7
votes
Accepted
Estimating CES utility (not production) function parameters
It may be interesting to exploit the homothetic separability of the CES utility function in $x$. It implies that
$$\frac{x_i}{x_j} = \left( \frac{\alpha_i}{\alpha_j}\frac{p_j}{p_i} \right)^\sigma $$
...
- 2,527
6
votes
Accepted
Confusing on the CRS Property of CES Function
Consider the function $f(K,L) = [\alpha K^\rho + \beta L^\rho]^{1/\rho}$. We want to evaluate the limit of $f$ when $\rho \to 0$.
$$
\lim_{\rho \to 0} f(K,L) = \lim_{\rho \to 0} [\alpha K^\rho + \beta ...
- 8,737
5
votes
Accepted
Convex CES Aggregator
Let $N=\max\{N_1,\ldots, N_J\}$ and $\sigma<0$.
$$N=\left[N^{(\sigma-1) / \sigma}\right]^{\sigma /(\sigma-1)}\leq\left[\sum_{j=1}^{J} N_{j}^{(\sigma-1) / \sigma}\right]^{\sigma /(\sigma-1)}\leq \...
- 9,415
5
votes
Accepted
Is there a name for this type of CES look-alike utility function?
I believe it can be found as "nested CES"
See for example:
Nested CES
- 445
5
votes
Accepted
How to prove a generalised function is quasiconcave?
Note first that the function $r\mapsto A(r)^{\mu/p}$ is strictly increasing on $\mathbb{R}_+$. When you look at the minimum in the definition of quasi-concavity, you can therefore ignore this part and ...
- 9,415
5
votes
Estimating CES utility (not production) function parameters
This answer closely follows the logic of estimation of translog cost function presented in Section 4.7 of Fumio Hayashi's "Econometrics".
Define for convenience the CES aggregate price index ...
- 215
4
votes
Estimating CES utility (not production) function parameters
In this comment I simply show that
Under certain assumptions the problem is not an estimation problem, there is an exact solution for $\sigma$ and a solution for the structural errors $\alpha_i$ up ...
- 3,247
4
votes
Accepted
Bellman equation corresponding to stochastic EZW recursive utility
What you have there are the preferences under an arbitrary policy -- what some call the prevalue function. The only thing missing is the max operator. Written with maximization (and making the state ...
3
votes
Accepted
The Intuition of CES Utility
This is going to be a long answer, and I'm not completely sure if it is going to answer your questions as I'm mostly going to focus on the derivations of the own and cross price elasticities. Most of ...
- 8,737
3
votes
Accepted
CES utility function in an Edgeworth box
There seems to be some confusion in the expression for $x^*_i$ in the question that whether $i$ is for consumer of for the good. Assuming $i$ is for consumer:
Let $x^*_i = (x_1^i,x_2^i)'$ be the ...
- 1,630
3
votes
Estimating CES utility (not production) function parameters
These other answers seem to be citing some methods I haven't quite heard about yet however they all touch upon the idea developed by Czech economist named Jan Kmenta which has come to be known as the ...
- 7,685
3
votes
Accepted
CES production function profit and supply function
Hint: Solving for the FOC's assumes that the solution is interior, in this case, that profits are positive and smaller than $\infty$. I would recommend you to derive the cost function $c(y)$ and then ...
- 4,138
3
votes
Accepted
Cobb-Douglas nested in CES model
Think of your function as
$$Y=[A_1Q^\sigma+ A_2X^\sigma]^{1/\sigma}$$
where $Q=L^\alpha K^\beta$ (I removed unnecessary bits like $\gamma$ and exponent of $A_i$). This is a standard CES, where the ...
- 8,437
2
votes
CES function estimation
You should always validate statistically your model, running various model diagnostics. It appears you work with time series (single country?).
Here, certainly autocorrelation may be an issue. After ...
- 31.8k
2
votes
2
votes
Accepted
Nested/Recursive Dynastic Utility Functions
Let $\delta_i=N_i\beta_i$. I think what you want is for generation $i$'s utility to be something like:
\begin{equation}
U_i=u(x_i)+\delta_{i+1}U_{i+1}+\cdots+\delta_{i+n}U_{i+n},
\end{equation}
where $...
- 14.3k
2
votes
Nested/Recursive Dynastic Utility Functions
Here are two nice papers on recursive utility functions, a generalization of additive utility functions and compatible with "utility of the dynastic head to be partly a function of the utility of ...
- 2,527
2
votes
Accepted
Homogeneous Utilities: Anything other than CES?
There is an infinity of such functions. You can for instance construct a linear homogeneous function $u$ from any utility function $U$ by using a linear homogeneous function $h: \mathbb{R}^J \...
- 2,527
2
votes
Accepted
Non CES Production Functions
(1) why is imposing CES so important in our models?
Because although its relatively quite general (relatively to some other widely used production functions like Cobb-Douglas - which is a special ...
- 41.6k
1
vote
A utility function (neither perfect substitues nor perfect complements) which stems from a CES f. and leads to gross complements or gross substitutes
We can show if a utility function exhibits complementarity or substitutability just from its function, without having any information about prices. The utility function gives information about the ...
1
vote
Accepted
Can you set $C / P^{\eta}$ to be the numeraire in a NK model?
I'm going to answer my own question. Consider multiplying all prices and income (i.e., the wage) by a common factor $\lambda>0$. The new ideal price index is just $P' = \lambda P$. The new wage is ...
- 31
1
vote
CES production function application problem
Your y2 needs to be the output associated produced with those inputs. Given that you have a CES production function and you use World Bank Country data as inputs, you need output of the countries in ...
- 2,330
1
vote
Accepted
Nested CES Production Function
Consider the CES production function over four goods defined as follows:
$$ x = (\alpha j^{\gamma} + k^{\gamma})^{1/\gamma}$$
$$ y = (\delta l^{\beta} + m^{\beta})^{1/\beta }$$
$$ z = (\zeta x^{\xi} + ...
- 15.9k
Only top scored, non community-wiki answers of a minimum length are eligible