Volume of internationalization (VOI)

Country search scores focus on search volumes for objects in single countries. To compute an object’s volume of internationalization, we focus on global search volumes instead of country search volumes. Using the same approach as outlined above, globaltrends first downloads global search volumes for each control keyword and firm. Next, the package runs the control-object mapping and computes global search scores as the ratio of global search volumes for each object and global control search volumes.

Like country search scores, we can interpret global search scores as the proportion of global search volumes for an object of interest compared to global search volumes for control keywords. This allows researchers to track changes in global interest in objects and highlights phases of fast or receding internationalization. Since the computation of country and global search scores follows the same procedures, the two measures have the same properties. This provides for a direct comparison between country search scores and volume of internationalization in terms of global search scores.

Degree of internationalization (DOI)

As the main measure for degree of internationalization, the globaltrends package uses the global dispersion of country search scores. The more uniform the distribution of search scores across countries, the higher an object’s degree of internationalization. When the distribution of country search scores is highly skewed, with high search scores in the object’s country of origin and low search scores in other countries, the object has a low degree of internationalization. To compute an object’s degree of internationalization, the packages by default uses as the inverted Gini coefficient.

Setup and start database

Research projects that use Google Trends generate a substantial amount of data. To optimally handle this data, the globaltrends package uses an SQLite database to store and handle all data. This ensures efficiency and portability on the one hand and seamless integration with functions implemented in the DBI and dplyr packages on the other hand.

Users create the underlying database through the initialize_db command. The command creates a folder named db within the current working directory and creates an SQLite database file named globaltrends_db.sqlite within this folder. The command also creates all necessary tables within the database. For more information on database tables, please refer to their built-in documentation e.g., ?globaltrends::data_score. The database initialization is necessary only for the first usage of the globaltrends package.

# initialize_db ----------------------------------------------------------------
setwd("your/globaltrends/folder")
initialize_db()
#> Database has been created.
#> Table 'batch_keywords' has been created.
#> ...
#> Table 'data_global' has been created.
#> Successfully disconnected.

After initialization or when resuming work on an existing database it is sufficient to call start_db from the respective working directory. This command connects to the globaltrends_db.sqlite database in the folder db and creates connections to all tables in the database.

# start_db ---------------------------------------------------------------------
setwd("your/globaltrends/folder")
start_db()
#> Successfully connected to database.
#> Successfully exported all objects to .GlobalEnv.
print(ls())
#>  [1] "batch_keywords"   "batch_time"       "countries"        "data_control"
#>  [5] "data_doi"         "data_global"      "data_locations"   "data_mapping"
#>  [9] "data_object"      "data_score"       "dir_current"      "dir_wd"
#> [13] "globaltrends_db"  "keyword_synonyms" "keywords_control" "keywords_object"
#> [17] "time_control"     "time_object"      "us_states"

After work with the globaltrends package is complete, the user disconnects from the database with the command disconnect_db.

# disconnect_db ----------------------------------------------------------------
disconnect_db()
#> Successfully disconnected.

Download data from Google Trends

The next step in the globaltrends workflow is data download from Google Trends. The globaltrends package includes four types of download functions that we explain in detail below. Each of these functions uses the gtrendsR::gtrends function to access the Google Trends API. The Google Trends API allows inputs of up to five keywords for a given location and period. Therefore, the globaltrends package works with “keyword batches” that combine up to five keywords. The respective batch numbers are an input to all functions – either as list or as single integer objects. In the package, we distinguish two types of batches: control batches that include keywords indicating baseline search activity and object batches that include keywords relating to the objects of interest (e.g., firms, persons, products…). Currently, globaltrends only includes two sets of locations. The countries set, which covers all countries that generated at least 0.1% of world GDP in 2018 and the us_states set, covering all US states and Washington DC, see below for further details.

