cesModel: Fitting CES models
In EconModels/MacroGrowth: Economics Models

Description Usage Arguments Value Note Examples

This function fits a CES model with 2 or 3 factors of production. In principle, the CES model can handle up to 4 factors of production, but this is not supported by cesModel() at this time.

cesModel(formula, data, response, x1 = NULL, x2 = NULL, x3 = NULL,
  x4 = NULL, time = NULL, nest = 1:3, prevModel = NULL,
  algorithms = c("PORT", "L-BFGS-B"), multErr = TRUE, rho = c(9, 2,
  1, 0.43, 0.25, 0.1, -0.1, -0.5, -0.75, -0.9, -0.99), rho1 = c(9, 2, 1,
  0.43, 0.25, 0.1, -0.1, -0.5, -0.75, -0.9, -0.99), digits = 6,
  save.data = TRUE, constrained = TRUE, fitBoundaries = TRUE, ...)

`formula`	a formula of the form `response ~ a + b + c + d + time`. `c` and `d` are optional. The use of `d` had not yet been implemented.
`data`	a data frame, in which to evaluate the formula.
`response`	instead of specifying a formula, expressions for the components can be specified individually.
`x1`	instead of specifying a formula, expressions for the components can be specified individually as character strings.
`x2`	instead of specifying a formula, expressions for the components can be specified individually as character strings.
`x3`	instead of specifying a formula, expressions for the components can be specified individually as character strings.
`x4`	instead of specifying a formula, expressions for the components can be specified individually as character strings. Currently only 2 or 3 factors of production are supported. This is a placeholder for potential expansion of the package.
`time`	instead of specifying a formula, expressions for the components can be specified individually as character strings.
`nest`	a permutation (a,b,c,d) of the integers 1 through 4. For models with 3 factors, the nesting is (xa + xb) + xc. For 4 factors, the nesting is (xa + xb) + (xc + xd)
`prevModel`	a model used to start a gradient search. `prevModel` will be used as a starting point for a gradient search after both (a) grid search in `rho` and `rho1` and (b) a gradient search starting from the best grid search are complete. #' Use `NULL` (the default value) if you want to skip the gradient search from a previous model.
`multErr`	logical, tells whether errors are to be assessed in a multiplicative manner
`rho, rho1`	creates a grid upon which gradient searches in all other (free) parameters will be made. (I.e., when `rho` and/or `rho1` are specified, the algorithm performs gradient searches in the `scale` parameter, `lambda`, `delta`, and `delta1` (if 3 factors of production are given) with `rho` and `rho1` fixed.) Note that the default arguments for both `rho` and `rho1` include the value 0.25. 0.25 is also the starting value for both `rho` and `rho1` used by `cesEst` for gradient searches when `rho` and `rho1` are unspecified. Thus, if you accept the default arguments, there is no need to do an additional `cesEst` gradient search with `rho` and `rho1` unspecified. (`rho = 0.25` corresponds to `sigma = 0.8`.) After the grid search, a gradient search is performed in which all parameters are free (including `rho` and `rho1`), starting from the best grid search point.
`digits`	the number of sse digits that is to be considered significant when comparing one fit against another.
`save.data`	a logical indicating whether data is to be saved with the model. Be sure to set `TRUE` if resampling is needed later. Default is `TRUE`.
`constrained`	a logical indicating whether the parameters should be constrained in the fitting process. Default is `TRUE`.
`fitBoundaries`	a logical indicating whether fits should be performed along boundaries. Default is `TRUE`.

a cesEst model with additional information attached as attributes.

For now the components in f (or the arguments response, x1, x2, x3, x4, and time) must correspond to variables in data and may not be other kinds of expressions.

For now, this function works for only 2 or 3 factors of production. Setting the value of x4 or using f of the form y ~ a + b + c + d + time will not work.

if (require("EconData") & require("dplyr")) {
  cesModel(iGDP ~ iK + iL + iQp + iYear, data = filter(Calvin, Country=="US"), nest = c(1,2,3))
  cesModel(iGDP ~ iK + iL + iQp + iYear, data = filter(Calvin, Country=="US"), nest = c(2,3,1))
  cesModel(iGDP ~ iK + iL + iQp + iYear, data = filter(Calvin, Country=="US"), nest = c(3,1,2))
  cesModel(iGDP ~ iK + iL + iQp + iYear, data = filter(Calvin, Country=="ZM"), nest = c(3,1,2))
  cesModel(response="iGDP", x1="iK", x2="iL", x3="iQp", time="iYear",
           data = filter(Calvin, Country=="ZM"), nest = c(3,1,2))
}