Thanks, very interesting as usual. I do not understand Figure 3: why wouldn't the standard/Fed view be consistent with the academic one? By shifting the opportunity cost of current consumption, an increase in rates can push current consumption *levels* down, hence consumption *growth* up. What am I missing?
John, equations (2) and (3) include ß^t where ß^t = 1/(1+r). From your work, r is a stochastic discount rate. An individual risk averse consumer, given their subjective preferences, would take this into account as it relates to equation (3). Is it implied in the S.T. constraints? Individuals can manage risk exposure of financial assets with hedges and insurance in various trading markets.
This model assumes a constant real interest rate. But you're right, permanent income is not the properly stochastically discounted market value of income. Great insight! I'll update in a bit.
Equation (4) above is predicated on the individual's rate of time preference, δ, being equal to the real rate of interest, r. Hall, in his 1978 paper, states that r ≥ δ. If, however, r = δ, then because δ is strictly positive, the real rate of interest, r, is also strictly positive. As we know from the past decade, r is not strictly positive and may be non-positive at times.
The constant c* that appears in the quadratic utility function (equation (2) above) is the bliss level of consumption. Bliss being almost impossible to attain, the quadratic utility function is appropriate for c ₜ < c*. As in control engineering, the quadratic utility function is a useful approximation where the actual utility function is unknown. For variational analysis, such as modelling small excursions from equilibrium and where the pre-determined variable state equations are linear, assuming a quadratic utility function as the cost function to be optimized allows the use of quadratic-linear regulation models for solution of the optimization problem with lower expenditure of effort.
Hall (1988), in the section headed "Conclusions", observes (on pp. 36-37) "... if the economy contains isolated individuals with finite lifetimes, then the elasticity of substitution governs the extent to which redistribution of consumption within lifetimes offsets the government's attempt to redistribute consumption across generations. With low [elasticity of] substitution, redistribution is highly effective--unfunded social security really does create more consumption for the older generation in general equilibrium."
I love your blog, but you are overly kind to macro asset pricing. Consumption is too smooth to explain asset returns. Like Jason from "Friday the 13th", consumption gets killed in every paper, but reappears in the sequel.
We only "explain" the equity premium by adding an extra parameter. The variance premium is larger, and gets ignored.
The cross-section of expected asset returns seems unrelated to covariance. By contrast, there are large momentum and seasonal patterns in asset returns.
Efficient market theory made a surprising, far-reaching, and successful random walk prediction. It led to indexing and revolutionized investing. Macro finance, not so much.
You have a comment about it, but doesn't adding habits kind of reconcile the Fed view and the academic view? If I look at the movement of consumption in response to a (expansionary) monetary shock in Christiano, Eichenbaum, and Evans figure 1, I see that consumption gradually rises before falling back down. I think this is consistent with what policy makers would say happens? (and is broadly consistent with the empirical evidence)
I know that an important difference is they are considering a one-off shock that is allowed to revert, while you are considering a permanent shock. Is that where you think the tension arises?
As someone who works in the financial industry, I broadly agree with Disinfectant. It is much easier to apply and get value from the efficient market theory and random walks. But sometimes you do come across situations were explaining thing in terms of market factors doesnt have the level of insight needed. For example, situations where you are trying to embed longer term macro economic forecasts/insights into the modelling.
In situations like that I often come back to the economic finance stuff (and your writing). And then usually regret it! The literature is incredibly confusing, and the empirical results/studies seem endlessly conflicting. Often the modelling seems reductionist/ too low dimensional.
So a couple of naive questions:
You hint at the end towards the idea that longer term real rates might move in line with consumption growth. You contrast this with the monetary policy view that the two are negatively correlated. But you dont mention the idea of natural rate of interest which would the concept the New Keynsian models would say they are modelling, or longer dated real bond yields which is what finance practicioners would look at. Could you add either of these concepts to the models to make them just a bit more realistic/intuitive?
Also, my understanding is that if the IES is 1 then this implies the consumption to wealth ratio is held constant. A bit like the crew of a shipwrecked boat carefully rationing their supply of food. This seems like a V. strong statement, and the sort of thing which should be testable. Why isnt the view of say, Laubach and Williams, that this is evidenced in the dynamics of natural rate/long term trend growth not more broadly accepted?
