Questions tagged [academic-graduate]
Expert level questions which do not arise prior to graduate studies in economics.
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How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem?
How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem?
In Duffie's book "Dynamic Asset Pricing," he outlines the "Martingale method" of solving ...
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15
votes
1
answer
558
views
Stochastic growth in continuous time
Literature: See Chang (1988) for theoretical part and Achdou et
al. (2015) for numerical part respectively.
Model
Consider the following stochastic optimal growth problem in per capita notation.
\...
- 1,549
14
votes
1
answer
446
views
Barro's (2009) rare disaster model in the AER: How to derive equation (10)?
In Barro (2009) Rare disasters, asset prices and welfare costs Barro develops a Lucas tree model with Epstein-Zin preferences.
My question concerns the paper's equation (10). In this equation Barro ...
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12
votes
1
answer
1k
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Conventions for reading mathematically rigorous academic articles in economics
How would an informed reader typically go about reading a mathematically rigorous academic article in economics, with lots of notations, assumptions and postulations (e.g, a typical article published ...
- 419
12
votes
2
answers
3k
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What is the definition of a "Stackelberg leader-leader equilibrium"?
I have encountered the equilibrium concept of "Stackelberg leader-leader equilibrium" while reading Product Line Rivalry (AER, Brander and Eaton (1984). They say "we define a Stackelberg strategy as ...
- 123
12
votes
1
answer
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What are estimates of the elasticity of demand for credit with respect to interest rates?
When interest rates go up one percent (not one percentage point), what happens to demand for credit? I've only been able to find two papers in this area:
Gross and Souleles (2001) study credit cards ...
- 16.2k
11
votes
6
answers
2k
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Did previous researchers fail to detect the hot hand simply because of a statistical fallacy?
Many basketball fans/players believe that having made several shots in a row, the next shot is more likely to go in. This is sometimes called the hot hand.
Starting (I think) with Gilovich, Mallone, ...
user18
11
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2
answers
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Inflation and economic growth
Noticeable works about the impact of inflation on economic growth are dated back to the 90s.
For example, Barro (1995):
the impact effects from an increase in average inflation by 10 percentage ...
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10
votes
3
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1k
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Does risk aversion cause diminishing marginal utility, or vice versa?
Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
9
votes
1
answer
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Take-it-or-leave-it PBE
I've found an interesting question looking at perfect-bayesian-equilibrium. I haven't seen a question where beliefs are not discrete.
There is a single potential buyer of an object which has zero ...
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9
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1
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Piketty's Return on Capital
How exactly does Piketty et al's method (as in his book) for computing the interest rate over time and countries work?
I know that they use reported tax returns, and that some criticize them for also ...
- 10.6k
8
votes
2
answers
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Is there a way to link Berge's theorem of maximum to Envelope theorem?
Berge's theorem states
Let $X \in \mathbb R^m, \Theta \in \mathbb R^n $, $f : X \times \Theta \to \mathbb R$ be a jointly continuous function, $C : \Theta \rightrightarrows X$ be a continuous(both ...
- 441
8
votes
2
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312
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Solving Kaplan and Menzio: Shopping Time
Kaplan and Menzio's shopping time model is a search&matching unemployment model where we, for a steady state equilibrium, need to determine to variables:
$J$: Value of a worker
$u$: unemployment ...
- 10.6k
8
votes
1
answer
440
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Muth exposition of the rational expectations hypothesis
I am reading in statistical decision theory and stumbled upon the rational expectations literature (rationality with incomplete information->dynamic problem->N.L Stokey->husband). The assumption that ...
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1
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Optimal consumption in Merton-like portfolio choice model with constant wage
My Questions
Consider the following problem. It is almost identical to
the classic Merton portfolio choice problem. Here I'm solving it using
the so-called Martingale method. I have provided my ...
- 9,315
7
votes
2
answers
216
views
What is the usefulness of approximating an optimal decision rule that close enough to steadystate in RBC model?
I'm reading understanding real business cycle by Plosser.
Here's my crude understanding: For a RBC model, the FOCs of lagrangian together with transversality condition usually forms a nonlinear ...
- 441
7
votes
3
answers
143
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Interchangeability between knowing an event obtains with probability 1 and knowing an event obtains with absolute certainty?
