tag:blogger.com,1999:blog-26706564.post8884880137111486330..comments2020-03-24T11:05:18.939-04:00Comments on Thoughts On Economics: For Whatever Can Walk - It Must Walk Once MoreRobert Vienneauhttp://www.blogger.com/profile/14748118392842775431noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-26706564.post-75159006742962908552008-10-12T02:42:00.000-04:002008-10-12T02:42:00.000-04:00""Substitution" has nothing to do with it."Right, ...""Substitution" has nothing to do with it."<BR/><BR/>Right, which is exactly what I said. But still the fact that higher labor productivity can lead to a situation where unemployment goes 100% AND wages grow to zero definitely falls in the "bug not a feature of the model" category. Step back away from the model and ask if this makes sense. And why or why not? As workers become more productive not only are they gotten rid of but they get lower wages as well.<BR/><BR/>The problem arises simply because v is the main "jump" variable in the model so it always has to absorb any kind of exogenous shocks that occur. If these shocks occur "often enough" - continuously, at a high enough rate alpha, v is always absorbing those shocks (u also falls simply because, with fixed wages it's = constant*a). With a growing fast enough all the other adjustment dynamics don't matter and the whole thing has to go to (0,0).<BR/><BR/>In particular, what does it is the assumption that at all points in time q=al and q=k/o (hence k/l=ao). The model, unlike the traditional Harrod-Domar version, does not allow for capital under utilization. So v's is forced to go to zero to make sure those two equalities hold. It's not a good assumption - but I think it's pretty much how you got to close this model with the fixed coefficients technology.<BR/><BR/>Or think about it this way. Labor productivity can be thought of as including a certain level of "effort". It's not to much of a stretch to assume that workers can coordinate on their level of effort, since they can coordinate on the level of wages (as embodied in the Phillips curve, presumably embodying some kind of bargaining process and a wage/employment trade-off). But in this case, workers would have an incentive to reduce their effort - since lower a means higher v and u - so as to get to (1,1). That's crazy enough. But obviously that's not a steady state, since we got a limit cycle here. So even with the lower level of effort (a) the economy would start moving towards a lower v and u. But then the workers would have an incentive to lower their effort even further. In the end workers' effort is zero (well, epsilon) and they get (almost) full employment and (almost) full share of output. All this is without any kind of disembodied technological progress.<BR/>The case with such progress works in exactly opposite way (so even if you don't buy the 'effort' story, it's a useful way to think through how the model operates) except to the benefit of capitalists (workers, in the limit, infinitive productive (as opposed to zero effort)) but none of them (well, epsilon) employed and getting none of the output.<BR/><BR/>There's also other interesting parts to this;<BR/><BR/>Sticking with the Leontief function you can get stability (i.e. it circles inward) with a non-linear saving function. <BR/><BR/>Ignoring the weird effects noted above, it starts to matter WHEN technological progress occurs - if it's in hi-v, hi-u times, it's stabilizing (smaller cycles, at least for awhile), if it's during lo-v, lo-u times it's destabilizing and in other cases it destabilizes one but not the other. And some other stuff...YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-24060779216925143352008-10-11T05:31:00.000-04:002008-10-11T05:31:00.000-04:00The literature on this and related models is appar...The literature on this and related models is apparently immense and growing.<BR/><BR/>I drew the curves for α = 0.05, β = 0.1, δ = -0.1 (that's bad), γ = 0.95, ρ = 1, σ = 0.2, and <I>s</I> = 0.25. I haven't done much in the way of numeric experimentation.<BR/><BR/>Think of that limit point in the special case where the rate of growth of productivity is zero. Then growth will be smooth. Now introduce productivity growth, keeping the rate of growth of output unchanged. Less labor will be needed over time to make the same stuff. Unemployment will rise and wages will fall. But if the rate of growth of output were increased by the rate of growth of productivity, the level of employment would remain unchanged. "Substitution" has nothing to do with it.<BR/><BR/>An objection to my formulation of the model is that savings drives investment. In a sense, the cyclical growth curve in the model is a warranted growth curve. Sordi (2008) addresses this objection, and introduces an investment function. That generalization has a varying capital-output ratio and relates the model to the Kaldor-Pasinetti-Robinson <A HREF="http://robertvienneau.blogspot.com/2007/01/post-keynesian-model-of-growth-and_10.html" REL="nofollow">theory</A> of income distribution.<BR/><BR/>One would like to tell tales that generalize, at least qualitatively, to multi-sector models. One cannot do that with neoclassical aggregate models in which the interest rate equaling the marginal product of capital is a central mechanism.