The download for a single keyword batch for a single location takes about 10 seconds. This includes a randomized waiting period of 5-10 seconds between downloads. Depending on download frequency, Google Trends might block users for some time. Unfortunately, the exact download limits are unknown (Issue #140, Issue #255). In this case, globaltrends waits 1 minute before it retries the download.

# add_control_keyword ----------------------------------------------------------
new_control <- add_control_keyword(
  keyword = c("gmail", "maps", "translate", "wikipedia", "youtube"),
  time = "2010-01-01 2020-12-31"
)
#> Successfully created new control batch 1 (gmail ... youtube, 2010-01-01 2020-12-31).

# keywords_control and dplyr interaction ---------------------------------------
dplyr::filter(keywords_control, keyword == "gmail")
#> # A tibble: 1 x 2
#>   batch keyword
#>   <int> <chr>
#> 1     1 gmail

# download_control -------------------------------------------------------------
download_control(control = new_control, locations = countries)
#> Successfully downloaded control data | control: 1 | location: US [1/66]
#> ...
#> Successfully downloaded control data | control: 1 | location: DO [66/66]

# download_control_global ------------------------------------------------------
download_control_global(control = new_control)
#> Successfully downloaded control data | control: 1 | location: world [1/1]

# add_object_keyword -----------------------------------------------------------
new_object <- add_object_keyword(
  keyword = list(
    c("coca cola", "facebook", "microsoft"),
    c("alaska air group", "illinois tool works", "jm smucker")
  ),
  time = "2010-01-01 2020-12-31"
)
#> Successfully created new object batch 1 (coca cola ... microsoft, 2010-01-01 2020-12-31).
#> Successfully created new object batch 2 (alaska air group ... jm smucker, 2010-01-01 2020-12-31).

# keywords_object and dplyr interaction ----------------------------------------
dplyr::filter(keywords_object, keyword == "coca cola")
#> # A tibble: 1 x 2
#>   batch keyword
#>   <int> <chr>
#> 1     1 coca cola

# download_object --------------------------------------------------------------
download_object(object = new_object, locations = countries)
#> Successfully downloaded object data | object: 1 | location: US [1/66]
#> ...
#> Successfully downloaded object data | object: 2 | location: DO [66/66]

# download_object_global -------------------------------------------------------
download_object_global(object = new_object)
#> Successfully downloaded object data | object: 1 | location: world [1/1]
#> Successfully downloaded object data | object: 2 | location: world [1/1]

Compute search scores and internationalization

Once the user has completed all control and object downloads, globaltrends computes search scores for each keyword-time-location combination and at a global level (volume of internationalization). Next, the package uses the across-country distribution of these search scores to measure the degree of internationalization of an object keyword.

# compute_score ----------------------------------------------------------------
compute_score(control = new_control[[1]], object = new_object, locations = countries)
#> Successfully computed search score | control: 1 | object: 1 | location: US [1/66]
#> ...
#> Successfully computed search score | control: 1 | object: 2 | location: DO [66/66]

# compute_voi ------------------------------------------------------------------
compute_voi(control = new_control[[1]], object = new_object)
#> Successfully computed search score | control: 1 | object: 1 | location: world [1/1]
#> Successfully computed search score | control: 1 | object: 2 | location: world [1/1]

# compute_doi ------------------------------------------------------------------
compute_doi(control = new_control[[1]], object = new_object, locations = "countries")
#> Successfully computed DOI | control: 1 | object: 1 [1/2]
#> Successfully computed DOI | control: 1 | object: 2 [2/2]

Exports and plots

Functions in globaltrends write all data directly to tables in the database. With the help of functions from the dplyr package and connections exported from start_db, users can access database tables and prepare their own analysis.

