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ffer importantly from linear results are few and far between the premise behind adopting a non linear approach is that knowing about the slopes or elasticities of the demand and supply curves is not sufficient we have to know about the curvatures of the demand and supply curves too on top of the fact that we don t really know much about these curvature terms the presumption itself is highly suspect if we are picking teams i ll pick the first order terms and let you pick all of the higher order terms you want any day of the week and i ll win in cases in which we can calculate linear vs non linear solutions the differences are typically embarrassingly small and even when there are noticeable differences they often go away as we improve the non linear solution a common exercise is to calculate the growth convergence path for the neoclassical ramsey growth model using discrete dynamic programming techniques and then compare the solution to the one you get from a linearized solution in the neighborhood of the balanced growth path the dynamic programming approach is non linear it allows for an arbitrary reaction on a discrete grid space when you plot out the two responses it is clear that the two solutions aren t the same however as we add more and more grid points the two solutions start to look closer and closer the time required for computation of the dynamic programming solution grows of course 5 unlike non linear models approximate analytical results can be recovered from the linear systems this is an underappreciated side benefit of adopting a linear approach the linear equations can be solved by hand to yield productive insights there are many famous examples of log linear relationships that have led to well known empirical studies based on their predictions hall s log linear euler equation the new keynesian phillips curve log linear labor supply curves etc mankiw romer and weil 1992 used a linear approximation to crack open the important relationship between human capital and economic growth given the huge benefits to linear approaches in the field the main question i have is not why researchers don t adopt non linear global solution approaches but rather why linear methods aren t used even more widely than they already are one example in particular concerns the field of industrial organization io io researchers are famous for adopting complex non linear modelling techniques that are intimidating and impressive they often seem to brag about how it takes even the most powerful computers weeks to solve their models i ve never understood this aspect of io io is also known to feature the longest publication lags and revision lags of any field it s possible that some of this is due to the techniques that they are using i m not sure i have asked friends in io why they don t use linear solutions more often and the impression i am left with is that it is a combination of an assumption that a linear solution simply won t work for the kinds of problems they analyze together with a lack of familiarity with linear methods there are of course cases in which there is important non linear behavior that needs to be featured in the results for these cases it does indeed seem like a linear approach is not appropriate brad delong argued that accommodating the zero lower bound on interest rates i e the flat part of the lm curve is such a case i agree there are cases like the liquidity trap that clearly entail important aggregate non linearities and in those instances you are forced to adopt a non linear approach for most other cases however i ve already chosen my team fn 1 this reminds me of a joke from the consulting business i once asked an economic consultant why he thought he could give valuable advice to people who have been working in an industry their whole lives he told me that i was overlooking one important fact the consultants charge a lot of money 14 comments may 10 2015 by chris house back to blogging i haven t written a post in a long long time research referee reports teaching and administrative work have all been preventing me from contributing to the blog this summer i m going to try to get back into writing somewhat regularly famous last words leave a comment october 27 2014 by chris house the lure of capital taxation the taxation of capital income corporate profits capital gains interest dividends etc has always been attractive to both politicians and to economists politicians are drawn to capital taxation because it presents an opportunity to raise a substantial amount of income but at the same time is politically popular in a way that labor income taxation or the elimination of the home mortgage interest deduction isn t economists are drawn to capital income taxation not because it is a good idea many most economists oppose taxing capital income but because it presents a number of academically interesting features that are worthy of study in particular capital income taxation presents several tricky dynamic considerations that many other forms of taxation do not suppose the united states government sharply increases taxes on business income say by increasing the corporate profit tax rate what are the short run and long run consequences of such a policy in the immediate wake of the higher tax standard theory would predict that basically nothing would happen to production or employment this probably strikes many of you as puzzling if i tax business income shouldn t i discourage the creation of this income according to standard economic analysis such a tax should not the reason is that real business capital the equipment machines factories etc are inelastically supplied in the short run the factories are all still here the grills ovens and sinks still work as do the espresso machines the excavators still run all of the capital that was functioning before the tax is functioning after the tax moreover businesses cannot escape capital taxes by laying off workers the firm s wage bill is already tax deductible as a result the firm should behave the same in the face of the capital tax hike the immediate effects of the capital tax increase are simply a reduction in the after tax capital income for owners investors and savers put differently it is the capitalists bear all of the burdens on the tax increase as time passes however the burden of the tax hike shifts to workers rather than capital owners while the tax increase doesn t influence the supply of capital in the short run according to the standard model it discourages the capital accumulation over time in particular it should discourage capital accumulation and thus reduce the capital stock to the point at which the after tax real rate of return is in its long run equilibrium in the standard model this is usually the exact same rate of return that the economy began with at the same time the reduction in capital also reduces the demand for labor and so wages fall so in the long run the consequences of an increase in capital taxation are the opposite of the short run in the long run the workers bear all of the tax burden and the capitalists bear none of it the fact that the economic incidence of a tax increase is different from the statutory incidence is one of the classic insights of public finance economics the dynamic effects of a change in capital taxes is a particularly stark example of such a distinction the difference between the short run and long run effects of the tax changes comes from the