# PriceIndices

# PriceIndices – a Package for Bilateral and Multilateral Price Index Calculations

author: Jacek Białek, University of Lodz, Statistics Poland

Goals of PriceIndices are as follows: a) data processing before price index calculations; b) bilateral and multilateral price index calculations; c) extending multilateral price indices. You can download the package documentation from here. This vignette with all graphical results can be download from here.

## Installation

You can install the released version of PriceIndices from CRAN with:

    install.packages("PriceIndices")

You can install the development version of PriceIndices from GitHub with:

    library("remotes")
    remotes::install_github("JacekBialek/PriceIndices")

## The functionality of this package can be categorized as follows:

1. Data sets included in the package and generating artificial scanner data sets
2. Functions for data processing
3. Functions providing dataset characteristics
4. Functions for bilateral unweighted price index calculation
5. Functions for bilateral weighted price index calculation
6. Functions for chain price index calculation
7. Functions for multilateral price index calculation
8. Functions for extending multilateral price indices by using splicing methods
9. Functions for extending multilateral price indices by using the FBEW method
10. Functions for extending multilateral price indices by using the FBMW method
11. General functions for price index calculations
12. Functions for comparisons of price indices

### Data sets included in the package and generating artificial scanner data sets

This package includes seven data sets: artificial and real.

1) dataAGGR

The first one, dataAGGR, can be used to demonstrate the data_aggregating function. This is a collection of artificial scanner data on milk products sold in three different months and it contains the following columns: time - dates of transactions (Year-Month-Day: 4 different dates); prices - prices of sold products (PLN); quantities - quantities of sold products (liters); prodID - unique product codes (3 different prodIDs); retID - unique codes identifying outlets/retailer sale points (4 different retIDs); description - descriptions of sold products (two subgroups: goat milk, powdered milk).

2) dataMATCH

The second one, dataMATCH, can be used to demonstrate the data_matching function and it will be described in the next part of the guidelines. Generally, this artificial data set contains the following columns: time - dates of transactions (Year-Month-Day); prices - prices of sold products; quantities - quantities of sold products; codeIN - internal product codes from the retailer; codeOUT - external product codes, e.g. GTIN or SKU in the real case; description - descriptions of sold products, eg. 'product A', 'product B', etc.

3) dataCOICOP

The third one, dataCOICOP, is a collection of artificial scanner data on the sale of tomatoes, fruit juices, low fat milk, full fat milk, sugar, chocolate, yoghurt, coffee, eggs and salt in the period from December 2018 to October 2020. It is a data frame with 8 columns and 96600 rows. The used variables are as follows: time - dates of transactions (Year-Month-Day); prices - prices of sold products (PLN); quantities - quantities of sold products (liters); prodID - unique product codes obtained after product matching (data set contains 331 different prodIDs); retID - unique codes identifying outlets/retailer sale points (data set contains 10 different retIDs); description - descriptions of sold products (data set contains 12 different product descriptions), unit - sales units, e.g. 'kg', 'ml', etc.; coicop - identifiers of COICOP groups (10 groups). Please note that this data set can serve as a training or testing set in product classification using machine learning methods (see the functions: model_classification and data_classifying).

4) milk

This data set, milk, is a collection of scaner data on the sale of milk in one of Polish supermarkets in the period from December 2018 to August 2020. It is a data frame with 6 columns and 4386 rows. The used variables are as follows: time - dates of transactions (Year-Month-Day); prices - prices of sold products (PLN); quantities - quantities of sold products (liters); prodID - unique product codes obtained after product matching (data set contains 68 different prodIDs); retID - unique codes identifying outlets/retailer sale points (data set contains 5 different retIDs); description - descriptions of sold milk products (data set contains 6 different product descriptions corresponding to subgroups of the milk group).

5) coffee

This data set, coffee, is a collection of scanner data on the sale of coffee in one of Polish supermarkets in the period from December 2017 to October 2020. It is a data frame with 6 columns and 42561 rows. The used variables are as follows: time - dates of transactions (Year-Month-Day); prices - prices of sold products (PLN); quantities - quantities of sold products (kg); prodID - unique product codes obtained after product matching (data set contains 79 different prodIDs); retID - unique codes identifying outlets/retailer sale points (data set contains 20 different retIDs); description - descriptions of sold coffee products (data set contains 3 different product descriptions corresponding to subgroups of the coffee group).

6) sugar

This data set, sugar, is a collection of scanner data on the sale of coffee in one of Polish supermarkets in the period from December 2017 to October 2020. It is a data frame with 6 columns and 7666 rows. The used variables are as follows: time - dates of transactions (Year-Month-Day); prices - prices of sold products (PLN); quantities - quantities of sold products (kg); prodID - unique product codes obtained after product matching (data set contains 11 different prodIDs); retID - unique codes identifying outlets/retailer sale points (data set contains 20 different retIDs); description - descriptions of sold sugar products (data set contains 3 different product descriptions corresponding to subgroups of the sugar group).

7) dataU

This data set, dataU, is a collection of artificial scanner data on 6 products sold in Dec, 2018. Product descriptions contain the information about their grammage and unit. It is a data frame with 5 columns and 6 rows. The used variables are as follows: time - dates of transactions (Year-Month-Day); prices - prices of sold products (PLN); quantities - quantities of sold products (item); prodID - unique product codes; description - descriptions of sold products (data set contains 6 different product descriptions).

