tag:blogger.com,1999:blog-4409551172339639840.post1436315104877424153..comments2018-04-19T00:36:47.114-07:00Comments on Douglas L. Campbell: On the Uses (and Abuses) of Economath: The Malthusian ModelsDoug Campbell http://www.blogger.com/profile/11028049845008665877noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-4409551172339639840.post-56704801848001741022018-04-17T20:03:24.772-07:002018-04-17T20:03:24.772-07:00thank you for sharing
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I have never unde...Grad student in economics here.<br /><br />I have never understood why mathematics was way too important in economics. If you do not take additional math classes from math department during your undergrad years, you are screwed. You will not be able to get into a decent phd program. Suppose that you have entered into a phd program and you are a possible candidate for becoming a brilliant social scientist, with a great intuition and grasp, but unable to demonstrate some proofs in your prelims, you will be get kicked out from the program. But I think, there is no penalty for any academic who is manipulating or overselling mathematical models.<br /><br />I need to quote George Box: "All models are wrong, some are useful". In contemporary economics, all models are wrong and nothing is useful.<br /><br />By the way, I think we need a blog post about your precious advices for prospective students (for phd applicant and JMCs)nexus66http://nexus66.livejournal.com/noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-29251460096596866402018-02-08T22:55:11.814-08:002018-02-08T22:55:11.814-08:00Hey Chris,
If their main point is that populati...Hey Chris,<br /><br /> If their main point is that population density will not be a decent proxy for income in a Malthusian world, why do the first two lines of the abstract read "Among countries colonized by European powers during the past 500 years, those that were relatively rich in 1500 are now relatively poor. We document this reversal using data on urbanization patterns and population density, which, we argue, proxy for economic prosperity."<br /><br /> Seems pretty clear.<br /><br /> Sure, they acknowledge a caveat that, in their Malthusian model, there are two opposing forces. But without the unrealistic assumption highlighted in my post, there won't be two opposing forces. Population density won't proxy prosperity period. This is why hunter-gatherers are often recorded as having higher incomes than settled agrarian societies. <br /><br /> Best,<br /> Doug<br /><br /> <br /><br /> <br /><br />Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-22189125609024635902018-02-08T12:50:03.481-08:002018-02-08T12:50:03.481-08:00Hi Doug,
You claim that the point they are making...Hi Doug,<br /><br />You claim that the point they are making is "population density will be a decent proxy for income in a Malthusian model." The point they are making is explicitly the exact opposite: that "caution is required in interpreting population density as a proxy for income per capita." This, as their little, pedagogical model shows, is at least in part because of simultaneous causality between income and population. They are not simply focusing on the equilibrium steady-state relationship, you are taking the quote about variance in technology and the induced positive association between income and population density out of context.<br /><br />Further, as I keep saying, the point they're making doesn't hinge on the goofy assumption you highlight. For example, consider what happens if we rewrite equation (2) as an AR(1) process in the log rather than the level of population density. We still get a positive association between income and density across steady-states if we assume that all that's driving variation across countries is variation in technology, but this slightly different specification does not have the problem you highlight. <br /><br />The point, as I say above, is that it doesn't really matter. They're not taking this model directly to data, they're just using it to make a simple point about identification in this context, and it's not the point you claim they're making. It would also, as I noted, be a point which would be extremely difficult to make if they couldn't use mathematics to express the argument.<br /><br />Chris.<br /><br />Chris Ahttps://www.blogger.com/profile/15553934787026424150noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-53237150505280429632018-02-08T12:34:27.276-08:002018-02-08T12:34:27.276-08:00Here's another tweet from Chris: "Again, ...Here's another tweet from Chris: "Again, the basic point Acemoglu et al are making, which you're misconstruing, is robust to that assumption. This is not "bullshit" math being used to "trick people," particularly the "feebleminded." These are remarkable, uncharitable, and wrong, claims. Dear Lord, indeed."<br /><br />My response: Chris -- have another look at the model. If you set rho = 1, you get back to the classic Malthusian model, where there is no correlation between income and population density. Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-21902534629399474902018-02-08T12:30:14.514-08:002018-02-08T12:30:14.514-08:00This comment has been removed by the author.Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-4995758436824588522018-02-08T10:58:23.609-08:002018-02-08T10:58:23.609-08:00Chris -- if you really want to show me up, the way...Chris -- if you really want to show me up, the way you can do it is by showing with algebra that the positive steady state relationship between income and population doesn't actually hold in this model. This would prove I'm wrong once and for all. Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-25973955382778396992018-02-08T10:54:44.528-08:002018-02-08T10:54:44.528-08:00Chris replies again on twitter: "Again, Doug,...Chris replies again on twitter: "Again, Doug, you're entirely missing the point of the model, which is that there's an "identification problem," as the authors put it---they're not limiting attention to SS. Their point is precisely the opposite of the claim you appear to think they're making, see last par. p10."