7 votes
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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 $$\frac{x_i}{x_j} = \left( \frac{\alpha_i}{\alpha_j}\frac{p_j}{p_i} \right)^\sigma $$ ...
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  • 2,527
6 votes
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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 ...
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  • 8,737
5 votes
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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 \...
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5 votes
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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
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  • 445
5 votes
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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 ...
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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 ...
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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 ...
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  • 3,247
4 votes
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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 ...
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3 votes
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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 ...
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  • 8,737
3 votes
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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 ...
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  • 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 ...
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  • 7,685
3 votes
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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 ...
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  • 4,138
3 votes
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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 ...
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  • 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 ...
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2 votes

Choosing Data for CES Production Function

The Penn Wolrd Tables have the data you need.
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2 votes
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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 $...
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  • 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 ...
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  • 2,527
2 votes
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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 \...
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  • 2,527
2 votes
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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 ...
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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 ...
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1 vote
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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 ...
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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 ...
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  • 2,330
1 vote
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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} + ...
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