# manual exports ---------------------------------------------------------------
library(dplyr)
data_score %>%
  filter(keyword == "coca cola") %>%
  collect()
#> # A tibble: 8,040 x 8
#>    location keyword    date score_obs score_sad score_trd batch_c batch_o
#>    <chr>    <chr>     <int>     <dbl>     <dbl>     <dbl>   <int>   <int>
#>  1 US       coca cola 14610   0.00362   0.00381   0.00548       1      1
#>  ...
#> 10 US       coca cola 14883   0.00347   0.00365   0.00389       1      1
#> # ... with 8,030 more rows

To enhance usability, the globaltrends package includes a set of export functions that offer filters and return data as tibble. The default value for the batch/keyword, for which export_xxx exports data is NULL. In this case, all values from the database are exported. Alternatively, users can specify filters (e.g., keywords, batches, locations) individually, as vector or as list.

# export_control ---------------------------------------------------------------
export_control(control = 1)
#> # A tibble: 39,600 x 5
#>    location keyword date        hits control
#>    <chr>    <chr>   <date>     <dbl>   <int>
#>  1 US       gmail   2010-01-01    22       1
#>  ...
#> 10 US       gmail   2010-10-01    27       1
#> # ... with 39,590 more rows

# export_score -----------------------------------------------------------------
export_score(object = 1, control = 1)
#> # A tibble: 23,760 x 8
#>    location keyword   date       score_obs score_sad score_trd control object
#>    <chr>    <chr>     <date>         <dbl>     <dbl>     <dbl>   <int>  <int>
#>  1 US       coca cola 2010-01-01   0.00362   0.00381   0.00548       1     1
#>  ...
#> 10 US       coca cola 2010-10-01   0.00347   0.00365   0.00389       1     1
#> # ... with 23,750 more rows

# export_doi and purrr interaction ---------------------------------------------
purrr::map_dfr(c("coca cola", "microsoft"), export_doi, control = 1, type = "obs")
#> # A tibble: 240 x 9
#>    keyword   date       type       gini   hhi entropy control object locations
#>    <chr>     <date>     <chr>     <dbl> <dbl>   <dbl>   <int>  <int> <chr>    
#>  1 coca cola 2010-01-01 score_obs 0.397 0.874  -0.938       1     1 countries
#>  ...
#> 10 coca cola 2010-10-01 score_obs 0.574 0.968  -0.303       1     1 countries
#> # ... with 230 more rows

The export functions from globaltrends also allow direct interaction with dplyr or other packages for further analysis.

# export and dplyr interaction -------------------------------------------------
library(dplyr)
export_doi(object = 1, control = 1, type = "obs") %>%
  filter(lubridate::year(date) == 2019) %>%
  group_by(keyword) %>%
  summarise(gini = mean(gini), .groups = "drop")
#> # A tibble: 3 x 2
#>   keyword    gini
#>   <chr>     <dbl>
#> 1 coca cola 0.615
#> 2 facebook  0.707
#> 3 microsoft 0.682

Exports from globaltrends also serve as input for plot functions and the computation of abnormal changes in internationalization implemented in the package. Except for plot_voi_doi, plot functions have methods for classes of outputs from export_score, export_voi, and export_doi. Alternatively, all plot-functions provide options to work without the respective class e.g., for cases where the class gets lost in a join. The function plot_bar uses the output from export_score as input and shows the locations with the highest search scores for a given object keyword. The function uses only the first keyword in the dataset and averages the search scores for the input dataset – we therefore suggest filtering the output from export_score to a specific period. The plot shows that Coca-Cola has high search scores across Latin America and India.

# plot_score -------------------------------------------------------------------
library(dplyr)
export_score(keyword = "coca cola", control = 1) %>%
  filter(lubridate::year(date) == 2019) %>%
  plot_bar()

The functions plot_box and plot_ts have methods for classes of output from export_score, export_voi, and export_doi. The time series plot function plot_ts shows how search scores and volume or degree of internationalization for objects of interest develops over time. The function plot_box generates boxplots of search score and volume or degree of internationalization distributions. The four plots below compare volume and degree of internationalization for the six companies in our sample. At first glance, we see that Coca-Cola, Facebook, and Microsoft have higher degrees of internationalization than Alaska Air Group, Illinois Tool Works, and J.M. Smucker. It seems as if the degree of internationalization of Facebook and Microsoft increased slightly from 2010 to 2015. Although the overall trend remains stable, Coca-Cola shows greater variation than the other companies.

