IndexNumR: A package for computing index numbers

Description

IndexNumR is a package for computing bilateral and multilateral index numbers. The package has been designed with performance in mind, to enable computing index numbers on large datasets within a reasonable timeframe. It also aims to make a large number of index number methods available, along with access to datasets to enable research and experimentation.

Author

Graham White

Notes

I'd like to thank all those that have commented on, or tested the code so that it could be improved. In particular, I'd like to thank Professor Kevin Fox at the University of New South Wales for his support and input.

Some function parameters can have a considerable impact on the outputs, so it is recommended that the user read the documentation for these functions carefully.

Vignettes

There is very detailed information about the functions in the package vignette, which can be accessed with,

browseVignettes("IndexNumR").

Bilateral index functions

Compute bilateral indexes

• priceIndex

• quantityIndex

Similarity chain linking

Compute dissimilarity measures or chain links.

• relativeDissimilarity

• mixScaleDissimilarity

• maximumSimilarityLinks

Multilateral index functions

Compute multilateral indexes

• GEKSIndex

• GKIndex

• WTPDIndex

Other index number functions

• groupIndexes

• yearOverYearIndexes

Data preparation functions

Perform various operations on the data before using other functions, such as index number functions.

• unitValues

• imputeCarryPrices

• imputeQuantities

Data exploration functions

Learn more about the characteristics of your dataset.

• evaluateMatched

• values

Sample data

IndexNumR has one sample dataset,

• CES_sigma_2,

and a function for generating small datasets,

• CESData,

and a function for accessing the Dominicks Finer Foods scanner data,

• dominicksData.

Differences approach to index numbers

These functions are referred to as indicators, to distinguish them from the bilateral and multilateral index functions which use the ratio approach.

• priceIndicator

• quantityIndicator

Time index functions

Index functions in IndexNumR generally need a time period variable. These functions will compute the required time period variable, depending on the frequency required.

• weekIndex

• monthIndex

• quarterIndex

• yearIndex

See Also

Useful links:

• https://github.com/grahamjwhite/IndexNumR

Generate data assuming CES preferences

Description

This function is useful for generating datasets that can be used for testing where the 'true' price index is known. The data are constructed using assumed prices and total expenditure in each period. Expenditure shares and quantities are then computed assuming CES preferences. For further details, see the references.

Usage

CESData(sigma)

Arguments

Value

a dataframe containing time period, prices, quantities and product identifier.

References

W.E. Diewert and K.J. Fox (2017), "Substitution Bias in Multilateral Methods for CPI Construction Using Scanner Data", Discussion Paper 17-02, Vancouver School of Economics, The University of British Columbia.

Examples

## Not run: 
# generate data assuming the elasticity of substitution is 2
CESData(2)

## End(Not run)

Dataset of prices and quantities on four products

Description

A constructed dataset containing the prices and quantities of four products over a twelve month period, assuming CES preferences.

Usage

CES_sigma_2

Format

A data frame with 48 rows and 4 columns:

time

time period

prices

constructed prices

quantities

constructed quantities

prodID

product identifier

Source

Computed using procedure in W.E. Diewert and K.J. Fox (2017), "Substitution Bias in Multilateral Methods for CPI Construction Using Scanner Data", Discussion Paper 17-02, Vancouver School of Economics, The University of British Columbia.

Date information for the Dominicks data

Description

Table from the Dominicks Data Manual, that gives the start and end date of each of the weeks in the movement files.

Usage

DominicksWeeks

Format

A data frame with 400 rows and 4 columns:

week

the number of the week

start

date the week started

end

date the week ended

specialEvents

special events, such as Halloween, that occurred during the week

Source

Dominicks Data Manual, Chicago Booth Kilts Center for Marketing, 2018, pages 21-28.

Compute a GEKS multilateral index

Description

A function to calculate a GEKS multilateral price index

Usage

GEKSIndex(
  x,
  pvar,
  qvar,
  pervar,
  indexMethod = "tornqvist",
  prodID,
  sample = "matched",
  window = 13,
  splice = "mean",
  biasAdjust = FALSE,
  weights = "average",
  intGEKS = FALSE,
  imputePrices = NULL
)

Arguments

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.

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.

Lamboray, C. and F. Krsinich (2015), "A Modification of the GEKS Index When Product Turnover is High", Paper presented at the fourteenth Ottawa Group meeting, 20-22 May 2015, Tokyo, Japan.

