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Sjysnyc
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I thought we weren’t supposed to use argument from authority anymore? Then wouldn’t we just say Mike Woodford is really smart and has lots of published papers that use NK models so they must be right. The monopolistic competition does make a difference—or at least so it seems to me—as now you’re bringing in the very adjustment mechanisms that get you back to what counts as full employment in the NK model: allowing labor supply to increase and prices to adjust. So take the fraction of intermediate firms that do adjust prices. They drop their prices substantially and hire lots of labor. They have enough demand at those new lower prices now, and can actually expand their production. So output goes up at those firms that adjusted their prices. And unless you’ve got some strange aggregation function overall demand should be greater than 50. At the same time, wages go down not only at those firms but at all firms. [In the background workers are getting not just wages but also the profits from the firms who have cut prices.] And for all the identical workers in the economy they are back on the equilibration of marginal utility of consumption and marginal disutility of labor. You’ve got the mechanism that allows labor supply to increase through the extra hiring—the other equilibrium condition I was talking about earlier. In contrast to your 9/11 648 post there _is_ an incentive to hire that extra labor now. Or are you still saying that despite drop in price there can be no more than 50 total haircuts in the economy? Or that the extra haircuts just happen to be exactly canceled out by less at others? Despite the fact that nominal wages have now dropped substantially across the economy and you no longer have a difference between the marginal utility of consumption and the marginal disutility of labor? And then if you think of dynamics that happens again next period as output goes up again as more firms have the ability to adjust their prices. So some further fraction now are producing more, and so it goes on each period with production slowly inching back up, and hence pushing employment back toward the NK model’s concept of full employment. [Well, kind of. This is all a little off as there isn’t any actual way for the consumption to fall from animal spirits in the model, but it does outline the equilibrium forces that push employment back to the model’s concept of full employment.]
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You posit a hard cutoff of demand at 50 and no matter what you can’t get demand beyond that. And are stripping down the implicit model by only looking at one good. Again, this is a different model than the NK one. Whether it is a better model or not is a separate question. But it isn’t how the NK model works. In the NK, there is the composite good made up of all the different monopolistically competitive firms goods. Each of those firms hires the non-differentiated labor in the market, and it’s all at the same wage. And if the prices of one of the intermediate goods is lower, then more of that is bought and goes into the composite good. So suppose you have that initial drop in expectations down to producing 50. The Calvo pricing assumption in the model is that a fraction theta of the intermediate goods producers lower their prices substantially and increase their output. The model has smooth demand curves for all firms by the technology of the model—you can’t get the sharp drop off in demand you posit. These intermediate goods producers who adjust then hire a large amount of labor in the spot market at the new lower wage but that still means that overall labor supply rises relative to the just 50 expectation. And all wages in the economy sink to that new lower level because the model has the labor market clearing. The marginal utility of consumption and marginal disutility of labor are equalized. Those firms that can’t adjust their prices see their demand cut back. Not sure of the sign of the change in profits for those firms since you have lower output, but costs of their only input (labor) has also declined, but those profits continue to be sent back to all the households in the economy since they all own equal shares of each company, so the households have income from that source as well. But in the model, as stated and not saying the model is a good approximation of reality, there are forces that push back to what it calls the full employment equilibrium. Now does this labor market make any sense? Nope, none at all. That was what I alluded to in my post on the other thread. There is no involuntary unemployment and attempted fixes such lotteries across agents are even worse. And as Andy notes above this makes the NK model not a great guide to think about what’s happening in the economy during a recession. And is one of the places where I have the major issues with the model. But the ability of firms to sell more output at a low enough price isn’t where I think the NK really falls down.
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I think – though am not sure – that you’re right about the diminishing returns to labor not mattering. I’d have to crank through the algebra to be sure. But to be fair you’re simplifying away from their model. But here is the rub: “In my underemployment equilibrium, where C(t)=50, it is indeed true that the self-employed hairdressers want to sell more labour (i.e. sell more haircuts). But they can't, because nobody will buy any more than 50 haircuts. So yes, they are "off" their labour supply curves (i.e. "off" their output supply curves). That FOC is not satisfied. But the individual agent can't do anything about it. He is sales-constrained.” In the NK model that isn’t the way it works. There is a perfectly competitive market for labor among all the differentiated good producing firms and the workers. That market clears (by assumption) in the model and the wage is the same across all the differentiated product producers. In your example, though not in all NK models, wages are perfectly flexible every period. So any worker who drops there wage has infinite demand for labor. Each worker is infinitesimally small relative to the economy as a whole, so they have no effect on overall wages or labor supply. You note “an individual hairdresser will cut his price (cut his wage) when the Calvo fairy touches him with her wand. But that makes no difference to my argument here.” But that isn’t the case. Price and wage are different in the model. Prices are what the individual firms charge while wages are what workers are paid. In your scenario there is a _permanent_ difference between the marginal utility of consumption and the marginal disutility of labor. You’re implicitly not allowing the wage to adjust to clear that market. Each of the workers is happy to lower their wage and work more. Each of the firms would be happy to hire at a lower wage and increase their production (since production isn’t fixed, just the price of output). Instead you’re saying that doesn’t happen. What you want is a different model. One where those adjustments cannot occur for some reason. Which is fine. But that doesn’t mean that under its own terms the NK model doesn’t have a equilibrating force. Half the consumption simply isn’t an equilibrium because every agent has an incentive to push away from it.