# plot_doi_ts and plot_doi_box -------------------------------------------------
data <- purrr::map_dfr(1:2, export_doi, keyword = NULL, control = 1, type = "obs")
plot_ts(data)
plot_box(data)

With the function plot_voi_doi, users can compare the volume of internationalization for an object of interest to its degree of internationalization. Like plot_bar, the function uses only the first keyword in a dataset, filtering might be necessary. In the plot below, we compare Facebook’s volume of internationalization to its degree of internationalization. While volume of internationalization indicates the level of global search scores, degree of internationalization relates to the global distribution of search scores. We see that Facebook’s volume of internationalization constantly decreased after its peak in 2013. At the same time, we observe that its degree of internationalization grew from 2010 before peaking in 2013.

# plot_voi_doi -----------------------------------------------------------------
out_voi <- export_voi(keyword = "facebook", type = "obs")
out_doi <- export_doi(keyword = "facebook", object = 1, type = "obs")
plot_voi_doi(data_voi = out_voi, data_doi = out_doi)

Abnormal changes in internationalization

A unique feature of internationalization data from globaltrends is that it allows time series analysis. For a better understanding of changes in the data, the function provides the get_abnorm_hist function that implements functionality used in financial event studies (MacKinlay, 1997; McWilliams & Siegel, 1997). The function compares search scores and volume or degree of internationalization to a historic baseline. By default, the historic baseline is the average from the preceding twelve months. Users can specify the window of the baseline period (train_win) and a can use a break between baseline and date of interest (train_break). Since they are used as baseline, the first train_win + train_break abnormal changes are NA. The get_abnorm_hist function has methods for classes of outputs from export_score, export_voi, and export_doi. For each month in the dataset, the deviation from the historic baseline is computed. To identify abnormal changes, the function provides the percentile rank for each change within the distribution of changes.

data <- export_score(keyword = "facebook", locations = countries)
out <- get_abnorm_hist(data)
na.omit(out) # to drop baseline NA values
#> # A tibble: 7,590 x 8
#>   keyword  location date       control object score score_abnorm quantile
#>   <chr>    <chr>    <date>       <int>  <int> <dbl>        <dbl>    <dbl>
#>  1 facebook US       2011-01-01       1      1  1.19      0.0220     0.728
#>  ...
#> 10 facebook US       2011-10-01       1      1  1.32     -0.0669     0.456
#> # ... with 7,580 more rows

data <- export_voi(object = 1)
out <- get_abnorm_hist(data)
na.omit(out) # to drop baseline NA values
#> # A tibble: 345 x 7
#>    keyword   date       control object     voi voi_abnorm quantile
#>    <chr>     <date>       <int>  <int>   <dbl>      <dbl>    <dbl>
#>  1 coca cola 2011-01-01       1      1 0.00320  -0.000299    0.316
#>  ...
#> 10 coca cola 2011-10-01       1      1 0.00274  -0.000458    0.193
#> # ... with 335 more rows

data <- export_doi(keyword = "microsoft", locations = "us_states")
out <- get_abnorm_hist(data)
na.omit(out) # to drop baseline NA values
#> # A tibble: 345 x 9
#>    keyword   date       type      control object locations   doi doi_abnorm quantile
#>    <chr>     <date>     <chr>       <int>  <int> <chr>     <dbl>      <dbl>    <dbl>
#>  1 microsoft 2011-01-01 score_obs       1      1 us_states 0.919    0.0330     0.991
#>  ...
#> 10 microsoft 2011-04-01 score_obs       1      1 us_states 0.909    0.0171     0.886
#> # ... with 335 more rows

