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Proportionally Calibrated Almost Ideal Demand System (PCAIDS) in R

Overview

This repository contains R functions for the calculation of own- and cross-price elasticities of goods in the PCAIDS framework as described in,

Use

The process workflow for these scripts is to estimate the market share equations and the aggregate demand curve and store them as R linear (or robust linear) model objects. These objects are the input arguments for the elasticity calculation functions.

The user simply downloads pcaids_functions.R and sources them in their R script with a command such as,

source("pcaids_functions.R")

This gives access to the elasticity functions in pcaids_functions.R.

Two-Good Problems

Importing pcaids_functions.R provides access to the pcaids2good function which is used for two-good problems. Given the assumptions in Coloma (2006), only one regression (for good $i$) is needed along with the aggregate demand curve regression.

Two-Good Methodology

Following the methodology of Coloma (2006), the pcaids2good function calculates own- and cross-price elasticities following,

$$\eta_{own} = -1 + \frac{a_{ii}}{S_i}+S_i(\eta + 1)$$

$$\eta_{cross} = \frac{a_{ij}}{S_i}+S_j(\eta + 1)$$

The function calculates the mean and median of these elasticities as well as a t-stat test with the null hypothesis that the elasticity is zero.

pcaids2good(regression_good_i, aggregate_market_demand)

  Calculates own- and cross-price elasticities for a two-good PC-AIDS.

  Calculates own- and cross-price elasticities for a two-good PC-AIDS based on
  the equations from Coloma (2006).

  Parameters
  ---
  reg_i : R object of class("rlm","lm")
      R regression object for good i
  aggregate_market_demand : R object of class("rlm","lm")
      R regression object for the aggregate demand curve

  Returns
  ---
  A list containing two sub-lists: 1) own-price estimates, and 2) cross-price
  estimates.
    - own_price
      - own_price[1] : Mean Own-price elasticity of demand for good i
      - own_price[2] : Median Own-price elasticity of demand for good i
      - own_price[3] : T-statistic: Test Statistic (Ho: elasticity = 0)
      - own_price[4] : T-statistic: P Value
      - own_price[5] : T-statistic: Lower Bound 95% Confidence Interval
      - own_price[6] : T-statistic: Upper Bound 95% Confidence Interval
    - cross_price
      - cross_price[1] : Mean Cross-price elasticity of demand for good i
      - cross_price[2] : Median Cross-price elasticity of demand for good i
      - cross_price[3] : T-statistic: Test Statistic (Ho: elasticity = 0)
      - cross_price[4] : T-statistic: P Value
      - cross_price[5] : T-statistic: Lower Bound 95% Confidence Interval
      - cross_price[6] : T-statistic: Upper Bound 95% Confidence Interval

  Notes
  ---
  This does not check for any assumption requirements associated with the PC-
  AIDS model presented in Epstein and Rubinfeld (2002) and Coloma (2006). It
  is your responsibility to make sure these assumptions hold.

  Warnings
  ---
    - This does not check for any assumption requirements associated with the PC-
      AIDS model presented in Epstein and Rubinfeld (2002) and Coloma (2006). It
      is your responsibility to make sure these assumptions hold.
    - This function only allows linear models and/or robust linear models.
    - The first predictor in the model must be the price variable.
    - This model does not support repressed intercepts.

Future Models

I am currently working to expand the elasticity model to n goods but this is forthcoming.