Examples

# compute a GEKS mutlilateral index with mean splicing
GEKSIndex(CES_sigma_2, pvar = "prices", qvar = "quantities", pervar = "time",
prodID = "prodID", indexMethod = "tornqvist", window=11, splice = "mean")

# compute a GEKS multilateral index with window splicing and the Fisher index method
GEKSIndex(CES_sigma_2, pvar = "prices", qvar = "quantities", pervar = "time",
prodID = "prodID", indexMethod = "fisher", window=11, splice = "mean")

Compute the Geary-Khamis index

Description

Compute the Geary-Khamis index

Usage

GKIndex(
  x,
  pvar,
  qvar,
  pervar,
  prodID,
  sample = "",
  window,
  splice = "mean",
  imputePrices = NULL,
  solveMethod = "inverse",
  tolerance = 1/1000000000000,
  maxIter = 100
)

Arguments

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

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

Compute a weighted time-product-dummy multilateral index

Description

A function to calculate a weighted-time-product-dummy multilateral index.

Usage

WTPDIndex(
  x,
  pvar,
  qvar,
  pervar,
  prodID,
  sample = "",
  window = 13,
  splice = "mean",
  imputePrices = NULL
)

Arguments

Details

When there are missing values in the dataset (e.g., from new or disappearing products), the default option is to treat the missing prices and quantities as zero. An alternative is to use a matched sample, where only products that appear throughout each window in the calculation are kept.

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.

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.

Examples

# compute a wtpd index with mean splicing
WTPDIndex(CES_sigma_2, pvar = "prices", qvar = "quantities", pervar = "time",
prodID = "prodID", window=11, splice = "mean")

Get data from the Dominicks dataset

Description

The Dominicks Scanner data, provided by the University of Chicago Booth School of Business, contains around 5 years of product-level data from over 100 stores, collected from 1989-1994. The data consist of a UPC file that contains information on the products, and a movement file that contains the information on prices and sales. For a complete description of the data, see Dominicks data website and the Dominicks data user manual. This function downloads and merges the movement and UPC files, then merges the result with data detailing the dates of each of the weeks in the movement file.

Usage

dominicksData(x, movementcsv = NULL, UPCcsv = NULL)

Arguments

Details

The following transformations are performed on the data:

• The quantity variable is set to MOVE, which is the number of individual units sold

• The price variable is set to PRICE/QTY, which is the unit price. This accounts for the fact that sometimes products are sold in bundles (e.g., two-for-one promotions).

• expenditure is given by PRICE*MOVE/QTY.

• All observations where the variable OK equals 0, or price is less than or equal to 0, are dropped.

If you have already downloaded the movement and UPC csv files for a category from the website, then you can pass the file paths of those files to the function and just have it combine them with the weeks dataset. The default is to download the files for you from the website.

The products available are:

• Analgesics

• Bath Soap

• Beer

• Bottled Juices

• Cereals

• Cheeses

• Cigarettes

• Cookies

• Crackers

• Canned Soup

• Dish Detergent

• Front-end-candies

• Frozen Dinners

• Frozen Entrees

• Frozen Juices

• Fabric Softeners

• Grooming Products

• Laundry Detergents

• Oatmeal

• Paper Towels

• Refrigerated Juices (not currently available)

• Soft Drinks

• Shampoos

• Snack Crackers

• Soaps

• Toothbrushes

• Canned Tuna

• Toothpastes

• Bathroom Tissues

References

James M. Kilts Center, University of Chicago Booth School of Business

Examples

## Not run: 
analgesics <- dominicksData("Analgesics")

## End(Not run)

Computes the elasticity of substitution

Description

A function to estimate the elasticity of substitution

Usage

elasticity(
  x,
  pvar,
  qvar,
  pervar,
  prodID,
  compIndex = "ces",
  lower = -20,
  upper = 20
)

Arguments

Value

A list with three elements: sigma (the average elasticity over all time periods); allsigma (a T-1 by 1 matrix of the estimated elasticities for each time period, except period one); and diff (the value of the difference between the two indexes, check this is zero for all time periods).

Examples

elasticity(CES_sigma_2,pvar="prices",qvar="quantities",pervar="time",
prodID = "prodID")

Evaluate product overlap between periods

Description

Evaluate the counts and expenditure for each period with and without matching items across periods.