The functions plot_bar, plot_box, and plot_ts have methods for classes of output from get_abnorm_hist. This allows seamless plotting of changes in internationalization. The function plot_bar shows the five locations with the highest and lowest changes in search scores for a given object keyword. The function uses only the first keyword in the dataset and averages changes in search scores for the input dataset – we therefore suggest filtering the output from get_abnorm_hist to a specific period. The plot shows that while positive abnormal changes in search scores for Facebook were greatest in Ecuador and Myanmar, negative abnormal changes were greatest in Italy and Argentina.

data <- export_score(object = 1, locations = countries)
data <- dplyr::filter(data, keyword == "facebook" & lubridate::year(date) >= 2018)
# use 2018 as baseline to compute abnormal changes in 2019
out <- get_abnorm_hist(data)
plot_bar(out)

The time series plot function plot_ts shows how search scores and volume or degree of internationalization for objects of interest changed over time. The function plot_box generates boxplots of changes in search score and volume or degree of internationalization distributions. The input ci allows users to set a confidence interval for plotting. Changes with percentile ranks outside this two-tailed confidence interval are highlighted with red dots. The left-hand plot shows abnormal changes in Facebook’s search score for Germany. Search scores increased “abnormally” (i.e., compared to the historic average) in 2012 and decreased abnormally in 2014. The right-hand plot shows the distribution for Coca Cola’s degree of internationalization and indicates abnormal changes.

data <- export_score(keyword = "facebook", locations = "DE")
out <- get_abnorm_hist(data)
plot_ts(out)

data <- export_doi(keyword = "coca cola", locations = "countries")
out <- get_abnorm_hist(data)
plot_box(out)

Additional options

The globaltrends package offers several options that allow robustness checks and adjustments for default computations. Users can compute global trend dispersion based on different types of time series, use other measures than the inverted Gini-coefficient, or change the set of locations.

Time series adjustments

The computation of search scores in the globaltrends package compares a time series of search volumes for object keywords to the time series of search volumes for control keywords. Noise and seasonality in search volume time series could affect the resulting search scores. The globaltrends package offers two time series adjustments as robustness checks. In the data_score table, column score_obs refers to values without adjustment. Column score_trd uses the underlying time series’ trend for computation.

# computation seasonally adjusted ----------------------------------------------
search_score <- ts(data$hits, frequency = 12)
fit <- stl(search_score, s.window = "period")
trend <- fit$time.series[, "trend"]
# computation trend only -------------------------------------------------------
search_score <- ts(data$hits, frequency = 12)
fit <- stl(search_score, s.window = "period")
seasad <- forecast::seasadj(fit)

Column score_sad corrects the time series for seasonal patterns. In general, outcomes for all three types of time series are similar. Column score_trd applies the greatest smoothing, while score_sad reduces some noise.

The export_doi, get_abnorm_hist, plot_bar, plot_ts, plot_box, and plot_voi_doi functions allow filtering for the type of time series through the type input.

# adapt export and plot options ------------------------------------------------
data_score <- export_score(keyword)
data_voi <- export_voi(keyword)
data_doi <- export_doi(keyword, type = "obs")

plot_bar(data_score, type = "obs")
plot_ts(data_voi, type = "sad")
plot_box(data_doi, type = "trd")
plot_voi_doi(data_voi, data_doi, type = "obs")

get_abnorm_hist(data_voi, type = "obs")

Alternative dispersion measures

The globaltrends package computes degree of internationalization based on the across-location distribution of search scores. By default, the package uses an inverted Gini-coefficient. In addition, the package provides inverted Herfindahl index and inverted Entropy as robustness checks. In general, outcomes for all three dispersion measures are similar.