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I'm moving my (slightly modified) comment from the other thread over since the discussion has moved over here. Hopefully that's okay. In that prior discussion I had an aside about the issue of labor markets in the NK model wasn't particularly useful -- indeed it was a distraction. I was expressing my skepticism about the usefulness of the NK/DSGE blend in general, and specifically about their labor market modeling assumptions as being the worst part. But that's not particularly relevant to the discussion at hand. Which I take as to whether there is a meaningful trend/equilibrium/full employment that the model comes back to because of equilibriating forces within the model. In the terms you were asking: is consumption halving for everyone an equilibrium? There I think the answer is no. There isn't just a optimization over consumption but over labor supply -- and as you note in your response to me the model assumes that the agent can work as much as he wants at the prevailing wage. And in the case where you halve consumption the agent would want to work substantially more. There is lurking somewhere in the depths of the model a first order condition with respect to labor supply as well. With a diminishing returns to labor production function around too. It's just when reducing it to the 3 variable system that gets swept under the table. Or think about it in terms of the individual agents. Suppose one halves her consumption and expects everyone else to do the same. Then, at the prevailing wage she has an incentive to increase her hours of work. And by the assumptions of the model she can do so without affecting wages. She can consume more, but because she is also working more will not violate the transversality condition. But then, so does everyone else. And that gets you on the way back to an equilibrium with what they call full employment in the model. With respect to your response to David above, the production function isn't one hair cut per hour. Instead it is F(n) = A_t * n^alpha (eq 5 in the Gali paper linked to earlier). There are diminishing returns to labor on the aggregate level and that matters.
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So my aside about the issue of labor markets in the NK model wasn't particularly useful -- indeed it was a distraction. I was expressing my skepticism about the usefulness of the NK/DSGE blend in general, and specifically about their labor market modeling assumptions as being the worst part. But that's not particularly relevant to the discussion at hand. Which I take as to whether there is a meaningful trend/equilibrium/full employment that the model comes back to because of equilibriating forces within the model. In the terms you were asking: is consumption halving for everyone an equilibrium? There I think the answer is no. There isn't just a optimization over consumption but over labor supply -- and as you note in your response to me the model assumes that the agent can work as much as he wants at the prevailing wage. And in the case where you halve consumption the agent would want to work substantially more. There is lurking somewhere in the depths of the model a first order condition with respect to labor supply as well. With a diminishing returns to labor production function around too. It's just when reducing it to the 3 variable system that gets swept under the table. That's why there is a equilibrium to which it makes sense to talk about returning to as time goes to infinity. Or think about it in terms of the individual agents you were talking about with JW. Suppose one halves her consumption and expects everyone else to do the same. Then, at the prevailing wage she has an incentive to increase her hours of work. And by the assumptions of the model she can do so without affecting wages. She can consume more, but because she is also working more will not violate the transversality condition. But then, so does everyone else. And that gets you back to an equilibrium with what they call full employment.
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Simplification is good. But I think you're simplifying too much. So I can't see the entire Gali derivation in the book, but it looks like his underlying utility function has both consumption and labor supply in it. That means instead of your simplification of u = ln(c) it should be u = ln(c) - ln(n) And that gives you a stable path. Intuitively what it means is if you halve consumption then you also drastically reduce labor supply. The marginal utility of additional consumption is then much higher than the marginal disutility of additional work. You're no longer in an equilibrium since the assumption of these models is that labor supply and labor demand match -- this is one of the much more problematic areas in my view. So essentially what the model has is something like the phase diagrams mentioned for the Ramsey model above implicitly in it, just that somewhere in the algebra the labor part gets subsumed into the deviation of output from trend and doesn't show up in the 3 equation version. That's why the "under the assumption that the nominal rigidities vanish asymptotically" isn't really sweeping it under the rug. What it's saying is if the nominal rigidities go away there is a stable saddle path back to y=y* that he assumes the economy follows. I think some derivations may be a bit murky that this is going on. And if you didn't have the disutility of labor in here I don't think it would work. Or I could be wrong -- it's been a couple of years since graduate school and I've fled academic economics.
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Sep 10, 2013