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l augmented to include human capital skills know how the model is essentially a one good economy with exogenous savings rates in some corners of the profession using a model with an exogenous savings rate might be viewed as a stoning offense but it is perfectly fine in this context the paper is about human capital not about the determinants of the saving rate but that s not the end of the mathiness their analysis proceeds by constructing a linear approximation to the growth paths of the model and then using standard linear regression methods together with aggregate data naturally such regressions are typically not identified but mankiw romer and weil don t let that interfere with the paper they simply assume that the error terms in their regressions are uncorrelated with the savings rates and proceed with ols there is a ton of mathiness in this work and the consequence mankiw romer and weil s 1992 paper is one of the most cited and influential papers in the field of economic growth think about how this paper would be changed if some idiot referee decided that it needed optimizing savings decisions after all we can t allow hand waving about exogenous savings rates multiple goods and a separate human capital production function no hand waving about an aggregate production function or one good economies micro data no hand waving about aggregate data and instruments for savings rates population growth rates and human capital savings rate no hand waving about identification the first three modifications suggested by the referee would simply be a form of hazing combined with obfuscation the modifications make the authors jump through hoops for no good reason and the end product has an analysis that is less clear the last one insistence on a valid instrument would probably be the end of the paper since such instruments probably don t exist thank god this paper didn t run into a referee like this my own opinion is that mathematical sloppiness can be perfectly fine if it deals with a feature that is not a focus of the paper hand waving of this sort likely comes at very little cost and may have benefits by eliminating a lengthy discussion of issues only tangentially related to the paper on the other hand if the hand waving occurs when analyzing or discussing central features of the paper then i am much more inclined to ask the researcher to do the analysis right this type of hand waving happens sometimes but it is not clear that it happens more often in macroeconomics or in freshwater macro at that ironically the freshwater guys that romer criticizes are much more likely to demand a tight specification and precise analysis of the model whether it is called for or not fn1 if you are interested in the modern proof of fermat s last theorem i highly recommend this documentary 13 comments may 10 2015 by chris house in praise of linear models noah smith and francis coppola have recent columns discussing the prevalence of linear methods in economics and in particular in macroeconomics coppola acknowledges that adding financial components to dsge models is a step in the right direction but that it does not begin to address the essential non linearity of a monetary economy until macroeconomists understand this their models will remain inadequate this is ok but to me it sounds like she s going into deepak chopra mode a bit noah gives a good description of the properties and benefits of linear models linear models are easy to work with lines can only intersect at one point so there s only one thing that can happen in non linear models the curves can bend back around and could meet in some faraway location then you have a second equilibrium another possible future for the economy if you go with the full correct non linear versions of your models you stop being able to make predictions about what s going to happen to the economy also linearized models are a heck of a lot easier to work with mathematically as formal macroeconomic models have become more realistic they ve become nastier and less usable maybe their days are simply numbered there are elements of truth in both columns but on the whole i don t share their assessments in fact i am firmly of the opinion that linear solution methods are simply superior to virtually any other solution method in macroeconomics or any other field of economics for that matter moreover i suspect that many younger economists and many entering graduate students are gravitating towards non linear methods for no good reason and i also suspect they will end up paying a price if they adopt the fancier modelling techniques why am i so convinced that linear methods are a good way to proceed let me count the ways 1 most empirical work is done in a log linear context in particular regressions are linear this is important because when macroeconomists or any economist tries to compare predictions with the data the empirical statements are usually stated in terms that are already linear this comparison between theory and data is easier if the models are making predictions that are couched in a linear framework in addition there aren t many empirical results that speak clearly on non linearities in the data there is a statement that i ve been told by empirical economists several times that a well known economist said that either the world is linear or it s log linear or god is a son of a bitch 2 linear doesn t mean simple when i read francis column it seems that her main complaint lies with the economic substance of the theories rather than the solution method or the approximate linearity of the solutions she talks about lack of rationality heterogeneity financial market imperfections and so forth none of these things requires a fundamentally non linear approach on the contrary the more mechanisms and features you shove into a theory the more you will benefit from a linear approach linear systems can accommodate many features without much additional cost 3 linear dsge models can be solved quickly and accurately noah mentioned this but it bears repeating one of the main reasons to use linear methods is that they are extremely efficient and extremely powerful they can calculate accurate linear solutions in milliseconds in comparison non linear solutions often require hours or days or weeks to converge to a solution fn 1 4 the instances where non linear results differ 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 ar...
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