# computation inverted gini coefficient ----------------------------------------
dplyr::coalesce(1 - ineq::ineq(search_score, type = "Gini"), 0)
# computation inverted herfindahl index ----------------------------------------
dplyr::coalesce(1 - sum((search_score / sum(search_score))^2), 0)
# computation inverted entropy -------------------------------------------------
dplyr::coalesce(-1 * ineq::ineq(search_score, parameter = 1, type = "entropy"), 0)

The export_doi, get_abnorm_hist, plot_ts, plot_box, and plot_voi_doi functions allow filtering for the type of dispersion measures through the measure input.

# adapt export and plot options ------------------------------------------------
data_voi <- export_voi(keyword)
data_doi <- export_doi(keyword, measure = "gini")

plot_ts(data_doi, measure = "gini")
plot_box(data_doi, measure = "hhi")
plot_voi_doi(data_voi, data_doi, measure = "entropy")

get_abnorm_hist(data_doi, measure = "hhi")

# change locations -------------------------------------------------------------
download_control(control = 1, locations = us_states)
download_object(object = list(1,2), locations = us_states)
download_mapping(control = 1, object = 2, locations = us_states)
compute_score(control = 1, object = 2, locations = us_states)
compute_doi(control = 1, object = list(1,2), locations = "us_states")

add_locations(c("AT", "CH", "DE"), type = "dach")
#> Successfully created new location set dach (AT, CH, DE).
data <- export_score(keyword = "coca cola", locations = dach)
dplyr::count(data, location)
#> # A tibble: 3 x 2
#>   location     n
#>   <chr>    <int>
#> 1 AT         127
#> 2 CH         127
#> 3 DE         127

Relevelling of search volumes

Google Trends does not provide raw search queries for downloads. Instead, Google Trends expresses the number of search queries as search volumes relative to the total number of search queries and then normalizes this data. To use Google Trends data, we first have to bring all search volumes to the same level.
For object keyword \(ko\), included in object batch \(bo\), Google Trends observes \(SQ_{ko,bo,l,t}\) search queries for location \(l\) at time \(t\). The number of raw search queries is transformed to search volumes \(SV_{ko,bo,l,t}\) by division through the total number of search queries for the given location-time pair \(l,t\):

\[\begin{equation} SV_{ko,bo,l,t}=\frac{SQ_{ko,bo,l,t}}{\sum SQ_{l,t}}. \tag{1} \end{equation}\]

Next, Google Trends divides search volumes \(SV_{ko,bo,l,t}\) by the maximum search value within object batch \(bo\) at location \(l\) to normalize search volumes to \(\tilde{SV}_{ko,bo,l,t}\):

\[\begin{equation} \tilde{SV}_{ko,bo,l,t}=\frac{SV_{ko,bo,l,t}}{max(SV_{bo,l})*100}. \tag{2} \end{equation}\]

Since this normalization step is contingent on the maximum search volume within object batch \(bo\), normalized search volumes \(\tilde{SV}\) depend on the other keywords included in the object batch, the choice of location, and time span \(T\) (\(t \in T\)) for which data is obtained. To prepare normalized search volumes \(\tilde{SV}\) for further usage, the globaltrends packages follows Castelnuovo and Tran (2017, pp. A1-A2) to relevel \(\tilde{SV}\) through mapping to a benchmark. To this end, we map all \(\tilde{SV}\) values in object batch \(bo\) to the same level as \(\tilde{SV}\) values in control batch \(bc\). The function download_object automatically adds a control keyword \(kc\) to all object batches \(bo\). In functions compute_score and compute_voi, \(\tilde{SV}_{kc,bc,l,t}\) of control keyword \(kc\) in control batch \(bc\) is divided by \(\tilde{SV}_{ko,bc,l,t}\) in object batch \(bo\). By multiplying the result of this division with normalized search volumes \(\tilde{SV}_{ko,bo,l,t}\), we get releveled search volumes \(\tilde{SV}_{ko,bc,l,t}\) for object keyword \(ko\), at location \(l\), at time \(t\):

\[\begin{equation} \tilde{SV}_{ko,bc,l,t}=\tilde{SV}_{ko,bo,t,l}*\frac{\tilde{SV}_{kc,bc,l,t}}{\tilde{SV}_{kc,bo,l,t}}. \tag{3} \end{equation}\]

After the relevelling, search volumes from all object batches use control batch \(bc\) as basis for normalization.

