Questions tagged [academic-graduate]

Expert level questions which do not arise prior to graduate studies in economics.

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15
votes
0answers
416 views

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 ...
13
votes
1answer
318 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 ...
13
votes
1answer
421 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. \...
12
votes
2answers
3k views

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 ...
12
votes
1answer
679 views

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 ...
11
votes
6answers
1k views

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, ...
11
votes
2answers
970 views

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 ...
9
votes
1answer
1k views

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 ...
9
votes
1answer
442 views

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 ...
8
votes
3answers
991 views

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 $A$. ...
8
votes
2answers
604 views

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 ...
8
votes
1answer
326 views

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 ...
7
votes
2answers
204 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 ...
7
votes
3answers
131 views

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 (...
6
votes
2answers
164 views

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, ...
6
votes
2answers
277 views

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 ...
6
votes
1answer
105 views

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 ...
6
votes
1answer
151 views

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, ...
6
votes
1answer
118 views

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 ...
6
votes
1answer
243 views

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 ...
6
votes
0answers
211 views

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 ...
5
votes
1answer
321 views

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 ...
5
votes
2answers
548 views

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 ...
5
votes
1answer
129 views

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} ...
5
votes
0answers
95 views

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 ...
4
votes
2answers
667 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 ...
4
votes
3answers
153 views

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 ...
4
votes
3answers
226 views

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 ...
4
votes
1answer
1k views

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
votes
2answers
262 views

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.
4
votes
1answer
80 views

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 ...
4
votes
1answer
150 views

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}{\...
4
votes
1answer
82 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 ...
4
votes
1answer
109 views

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 ...
4
votes
1answer
76 views

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. ...
4
votes
1answer
142 views

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 ...
4
votes
2answers
193 views

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})+\...
4
votes
1answer
170 views

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 ...
4
votes
1answer
57 views

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 ...
3
votes
2answers
499 views

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
votes
1answer
314 views

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" ...
3
votes
1answer
1k views

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 ...
3
votes
2answers
328 views

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?
3
votes
1answer
71 views

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 ...
3
votes
1answer
44 views

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 ...
3
votes
1answer
50 views

What is the difference between a power law exponent and the Pareto exponent?

I use the poweRlaw package in R to fit a power law to my data. I am trying to figure out what is the value of the Pareto exponent. Assume the probability mass function is defined by: $$ p(x) = \...
3
votes
1answer
103 views

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 ...
3
votes
0answers
95 views

Solving this system of ODE

I have the following system of equations $$ \rho V(u, \epsilon^i) = F(u, \epsilon^i) + V_u(u, \epsilon^i)g(u, V(u, \epsilon^i) + \lambda^i \left(V(u, \epsilon^{-i}) - V(u, \epsilon^i)\right)$$ with $...
2
votes
1answer
94 views

A general formulation to capture price stickiness

In Wickens' macro book, page 227 (1st edition), the author states where $p^*_t$ is the optimal price at time $t$. The three theories he is referring to are: Taylor Model of Overlapping contracts, ...
2
votes
0answers
182 views

Hot Topics in Labor-Macro

I'm interested in currently hot research topics within Labor Macro. I'm only aware of the debate on the recent shift in the US Beveridge curve, and, of course, the olden but golden Shimer puzzle. ...