10 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 $$\frac{x_i}{x_j} = \left( \frac{\alpha_i}{\alpha_j}\frac{p_j}{p_i} \right)^\sigma $$ ...
Bertrand's user avatar
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8 votes

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 ...
tdm's user avatar
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7 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 ...
Konstantin's user avatar
6 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 ...
Jesper Hybel's user avatar
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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 \...
Michael Greinecker's user avatar
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 ...
Michael Greinecker's user avatar
5 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 ...
EconJohn's user avatar
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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
qwerty's user avatar
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4 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 ...
Dayne's user avatar
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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 ...
penGuinKeeper's user avatar
4 votes

CES production function: How to show that $\sigma < 1$ implies essentialness?

The problem is that, with an elasticity of substitution $\sigma<1$, in the CES production function we have negative exponents.$^1$ I rewrite your CES production function: $$Y = f(K, L) = (a \cdot K^...
BakerStreet's user avatar
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3 votes

Balanced growth path in the Hicks neutral technology and CES function

The problem is that, as in most cases for the Solow model, we don't know an explicit analytical solution of the differential equation for $k_t$, the so-called fundamental equation of growth, and in ...
BakerStreet's user avatar
  • 3,672
3 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 ...
1muflon1's user avatar
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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 ...
tdm's user avatar
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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 ...
Regio's user avatar
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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 ...
luchonacho's user avatar
  • 8,591
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 ...
Alecos Papadopoulos's user avatar
2 votes

Choosing Data for CES Production Function

The Penn Wolrd Tables have the data you need.
Alecos Papadopoulos's user avatar
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 $...
Herr K.'s user avatar
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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 ...
Bertrand's user avatar
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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 \...
Bertrand's user avatar
  • 3,351
2 votes

What is an example of utility function where the proportion of one goes to zero?

Consider quasi-linear utility function: $u(x_1,x_2)=2\sqrt{x_1}+x_2$ Here demand for $x_1$ is $x_1^d = \min(y, 1)$, and demand for $x_2^d = \max(0, y-1)$. Clearly, $\lim_{y\rightarrow\infty} \frac{...
Amit's user avatar
  • 8,456
2 votes

Tastes in Cobb-Douglas vs CES: Different degree of homogeneity

Consider the CES production function: $$ f(x_1, x_2) = (\alpha x_1^\rho + \beta x_2^\rho)^{1/\rho}. $$ The limit for $\rho$ going to zero of this function gives a Cobb-Douglas function: $$ g(x_1, x_2) ...
tdm's user avatar
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2 votes
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Tastes in Cobb-Douglas vs CES: Different degree of homogeneity

(I am adding another answer since the question has been reworded.) I think your question contains a misunderstanding which stems from your usage of the same parameter names $\alpha_1$ and $\alpha_2$ ...
VARulle's user avatar
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2 votes
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LSE EC417 2023: Markup as Elasticity Tends to Unity

A monopolist will always produce on the elastic part of the demand curve. The idea is the following: if the output level is on the inelastic pat of the demand curve, then increasing prices, by 1% will ...
tdm's user avatar
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1 vote

Cost function from a weighted CES production function

I'll use $(w_1, w_2)$ to denote the factor prices instead of $(p_1, p_2)$ as the latter is traditionally used for output prices. $c(w_1, w_2, y)$ solves the maximization problem: $$\max_{x_1, x_2 \ \...
uninterestedacademic's user avatar
1 vote

Are homothetic additively separable preferences always equivalent to CES?

The second to top "Related" question (What utility functions are equivalent to additive functions?) contained a link to Ted Bergstrom's Lecture Notes on Separable Preferences, which answered ...
cfp's user avatar
  • 252
1 vote

What is an example of utility function where the proportion of one goes to zero?

$U(x_1,x_2)=\min\{x_1^2,x_2\}$.
Michael Greinecker's user avatar
1 vote
Accepted

Elasticity of substitution by regression: Biased results (simulation)

I am answering my question because I have found the solution. The thing is: I have started with the wrong premise and therefore reached poor conclusion. Due to this I will edit the question a little ...
Athaeneus's user avatar
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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 ...
enthusiastic economist's user avatar

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