In the literature of interactive epistemology, for a player, knowing an event obtains with probability one and knowing an event obtains with absolute certainty are different. Is there a nontrivial (...
- 1,416
7
votes
1
answer
236
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Splittet Value Function and Hamilton-Jacobi-Bellman equation
General Problem
Let $k\in\mathbb{R}_+$ be the state variable, $k=k^*$ a fixed point (saddle) and $v(k)$ a value function. The problem is, that the value function has two distinct functional forms, ...
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Has any progress been made on the Pacman Conjecture on Finite Time Horizons?
The Pacman conjecture states that the optimal strategy for monopolistic durable goods manufacturers is to set price high and slowly drop it (i.e. eating their way down the demand curve).
Empirically ...
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3
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Does julia's speed advantage over python make any difference for DSGE modeling?
When compared to Python the main selling point of Julia is its speed as it is often argued. However, from my own personal experience I never noticed any significant difference in speed between Julia ...
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6
votes
2
answers
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Are there conventions in economics for coding the distance between states?
I know there are lots of gravity models in economics that take as an input distance between countries. My understanding is distance is typically coded based on the distance between capital cities, ...
- 16.2k
6
votes
1
answer
246
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Optimal price function: application of calculus of variations
The problem, I am trying to solve is based on the paper by Rochet and Vila 1994 (see literature below). In fact, it is a variant of the seminal paper of Kyle 1985 in the finance/economics literature. ...
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Is there any article or paper that describes what Thomas Sargent thinks of New Keynesian economics/models?
Is there any article or paper that describes what Thomas Sargent thinks of New Keynesian economics/models?
I am asking this question, because we all know what Thomas Sargent thinks of Old Keynesian ...
- 61
6
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1
answer
271
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Solving Leeper (1991) model
I am attempting to solve a variation of Leeper's (1991) model, which deals with the FTPL. This is what I have done so far:
The utility function is $\log(c_t)+\delta\log(M_t/p_t)$.
I obtain two ...
- 61
6
votes
1
answer
139
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Gali and van Rens: The Vanishing Procyclicality of Labor Productivity
Let's see how questions like the following are taken here.
Gali and van Rens, 2014 show that empirically, the correlation between $Y, Y/L$ has been declining over time. In fact, it only was a "real ...
- 10.6k
5
votes
1
answer
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Learning post-keynesian and marxist economics
My question here is not about theory, but more about the teaching landscape. I'm currently learning economics in Canada, and I realize that the academic world is very homogeneous. I'm quite impressed ...
5
votes
1
answer
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If $a$ and $b$ are two pure rationalizable strategies, can $0.5a+0.5b$ fail to be a rationalizable strategy?
It is easy to see that if $\sigma$ is mixed rationalizable strategy, then a pure strategy $a$ such that $\sigma(a)>0$ is also rationalizable, but it seems not vice versa.
For a two-player finite ...
- 1,416
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Housing Supply Elasticity: Proxy for Exogenous House Price Movements
Mian and Sufi (2014) say
We use individual and zip code level data, and exploit cross-sectional variation in house price growth to estimate the impact of rising home values on borrowing and ...
- 10.6k
5
votes
2
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745
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One-shot deviation principle for infinite repeated games and dynamic programming
In a context that future return is discounted by a constant parameter, one-shot deviation principle holds for both repeated games and dynamic programming.
Because, in repeated games, a one-shot ...
- 1,416
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1
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How to write the dual problem of this maximization problem?
On this note for Shapley-Shubik model, there's a maximization problem:
$$\max_{x_{ij} \in \mathbb{R}^{M \times N}}\sum_{j \in N}\sum_{i \in M}v_{ij}x_{ij}$$
$$\text{s.t.} \ \sum_{j \in N}x_{ij} \...
- 1,416
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0
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103
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Can repeated bidding in an auction make each player's type common knowledge?
In Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007), there's a hand-waving argument to justify their setting as a game of complete information:
we assume that all values are common
...
- 1,416
4
votes
2
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706
views
Why are some economists remarkably productive?
I'm a first year PhD student and I randomly go to different professors' websites to admire their works. Usually an economist has around 20 published papers when he/she reaches professorship. But there ...
- 505
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3
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230
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How to close the gap between non-Econ background and Macroeconomics
I'm a first year PhD student with mathematical finance background, and am not quite familiar with all the assumptions/setup for macroeconomics. During study I found the math relatively easy but I'm ...
