Timeline for Why utility rather than expected utility in Cochrane's "Asset Pricing"?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 20, 2022 at 9:58 | vote | accept | Richard Hardy | ||
| Feb 23, 2021 at 0:24 | comment | added | Michael Greinecker | @1muflon1 It is more complicated than that. The expectation is the conditional expectation given $t$, which cannot be chosen independently of $c_t$. And Cochrane's clarification "where $c_t$ denotes consumption at date $t$." certainly suggests that $c_{t+1}$ denotes consumption at $t+1.$ At the next page, he even writes "Consumption $c_{t+1}$ is also random." which clarifies that he talks about the value. I really don't see what is controversial about my statement that it does not make sense. | |
| Feb 23, 2021 at 0:02 | comment | added | 1muflon1♦ | @MichaelGreinecker but in this case $U$ is clearly composite function, so here I think Cochrane is just bit sloppy as clearly the function is actually a composite one $U(u_t(c_t),E[u_{t+1}(c_{t+1})] )$ | |
| Feb 22, 2021 at 23:52 | comment | added | Michael Greinecker | @1muflon1 The normal way to read $U(c_t,c_{t+1})$ is that $U$ is a function of two numbers, $c_t$ and $c_{t+1}$. Indeed, Cochrane write that utility is "defined over current and future values of consumption" But $U$ does not just depend on the current and future values of consumption, it depends on the current value and the conditional expaction over all possible future values. You are not going to read that in a math paper. | |
| Feb 22, 2021 at 20:21 | history | became hot network question | |||
| Feb 22, 2021 at 17:06 | answer | added | 1muflon1♦ | timeline score: 4 | |
| Feb 22, 2021 at 16:49 | comment | added | Richard Hardy | @1muflon1, I must agree. Thank you for a thoughtful comment! I think you could post it as an answer. | |
| Feb 22, 2021 at 16:43 | comment | added | 1muflon1♦ | @RichardHardy but note that is not what Cochrane is stating there. He states that the overall utility $U$ is sum of present utility of consumption $u_t(c_t)$ and expected utility of future consumption $E_t(u_{t+1}(c_{t+1}))$. Is it non-standard? Yes! Does it offend my sense of aesthetics? A bit. Is it Incorrect? I don't think that it is incorrect to have composite utility function which is sum of present utility that is known and expected utility from future consumption - I consider it less elegant as just having $E[U]$ but I would not go as far as saying its nonsense. | |
| Feb 22, 2021 at 16:38 | comment | added | Richard Hardy | @1muflon1, it is weird and I think incorrect to say someone's utility is a function of consumption today and expected consumption tomorrow. People do not derive utiity from expected vaules of consumption, only from actual consumption. In that sense I think it is justifiable to have a harsh comment. | |
| Feb 22, 2021 at 16:02 | comment | added | 1muflon1♦ | I agree that this comes to the stylistic choice, but I also think previous comment is bit too harsh saying it does not make sense. It is like saying using sing $2 \cdot 5$ and calling it a product of integer is more/less correct than using 10 and calling it integer. To be clear most of the literature would use the RHS and write it as $E_t[U]$ instead of LHS $U(u_t,E_t(u_{t+1}))$, but due to expectations being applied only to the argument it could be called just utility with $u_{t+1}$ being expected utility even when it’s completely equivalent to having expected utility of whole function | |
| Feb 22, 2021 at 13:42 | comment | added | Michael Greinecker | The theory here uses expected utility. Not all authors are equally careful when it comes to formal details. | |
| Feb 22, 2021 at 13:38 | comment | added | Richard Hardy | I will probably discover the answer somewhere later in the book, but I found the discrepancy between the language/text and the formulas quite striking. | |
| Feb 22, 2021 at 13:37 | comment | added | Michael Greinecker | This seems to be more a question about Mr. Cochrane and his stylistic choices than about economics. But the right-hand side is clearly expected utility, and the left-hand side does not make much sense- but is not used anyways. | |
| Feb 22, 2021 at 13:36 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| Feb 22, 2021 at 12:19 | history | asked | Richard Hardy | CC BY-SA 4.0 |