elasticity {PriceIndices}

Calculating the elasticity of substitution

Description

This function returns a value of the elasticity of substitution

Usage

elasticity(
  data,
  start,
  end,
  method = "lm",
  left = -10,
  right = 10,
  precision = 1e-06
)

Arguments

data

The user's data frame with information about sold products. It must contain columns: time (as Date in format: year-month-day,e.g. '2020-12-01'), prices (as positive numeric), quantities (as positive numeric) and prodID (as numeric, factor or character).

start

The base period (as character) limited to the year and month, e.g. "2020-03".

end

The research period (as character) limited to the year and month, e.g. "2020-04".

method

The index formula for which the CES index will be equated to calculate the elasticity. Acceptable options are lm, f, t, w and sv.

left

The beginning of an interval for estimation of the elasticity of substitution (its default value is -10).

right

The end of an interval for estimation of the elasticity of substitution (its default value is 10).

precision

The precision of estimation (a 'stop' condition for the procedure). A default value of this parameter is 0.000001.

Value

This function returns a value of the elasticity of substitution. If the method parameter is set to lm, the procedure of estimation solves the equation: LM(sigma)-CW(sigma)=0 numerically, where LM denotes the Lloyd-Moulton price index, the CW denotes a current weight counterpart of the Lloyd-Moulton price index, and sigma is the elasticity of substitution parameter, which is estimated. If the method parameter is set to f, the Fisher price index formula is used instead of the CW price index. If the method parameter is set to t, the Tornqvist price index formula is used instead of the CW price index. If the method parameter is set to w, the Walsh price index formula is used instead of the CW price index. If the method parameter is set to sv, the Sato-Vartia price index formula is used instead of the CW price index.The procedure continues until the absolute value of this difference is greater than the value of the 'precision' parameter.

References

de Haan, J., Balk, B.M., Hansen, C.B. (2010). Retrospective Approximations of Superlative Price Indexes for Years Where Expenditure Data Is Unavailable. In: Biggeri, L., Ferrari, G. (eds) Price Indexes in Time and Space. Contributions to Statistics. Physica-Verlag HD.

(2004). Consumer Price Index Manual. Theory and practice. ILO/IMF/OECD/UNECE/Eurostat/The World Bank, International Labour Office (ILO), Geneva.

Examples

elasticity(coffee, start = "2018-12", end = "2019-01")
elasticity(coffee, start = "2018-12", end = "2019-01", method = "f")
elasticity(coffee, start = "2018-12", end = "2019-01", method = "sv")