translogMonoRestr: Monotonicity Restrictions of a Translog Function

Description

Create matrix to check or impose the monotonicity restrictions of a translog function.

Usage

translogMonoRestr( xNames, data,
   dataLogged = FALSE, box = FALSE )

Value

translogMonoRestr returns a matrix of dimension

$( n \cdot N ) \times c$, where $n$ is the number of independent varables,

$N$ is the number of data points at which monotonicity should be imposed (if argument box is FALSE,

$N$ is the number of rows in data; if argument box is TRUE, $N = 2^n$), and $c = 1 + n ( n + 3 ) / 2$ is the number of (linearly independent) coefficients. Multiplying a row of this matrix (e.g.\ the $k$th row of $M$) by the vector of coefficients ($\beta$) results in the derivative of the dependent variable ($y$) with respect to one independent variable (e.g.\ $x_i$) at one data point (e.g.\ $j$):

$$M[k,] \cdot \beta = \frac{ \partial \ln y }{ \partial \ln x_i}$$, evaluated at $x_{1j}$, ..., $x_{nj}$, where $k = ( i - 1 ) N + j$. Hence, the observations run faster than the independent variables.

Arguments

xNames: a vector of strings containing the names of the independent variables.
data: dataframe containing the data.
dataLogged: logical. Are the values in data already logged?
box: logical. Should monotonicity be imposed within an $n$-dimensional box that includes all points in data? If FALSE, monotonicity is imposed (only) within an $n$-dimensional polygon that includes all points in data. ($n$ is the number of independent varables.)

Author

Arne Henningsen

Examples

Run this code

   data( germanFarms )
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput

   # matrix to check or impose monotonicity at all observations
   monoRestrObs <- translogMonoRestr( c( "qLabor", "land", "qVarInput" ),
      germanFarms )

   # matrix to check or impose monotonicity within a box that includes all 
   # observations
   monoRestrBox <- translogMonoRestr( c( "qLabor", "land", "qVarInput" ),
      germanFarms, box = TRUE )