Usage

evaluateMatched(x, pvar, qvar, pervar, prodID, output = "chained")

Arguments

Value

A list of two matrices, one for expenditures and one for counts. The first four columns present the base period information base_index (the base time period), base (base period expenditure or count), base_matched (the expenditure or count of the base period after matching), base_share (share of total expenditure in the base period that remains after matching). Columns 5-8 are defined analogously for the current period. The matched numbers for the base period should be interpreted as the count or expenditure that remains after removal of products that exist in the base period, but not in the current period. That is, products that existed in the base period but no longer exist in the current period are removed by the matching. If new products exist in the current period that were not available in the base period, this does not affect the matched base period expenditure or count. The appearance of new products is captured in the current period matched expenditure and counts. Therefore, a base period share that is less than 1 indicates that products have disappeared, while a current period share less than 1 indicates that new products have appeared.

The count matrix has two additional columns, "new" and "leaving". The new column gives the number of products that exist in the current period but not the base period. The leaving column gives the count of products that exist in the base period but not the current period. Matching removes both of these types of products.

Examples

# create CES_sigma_2 dataset removing the observation in time period 4
# on product 1
df <- CES_sigma_2[!(CES_sigma_2$time==4 & CES_sigma_2$prodID==1),]
# evaluate the overlap between periods for this dataset assuming
# a chained index
evaluateMatched(df, pvar="prices", qvar="quantities", pervar="time",
prodID = "prodID", output="chained")

Calculate price indexes for product groups

Description

Calculate price indexes for product groups

Usage

groupIndexes(group, indexFunction, indexArgs)

Arguments

Value

a list of indexes, one for each group

Examples

df <- CES_sigma_2
df$groupID <- c(rep(1, 24), rep(2, 24))

argsList <- list(x = df, pvar = "prices", qvar = "quantities", pervar = "time",
prodID = "prodID", indexMethod = "fisher", output = "chained")

groupIndexes("groupID", "priceIndex", argsList)

Fill all missing prices with carry forward/backward prices

Description

If a missing product has a previous price then that previous price is carried forward until the next real observation. If there is no previous price then the next real observation is found and carried backward. If a price observation is filled, and a quantity variable is specified, then the corresponding quantity is set to zero. Prices can be filled with no quantity variable by specifying qvar = "".

Usage

imputeCarryPrices(x, pvar, qvar, pervar, prodID)

Arguments

Value

the input data frame with missing observations filled

Examples

# create a dataset with missing prices for products 1 and 2
df <- CES_sigma_2[-c(1,2,14,15),]
imputeCarryPrices(df, "prices", "quantities", "time", "prodID")

Impute quantities when only prices are available

Description

This procedure calculates quantities in such a way that the expenditure shares on all products are equal in each period. It is used to compute quantities for the predicted share measure of relative price dissimilarity when there are none available.

Usage

imputeQuantities(x, pvar, pervar, prodID)

Arguments

Finds periods to link using minimum dissimilarity.

Description

Function to compute the maximum similarity chain links from a measure of dissimilarity. The procedure works as described in Diewert and Fox (2017). It first links period 2 to period 1. Then for each period t, from periods 3,...,T it searches among the periods 1,...,t-1 for the period that is most similar (least dissimilar) to period t.

Usage

maximumSimilarityLinks(x)

Arguments

Examples

# find the linking periods in the CES_sigma_2 dataset that maximise
# the similarity between periods, using the absolute dissimilarity measure.
disMat <- mixScaleDissimilarity(CES_sigma_2, pvar = "prices", qvar = "quantities",
pervar = "time", prodID = "prodID", measure = "absolute",
combine = "geomean")
maximumSimilarityLinks(disMat)

Computes mix, scale and absolute dissimilarity measures

Description

This is a function to compute the Fox, Hill and Diewert 2004 dissimilarity measures.

Usage

mixScaleDissimilarity(
  x,
  pvar,
  qvar,
  prodID,
  pervar,
  measure = "absolute",
  combine = "geomean"
)

Arguments

Value

A matrix where the first two columns are the possible combinations of periods and the third column is the dissimilarity measure.

References

Fox, K.J., R.J. Hill and W.E. Diewert (2004), "Identifying outliers in multi-output models", Journal of Productivity Analysis, 22, 73-94, 2004.

Examples

# estimate the dissimilarity between periods in the CES_sigma_2 dataset
# using the absolute measure of dissimilarity and the geometric mean
# to combine price and quantity information.
mixScaleDissimilarity(CES_sigma_2, pvar = "prices", qvar = "quantities",
pervar = "time", prodID = "prodID", measure = "absolute",
combine = "geomean")

Generate an index of months

Description

A function to create a month index variable

Usage

monthIndex(x, overlapWeeks = "naive")

Arguments

Examples

# given a vector of dates
df <- data.frame(date = as.Date(c("2017-01-01","2017-02-01","2017-03-01","2017-04-01"),
format = "%Y-%m-%d"))
# calculate the time period variable
df$period <- monthIndex(df$date, overlapWeeks = "naive")
df

Predicted shares for predicted share relative price dissimilarity

Description

You should not need to call this function directly unless the shares themselves are of interest. Other functions will call this function internally.