The set milk represents a typical data frame used in the package for most calculations and is organized as follows:

    library(PriceIndices)
    head(milk)

Available subgroups of sold milk are

    unique(milk$description)

Generating artificial scanner data sets in the package

The package includes the generate function which provides an artificial scanner data sets where prices and quantities are lognormally distributed. The characteristics for these lognormal distributions are set by pmi, sigma, qmi and qsigma parameters. This function works for the fixed number of products and outlets (see n and r parameters). The generated data set is ready for further price index calculations. For instance:

    dataset<-generate(pmi=c(1.02,1.03,1.04),psigma=c(0.05,0.09,0.02),
                      qmi=c(3,4,4),qsigma=c(0.1,0.1,0.15),
                      start="2020-01")
    head(dataset)

From the other hand you can use tindex function to obtain the theoretical value of the unweighted price index for lognormally distributed prices (the month defined by start parameter plays a role of the fixed base period). The characteristics for these lognormal distributions are set by pmi and sigma parameters. The ratio parameter is a logical parameter indicating how we define the theoretical unweighted price index. If it is set to TRUE then the resulting value is a ratio of expected price values from compared months; otherwise the resulting value is the expected value of the ratio of prices from compared months.The function provides a data frame consisting of dates and corresponding expected values of the theoretical unweighted price index. For example:

    tindex(pmi=c(1.02,1.03,1.04),psigma=c(0.05,0.09,0.02),start="2020-01",ratio=FALSE)

### Functions for data processing

data_preparing

This function returns a prepared data frame based on the user's data set (you can check if your data set it is suitable for further price index calculation by using data_check function). The resulting data frame is ready for further data processing (such as data selecting, matching or filtering) and it is also ready for price index calculations (if only it contains the required columns). The resulting data frame is free from missing values, zero or negative prices and quantities. As a result, the column time is set to be Date type (in format: 'Year-Month-01'), while the columns prices and quantities are set to be numeric. If the description parameter is set to TRUE then the column description is set to be character type (otherwise it is deleted). Please note that the milk set is an already prepared dataset but let us assume for a moment that we want to make sure that it does not contain missing values and we do not need the column description for further calculations. For this purpose, we use the data_preparing function as follows:

    head(data_preparing(milk, time="time",prices="prices",quantities="quantities"))

data_aggregating

The function aggregates the user's data frame over time and/or over outlets. Consequently, we obtain monthly data, where the unit value is calculated instead of a price for each prodID observed in each month (the time column gets the Date format: "Year-Month-01"). If paramter join_outlets is TRUE, then the function also performs aggregation over outlets (retIDs) and the retID column is removed from the data frame. The main advantage of using this function is the ability to reduce the size of the data frame and the time needed to calculate the price index. For instance, let us consider the following data set:

    dataAGGR

After aggregating this data set over time and outlets we obtain:

    data_aggregating(dataAGGR)

data_unit

The function returns the user's data frame with two additional columns: grammage and unit (both are character type). The values of these columns are extracted from product descriptions on the basis of provided units. Please note, that the function takes into consideration a sign of the multiplication, e.g. if the product description contains: '2x50 g', we will obtain: grammage: 100 and unit: g for that product (for multiplication set to 'x'). For example:

    data_unit(dataU,units=c("g","ml","kg","l"),multiplication="x")

data_norm

The function returns the user's data frame with two transformed columns: grammage and unit, and two rescaled columns: prices and quantities. The above-mentioned transformation and rescaling take into consideration the user rules. Recalculated prices and quantities concern grammage units defined as the second parameter in the given rule. For instance:

    # Preparing a data set
    data<-data_unit(dataU,units=c("g","ml","kg","l"),multiplication="x")
    # Normalization of grammage units
    data_norm(data, rules=list(c("ml","l",1000),c("g","kg",1000)))

data_selecting

The function returns a subset of the user's data set obtained by selection based on keywords and phrases defined by parameters: include, must and exclude (an additional column coicop is optional). Providing values of these parameters, please remember that the procedure distinguishes between uppercase and lowercase letters only when sensitivity is set to TRUE.

For instance, please use

    subgroup1<-data_selecting(milk, include=c("milk"), must=c("UHT"))
    head(subgroup1)

to obtain the subset of milk limited to UHT category:

    unique(subgroup1$description)

You can use

    subgroup2<-data_selecting(milk, must=c("milk"), exclude=c("past","goat"))
    head(subgroup2)

to obtain the subset of milk with products which are not pasteurized and which are not goat:

    unique(subgroup2$description)

data_classifying

This function predicts product COICOP levels using the selected machine learning model (see the model parameter). It provides the indicated data set with an additional column, i.e. coicop_predicted. The selected model must be built previously (see the model_classification function) and after the training process it can be saved on your disk (see the save_model function) and then loaded at any time (see the load_model function). Please note that the machine learning process is based on the XGBoost algorithm (from the XGBoost package) which is an implementation of gradient boosted decision trees designed for speed and performance. For example, let us build a machine learning model

    my.grid=list(eta=c(0.01,0.02,0.05),subsample=c(0.5))
    data_train<-dplyr::filter(dataCOICOP,dataCOICOP$time<=as.Date("2020-08-01"))
    data_test<-dplyr::filter(dataCOICOP,dataCOICOP$time>as.Date("2020-08-01"))
    ML<-model_classification(data_train,
                             data_test,
                             grid=my.grid,
                             indicators=c("prodID","unit","description"),
                             key_words=c("milk"),rounds=50)

We can watch the results of the whole training process:

    ML$figure_training

or we can observe the importance of the used indicators:

    ML$figure_importance

We can save the model on the disk, load it and use it at any time by using save_model() and load_model() functions. We can use the model for COICOP predictions

    data_predicted<-data_classifying(ML, data_test)
    head(data_predicted)

data_matching

If you have a dataset with information about products sold but they are not matched you can use the data_matching function. In an optimal situation, your data frame contains the codeIN, codeOUT and description columns (see documentation), which in practice will contain retailer codes, GTIN or SKU codes and product labels, respectively. The data_matching function returns a data set defined in the first parameter (data) with an additional column (prodID). Two products are treated as being matched if they have the same prodID value. The procedure of generating the above-mentioned additional column depends on the set of chosen columns for matching (see documentation for details). For instance, let us suppose you want to obtain matched products from the following, artificial data set:

    head(dataMATCH)