<BR/><BR/>I resist the urge to describe continuously differentiable production functions and discrete-coefficient production functions as "neoclassical" and "non-neoclassical", respectively.Robert Vienneauhttps://www.blogger.com/profile/14748118392842775431noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-4393978264243397452008-10-10T03:44:00.000-04:002008-10-10T03:44:00.000-04:00I was right that you can do this in a neoclassical...I was right that you can do this in a neoclassical model (I actually got excited for a second thinking it hadn't been done before):<BR/><BR/>http://www3.eeg.uminho.pt/economia/nipe/docs/2007/NIPE_WP_5_2007.pdf<BR/><BR/>In fact it's pretty interesting as that paper considers both the possibility of substitution between capital and labor as well as increasing returns to scale. <BR/><BR/>Basically what you get(from my own playing around with it):<BR/>With CRS <BR/>- with Leontief you get the limit cycle as in your post<BR/>- with substitution (even just a little bit of it) you get fluctuations but it gets to the steady state rather than orbiting around it. With Cobb-Douglas you get constant shares of course but v fluctuates as does K/L (which is assumed constant in your post)<BR/>- with a lot of substitution you get wild swings in employment even as capital keeps growing (as in AK model) simply because it's either all or nothing; wages are either crazy high with zero employment or they're really low with full (slavery) employment. Since in this case K - and adjustments in it - doesn't affect labor productivity v never settles down.<BR/><BR/>With IRS (I haven't played with this version as much - it's from the paper) you get more more "destabilizing effects" which here I take it to mean you're more likely to get the limit cycle rather than the darned thing making its way to where some two curves cross (either v and u, or v and k). But apparently the effect of allowing some substitutability dominates the IRS of it - you need only a bit of substitution to make up for a lot of IRS to get to where the two curves cross.<BR/><BR/>Anyway, it's pretty interesting. But it's pretty much a neoclassical model. Homogeneous capital and all.YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-5476399232074586982008-10-09T14:13:00.000-04:002008-10-09T14:13:00.000-04:00Quick question, what parameter values did you use ...Quick question, what parameter values did you use for Figure 1?YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-87593116965858319482008-10-08T02:03:00.000-04:002008-10-08T02:03:00.000-04:00Yes, that's clear. But what is the intuitive expla...Yes, that's clear. But what is the intuitive explanation for why a really high rate of productivity growth rate causes convergence to the crash state (share of labor income, as well as the employment rate going to 0)?<BR/><BR/>(we can find the (dv/dt)/v=0 line by setting the relevant equation to zero. It's a vertical line whose position depends negatively on alpha. So a high enough alpha pushes the line past zero, insuring that (0,0) is the only steady state (no cycle in this case))<BR/><BR/>One may be tempted to say "machines replacing capital" but with a Leontief PF there's no substitution. So I'm on clear on the reasons.<BR/><BR/>Also, it might also be worth noting that the 'pump' that is doing the work here of creating the fluctuations is not the particular form of the production function but rather the Phillips curve equation. I think a very similar result can be obtained with a version of the Solow model with unemployment, in which wages are given (by the PC as here) but marginal product is equal to them (hence resulting in unemployment if they go too high). Of course there the K/Y and K/L ratios aren't constant so it's substitution between K and L that is doing the work of changes in labor's share (which is constant).<BR/><BR/>Also, I assume that when you say "This model has some features that I find objectionable, but I find it interesting nonetheless." you are referring to the homogeneous capital of the model. But then why not take the same open minded approach to other models that commit the same sin?YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-55685050290646925542008-10-07T20:06:00.000-04:002008-10-07T20:06:00.000-04:00There are probably conditions to ensure that neith...There are probably conditions to ensure that neither component of that limit points exceeds unity. And maybe some conditions are needed to ensure that limit point is dynamically unstable, with periodic orbits around it.<BR/><BR/>Anyways, think of the special case where the rate of growth of productivity is zero (α = 0), the rate of growth of the labor force is zero (β = 0), and all capital is circulating capital (δ = 1). Then that condition is that σ < <I>s</I>. In words, it must be possible for savings to at least replace the capital used up in production. If some of the capital is fixed capital - so δ is less - not as much savings is needed. But if population or productivity grows, more savings is needed to maintain the natural rate of growth. In the sort of growth models I like, the rate of population growth and the rate of growth in productivity sum together to comprise the natural rate of growth.Robert Vienneauhttps://www.blogger.com/profile/14748118392842775431noreply@blogger.comtag:blogger.com,1999:blog-26706564.post-12542980973276489542008-10-06T16:57:00.000-04:002008-10-06T16:57:00.000-04:00This is a very cool model and you've got a ver...This is a very cool model and you've got a very nice presentation there. But you leave it a bit under analyzed. <BR/>For example, there's some parameter restrictions for that non-origin limit point to exist. Specifically, you need (d+a+b)(o/s)<1 (where d is delta, a is alpha, b is beta, o is sigma). Otherwise the only stable limit point is the crash state (0,0). While it is intuitive that higher depreciation and pop growth, as well as lower saving rate on the part of the capitalist would make that more likely, it is a bit strange that a higher rate of productivity growth (a) also makes the crash state more likely. What's going on in intuitive terms? <BR/>Also, I'm having trouble figuring out if there's a "golden rule" of s here, say, with alpha and beta = 0. <BR/>I might draw up some phase diagrams for this.YouNotSneaky!https://www.blogger.com/profile/06378267534638281151noreply@blogger.com