Usage

predictedShares(x, pvar, qvar, pervar, prodID)

Arguments

Value

a list of matrices

Computes a bilateral price index

Description

A function to compute a price index given data on products over time

Usage

priceIndex(
  x,
  pvar,
  qvar,
  pervar,
  indexMethod = "laspeyres",
  prodID,
  sample = "matched",
  output = "pop",
  chainMethod = "pop",
  sigma = 1.0001,
  basePeriod = 1,
  biasAdjust = TRUE,
  weights = "average",
  loweYoungBase = 1,
  imputePrices = NULL,
  ...
)

Arguments

Examples

# period-on-period Laspeyres index for the CES_sigma_2 dataset
priceIndex(CES_sigma_2, pvar="prices", qvar="quantities", pervar="time",
prodID = "prodID", indexMethod = "laspeyres")

# chained Fisher index
priceIndex(CES_sigma_2, pvar="prices", qvar="quantities", pervar="time",
prodID = "prodID", indexMethod = "fisher", output="chained")

# chained Tornqvist index, with linking periods chosen by the
# weighted log-quadratic dissimilarity measure
priceIndex(CES_sigma_2, pvar="prices", qvar="quantities", pervar="time",
prodID = "prodID", indexMethod = "tornqvist", output="chained",
chainMethod = "logquadratic")

Calculate a price indicator

Description

This calculates a price indicator. This is calculated using the differences approach to index number theory, where the change in prices and quantities from one period to the next is additive. Therefore, the change in total value is the sum of the change in prices and the change in quantities. Such a value decomposition can be obtained using valueDecomposition.

See the vignette for more information on the calculations.

vignette(topic = "indexnumr", package = "IndexNumR")

Usage

priceIndicator(x, pvar, qvar, pervar, prodID, method, sample = "matched")

Arguments

Value

an nx1 matrix containing the indicator

Examples

# compute a price indicator using the Montgomery method
priceIndicator(CES_sigma_2, pvar = "prices", qvar = "quantities",
prodID = "prodID", pervar = "time", method = "montgomery")

Product ID's for appearing/disappearing products

Description

This function will give the product ID's of products that appear or disappear in each period.

Usage

productChanges(x, pervar, prodID)

Arguments

Value

a list containing one element for each time period, each element of which contains two vectors (one for appearing products, and one for disappearing products)

Examples

# create a dataset with some missing products
df <- CES_sigma_2[-c(3,4,15),]

# show the products that changed
productChanges(df, "time", "prodID")

Computes a bilateral quantity index

Description

A function to compute a quantity index given data on products over time

Usage

quantityIndex(
  x,
  pvar,
  qvar,
  pervar,
  indexMethod = "laspeyres",
  prodID,
  sample = "matched",
  output = "pop",
  chainMethod = "pop",
  sigma = 1.0001,
  basePeriod = 1,
  biasAdjust = TRUE,
  weights = "average",
  loweYoungBase = 1,
  imputePrices = NULL,
  ...
)

Arguments

Examples

# chained Fisher quantity index for the CES_sigma_2 dataset
quantityIndex(CES_sigma_2, pvar="prices", qvar="quantities", pervar="time",
prodID = "prodID", indexMethod = "fisher", output="chained")

Compute a quantity indicator

Description

This calculates a quantity indicator. This is calculated using the differences approach to index number theory, where the change in prices and quantities from one period to the next is additive. Therefore, the change in total value is the sum of the change in prices and the change in quantities. Such a value decomposition can be obtained using valueDecomposition.

See the vignette for more information on the calculations.

vignette(topic = "indexnumr", package = "IndexNumR")

Usage

quantityIndicator(x, pvar, qvar, pervar, prodID, method, sample = "matched")

Arguments

Value

an nx1 matrix containing the indicator

Examples

# compute a quantity indicator using the Bennet method
quantityIndicator(CES_sigma_2, pvar = "prices", qvar = "quantities",
prodID = "prodID", pervar = "time", method = "bennet")

Generate an index of quarters

Description

A function to create a quarter index variable

Usage

quarterIndex(x)

Arguments

Examples

# given a vector of dates
df <- data.frame(date = as.Date(c("2017-01-01","2017-04-01","2017-07-01","2017-08-01"),
format = "%Y-%m-%d"))
# calculate the time period variable
df$period <- quarterIndex(df$date)
df

Computes measures of relative dissimilarity between all periods

Description

A function to compute the relative price dissimilarity between two vectors of prices.