<br /><br />Response: Dear Lord Chris. For the last time, I'm taking issue with the positive steady state relationship between population and income, and the fallacious assumption which yields it.<br /><br />The point I think they are making with the model is that there is good reason to think that population and income will be positively correlated in a Malthusian economy. I'm saying, this comes from a bad assumption. Correct that assumption, and this positive SS relationship doesn't hold, and thus, there is no reason to think income and population will be correlated in a Malthusian world. Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-49576681021755212232018-02-08T10:21:09.812-08:002018-02-08T10:21:09.812-08:00Chris replies again: "Nope, you misunderstood...Chris replies again: "Nope, you misunderstood the key piece of logic, which is that even assuming there's a positive causal effect of income on pop. density, we could observe any association between those outcomes. It isn't those three MIT profs (and me) who are confused by this model...."<br /><br />Hate to sound like a broken record here Chris, but, once again, we're talking about the steady state. In the steady state, there is, in fact, necessarily a positive relationship between p* and y* in their model (just not in real life). Yes, I realize that out of the SS a different relationship could materialize. However, I actually would like to defend AJR here -- differences in technology were enormous between hunter-gatherer groups and agricultural groups in the Americas, so that, even away from the SS, differences in A were likely to be dominant. Thus, given their model, applying it to data, while not perfect, is not necessarily without reason. The problem is about the model, and particularly with the SS relationship. Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-62017291698088192362018-02-08T10:15:48.244-08:002018-02-08T10:15:48.244-08:00On twitter, Chris replies again: "Yes, if onl...On twitter, Chris replies again: "Yes, if only A varies, that's so. And if only epsilon varies, there will be a negative association! The point, as they say, is that there's an identification problem. You have yet again just pulled one equation out of a sim. system and drawn erroneous conclusions."<br /><br />My response: OK, but in the blog post, it's clear I'm talking about the steady state. I don't see how pointing out that, outside of the steady state, things are different refutes the steady state positive relationship between p* and y*. It's this positive SS relationship which I take issue with. You seem to be saying that this positive steady state relationship between p* and y* is valid. However, I'm saying it's counterfactual, and comes from a specific, invalid assumption in AJR. <br /><br /><br /><br /><br /><br /><br /><br />Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-1035146111593016752018-02-08T07:24:34.846-08:002018-02-08T07:24:34.846-08:00Economath could be useful but one have to be very ...Economath could be useful but one have to be very wary of the model limitations which are often dismissed.<br /><br />Finally, Economath need to be supported by Econostat. Your model need to support the observed data and be estimated via ecnometric analysis. So many models, including many DESG models, fail this tests and should only be taken as incomplete theory and interesting exercise.Philippe Marcilhttps://www.blogger.com/profile/01040870749107318765noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-62127926591718842662018-02-08T00:26:34.692-08:002018-02-08T00:26:34.692-08:00On twitter, Chris replies: "That's not ri...On twitter, Chris replies: "That's not right and not what they say. Again, the model says income and population are sim. determined, but you are taking the implications of equation (2) in isolation. Eq (1) says higher pop -> lower income. In data, sign of corr. depends on what is varying across countries."<br /><br />First, Chris is quite correct that I did not present the full model above, only the offending bit of logic. However, you can plug in for p* in the equation above using the production function, set y-bar to zero for simplicity, and then, I hope, you'd find truth to AJR's claim that "As long as ρ < 1, there will be a steady-state level of income per capita, y∗, and steady state<br />population density, p∗, both strictly increasing in productivity A." It does seem to me that Chris is speaking away from the steady-state, in which his argument sounds quite correct. However, in the steady state, I actually buy AJR's argument. <br /><br />Let's suppose Chris is correct here that AJR are wrong, and that an editor of Econometrica and tenured professors at MIT themselves did not even understand the implications of a very simple model. Does this make the use of math look better? Or, instead, if Chris, a tenured economics professor, is wrong and AJR are right, doesn't this anecdote also provide a cautionary tale about how tricky even a simple mathematical model can be? <br />Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-22944283558100983002018-02-07T20:29:16.236-08:002018-02-07T20:29:16.236-08:00I actually do think that the intentions of these r...I actually do think that the intentions of these researchers were pure. I suspect they actually do believe that this algebra allowed them to overturn a basic result of the classic Malthusian model. But, math was still a tool in this case for an elaborate self-deception. Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-73259128575402621542018-02-07T12:44:53.672-08:002018-02-07T12:44:53.672-08:00"Math in this case is used as little more tha..."Math in this case is used as little more than a literary device designed to fool the feebleminded."