Thanks, very interesting as usual. I do not understand Figure 3: why wouldn't the standard/Fed view be consistent with the academic one? By shifting the opportunity cost of current consumption, an increase in rates can push current consumption *levels* down, hence consumption *growth* up. What am I missing?
That's right, as expressed in the lower blue line. But the Fed / policy view thinks like the bottom red line.
John, equations (2) and (3) include ß^t where ß^t = 1/(1+r). From your work, r is a stochastic discount rate. An individual risk averse consumer, given their subjective preferences, would take this into account as it relates to equation (3). Is it implied in the S.T. constraints? Individuals can manage risk exposure of financial assets with hedges and insurance in various trading markets.
Again...really good stuff!
This model assumes a constant real interest rate. But you're right, permanent income is not the properly stochastically discounted market value of income. Great insight! I'll update in a bit.
Thank you for your kind comment.
Equation (4) above is predicated on the individual's rate of time preference, δ, being equal to the real rate of interest, r. Hall, in his 1978 paper, states that r ≥ δ. If, however, r = δ, then because δ is strictly positive, the real rate of interest, r, is also strictly positive. As we know from the past decade, r is not strictly positive and may be non-positive at times.
The constant c* that appears in the quadratic utility function (equation (2) above) is the bliss level of consumption. Bliss being almost impossible to attain, the quadratic utility function is appropriate for c ₜ < c*. As in control engineering, the quadratic utility function is a useful approximation where the actual utility function is unknown. For variational analysis, such as modelling small excursions from equilibrium and where the pre-determined variable state equations are linear, assuming a quadratic utility function as the cost function to be optimized allows the use of quadratic-linear regulation models for solution of the optimization problem with lower expenditure of effort.
Hall (1988), in the section headed "Conclusions", observes (on pp. 36-37) "... if the economy contains isolated individuals with finite lifetimes, then the elasticity of substitution governs the extent to which redistribution of consumption within lifetimes offsets the government's attempt to redistribute consumption across generations. With low [elasticity of] substitution, redistribution is highly effective--unfunded social security really does create more consumption for the older generation in general equilibrium."
I love your blog, but you are overly kind to macro asset pricing. Consumption is too smooth to explain asset returns. Like Jason from "Friday the 13th", consumption gets killed in every paper, but reappears in the sequel.
We only "explain" the equity premium by adding an extra parameter. The variance premium is larger, and gets ignored.
The cross-section of expected asset returns seems unrelated to covariance. By contrast, there are large momentum and seasonal patterns in asset returns.
Efficient market theory made a surprising, far-reaching, and successful random walk prediction. It led to indexing and revolutionized investing. Macro finance, not so much.
You have a comment about it, but doesn't adding habits kind of reconcile the Fed view and the academic view? If I look at the movement of consumption in response to a (expansionary) monetary shock in Christiano, Eichenbaum, and Evans figure 1, I see that consumption gradually rises before falling back down. I think this is consistent with what policy makers would say happens? (and is broadly consistent with the empirical evidence)
I know that an important difference is they are considering a one-off shock that is allowed to revert, while you are considering a permanent shock. Is that where you think the tension arises?
As someone who works in the financial industry, I broadly agree with Disinfectant. It is much easier to apply and get value from the efficient market theory and random walks. But sometimes you do come across situations were explaining thing in terms of market factors doesnt have the level of insight needed. For example, situations where you are trying to embed longer term macro economic forecasts/insights into the modelling.
In situations like that I often come back to the economic finance stuff (and your writing). And then usually regret it! The literature is incredibly confusing, and the empirical results/studies seem endlessly conflicting. Often the modelling seems reductionist/ too low dimensional.
So a couple of naive questions:
You hint at the end towards the idea that longer term real rates might move in line with consumption growth. You contrast this with the monetary policy view that the two are negatively correlated. But you dont mention the idea of natural rate of interest which would the concept the New Keynsian models would say they are modelling, or longer dated real bond yields which is what finance practicioners would look at. Could you add either of these concepts to the models to make them just a bit more realistic/intuitive?
Also, my understanding is that if the IES is 1 then this implies the consumption to wealth ratio is held constant. A bit like the crew of a shipwrecked boat carefully rationing their supply of food. This seems like a V. strong statement, and the sort of thing which should be testable. Why isnt the view of say, Laubach and Williams, that this is evidenced in the dynamics of natural rate/long term trend growth not more broadly accepted?