elasticities: Estimation of elasticities of the (Quadratic) Almost-Ideal...

In JanMarvin/nlsur: Estimating Nonlinear Least Squares for Equation Systems

Estimation of elasticities of the (Quadratic) Almost-Ideal Demand System

Description

Estimates the income/expenditure elasticity, the uncompensated price elasticity and the compensated price elasticity

Usage

elasticities(object, data, type = 1, usemean = FALSE)

Arguments

object	qai result
data	data vector used for estimation
type	1 = expenditure; 2 = uncompensated; 3 = compensated
usemean	evaluate at mean

Details

Formula for the expenditure (income) elasticity

\mu_i = 1 + \frac{1}{w_i} \left[ \beta_i + \frac{2\lambda_i}{b(\mathbf{p})} * ln \left\{\frac{m}{a(\mathbf{p})} \right\}\right]

Formula for the uncompensated price elasticity

\epsilon_{ij} = \delta_{ij} + \frac{1}{w_i} \left( \gamma_{ij} - \beta_i + \frac{2\lambda_i}{b(\mathbf{p})} \right) \left[\ln \left\{ \frac{m}{a(\mathbf{p})}\right\} \right] \times \\ \left(\alpha_j + \sum_k \gamma_{jk} \ln p_k \right) - \frac{\beta_j \lambda_i}{b(\mathbf{p})} \left[ \ln \left\{ \frac{m}{a(\mathbf{p})} \right\}\right]

Compensated price elasticities (Slutsky equation)

\epsilon_{ij}^{C} = \epsilon_{ij} + \mu_i w_j

References

Banks, James, Blundell, Richard, Lewbel, Arthur: Quadratic Engel Curves and Consumer Demand, The Review of Economics and Statistics 79(4), The MIT Press, 527-539, 1997

Poi, Brian P.: Easy demand-system estimation with quaids, The Stata Journal 12(3), 433-446, 2012

See Also

ai and qai

Examples

## Not run: 
library(nlsur)
library(readstata13)

dd <- read.dta13("http://www.stata-press.com/data/r15/food.dta")

w <- paste0("w", 1:4); p <- paste0("p", 1:4); x <- "expfd"

est <- ai(w = w, p = p, x = x, data = dd, a0 = 10, scale = FALSE,
          logp = F, logexp = F)

mu <- elasticities(est, data = dd, type = 1, usemean = FALSE)

ue <- elasticities(est, data = dd, type = 2, usemean = FALSE)

ce <- elasticities(est, data = dd, type = 3, usemean = FALSE)
## End(Not run)

JanMarvin/nlsur documentation built on June 24, 2024, 2:58 a.m.