Let us assume that products with two identical codes (codeIN and codeOUT) or one of the codes identical and an identical description are automatically matched. Products are also matched if they have one of the codes identical and the Jaro-Winkler distance of their descriptions is bigger than the fixed precision value (see documentation - Case 1). Let us also suppose that you want to match all products sold in the interval: December 2018 - February 2019. If you use the data_matching function (as below), an additional column (prodID) will be added to your data frame:

    data1<-data_matching(dataMATCH, start="2018-12",end="2019-02", codeIN=TRUE, codeOUT=TRUE, precision=.98, interval=TRUE)
    head(data1)

Let us now suppose you do not want to consider codeIN while matching and that products with an identical description are to be matched too:

    data2<-data_matching(dataMATCH, start="2018-12",end="2019-02",
                         codeIN=FALSE, onlydescription=TRUE, interval=TRUE)
    head(data2)

Now, having a prodID column, your datasets are ready for further price index calculations, e.g.:

    fisher(data1, start="2018-12", end="2019-02")
    jevons(data2, start="2018-12", end="2019-02")

data_filtering

This function returns a filtered data set, i.e. a reduced user's data frame with the same columns and rows limited by a criterion defined by the filters parameter (see documentation). If the set of filters is empty then the function returns the original data frame (defined by the data parameter). On the other hand, if all filters are chosen, i.e. filters=c(extremeprices, dumpprices, lowsales), then these filters work independently and a summary result is returned. Please note that both variants of the extremeprices filter can be chosen at the same time, i.e. plimits and pquantiles, and they work also independently. For example, let us assume we consider three filters: filter1 is to reject 1% of the lowest and 1% of the highest price changes comparing March 2019 to December 2018, filter2 is to reject products with the price ratio being less than 0.5 or bigger than 2 in the same time, filter3 rejects the same products as filter2 rejects and also products with relatively low sale in compared months, filter4 rejects products with the price ratio being less than 0.9 and with the expenditure ratio being less than 0.8 in the same time.

    filter1<-data_filtering(milk,start="2018-12",end="2019-03",
                            filters=c("extremeprices"),pquantiles=c(0.01,0.99))
    filter2<-data_filtering(milk,start="2018-12",end="2019-03",
                            filters=c("extremeprices"),plimits=c(0.5,2))
    filter3<-data_filtering(milk,start="2018-12",end="2019-03",
                            filters=c("extremeprices","lowsales"),plimits=c(0.5,2))
    filter4<-data_filtering(milk,start="2018-12",end="2019-03",
                            filters=c("dumpprices"),dplimits=c(0.9,0.8))

These three filters differ from each other with regard to the data reduction level:

    data_without_filters<-data_filtering(milk,start="2018-12",end="2019-03",filters=c())
    nrow(data_without_filters)
    nrow(filter1)
    nrow(filter2)
    nrow(filter3)
    nrow(filter4)

You can also use data_filtering for each pair of subsequent months from the considered time interval under the condition that this filtering is done for each outlet (retID) separately, e.g.

    filter1B<-data_filtering(milk,start="2018-12",end="2019-03",
                             filters=c("extremeprices"),pquantiles=c(0.01,0.99),
                             interval=TRUE, retailers=TRUE)
    nrow(filter1B)

### Functions providing dataset characteristics

available

The function returns all values from the indicated column (defined by the type parameter) which occur at least once in one of compared periods or in a given time interval. Possible values of the type parameter are: retID, prodID, codeIN, codeOUT or description (see documentation). If the interval parameter is set to FALSE, then the function compares only periods defined by period1 and period2. Otherwise the whole time period between period1 and period2 is considered. For example:

    available(milk, period1="2018-12", period2="2019-12", type="retID",interval=TRUE)

matched

The function returns all values from the indicated column (defined by the type parameter) which occur simultaneously in the compared periods or in a given time interval.Possible values of the type parameter are: retID, prodID, codeIN, codeOUT or description (see documentation). If the interval parameter is set to FALSE, then the function compares only periods defined by period1 and period2. Otherwise the whole time period between period1 and period2 is considered. For example:

    matched(milk, period1="2018-12", period2="2019-12", type="prodID",interval=TRUE)

matched_index

The function returns a ratio of values from the indicated column that occur simultaneously in the compared periods or in a given time interval to all available values from the above-mentioned column (defined by the type parameter) at the same time. Possible values of the type parameter are: retID, prodID, codeIN, codeOUT or description (see documentation). If the interval parameter is set to FALSE, then the function compares only periods defined by period1 and period2. Otherwise the whole time period between period1 and period2 is considered. The returned value is from 0 to 1. For example:

    matched_index(milk, period1="2018-12", period2="2019-12", type="prodID",interval=TRUE)

matched_fig

The function returns a data frame or a figure presenting the matched_index function calculated for the column defined by the type parameter and for each month from the considered time interval. The interval is set by the start and end parameters. The returned object (data frame or figure) depends on the value of the figure parameter. Examples:

    matched_fig(milk, start="2018-12", end="2019-12", type="prodID")

    matched_fig(milk, start="2018-12", end="2019-04", type="prodID", figure=FALSE)

prices

The function returns prices (unit value) of products with a given ID (prodID column) and being sold in the time period indicated by the period parameter. The set parameter means a set of unique product IDs to be used for determining prices of sold products. If the set is empty the function returns prices of all products being available in the period. To get prices (unit values) of all available milk products sold in July, 2019, please use:

    prices(milk, period="2019-06")

quantities

The function returns quantities of products with a given ID (prodID column) and being sold in the time period indicated by the period parameter. The set parameter means a set of unique product IDs to be used for determining prices of sold products. If the set is empty the function returns quantities of all products being available in the period. To get quantities of milk products with prodIDs: 400032, 71772 and 82919, and sold in July, 2019, please use:

    quantities(milk, period="2019-06", set=c(400032, 71772, 82919))

sales

The function returns values of sales of products with a given ID (prodID column) and being sold in the time period indicated by period parameter. The set parameter means a set of unique product IDs to be used for determining prices of sold products. If the set is empty the function returns values of sales of all products being available in the period. To get values of sales of milk products with prodIDs: 400032, 71772 and 82919, and sold in July, 2019, please use:

    sales(milk, period="2019-06", set=c(400032, 71772, 82919))

sales_groups

The function returns values of sales of products from one or more datasets or the corresponding barplot for these sales (if barplot is set to TRUE). Alternatively, it calculates the sale shares (if the shares parameter is set to TRUE). Please see also the sales_groups2 function. As an example, let us create 3 subgroups of milk products and let us find out their sale shares for the time interval: April, 2019 - July, 2019. We can obtain precise values for the given period:

    ctg<-unique(milk$description)
    categories<-c(ctg[1],ctg[2],ctg[3])
    milk1<-dplyr::filter(milk, milk$description==categories[1])
    milk2<-dplyr::filter(milk, milk$description==categories[2])
    milk3<-dplyr::filter(milk, milk$description==categories[3])
    sales_groups(datasets=list(milk1,milk2,milk3),start="2019-04", end="2019-07")
    sales_groups(datasets=list(milk1,milk2,milk3),start="2019-04", end="2019-07", shares=TRUE)

or a barplot presenting these results:

    sales_groups(datasets=list(milk1,milk2,milk3),start="2019-04", end="2019-07",
                 barplot=TRUE, shares=TRUE, names=categories)

pqcor

The function returns Pearson's correlation coefficient for price and quantity of products with given IDs (defined by the set parameter) and sold in the period. If the set is empty, the function works for all products being available in the period. The figure parameter indicates whether the function returns a figure with a correlation coefficient (TRUE) or just a correlation coefficient (FALSE). For instance:

    pqcor(milk, period="2019-05")
    pqcor(milk, period="2019-05",figure=TRUE)

pqcor_fig

The function returns Pearson's correlation coefficients between price and quantity of products with given IDs (defined by the set parameter) and sold in the time interval defined by the start and end parameters. If the set is empty the function works for all available products. Correlation coefficients are calculated for each month separately. Results are presented in tabular or graphical form depending on the figure parameter. Both cases are presented below:

    pqcor_fig(milk, start="2018-12", end="2019-06", figure=FALSE)
    pqcor_fig(milk, start="2018-12", end="2019-06")

dissimilarity

This function returns a value of the relative price (dSP) and/or quantity (dSQ) dissimilarity measure. In a special case, when the type parameter is set to pq, the function provides the value of dSPQ measure (relative price and quantity dissimilarity measure calculated as min(dSP,dSQ). For instance:

    dissimilarity(milk, period1="2018-12",period2="2019-12",type="pq")

dissimilarity_fig

This function presents values of the relative price and/or quantity dissimilarity measure over time. The user can choose a benchmark period (defined by benchmark) and the type of dissimilarity measure is to be calculated (defined by type). The obtained results of dissimilarities over time can be presented in a dataframe form or via a figure (the default value of figure is TRUE which results a figure). For instance:

    dissimilarity_fig(milk, start="2018-12",end="2019-12",type="pq",benchmark="start")

### Functions for bilateral unweighted price index calculation

This package includes 6 functions for calculating the following bilateral unweighted price indices:

Price Index | Function
--- | ---
BMW (2007) | bmw
Carli (1804) | carli
CSWD (1980,1992) | cswd
Dutot (1738) | dutot
Jevons (1865) | jevons
Harmonic | harmonic

Each of these functions returns a value (or vector of values) of the choosen unweighted bilateral price index depending on the interval parameter. If the interval parameter is set to TRUE, the function returns a vector of price index values without dates. To get information about both price index values and corresponding dates please see general functions: price_index, price_indices or final_index. None of these functions takes into account aggregating over outlets or product subgroups (to consider these types of aggregating please use the final_index function.) Below are examples of calculations for the Jevons index (in the second case a fixed base month is set to December 2018):

    jevons(milk, start="2018-12", end="2020-01")
    jevons(milk, start="2018-12", end="2020-01", interval=TRUE)

### Functions for bilateral weighted price index calculation

This package includes 26 functions for calculating the following bilateral weighted price indices:

Price Index | Function
--- | ---
AG Mean (2009) | agmean
Banajree (1977) | banajree
Bialek (2012,2013) | bialek
Davies (1924) | davies
Drobisch (1871) | drobisch
Fisher (1922) | fisher
Geary-Khamis (1958,1970) | geary_khamis
Geo-Laspeyres | geolaspeyres
Geo-Lowe | geolowe
Geo-Paasche | geopaasche
Geo-Young | geoyoung
Geo-hybrid (2020) | geohybrid
Hybrid (2020) | hybrid
Laspeyres (1871) | laspeyres
Lehr (1885) | lehr
Lloyd-Moulton (1975,1996) | lloyd_moulton
Lowe | lowe
Marshall-Edgeworth (1887) | marshall_edgeworth
Paasche (1874) | paasche
Palgrave (1886) | palgrave
Sato-Vartia (1976) | sato_vartia
Stuvel (1957) | stuvel
Tornqvist (1936) | tornqvist
Vartia (1976) | vartia
Walsh (1901) | walsh
Young | young