Usage

relativeDissimilarity(
  x,
  pvar,
  qvar,
  pervar,
  prodID,
  indexMethod = "fisher",
  similarityMethod = "logquadratic"
)

Arguments

Value

A matrix of dissimilarity measures. The first two columns are the possible combinations of bilateral comparisons and the third column is the dissimilarity measure.

References

Diewert, W.E. (2002). "Similarity and Dissimilarity Indexes: An Axiomatic Approach" Discussion Paper No. 0210, Department of Economics, University of British Columbia.

Examples

# estimate the dissimilarity between periods in the CES_sigma_2 dataset
# using the log quadratic measure of dissimilarity
relativeDissimilarity(CES_sigma_2, pvar = "prices", qvar="quantities",
pervar = "time", prodID = "prodID", indexMethod="fisher",
similarityMethod = "logquadratic")

Compute expenditure shares for each product and time period

Description

Compute expenditure shares for each product and time period

Usage

shares(x, pvar, qvar, pervar, prodID)

Arguments

Value

an n by p data frame of expenditure shares

Aggregates prices to unit values and quantities to sums

Description

A function to aggregate price and quantity data to unit values

Usage

unitValues(x, pvar, qvar, pervar, prodID)

Arguments

Value

A dataframe containing columns for product identifier, time period, quantities, and unit values.

Examples

# suppose the CES_sigma_2 dataset contains 12 monthly observations
# and suppose we want quarterly unit values.
df <- CES_sigma_2
# convert the monthly time variable into quarterly
df$time <- ceiling(CES_sigma_2$time/3)
# compute unit values using the quarterly time variable
unitValues(df,pvar="prices",qvar="quantities",pervar="time",prodID="prodID")

valueDecomposition

Description

Perform a decomposition of value change using price and quantity indicators. This is an additive decomposition so that change due to price plus change due to quantity equals the total value change.

Usage

valueDecomposition(
  x,
  pvar,
  qvar,
  pervar,
  prodID,
  priceMethod,
  sample = "matched"
)

Arguments

Value

a dataframe containing the price indicator, quantity indicator the value change and the value level.

Examples

# decompose the value changes in the CES_sigma_2 dataset using the Bennet method
valueDecomposition(CES_sigma_2, pvar = "prices", qvar = "quantities",
prodID = "prodID", pervar = "time", priceMethod = "bennet")

Compute values (price x quantity)

Description

Compute the total value (expenditure), for each time period in the sample.

Usage

values(
  x,
  pvar,
  qvar,
  pervar,
  prodID,
  sample = "matched",
  matchPeriod = "previous"
)

Arguments

Examples

values(CES_sigma_2, pvar = "prices", qvar = "quantities", pervar = "time",
prodID = "prodID", matchPeriod = "previous")

Generate an index of weeks

Description

Function to create a week index variable with weeks determined as defined in ISO 8601. If the week (starting on Monday) containing 1 January has four or more days in the new year, then it is considered week 1. Otherwise, it is the 53rd week of the previous year, and the next week is week 1.

Usage

weekIndex(x)

Arguments

Examples

# given a vector of dates
df <- data.frame(date = as.Date(c("2016-12-20","2016-12-27","2017-01-01","2017-01-07"),
format = "%Y-%m-%d"))
# calculate the time period variable
df$period <- weekIndex(df$date)
df

Generate an index of years

Description

Function to create a year index variable

Usage

yearIndex(x)

Arguments

Examples

# given a vector of dates
df <- data.frame(date = as.Date(c("2017-01-01","2018-04-01","2019-07-01","2019-08-01"),
format = "%Y-%m-%d"))
# calculate the time period variable
df$period <- yearIndex(df$date)
df

Estimate year-over-year indexes

Description

Year-over-year indexes are indexes where the months or quarters of the year are split in separate datasets and an index estimated on each. Therefore, year-over-year indexes estimated on a dataset with five full years of observations at a monthly frequency will have 12 separate indexes, each with 5 observations.

Usage

yearOverYearIndexes(freq, indexFunction, indexArgs)

Arguments

Value

a list of indexes with one element for each month or quarter

Examples

argsList <- list(x = CES_sigma_2, pvar = "prices", qvar = "quantities", pervar = "time",
prodID = "prodID", indexMethod = "fisher", output = "chained")

yearOverYearIndexes("quarterly", "priceIndex", argsList)