differences between the short run and the long run supply of capital in the short run the capital stock is what it is over time however capital can be accumulated or decumulated that is the long run supply is relatively elastic this simply insight alone strongly suggests that the optimal taxation of capital income should be higher in the short run that in the long run the tension between long run and short run optimal taxes also presents a problem for policy makers while they will constantly be tempted to tax capital they will also want to commit to lower taxes in the future among the most famous results in modern public finance is the chamley judd theorem see c chamley 1986 and k judd 1985 this result says that if tax rates are chosen optimally then if the economy attains a steady state the tax rate on capital income should be zero many economists myself included have interpreted this result as a formal articulation of the intuitions above recently there may have been an important development in the literature on optimal capital taxation ivan werning and ludwig straub mit have circulated a paper in which they argue that the chamley judd result is of more limited importance that is commonly believed they argue that under certain circumstances optimal tax paths do not lead to a steady state the way we normally think of it and in these cases the tax on capital income can be positive in other cases while the chamley judd result technically holds the steady state is attained only after an extended period of time centuries in their examples and is thus of limited relevance i am not going to go into the details of the straub and werning paper in a blog post the short version of the explanation is that the suppositions required for the chamley judd result are more stringent than one would imagine for the textbook chamley judd result to hold the economy must approach an interior steady state with finite lagrange multipliers for the various constraints in the model in many of the solutions in the new paper the economy converges to a rest point with zero capital and is thus not interior in other solutions the lagrange multipliers do not converge in fairness the counter examples straub and werning provide are all in the family of isoelastic preferences which sometimes have weird features in certain settings it is not clear to me whether the authors findings will necessarily extend to more malleable preference specifications but what is clear is that researchers will have to look much closer at the meaning of one of the most prominent results in modern public finance theory more to come i m sure 10 comments september 10 2014 by chris house feels like it was yesterday stay safe everyone 3 comments september 3 2014 by chris house end of an era on august 13 judit polgar announced that she was retiring from competitive chess this came as a shock to most people who follow chess it certainly came as a shock to me though i have heard on several occasions that judit wanted to put more emphasis on raising her family on her website she said that she was going to spend more time with her children and developing her foundation the judit polgar chess foundation promotes pioneering cognitive skills development for school children judit is often described as the strongest female chess player ever and i have no reason to doubt that assessment at the peak of her career judit was one of the strongest players of either gender her highest elo ranking was a staggering 2735 and she was ranked 8 overall in the world in 2005 according to wikipedia she has been the 1 rated female chess player in the world since 1989 judit typically played in the general tournaments she actually never competed for the women s world championship over her career she has defeated a slew of famous players including magnus carlsen the current world 1 and current chess champion viswanathan anand the previous world 1 anatoly karpov boris spassky the list goes on and on 1 there is a famous anecdote that gary kasparov once described judit as a circus puppet and asserted that women chess players should stick to having children i m not actually sure where this story comes from it was relayed by the guardian in 2002 without further elaboration the statement is so over the top that i wonder whether it s actually true it s might be true chess players are known for making zany statements like this from time to time bobby fischer comes to mind perhaps kasparov was trying to stir up some controversy who knows in any case kasparov asked for it and he got it in 2002 polgar beat kasparov and added to her trophy room kasparov was the worlds 1 ranked player at the time another fascinating aspect of judit s chess life is that her father laszlo polgar apparently decided to use his children to prove that geniuses are made not born he made a conscious effort to train his children in chess starting when they were each very young perhaps laszlo was right in addition to judit her sisters susan and sofia are also established chess grandmasters speaking for myself judit has been my favorite active chess player for a while now her style is somewhat of an anachronism she is known for a hyper aggressive dramatic playing style she often sacrifices pieces trying to gain initiative and attacking positions for the most part men s chess is actually much tamer many of the best male players are positional players who grind out games looking for small advantages which they eventually convert for a win alexey shirov is a counter example see below stylistically judit reminds me a lot of mikhail tal perhaps the greatest chess tactician of all below is a video of one of judit s most famous games in the game judit plays against alexey shirov the game commentary is by mato jelic if you are interested in learning more about chess or about judit s games mato s youtube channel is a great place to start among other things mato has a great collection of judit polgar s games with commentary 1 here s a funny quote from judit about her sister susan my sister susan she was 16 or 17 said that she never won against a healthy man after the game there was always an excuse i had a headache i had a stomach ache there is always something 6 comments september 3 2014 by chris house more thoughts on agent based models my recent post on agent based models abms generated a few interesting responses and i thought i would briefly reply to a couple of them in this post in particular two responses came from people who actually have direct experience with abms rajiv sethi posts a response on his own blog some excerpts chris house has managed to misrepresent the methodology so completely that his post is likely to do more harm than good well that doesn t sound too good agents can be as sophisticated and forward looking in their pursuit of self interest in an abm as you care to make them they can even be set up to make choices based on solutions to dynamic programming problems provided that these are based on private beliefs about the future that change endogenously over time what you cannot have in an abm is the assumption that from the outset individual plans are mutually consistent that is you cannot simply assume that the economy is tracing out an equilibrium path the agent based approach is at heart a model of disequilibrium dynamics in which the mutual consistency of plans if it arises at all has to do so endogenously through a clearly specified adjustment process this is the key 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