Each of these functions returns a value (or vector of values) of the choosen weighted bilateral price index depending on the interval parameter. If interval parameter is set to TRUE, the function returns a vector of price index values without dates. To get information about both price index values and corresponding dates please see general functions: price_index, price_indices or final_index. None of these functions takes into account aggregating over outlets or product subgroups (to consider these types of aggregating please use the final_index function.) Below are examples of calculations for the Fisher, the Lloyd-Moulton and the Lowe indices (in the last case, the fixed base month is set to December 2019 and the prior period is December 2018):

    fisher(milk, start="2018-12", end="2020-01")
    lloyd_moulton(milk, start="2018-12", end="2020-01", sigma=0.9)
    lowe(milk, start="2019-12", end="2020-02", base="2018-12", interval=TRUE)

### Functions for chain price index calculation

This package includes 32 functions for calculating the following chain price indices (weighted and unweighted):

Price Index | Function
--- | ---
Chain BMW | chbmw
Chain Carli | chcarli
Chain CSWD | chcswd
Chain Dutot | chdutot
Chain Jevons | chjevons
Chain Harmonic | chharmonic
Chain AG Mean | chagmean
Chain Banajree | chbanajree
Chain Bialek | chbialek
Chain Davies | chdavies
Chain Drobisch | chdrobisch
Chain Fisher | chfisher
Chain Geary-Khamis | chgeary_khamis
Chain Geo-Laspeyres | chgeolaspeyres
Chain Geo-Lowe | chgeolowe
Chain Geo-Paasche | chgeopaasche
Chain Geo-Young | chgeoyoung
Chain Geo-hybrid | chgeohybrid
Chain Hybrid | chhybrid
Chain Laspeyres | chlaspeyres
Chain Lehr | chlehr
Chain Lloyd-Moulton | chlloyd_moulton
Chain Lowe | chlowe
Chain Marshall-Edgeworth | chmarshall_edgeworth
Chain Paasche | chpaasche
Chain Palgrave | chpalgrave
Chain Sato-Vartia | chsato_vartia
Chain Stuvel | chstuvel
Chain Tornqvist | chtornqvist
Chain Vartia | chvartia
Chain Walsh | chwalsh
Chain Young | chyoung

Each time, the interval parameter has a logical value indicating whether the function is to compare the research period defined by end to the base period defined by start (then interval is set to FALSE and it is a default value) or all fixed base indices are to be calculated. In this second case, all months from the time interval are considered and start defines the base period (interval is set to TRUE). Here are examples for the Fisher chain index:

    chfisher(milk, start="2018-12", end="2020-01")
    chfisher(milk, start="2018-12", end="2020-01", interval=TRUE)

### Functions for multilateral price index calculation

This package includes 18 functions for calculating multilateral price indices and one additional and general function (QU) which calculates the quality adjusted unit value index, i.e.:

Price Index | Function
--- | ---
CCDI | ccdi
GEKS | geks
WGEKS | wgeks
GEKS-J | geksj
GEKS-W | geksw
GEKS-L | geksl
WGEKS-L | wgeksl
GEKS-GL | geksgl
WGEKS-GL | wgeksgl
GEKS-AQU | geksaqu
WGEKS-AQU | wgeksaqu
GEKS-AQI | geksaqi
WGEKS-AQI | wgeksaqi
GEKS-GAQI | geksgaqi
WGEKS-GAQI | wgeksgaqi
Geary-Khamis | gk
Quality Adjusted Unit Value | QU
Time Product Dummy | tpd
SPQ | SPQ

The above-mentioned 18 multilateral formulas (the SPQ index is an exception) consider the time window defined by the wstart and window parameters, where window is a length of the time window (typically multilateral methods are based on a 13-month time window). It measures the price dynamics by comparing the end period to the start period (both start and end must be inside the considered time window). To get information about both price index values and corresponding dates, please see functions: price_index, price_indices or final_index. These functions do not take into account aggregating over outlets or product subgroups (to consider these types of aggregating please use functions: final_index or final_index2). Here are examples for the GEKS formula (see documentation):

    geks(milk, start="2019-01", end="2019-04",window=10)
    geksl(milk, wstart="2018-12", start="2019-03", end="2019-05")

The QU function returns a value of the quality adjusted unit value index (QU index) for the given set of adjustment factors. An additional v parameter is a data frame with adjustment factors for at least all matched prodIDs. It must contain two columns: prodID with unique product IDs and value with corresponding adjustment factors (see documentation). The following example starts from creating a data frame which includes sample adjusted factors:

    prodID<-base::unique(milk$prodID)
    values<-stats::runif(length(prodID),1,2)
    v<-data.frame(prodID,values)
    head(v)

and the next step is calculating the QU index which compares December 2019 to December 2018:

    QU(milk, start="2018-12", end="2019-12", v)

### Functions for extending multilateral price indices by using splicing methods

This package includes 17 functions for calculating splice indices:

Price Index | Function
--- | ---
Splice CCDI | ccdi_splcie
Splice GEKS | geks_splice
Splice weighted GEKS | wgeks_splice
Splice GEKS-J | geksj_splice
Splice GEKS-W | geksw_splice
Splice GEKS-L | geksl_splice
Splice weighted GEKS-L | wgeksl_splice
Splice GEKS-GL | geksgl_splice
Splice weighted GEKS-GL | wgeksgl_splice
Splice GEKS-AQU | geksaqu_splice
Splice weighted GEKS-AQU | wgeksaqu_splice
Splice GEKS-AQI | geksaqi_splice
Splice weighted GEKS-AQI | wgeksaqi_splice
Splice GEKS-GAQI | geksgaqi_splice
Splice weighted GEKS-GAQI | wgeksgaqi_splice
Splice Geary-Khamis | gk_splice
Splice Time Product Dummy | tpd_splice

