "experiments" as defined in the natural sciences cannot be in most cases be conducted. For example, an economists cannot analyze a country with "education" vs. one without and observes its effects on economic growth. Thus, economists are always looking for ways to control for as many effects as possible in their empirical research. Another more realistic problem is random sampling. For many cases, economists have to use nonramdom samples. Obviously such data leads to biased estimates. Thus, economists (or more specifically econometricians) has done a lot of research in dealing with these problems, and others.

For your macro model question, "things like politics, institutions..." for the most part are largely unquantifiable, and are also difficult to include them in a model. This does not mean that economists cannot find ways around this problem. Thus, the economic models may be context specific. It requires the economist to study the environment and the participating agents, and also any previous analyses and data in order to ascertain the magnitude of the government influence and of other factors. One point that is important is that governments hire economics to help them to dictate policy. Thus, economists can model outcomes without much government influence, and see if the results will be "better" relative to the current results.

 

[skilgannonau]

I understand that the lack of data constitutes the biggest hurtle in coming up with good models of economic behavior. I'm sure most of you did not watch the original lecture I posted (don't worry, I don't click on many links in forums either), but that guy is trying to identify ways to collect "better" data on social phenomena. Meaning that he's attempting to identify the best places to look when searching for an impending social trend. And he's had, if he's being honest with us, some serious success with his method.

I see that as the future: parsing the data for what's important. Certainly an economist doesn't need to know all the prices all the time to do scientific work. He needs reliable and objective measurements.

I actually did look at the TED lecture and while it’s novel it’s not so different in economic research. There are new novel methods being published in leading journals all the time. As I previously mentioned above the internet provides access to new (as well as better access to old) data and consequently there are new ideas on new applications being developed all the time which is reflected in research in economics and in other fields. Research in economics isn’t stagnant.

For those who are saying that macroeconomics will be microtized. How do the new models plan to cope with things like politics? Which is decidedly non micro and is a significant determinant of macroeconomic variables.

As already mentioned macroeconomics is already micro-based but they are simplistic (in order for them to be ‘tractable’ i.e usable). I say ‘simplistic’ in the sense they are just caricatures of reality but are order of magnitude mathematically more complex than old models.

Whether politics is a ‘significant determinant’ is an assertion that needs to be tested and in fact there are already models testing just that e.g. https://www.amazon.com/dp/0691092575/?tag=pfamazon01-20.

 

[Pyrrhus]

I actually did look at the TED lecture and while it’s novel it’s not so different in economic research. There are new novel methods being published in leading journals all the time. As I previously mentioned above the internet provides access to new (as well as better access to old) data and consequently there are new ideas on new applications being developed all the time which is reflected in research in economics and in other fields. Research in economics isn’t stagnant.



As already mentioned macroeconomics is already micro-based but they are simplistic (in order for them to be ‘tractable’ i.e usable). I say ‘simplistic’ in the sense they are just caricatures of reality but are order of magnitude mathematically more complex than old models.

Whether politics is a ‘significant determinant’ is an assertion that needs to be tested and in fact there are already models testing just that e.g. https://www.amazon.com/dp/0691092575/?tag=pfamazon01-20.

I agree. Network economics and Computational economics have been around for a while now. In fact, one of my colleagues in our research group studies transportation network growth, and his models are typically done using Agent-Based Modeling. Thus, his research deals with micro rules that lead to interesting macro results. Typically the case for complex systems.

For Macro and factors such as politics, institution, lobbying..., Yes they have been included in economic models (in fact, one my professors has done some research in two party lobbying). However, the main criticism with these models is validation of the "other factor" behavior. In some cases, it requires a lot of data analysis in order to define a possible function or other mathematical construct to represent the "other factor" reactions given a specific action. Thus, these "other factors" tend to be added in the most benign way into the models, or at least this is what I will recommend. Unless data says otherwise.

 

[skilgannonau]

I doubt even that, first there are about 10 billion SKUs traded in the US economy, let's say you consolidate them to a billion (i.e. collapse different sizes of toothpaste tubes, etc). An optimization routine on utility preferences, using complex, nonlinear utility functions, updated in real time is likely intractable even if you cold collect all the relevant information (which is impossible)

Have not seen an analysis of markets in regards to their computing power, but I think it would dwarf anything other than an extremely massive quantum computer

the other problem is that, of course, the forecasters and analysts cannot be kept outside the system. Any communication of their information or forecasts would change the potential outcomes

I was saying this is a capability economists wish they had (because it will go a long way to resolving a lot issues) not that it would be ever be possible. I think if the capability did exist we would solve a lot of issues for example I see tremendous application in general equilibrium by being able to observe the interaction of quantities and prices in real time. And general equilibrium is pretty much implicit in most micro and macro models.