elasticity {dsfa}

R Documentation

elasticity

Description

Calculates and plots the elasticity of a smooth function.

Usage

elasticity(object, select = NULL, plot = TRUE, se = TRUE)

Arguments

object	fitted mgcv object with family comper() or comper_mv().
select	specifying the smooth function for which the elasticity is calculated. If term=NULL the elasticities for all smooths of \mu are returned (excluding random and spatial effects).
plot	logical; if TRUE, plots the elasticities. If FALSE, returns the average elasticity.
se	logical; if TRUE, adds standard errors to the plot of elasticities.

Details

Calculates the marginal product for parametric terms. For smooth terms the average of the derivative is calculated.

Value

If plot is TRUE, plots the elasticities specified in select of the provided object. If plot is FALSE returns a named vector of the elasticity of the provided inputs.

References

• Schmidt R, Kneib T (2023). “Multivariate distributional stochastic frontier models.” Computational Statistics & Data Analysis, 107796.

• Kumbhakar SC, Wang H, Horncastle AP (2015). A practitioner's guide to stochastic frontier analysis using Stata. Cambridge University Press.

• Aigner D, Lovell CK, Schmidt P (1977). “Formulation and estimation of stochastic frontier production function models.” Journal of econometrics, 6(1), 21–37.

• Meeusen W, van Den Broeck J (1977). “Efficiency estimation from Cobb-Douglas production functions with composed error.” International economic review, 435–444.

Examples

#Set seed, sample size and type of function
set.seed(1337)
N=500 #Sample size
s=-1 #Set to production function

#Generate covariates
x1<-runif(N,-1,1); x2<-runif(N,-1,1); x3<-runif(N,-1,1)
x4<-runif(N,-1,1); x5<-runif(N,-1,1)

#Set parameters of the distribution
mu=2+0.75*x1+0.4*x2+0.6*x2^2+6*log(x3+2)^(1/4) #production function parameter
sigma_v=exp(-1.5+0.75*x4) #noise parameter
sigma_u=exp(-1+sin(2*pi*x5)) #inefficiency parameter

y<-rcomper(n=N, mu=mu, sigma_v=sigma_v, sigma_u=sigma_u, s=s, distr="normhnorm")
dat<-data.frame(y, x1, x2, x3, x4, x5)

#Write formulae for parameters
mu_formula<-y~x1+x2+I(x2^2)+s(x3, bs="ps")
sigma_v_formula<-~1+x4
sigma_u_formula<-~1+s(x5, bs="ps")

#Fit model
model<-dsfa(formula=list(mu_formula, sigma_v_formula, sigma_u_formula),
                 data=dat, family=comper(s=s, distr="normhnorm"), optimizer = c("efs"))

#Get elasticities
elasticity(model, plot=TRUE)

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