These functions return a value (or values) of the selected multilateral price index extended by using window splicing methods (defined by the splice parameter). Available splicing methods are: movement splice, window splice, half splice, mean splice and their additional variants: window splice on published indices (WISP), half splice on published indices (HASP) and mean splice on published indices (see documentation). The first considered time window is defined by the start and window parameters, where window is a length of the time window (typically multilateral methods are based on a 13-month time window). Functions measure the price dynamics by comparing the end period to the start period, i.e. if the time interval exceeds the defined time window then splicing methods are used. If the interval parameter is set to TRUE, then all fixed base multilateral indices are presented (the fixed base month is defined by start). To get information about both price index values and corresponding dates, please see functions: price_index, price_indices or final_index. These functions do not take into account aggregating over outlets or product subgroups (to consider these types of aggregating, please use the final_index function). For instance, let us calculate the extended Time Product Dummy index by using the half splice method with a 10-month time window:

    tpd_splice(milk, start="2018-12", end="2020-02",window=10,splice="half",interval=TRUE)

### Functions for extending multilateral price indices by using the FBEW method

This package includes 17 functions for calculating extensions of multilateral indices by using the Fixed Base Monthly Expanding Window (FBEW) method:

Price Index | Function
--- | ---
FBEW CCDI | ccdi_fbew
FBEW GEKS | geks_fbew
FBEW WGEKS | wgeks_fbew
FBEW GEKS-J | geksj_fbew
FBEW GEKS-W | geksw_fbew
FBEW GEKS-L | geksl_fbew
FBEW WGEKS-L | wgeksl_fbew
FBEW GEKS-GL | geksgl_fbew
FBEW WGEKS-GL | wgeksgl_fbew
FBEW GEKS-AQU | geksaqu_fbew
FBEW WGEKS-AQU | wgeksaqu_fbew
FBEW GEKS-AQI | geksaqi_fbew
FBEW WGEKS-AQI | wgeksaqi_fbew
FBEW GEKS-GAQI | geksgaqi_fbew
FBEW WGEKS-GAQI | wgeksgaqi_fbew
FBEW Geary-Khamis | gk_fbew
FBEW Time Product Dummy | tpd_fbew

These functions return a value (or values) of the selected multilateral price index extended by using the FBEW method. The FBEW method uses a time window with a fixed base month every year (December). The window is enlarged every month with one month in order to include information from a new month. The full window length (13 months) is reached in December of each year. These functions measure the price dynamics between the end and start periods. A month of the start parameter must be December (see documentation). If the distance between end and start exceeds 13 months, then internal Decembers play a role of chain-linking months. To get information about both price index values and corresponding dates please see functions: price_index, price_indices or final_index. These functions do not take into account aggregating over outlets or product subgroups (to consider these types of aggregating, please use the final_index function). For instance, let us calculate the extended GEKS index by using the FBEW method. Please note that December 2019 is the chain-linking month, i.e.:

    geks_fbew(milk, start="2018-12", end="2020-03")
      geks_fbew(milk, start="2018-12", end="2019-12")*
      geks_fbew(milk, start="2019-12", end="2020-03")

### Functions for extending multilateral price indices by using the FBMW method

This package includes 17 functions for calculating extensions of multilateral indices by using the Fixed Base Moving Window (FBMW) method:

Price Index | Function
--- | ---
FBMW CCDI | ccdi_fbmw
FBMW GEKS | geks_fbmw
FBMW WGEKS | wgeks_fbmw
FBMW GEKS-J | geksj_fbmw
FBMW GEKS-W | geksw_fbmw
FBMW GEKS-L | geksl_fbmw
FBMW WGEKS-L | wgeksl_fbmw
FBMW GEKS-GL | geksgl_fbmw
FBMW WGEKS-GL | wgeksgl_fbmw
FBMW GEKS-AQU | geksaqu_fbmw
FBMW WGEKS-AQU | wgeksaqu_fbmw
FBMW GEKS-AQI | geksaqi_fbmw
FBMW WGEKS-AQI | wgeksaqi_fbmw
FBMW GEKS-GAQI | geksgaqi_fbmw
FBMW WGEKS-GAQI | wgeksgaqi_fbmw
FBMW Geary-Khamis | gk_fbmw
FBMW Time Product Dummy | tpd_fbmw

These functions return a value (or values) of the selected multilateral price index extended by using the FBMW method. They measure the price dynamics between the end and start periods and it uses a 13-month time window with a fixed base month taken as year(end)-1. If the distance between end and start exceeds 13 months, then internal Decembers play a role of chain-linking months. A month of the start parameter must be December (see documentation). To get information about both price index values and corresponding dates, please see functions: price_index, price_indices or final_index. These functions do not take into account aggregating over outlets or product subgroups (to consider these types of aggregating, please use the final_index function). For instance, let us calculate the extended CCDI index by using the FBMW method. Please note that December 2019 is the chain-linking month, i.e.:

    ccdi_fbmw(milk, start="2018-12", end="2020-03")

    ccdi_fbmw(milk, start="2018-12", end="2019-12")*
    ccdi_fbmw(milk, start="2019-12", end="2020-03")

### General functions for price index calculations

This package includes 3 general functions for price index calculation. The start and end parameters indicate the base and the research period respectively. These function provide value or values (depending on the interval parameter) of the selected price index formula or formulas. If the interval parameter is set to TRUE then it returns a data frame with two columns: dates and index values. Functions price_index and price_indices do not take into account aggregating over outlets or product subgroups and to consider these types of aggregating, please use functions: final_index or final_index2.

