# summary.cesEst: Summarize Estimation of a CES Function In micEconCES: Analysis with the Constant Elasticity of Substitution (CES) function

## Description

`summary` method for objects of class `cesEst`.

## Usage

 ```1 2 3 4 5``` ```## S3 method for class 'cesEst' summary( object, rSquaredLog = object\$multErr, ela = TRUE, ... ) ## S3 method for class 'summary.cesEst' print( x, ela = TRUE, digits = max(3, getOption("digits") - 3), ... ) ```

## Arguments

 `object` an object returned by `cesEst`. `rSquaredLog` logical. If `FALSE` (the default for models with additive error term), the returned R^2-value measures the fraction of the explained variance of the dependent variable in natural units. If `TRUE` (the default for models with multiplicative error term), the returned R^2-value measures the fraction of the explained variance of the logarithmized dependent variable. `ela` logical. If `TRUE` (the default), the `summary` method calculates the (co)variances of the constant elasticities of substitution and the `print` method prints these elasticities together with corresponding summary statistics. If `FALSE`, the `summary` method does not calculate the (co)variances of the constant elasticities of substitution and the `print` method does not print these elasticities. `x` an object returned by `summary.cesEst`. `digits` number of digits. `...` further arguments are currently ignored.

## Value

`summary.cesEst` returns a list of class `summary.cesEst` that contains the elements of the provided `object` with with following changes or additions:

 `coefficients` a matrix with four columns: the estimated coefficients/parameters of the CES (including a possible fixed rho), their standard errors, the t-statistic, and corresponding (two-sided) P-values. `sigma` square root of the estimated (asymptotic) variance of the random error (calculated without correcting for degrees of freedom). `r.squared` R^2-value, i.e. the ‘fraction of variance explained by the model’. If argument `rSquaredLog` is `TRUE`, the R^2-value measures the fraction of the explained variance of the logarithmized dependent variable. `vcov` covariance matrix of the estimated parameters (including a possible fixed rho). `ela` a matrix with four columns: the estimated elasticities of substitution, their standard errors, the t-statistic, and corresponding (two-sided) P-values (only if argument `ela` is `TRUE`). `elaCov` covariance matrix of the estimated elasticities of substitution (only if argument `ela` is `TRUE`).

## Author(s)

Arne Henningsen

`cesEst` and `cesCalc`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ``` data( germanFarms, package = "micEcon" ) # output quantity: germanFarms\$qOutput <- germanFarms\$vOutput / germanFarms\$pOutput # quantity of intermediate inputs germanFarms\$qVarInput <- germanFarms\$vVarInput / germanFarms\$pVarInput ## CES: Land & Labor cesLandLabor <- cesEst( "qOutput", c( "land", "qLabor" ), germanFarms ) # print summary results summary( cesLandLabor ) ```