Elasticity function for lm() coefficient

Question

I wonder whether there is a function that calculates (economic) elasticity for models estimated with lm().

Elasticity for the percentage change of the dependent variable, around its mean Y, for a change of 1% in the independent variable, above its mean X, is calculated as follows: b*X/Y (b= model coefficient for the independent variable).

Below is the code for a Rmd File with a simple linear model and the elasticity of each coefficient. The output should be a table of the variable names and elasticity.

---
title: "Elasticity"
output: html_document
---

```{r}
N <- 1000
u <- rnorm(N)
x1 <- rnorm(N)
x2 <- 1 + x1 + rnorm(N)
y <- 1 + x1 + x2 + u
df <- data.frame(y,x1,x2)

fit <- lm(y ~ x1 + x2, data = df)

elax1 <- as.numeric(fit$coefficients["x1"] * mean(df$x1)/mean(df$y))
elax2 <- as.numeric(fit$coefficients["x2"] * mean(df$x2)/mean(df$y))

variable <-c ('x1','x2')
elasticity <-c (elax1,elax2)
a <- data.frame(variable,elasticity)

```

Output the results in a table:

```{r, message=FALSE,results='asis'}
require(stargazer)
stargazer(a, summary = FALSE,type = 'html',rownames=FALSE)
```

[This blog post](http://www.salemmarafi.com/code/price-elasticity-with-r/) seems to provide some simple code. — jbaums, Jan 22 '15 at 11:38
I had seen that post, but like you said it only has very simple code for the elasticity of two variables. The means and coefficients are selected individually using the variable names. I'm working on a quite large dataset and doing this 'by hand' for all regression would be very long. So this is why I thought someone here might take me to... — marco, Jan 22 '15 at 11:51
Maybe if you provide code to fit a simple model that we could use to write some general code. You should include in your post the fact that you want to automate this. Otherwise people are likely to provide solutions that aren't satisfactory for you. And if you can include the expected output for that example, even better. — jbaums, Jan 22 '15 at 12:46
I updated the question and included an example. Hope that helps. — marco, Jan 22 '15 at 20:20

marco · Accepted Answer · 2015-01-23T18:24:44.020

I came up with my own solution, maybe it can help others. Note that I have included an interaction in the model. Of course, improvements are welcome.

---
title: "Elasticity"
output: html_document
---

Generate data and linear model:
```{r}
N <- 1000
u <- rnorm(N)
x1 <- rnorm(N)
x2 <- 1 + x1 + rnorm(N)
y <- 1 + x1 + x2 + u
df <- data.frame(y,x1,x2)

fit <- lm(y ~ x1 * x2, data = df)

```


Function to calculate elasticities:
```{r,results='asis'}

elasticities <- function(linmod){
Ncoef <- nrow(data.frame(linmod$coefficients))
for(i in 2:Ncoef){
  el <- as.numeric(linmod$coefficients[i] * colMeans(model.matrix(linmod))[i]/colMeans(model.matrix(linmod))[1])
  ifelse (i== 2, elasticity <- el, elasticity <- rbind(elasticity,el))
}
rownames(elasticity) <- names(coef(linmod)[-1])
colnames(elasticity) <- 'elasticities'

return(data.frame(elasticity))
}
```

Run the elasticites function and produce a nice table:
```{r,results='asis',message=FALSE}
a <- elasticities(fit)

require(stargazer)
stargazer(a, summary = FALSE, type = 'html')

```

Elasticity function for lm() coefficient

1 Answers1