# snqProfitImposeConvexity: Imposing Convexity on a SNQ Profit function In micEconSNQP: Symmetric Normalized Quadratic Profit Function

## Description

Imposing Convexity on a Symmetric Normalized Quadratic (SNQ) Profit function.

## Usage

 ```1 2 3``` ```snqProfitImposeConvexity( estResult, rankReduction = 0, start = 10, optimMethod = "BFGS", control = list( maxit=5000 ), stErMethod = "none", nRep = 1000, verbose = 0 ) ```

## Arguments

 `estResult` object returned by `snqProfitEst`. `rankReduction` an integer specifying the reduction of the rank of the β matrix. `start` starting values of the triangular Cholesky matrix. `optimMethod` method to be used by `optim`. `control` list of control parameters passed to `optim`. `stErMethod` method to compute standard errors, either 'none', 'resample', 'jackknife' or 'coefSim' (see details). `nRep` number of replications to compute the standard errors if `stErMethod` is either 'resample' or 'coefSim'. `verbose` an integer idicating the verbose level.

## Details

The procedure proposed by Koebel, Falk and Laisney (2000, 2003) is applied to impose convexity in prices on an estimated symmetric normalized quadratic (SNQ) profit function.
The standard errors of the restricted coefficients can be either calculated by bootstrap resampling ('resampling'), jackknife ('jacknife') or by simulating the distribution of the unrestricted coefficients using its variance covariance matrix ('coefSim').

## Value

a list of class `snqProfitImposeConvexity` containing the same objects as an object of class `snqProfitEst` and additionally the objects:

 `mindist` object returned by `optim`. `sim` results of the simulation to obtain the standard errors of the estimated coefficients.

Arne Henningsen

## References

Koebel, B., M. Falk and F. Laisney (2000), Imposing and Testing Curvature Conditions on a Box-Cox Cost Function. Discussion Paper No. 00-70, ZEW, Mannheim, ftp://ftp.zew.de/pub/zew-docs/dp/dp0070.pdf.

Koebel, B., M. Falk and F. Laisney (2003), Imposing and Testing Curvature Conditions on a Box-Cox Cost Function. Journal of Business and Economic Statistics, 21, p. 319-335.

`snqProfitEst`.
 ``` 1 2 3 4 5 6 7 8 9 10``` ``` data( germanFarms, package = "micEcon" ) germanFarms\$qOutput <- germanFarms\$vOutput / germanFarms\$pOutput germanFarms\$qVarInput <- -germanFarms\$vVarInput / germanFarms\$pVarInput germanFarms\$qLabor <- -germanFarms\$qLabor priceNames <- c( "pOutput", "pVarInput", "pLabor" ) quantNames <- c( "qOutput", "qVarInput", "qLabor" ) estResult <- snqProfitEst( priceNames, quantNames, "land", data = germanFarms ) estResult # Note: it is NOT convex in netput prices estResultConvex <- snqProfitImposeConvexity( estResult ) estResultConvex # now it is convex ```