price_index

This function returns a value or values of the selected price index. The formula parameter is a character string indicating the price index formula is to be calculated (see documentation). If the selected price index formula needs some additional information it should be defined by additional parameters: window and splice (connected with multilateral indices), base (adequate for the Young and the Lowe indices) or sigma (for the Lloyd-Moulton or the AG mean indices). Sample use:

    price_index(milk, start="2019-05", end="2019-06", formula="fisher")
    price_index(milk, start="2018-12", end="2020-02",
                formula="tpd_splice",splice="movement",interval=TRUE)

price_indices

This is an extended version of the price_index function because it allows us to compare many price index formulas by using one command. The general character of this function mean that, for instance, your one command may calculate two CES indices for two different values of sigma parameter (the elasticity of substitution) or you can select several splice indices and calculate them by using different window lengths and different splicing method. You can control names of columns in the resulting data frame by defining additional parameters: namebilateral, namebindex, namecesindex, namefbmulti, namesplicemulti although their default values correspond to the used price index formulas. Please note that this function is not the most general in the package, i.e. all selected price indices are calculated for the same data set defined by the data parameter and the aggregation over subgroups or outlets are not taken into consideration here (to consider it, please use functions: final_index or final_index2).

For instance, let us use the milk data set and let us calculate the price dynamics for the time interval December 2019 - August 2020) using the following price index formulas: the Fisher index, the Young index with the prior period set to December 2018, the AG mean index with the elasticity of substitution parameter sigma=0.5, the full-window GEKS index with a 9-month window length, the full-window Geary-Khamis index with a 9-month window length, the splice TPD index using a 6-month time window and being extended by using the movement splice method:

    price_indices(milk, start="2019-12", end="2020-08", bilateral=c("fisher"),
                  bindex=c("young"), base=c("2018-12"),
                  cesindex=c("agmean"), sigma=c(0.5),
                  fbmulti=c("geks", "gk"), fbwindow=c(9,9),
                  splicemulti=c("tpd_splice"),splicewindow=c(6),
                  splice=c("movement"), interval=TRUE)

final_index

This function returns a value or values of the selected (final) price index taking into consideration aggregation over product subgroups and/or over outlets (retailer sale points defined in the retID column). If the interval parameter is set to TRUE, then it returns a data frame with two columns: dates and final index values (after optional aggregating). Please note that different index formulas may use different time intervals (or time periods) for calculations and, each time, if the aggrret parameter differs from "none", aggregation over outlets is done for the set of retIDs being available during all considered months. Moreover, for each outlet, i.e. each retID code, the set of considered prodID codes is limited to those codes which are available simultaneously in all considered months.

Details: the datasets parameter defines the user's list of data frames with subgroups of sold products (see documentation). The formula parameter is a character string indicating the price index formula is to be calculated (see documentation). If the selected price index formula needs some additional information, it should be defined by additional parameters: window and splice (connected with multilateral indices), base (adequate for the Young and the Lowe indices) or sigma (for the Lloyd-Moulton or the AG mean indices). The aggrret parameter is a character string indicating the formula for aggregation over outlets (retailer sale points defined in the retID column). Available options are: none, laspeyres, paasche, geolaspeyres, geopaasche, fisher, tornqvist, arithmetic and geometric. The first option means that there is no aggregating over outlets. The last two options mean unweighted methods of aggregating, i.e. the arithmetic or the geometric mean is used. Similarly, the aggrsets parameter is a character string indicating the formula for aggregation over product subgroups with identical options as previously.

Example. Let us define two subgroups of milk:

    g1<-dplyr::filter(milk, milk$description=="full-fat milk UHT")
    g2<-dplyr::filter(milk, milk$description=="low-fat milk UHT")

Now, for the fixed time interval: December 2018 - May 2019, let us calculate the (final) chain Walsh price index (the fixed base month is December 2018) taking into consideration the Laspeyres aggregation over subgroups g1 and g2 and the Fisher aggregation over outlets:

    final_index(datasets=list(g1,g2), start="2018-12", end="2019-05",
                formula="chwalsh",
                aggrsets = "laspeyres", aggrret = "fisher",
                interval=TRUE)

final_index2

This function returns a value or values of the selected (final) price index taking into consideration aggregation over product subgroups and/or over outlets. Optionally, the function returns a data frame or a figure presenting calculated indices, i.e. the price index for the whole data set and price indices for product subgroups. If the interval parameter is set to TRUE, then it returns a data frame (or a figure) with dates and final index values (after optional aggregating). Please note that different index formulas may use different time intervals (or time periods) for calculations and, each time, if the aggrret parameter differs from "none", aggregation over outlets is done for the set of retIDs being available during all considered months. Moreover, for each outlet, i.e. each retID code, the set of considered prodID codes is limited to those codes which are available simultaneously in all considered months.

Details: the data parameter defines the user's data frame with subgroups of sold products (see documentation). The by parameter indicates a grouping variable name, i.e. this column is used for creating subgroups of products. The all parameter is a logical value indicating whether the the selected price index is to be calculated only for the whole set of products or also for created subgroups of products (then all is set to TRUE). The formula parameter is a character string indicating the price index formula is to be calculated (see documentation). If the selected price index formula needs some additional information, it should be defined by additional parameters: window and splice (connected with multilateral indices), base (adequate for the Young and the Lowe indices) or sigma (for the Lloyd-Moulton or the AG mean indices). The aggrret parameter is a character string indicating the formula for aggregation over outlets (retailer sale points defined in the retID column). Available options are: none, laspeyres, paasche, geolaspeyres, geopaasche, fisher, tornqvist, arithmetic and geometric. The first option means that there is no aggregating over outlets. The last two options mean unweighted methods of aggregating, i.e. the arithmetic or the geometric mean is used. Similarly, the aggrsets parameter is a character string indicating the formula for aggregation over product subgroups with identical options as previously. Finally, the figure parameter is a logical value indicating whether the function returns a figure presenting all calculated indices (it works if all and interval are set to TRUE)