Computing search scores

The outcome of the relevelling is not a de-normalization but that search volumes are releveled to control batch \(bc\). This means that \(\tilde{SV}_{ko,bc,l,t}\) may still be distorted by \(max(SV_{bo,l})\). To overcome such distortion, functions compute_score and compute_voi divide \(\tilde{SV}_{ko,bc,l,t}\) by search volumes for a set of control keywords \(KC\). Since gmail, maps, translate, wikipedia, and youtube allow an approximation of “standard” search volumes on Google, we propose them as control keywords for global trend analysis. These keywords approximate the baseline search traffic on Google. For specific research settings, we suggest adapting control keywords to the respective setting and testing them on the Google Trends portal beforehand. To compute search score \(SC_{ko,l,t}\), we divide search volumes for object keywords by the sum of search volumes for control keywords \(kc \in KC\):

\[\begin{equation} SC_{ko,l,t}=\frac{\tilde{SV}_{ko,bc,l,t}}{\sum_{kc \in KC} \tilde{SV}_{kc,bc,l,t}}. \tag{4} \end{equation}\]

Using equation (3) for normalization from above, we can rewrite the equation (4) for \(SC\) as follows:

\[\begin{equation} SC_{ko,l,t}=\frac{\tilde{SV}_{ko,bo,t,l}*\frac{\tilde{SV}_{kc,bc,l,t}}{\tilde{SV}_{kc,bo,l,t}}}{\sum_{kc \in KC} \tilde{SV}_{kc,bc,l,t}} \tag{5} \end{equation}\]

\[\begin{equation} SC_{ko,l,t}=\frac{\frac{SV_{ko,bo,t,l}}{max(SV_{bo,l})*100}*\frac{\frac{SV_{kc,bc,l,t}}{max(SV_{bc,l})*100}}{\frac{SV_{kc,bo,l,t}}{ max(SV_{bo,l})*100}}}{\sum_{kc \in KC} \frac{SV_{kc,bc,l,t}}{ max(SV_{bc,l})*100}} \tag{6} \end{equation}\]

\[\begin{equation} SC_{ko,l,t}=\frac{SV_{ko,bo,t,l}*\frac{SV_{kc,bc,l,t}}{SV_{kc,bo,l,t}}}{\sum_{kc \in KC} SV_{kc,bc,l,t}} \tag{7} \end{equation}\]

\[\begin{equation} SC_{ko,l,t}=\frac{SV_{ko,bc,l,t}}{\sum_{kc \in KC} SV_{kc,bc,l,t}}. \tag{8} \end{equation}\]

Using the equation (1) for \(SV\) from above, we can reformulate \(SC\) as:

\[\begin{equation} SC_{ko,l,t}=\frac{\frac{SQ_{ko,l,t}}{\sum SQ_{l,t}}} {\sum_{kc \in KC} \frac{SQ_{kc,l,t}}{\sum SQ_{l,t}}}. \tag{9} \end{equation}\]

\[\begin{equation} SC_{ko,l,t}=\frac{SQ_{ko,l,t}}{\sum_{kc \in KC} SQ_{kc,l,t}}. \tag{10} \end{equation}\]

Based on these transformations, we can interpret search score \(SC\) as the ratio of search queries \(SQ_{ko,l,t}\) for object keyword \(ko\) divided by the sum of search queries \(SQ_{kc,l,t}\) for control keywords \(ko \in KC\) at location \(l\) for time \(t\). Since \(SC\) is independent from any keyword batch \(bo\) or \(bc\), search scores therefore allow comparison across objects of interest, time, and countries.