5 votes
Accepted

Stochastic AK model derivation

I think you may substitute it directly as mentioned? $$v(A,k) = \max log(c) + \beta E[v(A',k')|A]$$ Applying the value function expression (note period change): $v(A',k') = \frac{log(k')}{1-\beta} + v(...
qwerty's user avatar
  • 517
3 votes
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Bayes’ rule in "The sources of capital misallocation"

It follows immediately from Bayesian Updating using Bayes Rule for normal random variables. You can find derivations in e.g. Baley/Veldkamp (2021): Bayesian Learning See also the related answer at ...
jpfeifer's user avatar
  • 529
3 votes
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Bond Price expression

If $ \delta > 0 $ is very small, then the interest incurred during the small subperiod $[t, t + \delta]$ can be approximated using the simple interest formula. More specifically, the interest ...
user141240's user avatar
3 votes

Limit of random walk auto correlation function

Hi: The expression tends to 1.0. The intuition is that, as $t$ gets larger and larger, the $h$ lags that seperate the two processes become more and more negligible and the processes begin to look the ...
mark leeds's user avatar
3 votes

Application of Poisson process in economic modelling

Klette and Kortum (2004) develop a parsimonious model of innovating firms rich enough to confront firm-level evidence. It captures the dynamics of individual heterogenous firms, describes the behavior ...
emeryville's user avatar
  • 6,935
3 votes
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Purpose of Semidefinite Integral

It is just an opaque way to denote that the non-definite integration limit will take the value of the variable itself. Namely, $$\int_a g(x) dx \equiv \int_a^x g(s)ds$$ ... where $s$ is just the ...
Alecos Papadopoulos's user avatar
2 votes
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Profit maximization under uncertainity

Let $G$ be the cumulative distribution function for the buyers' willingness to pay. If there is no cost, expected profit is simply expected revenue. The revenue is quantity times price. If the unit of ...
Michael Greinecker's user avatar
2 votes

Given $\mathbb Q$ and $X_t$ is $\mathbb Q$-Brownian, find $\frac{d\mathbb Q}{d\mathbb P}$ / Uniqueness of Brownian or Radon-Nikodym derivative

As you say (how did $\sin t$ in the initial problem become $\cos t$?), $\mathbb{Q}$ is a measure under which $W_t$ becomes $\tilde{W}_t - \sin t$, where $\tilde{W}_t$ is a $\mathbb{Q}$-Brownian motion....
Michael's user avatar
  • 2,619
2 votes
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Decomposition of an additive functional into a Martingale part and other

Using the given formulas (inserting the expression for the $X$'s in the sum), we arrive at $$Y_t = (1-\beta_0)\alpha_0\cdot t + \beta_0\sum_{j=0}^{t-1}X_j +\sum_{j=1}^{t}W_j $$ We do not need a ...
Alecos Papadopoulos's user avatar
2 votes
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Are overlapping generation (OLG) models extensions of a DSGE model?

You can find OLG models that do not classify as DSGE (in particular, the model might not be stochastic) as well as DSGE with overlapping generations (contrary to those with infinitely lived agents). ...
Ali's user avatar
  • 852
2 votes
Accepted

Is playing against state of nature considered Stochastic game or Bayesian game?

To me, Bayesian games are usually "static" in the sense that no "time" is involved. The state is drawn once, and players make decisions, possibly sequentially, and the outcome is ...
Herr K.'s user avatar
  • 15.4k
1 vote

Granger-Sims causality and subtle differences

Let $\mathbf{X}$ be conditionally iid on $\{0,1\}$ with distribution $(P,1-P)$, with $P$ being a nontrivial random variable. Let $Y_t=\limsup_{T\to\infty} T^{-1}\sum_{i=1}^TX_{t-i}$. Then $\textbf{X}\...
Michael Greinecker's user avatar
1 vote

Stochastic optimal control problem (calculus)

I think there should be a minus before the final term in the expression you are looking for. In any case, you did not plug in the optimality condition for $w$, which is in your case $$ w = -\frac{V'(A)...
Wittgenstein's Poker's user avatar
1 vote

Derivation of autocovariances Lewis (2021) RES

A useful implication of conditional mean independence is: $E[\varepsilon_{it}|\varepsilon_{ks}]=0 \implies E[\varepsilon_{it}\varepsilon_{ks}]=0,$ and more generally, $E[\varepsilon_{it}|\varepsilon_{...
Bertrand's user avatar
  • 3,351
1 vote
Accepted

Expectational stability: adaptive learning of RE equilibria in dynamic systems

These are many questions. O.k., so let's go step by step: (Q1) What is a mapping actually? A map is just another term for a function. Here, every "law of motion", the actual one (ALM) and the ...
VARulle's user avatar
  • 6,805
1 vote

Autocorrelation function of a random walk process

By recursive substitution you obtain $y_t = \sum_{j=0}^t e_{t-j}.$ Thus $\forall p \in \mathbb{N} \hspace{.2cm} y_{t-p} = \sum_{j=0}^{t-p} e_{t-p-j}.$ Under the usual white noise assumption for the ...
Grada Gukovic's user avatar
1 vote

Decomposition of an additive functional into a Martingale part and other

Usually additive functionals are defined for (strong) Markov processes with continuous sample paths (diffusions) but I suppose you do have a Markov---AR(1)---time series and $\{ Y_t \}$ is indeed ...
Michael's user avatar
  • 2,619

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