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2

First, a caveat: I'm on the job market this year in the midst of the couple weeks when calls are rolling in. Hence, this seemed like a nice way to kill some time (semi-)productively. This is also a disclaimer in case I've made an error :) Now, let's look at the one you're suggested to try for, where player $1$ chooses $0$ with $p$ and $1$ with $1-p$. Again ...


1

Captive insurance is an insurance for purpose of insuring the owners of the said insurance. It’s a kind of self-insurance where multiple agents pool their capital together to insure themselves. So the term in that sentence refers to the pool of resources for insurance. It’s called captive because the modern concept of this kind of insurance was first ...


-1

Us coal follows a hubbert curve and seems to cause btoh 1930 and 08...


1

Well resource depletion could create recession as it could reduce the productive capability of economy. For example, if oil would suddenly run out tomorrow it would definitely cause supply side shock that would result in recession. Rather, the fallacy behind resource depletion scare is the resource depletion itself. For example, more oil is available now ...


5

One interpretation I can offer. The demand function can be expressed as: $$Q_1 = Q_1(p_1,p_2)$$ Let us take the total differential: $$dQ_1 = \frac{\partial Q_1(p_1,p_2)}{\partial p_1}dp_1+\frac{\partial Q_1(p_1,p_2)}{\partial p_2}dp_2$$ Assume that $Q_1$ remains unchanged with respect to a change in prices. This implies that $dQ_1=0$. Solving the ...


1

If GDP is measured (as it usually is) for a period such as a year, then number of hours worked ($h$) should be measured for the same period. Thus $h$ is dimensionless and the dimension of the right hand side is also value / time.


3

Rationality requires the following: Completeness For all $x, y \in X$, either $x \succsim y$ or $y \succsim x$ or both. Transitivity For all $x, y, z \in X$, if $x \succsim y$ and $y \succsim z$, then $x \succsim z$. Also note that if $x=y$ then completeness implies that $x\succsim x$. So reflexive preferences follow from completeness. So I would say ...


3

Reduced form is a regression of dependent variable on instrument directly without using some two stage approach. Consider the following example of endogenous system Second Stage: $$Y = \alpha + \beta X + \epsilon$$ First Stage: $$X = \mu + \gamma Z+ \eta $$ Where $Y$ is dependent variable $X$ endogenous regressor and $Z$ is your instrument. One ...


2

I am not an econometrician so this will be a very informal explanation how to get the Instrumental Variable (IV) estimates. Since $S_i$ is endogenous, $$\text{cov}(S_i,\epsilon_i)\neq0$$ We can think of it as having two components: $$S_i = v_i + u_i$$ Suppose, $\text{cov}(u_i,\epsilon_i) =0 $ and $\text{cov}(v_i,\epsilon_i)\neq0$. $v_i$ is the ...


3

FE logit requires the idiosyncratic errors to be IID across $i$ and $t$, quite a strong assumption. Also the regressors should be strictly exogenous, but it's the same for linear FE models. In your application, the fact that FE logit wouldn't converge will make a good argument against FE logit, and will satisfy some referees but not all. An important ...


6

Intuition Well, when $r$ is zero, you are just getting value $A$ per time unit, so total present value will be $A \cdot t$. The approximation You are asking about the approximation $$ \frac A {-r}(e^{-rt}-1) \approx A \cdot t. $$ This is equivalent to $$ \frac 1{rt}(1-e^{-rt}) \approx 1, $$ which is true for small $rt$ values. You can see this by taking ...


0

A pretty trivial assumption would do it: If the consumers preferences are strongly increasing, i.e. $$ x \succ_i y, \mbox{ if $x \geq y$ but $x \neq y$ }, $$ and unbounded for all $i$, then no $x$ can be an optimal bundle if $p \notin \mathbb{R}^C_{++}$ (assuming there are $C$ commodities). So zero price cannot arise in an Arrow-Debreu equilibrium.


0

For Bivariate Regression Your model would be : IQ = B0 + B1(Your Education) For Multiple Regression: You would use a correlation matrix/plot to do this. Basically it would give you a matrix with correlation values of all variables to each other 0 being none and 1 being perfect. This will also allow you to see the multicollinearity problem which is when ...


2

Your value function is as follows: $$ V_t[w] = \max_{c_t \in[0,w]} \left\{u(c_t) + \frac{1}{2}V_{t+1}[\alpha(w_t - c_t)] + \frac{1}{2}V_{t+1}[\beta(w_t-c_t)] \right\} $$ with the terminal condition $$ V_{T}[w_T] = \max_{c_T \in [0,w_T]} u(c_T) $$ So, we can solve this via backward induction. Clearly, at the final period $T$, since $u$ is monotonic, we ...


0

Assuming you are referring to the definition from the original Arrow & Debreu paper $x_i$ represents the units of good $x_i$ consumed. I would not call $Y$ technology, according to Arrow & Debreu $Y$ is set of production plans - so by that they mean production (which may make some assumptions on technological nature of the process). Also, from your ...


2

Remember that consistency describes how the estimator behaves in the limit as N asymptotically approaches infinity. Assuming no errors in your math up to this point, you need to consider how your error terms $U_i$ behave asymptotically as well.


1

What one needs are two facts: Scalarization/Sufficiency for Pareto Optimality Suppose the economy has finitely many agents $u_i$, $i = 1, \cdots, I$, with feasible allocations given by some $X \subset \mathbb{R}^I$. If $x = (x_1, \cdots, x_I) \in X$ solves the problem $$ \max_{x \in X} \sum_{i=1}^I \lambda_i u_i(x_i), $$ where $\lambda_i > 0$ for all $i$,...


1

This problem is quite specific to economics. The correct statement is: Proposition If $u(\cdot)$ is quasiconcave, strictly increasing, and continuous, then $\forall x$, there exists $p \gg 0$ and $w \geq 0$ such that $x \in x^*(p, w)$, where $x^*(p, w)$ is the Marshallian demand correspondence. Proof Quasiconcavity of $u$ means the upper-contour set $\...


2

Assumptions $1$ to $3$ are sufficient to obtain a linear representation when $X$ is open and convex. We proceed in two steps. Step $1$: We will repeatedely use the following consequence of continuity and $A1$: If $x \sim x^{\prime}$, then $x \sim x + \lambda (x^{\prime} - x)$ for every $\lambda \in \mathbb{R}$ such that $x + \lambda (x^{\prime} - x) \in X$....


0

Edit: My previous answer contained a mistake for the case where $x$ is restricted to $\mathbb{R}_{+}^{n}$. I removed this case from my answer. Take $\bar{U} > 0$. Let's denote $\delta = (\delta_{1}, \ldots, \delta_{n})$ and $p = (p_{1}, \ldots, p_{n})$. Assume $p \neq 0$. We want to solve \begin{align*} \min_{x\in\mathbb{R}^{n}} p \cdot x \qquad \text{...


0

The assumptions are that the agents understand the situation, model or game they are in, that they are rational - in economic sense of the word and try to maximize their utility. I think that one reason why you might have trouble finding a list of assumptions behind rational expectations is that rational expectations don’t really rely on their own ...


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