<br /><br />That's a pretty striking assumption of motive on the part of Acemoglu et al. What's your reason for thinking that they were out to fool people? JPGhttps://www.blogger.com/profile/02632504264072261599noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-87971656794655134092018-02-07T12:34:12.387-08:002018-02-07T12:34:12.387-08:00Well, if I had to assign importance, I would of co...Well, if I had to assign importance, I would of course have to say that signalling is dominant, as it is in most spheres, and second acknowledge the usefulness of math, and put subterfuge third. Note that, in fact, most economists actually are pure-hearted. They are generally innocent of any knowledge that they do so much math simply to signal, and they aren't lying on purpose. What also happens is an elaborate self-deception, which takes place with purely empirical researchers as well. Doug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-74096843270168826542018-02-07T12:26:10.841-08:002018-02-07T12:26:10.841-08:00So... economics grad students do lots of math so t...So... economics grad students do lots of math so they can learn how to lie better?<br /><br />I thought so, and that's why I'm transferring to a useful social science... Geography. I Will Never Accept The Terms of Servicehttps://www.blogger.com/profile/09422355923256894207noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-487360320987250872018-02-07T12:25:16.022-08:002018-02-07T12:25:16.022-08:00Hey Chris -- thanks for your post. I encourage you...Hey Chris -- thanks for your post. I encourage you to take a second look at the model above! If you impose a steady state, population is indeed increasing in income. And that is, in fact, a (wrong!) prediction about the data. Economath has struck again!<br /><br />All the best,<br />DougDoug Campbell https://www.blogger.com/profile/11028049845008665877noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-90398061397409209852018-02-07T11:11:45.331-08:002018-02-07T11:11:45.331-08:00The model in the working paper version of the pape...The model in the working paper version of the paper is there for a simple reason: to consider the implications of a *simultaneous* relationship between population and income. It is *not* true in this model that "population density (which is proportional to technology) will be proportional to income!" That claim is analogous to taking the demand equation out of a supply and demand model and claiming the model implies that we should see lower quantities traded in times and places where prices are higher. <br /><br />The equation in the post above is meant to capture the Malthusian notion that higher income causes higher population growth. The other equation in the model---which is important if we want to solve the model--- captures causality running in the other direction. That equation doesn't just say "income which is proportional to technology," it says<br /><br />y(t) = A p^{-\theta},<br /><br />which, for \theta>0, captures a negative causal effect of population density on income, a mechanism operating through diminishing returns to land, in this story. <br /><br />The observed relationship between income and population density can't be read off either of these equations alone. A more stylized version of their argument might run:<br /><br />population = f ( income, shocks )<br /><br />income = g( population, technology, shocks ),<br /><br />which means in part that either technology shocks or population shocks play out over time as changes in both income and population.<br /><br />It is true that the way expressed the first equation, their model makes absurd predictions about population growth rates. But it doesn't really matter, as they're just using the model to make the point above, not directly taking it to data, and the model could be easily rewritten in such a way as to address this problem without changing the point.<br /><br />Finally, note that the "economath" did exactly as it's supposed to do in this case: forced us to specify precisely the assumptions we need to make, and highlights where those assumptions may lead us astray. If these same arguments were expressed verbally, all of this would be much more opaque.<br /><br />I don't know, but I would guess that the model was removed from the publication version not because of this "mistake," but rather because it takes two pages of space elaborating on the idea that the relationship between population density is not as simple as Malthus predicted, but then goes ahead in the empirical work to largely, in contrast to what their model says, take population density as a proxy for income! Which is an actual problem with the analysis, but one dutifully highlighted in the paper.<br /><br />Chris.<br /><br /><br />Chris Ahttps://www.blogger.com/profile/15553934787026424150noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-10863260254134491812018-02-07T08:57:09.425-08:002018-02-07T08:57:09.425-08:00.
Is there anything stated in math that cannot ....<br /> Is there anything stated in math that cannot be clearly restated in English?<br />.Avraam J Dectishttps://www.blogger.com/profile/01098498673510354088noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-28509755365597557342018-02-06T23:05:53.908-08:002018-02-06T23:05:53.908-08:00I heard Richard Freeman (Harvard economist) say th...I heard Richard Freeman (Harvard economist) say that if he can’t explain something in words, he feels he hasn’t understood it. Seems a good rule. Freeman also says he loves math. Kienhttps://www.blogger.com/profile/15643929814291369340noreply@blogger.comtag:blogger.com,1999:blog-4409551172339639840.post-24852995645919413732018-02-06T17:23:57.762-08:002018-02-06T17:23:57.762-08:00In my experience, physicists are much less fussy a...In my experience, physicists are much less fussy about their math than economists. The physicists could afford to be a bit sloppy because experiments tended to catch their errors, whereas economists have so many fudge factors at hand that they better get the models formally correct. The world isn't going to provide a pony. To be sure, my experience is out-of-date. There are far more big data economists around these days who tend to use simpler models that make sense when described in English. So maybe things are different now, though you can fetishize data sets as well as system of differential equations. Jim Harrisonhttps://www.blogger.com/profile/16986759089669331171noreply@blogger.com