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1
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Doing a PhD Economics without background in formal theorems?
I could really use some advice. I am a new PhD student in Economics and Finance. My background is in economics, and while I did mathematics in my Master's course, it was more data-analysis based ...
4
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3
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Scaling Adjustment Costs
Take a cont. diff, convex and increasing cost function $c(X)$. Say you start with a stock $K$, and want to (dis)invest $I$. Many adjustment cost functions (for example, the first example on page 2 ...
- 10.6k
4
votes
2
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Is there a model for how much a philosopher produce in his lifespan?
Is there a model for how much a philosopher produce in his lifespan?
If not, state the economical reason for why we pay the philosopher.
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1
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Why does $\varepsilon_{x,p_x}^H =-s_y \sigma $?
Suppose I have two goods $x$ and $y$ and their associated prices $p_x$ and $p_y$. Income $m$. $x^H$ is Hicksian demand and $x^M$ is Marshallian demand.
Slutsky Equation:
$$\frac{\partial x^M}{\...
- 3,454
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votes
1
answer
90
views
Are there some nice properties for a finite two-player game having an increasing differences utility and a decreasing differences utility?
Nice properties of the set of Nash equilibria can be shown for supermodular games(see here). But for a two-player game in which
Strategy spaces for two player, $S_1$ and $S_2$ are finite, and both ...
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votes
1
answer
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What can we know for sure among ambiguous impulse responses in RBC?
I'm trying to understand the section on responses to productivity disturbances in Understanding Real Business Cycles by Plossor.
It seems to me ambiguity of representative agent's response in ...
- 441
4
votes
2
answers
289
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Solving rational expectations model - Sims form
I am trying to solve my first ratex model and make some impulse response functions using Dynare. I am following Leeper (1991). This is what I have done so far:
The utility function is $\log(c_{t})+\...
- 651
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1
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Markov decision processes, contractions and value iteration
I am reviewing Markov decision processes (MDP) and there is something I am missing with respect to the contraction argument. I am pretty sure it is a silly mistake somewhere (maybe computational), but ...
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1
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What's the status on uncertainty shocks?
Bloom (2009) analyzes the impact of uncertainty shocks, and Bloom et al (2014) propose a business cycle model based on these shocks.
It seems to be a young field, but is there any consensus on ...
- 10.6k
3
votes
2
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621
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Does there always exist a consumption bundle at which the indirect utility function is the inverse of the expenditure function?
Two questions:
Given $v(\vec{p},m)$ and $e(\vec{p},\bar{U})$, is there only a single point at which these are inverses of each other?
Does an inverse always exist for a given price vector $\vec{p}$,...
- 3,454
3
votes
1
answer
557
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What is an IOU?
I'm reading a paper right now that refers to divisible and one-period IOUs, but doesn't explain what the shorthand stands for.
I understand it's a unit of payment, and guess that is the same "thing" ...
- 10.6k
3
votes
1
answer
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Reverse auction formula
I am studing a little bit of auction theory. I found the optimal bid value in the Milgrom paper for the first price auction that is
$$
P=v \frac{n-1}{n}
$$
where $P$ is the optimal bid, $v$ is the ...
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2
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Using web scraped data for consumer price indices
Is there information and literature regarding comparative consumer price index methods? Specifically, the web scraping method of index construction?
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1
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Firm Sizes over the business cycle
There has been a lot of evidence about the firm size distribution (as measured in employment) being Pareto (see for example Luttmer 2007), but what are the properties of this distribution over the ...
- 10.6k
3
votes
1
answer
100
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Where to find the latest statistics of brain drain in the world?
Where to find the latest statistics of brain drain in the world?
I would appreciate your suggestions.
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1
answer
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Survival Rates of Firms
Jovanovic (1982) cites Du Rietz (1975) as a source for
Survival Rates of smaller firms are smaller than for larger firms
It's his doctoral thesis, and using Swedish data. Is there any recent ...
- 10.6k
3
votes
1
answer
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Value function iterations with hyperbolic discounting
I am currently working to the numerical solution of a model similar to the consumption-savings decision model with hyperbolic discounting as in Krussel et al. (2003).
Even if hyperbolic discounting ...
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