Examples. Let us calculate the final Fisher price index (with Laspeyres-type aggregation over subgroups) for the whole data set on coffee and for each product subgroup:

    final_index2(data=coffee, by="description",all=TRUE,
                 start="2018-12",end="2019-12",
                 formula="fisher",
                 interval=TRUE,
                 aggrsets="laspeyres",aggrret="none",
                 figure=FALSE)

and that can be presented in a figure:

    final_index2(data=coffee, by="description",all=TRUE,
                 start="2018-12",end="2019-12", formula="fisher",
                 interval=TRUE,
                 aggrsets="laspeyres",aggrret="none",
                 figure=TRUE)

Now, let us calculate and plot the same price index (with no aggregation) for each retID:

    final_index2(data=coffee, by="retID",all=TRUE,
                 start="2018-12",end="2019-12", formula="fisher",
                 interval=TRUE,
                 aggrsets="none",aggrret="none",
                 figure=TRUE)

### Functions for comparisons of price indices

This package includes two functions for a simple graphical comparison of price indices and one function for calculating distances between indices. The first one, i.e. compare_indices, is based on the syntax of the price_indices function and thus it allows us to compare price indices calculated on the same data set. The second function, i.e. compare_final_indices, has a general character since its first argument is a list of data frames which contain results obtained by using the price_index, final_index or final_index2 functions. The third one, i.e. compare_distances, calculates (average) distances between price indices, i.e. the mean absolute distance or root mean square distance is calculated.

compare_indices

This function calculates selected bilateral or/and multilateral price indices and returns a figure with plots of these indices (together with dates on X-axis and a corresponding legend). The function does not take into account aggregating over outlets or product subgroups (to consider these types of aggregating please use functions: final_index and compare_final_indices). Please note that the syntax of the function corresponds to the syntax of the price_indices function (the meaning of parameters is the same - see documentation). For instance, let us compare the price dynamics for the milk dataset for the time interval: December 2018 - December 2019, calculated by using two price index formulas: the chain Jevons index and the full-window GEKS index. The above-mentioned comparison can be made as follows:

    compare_indices(milk, start="2018-12",end="2019-12",bilateral=c("chjevons"),
                    fbmulti=c("geks"),fbwindow=c(13),
                    namebilateral=c("Chain Jevons"), namefbmulti=c("Full GEKS"))

compare_final_indices

This function returns a figure with plots of previously calculated price indices. It allows for graphical comparison of price index values which were previously calculated and now are provided as data frames. To be more precise: the finalindices parameter is a list of data frames with previously calculated price indices. Each data frame must consist of two columns, i.e. the first column must include dates limited to the year and month and the second column must indicate price index values for corresponding dates. The above-mentioned single data frame may be created manually in the previous step or it may be a result of functions: price_index or final_index. All considered data frames must have an identical number of rows. The names parameter is a vector of character strings describing names of presented indices.

For instance, let us compare the impact of the aggregating over outlets on the price index results (e.g. the Fisher formula is the assumed aggregating method). For this purpose, let us calculate the full-window TPD index in two cases: case1 without the above-mentioned aggregation and case2 which considers that aggregation. We use the milk dataset and the yearly time interval:

    case1<-price_index(milk, start="2018-12",end="2019-12",
                       formula="tpd", interval=TRUE)
    case2<-final_index(datasets=list(milk), start="2018-12", end="2019-12",
                       formula="tpd", aggrsets="none", aggrret = "fisher",
                       interval=TRUE)

The comparison of obtained results can be made as follows (it may be time-consuming on your computer):

    compare_final_indices(finalindices=list(case1, case2),names=c("TPD without aggregation","TPD with aggregation"))

compare_distances

The function calculates average distances between price indices and it returns a data frame with these values for each pair of price indices. The main data parameter is a data frame containing values of indices which are to be compared. The measure parameter specifies what measure should be used to compare the indexes. Possible parameter values are: "MAD" (Mean Absolute Distance) or "RMSD" (Root Mean Square Distance). The results may be presented in percentage points (see the pp parameter) and we can control how many decimal places are to be used in the presentation of results (see the prec parameter).

For instance, let us compare the Jevons, Dutot and Carli indices calculated for the milk data set and for the time interval: December 2018 - December 2019. Let us use the MAD measure for these comparisons:

    #Creating a data frame with unweighted bilateral index values
    df<-price_indices(milk, bilateral=c("jevons","dutot","carli"),
                      start="2018-12",end="2019-12",interval=TRUE)
    #Calculating average distances between indices (in p.p)
    compare_distances(df)

compare_to_target

The function calculates average distances between considered price indices and the target price index and it returns a data frame with: average distances on the basis of all values of compared indices (distance column), average semi-distances on the basis of values of compared indices which overestimate the target index values (distance_upper column) and average semi-distances on the basis of values of compared indices which underestimate the target index values (distance_lower column).

For instance, let us compare the Jevons, Laspeyres, Paasche and Walsh price indices (calculated for the milk data set and for the time interval: December 2018 - December 2019) with the target Fisher price index:

    #Creating a data frame with example bilateral indices
    df<-price_indices(milk,
                      bilateral=c("jevons","laspeyres","paasche","walsh"),
                      start="2018-12",end="2019-12",interval=TRUE)
    #Calculating the target Fisher price index
    target_index<-fisher(milk,start="2018-12",end="2019-12",interval=TRUE)
    #Calculating average distances between considered indices and the Fisher index (in p.p)
    compare_to_target(df,target=target_index)