# GKIndex: Compute the Geary-Khamis index In IndexNumR: Index Number Calculation

## Description

Compute the Geary-Khamis index

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```GKIndex( x, pvar, qvar, pervar, prodID, sample = "", window, splice = "mean", imputePrices = NULL, solveMethod = "inverse", tolerance = 1/1e+12, maxIter = 100 ) ```

## Arguments

 `x` A dataframe containing price, quantity, a time period identifier and a product identifier. It must have column names. `pvar` A character string for the name of the price variable `qvar` A character string for the name of the quantity variable `pervar` A character string for the name of the time variable. This variable must contain integers starting at period 1 and increasing in increments of 1 period. There may be observations on multiple products for each time period. `prodID` A character string for the name of the product identifier `sample` set to "matched" to only use products that occur across all periods in a given window. Default is not to match. `window` An integer specifying the length of the window. `splice` the splicing method to use to extend the index. Valid methods are window, movement, half, mean, fbew, fbmw, wisp, hasp or mean_pub. The default is mean. See details for important considerations when using fbew and fbmw. `imputePrices` the type of price imputation to use for missing prices. Currently only "carry" is supported to used carry-forward/carry-backward prices. Default is NULL to not impute missing prices. `solveMethod` the method to use to solve for the quality adjustment factors and the price levels. "inverse" uses a matrix inverse operation, is much more efficient, but may not work if there are many missing observations. "iterative" iterates between the equations for the quality adjustment factors and price levels and is much slower, but can be used even when there are a large number of missing observations. `tolerance` the tolerance for the iterative solving method. Smaller numbers will produce more accurate results, but take more iterations. Default is 1/1e12, which may be a little larger than machine precision, given by .Machine\$double.eps. `maxIter` the maximum number of iterations for the iterative solving method.

## Details

The splicing methods are used to update the price index when new data become available without changing prior index values. The window, movement, half and mean splices use the most recent index value as the base period, which is multiplied by a price movement computed using new data. The fbew (Fixed Base Expanding Window) and fbmw (Fixed Base Moving Window) use a fixed base onto which the price movement using new data is applied. The base period is updated periodically. IndexNumR calculates which periods are the base periods using `seq(from = 1, to = n, by = window - 1)`, so the data must be set up correctly and the right window length chosen. For example, if you have monthly data and want December of each year to be the base period, then the first period in the data must be December and the window must be set to 13.

It is recommended to use the matrix inverse method of solving the GK equations (the default) because the performance difference can be significant. If the matrix inverse method does not work then switch to the iterative method. The tolerance and maximum number of iterations in the iterative method can be adjusted to balance performance and precision.

## References

Ivancic, L., W.E. Diewert and K.J. Fox (2011), "Scanner Data, Time Aggregation and the Construction of Price Indexes", Journal of Econometrics 161, 24-35.

Geary, R. G. 1958. “A Note on Comparisons of Exchange Rates and Purchasing Power Between Countries.” Journal of the Royal Statistical Society Series A 121: 97–99.

Khamis, S. H. 1970. “Properties and Conditions for the Existence of a New Type of Index Number.” Sankhya: The Indian Journal of Statistics, Series B (1960-2002) 32: 81–98.

## Examples

 ```1 2 3``` ```# compute a Geary-Khamis index with mean splicing GKIndex(CES_sigma_2, pvar = "prices", qvar = "quantities", pervar = "time", prodID = "prodID", window=11, splice = "mean") ```

IndexNumR documentation built on Feb. 7, 2022, 5:09 p.m.