The goal here is to show how to run many regressions at once, allowing for very fast comparisons. We analyze the bahavior of economic openness through time for different countries. Openness is measured in % of GDP in current prices, a simple linear regression model is fit for each country, with year as the independent variable and openness as the dependent variable; data comes from Penn World Table 7.1.

First load the libraries and the data.

library(pwt)
library(dplyr)
library(tidyr)
library(purrr)
library(broom)
library(pander)

The code is written as sequence of dplyr pipes, but could be broken down into intermediate tibbles if desired. The “trick” is combining tidyr’s nest and purrr’s map functions. Nest will perform an operation similar to grouping and store the operation as a list; and map will apply a function, namely linear regression, to the list for each nested element. Broom’s tidy function will exctract coeffcients from the regression and this will allow the creation of a dataframe with intercepts and coefficients for each country.

open_coefs <- pwt7.1 %>% select(country, year, openc) %>% 
              na.omit( )%>%
              nest(-country) %>%
              mutate(model = map(data, ~lm(openc ~ year, data = .)),
                     tidied = map(model, tidy)) %>%
              unnest(tidied) %>%
              filter(term == "year") %>%
              mutate(adjusted = p.adjust(p.value)) %>%
              filter(adjusted < 0.05) %>%
              arrange(desc(estimate))

The result of this operation is a table of slope coefficients, one for each country, arranged by order of magnitude. Note that only significant coefficients are shown, selected via the p.adjust function, with p value correction for multiple hypothesis testing. The first 10 elements of this table are:

pander(head(open_coefs, 10))
country term estimate std.error statistic p.value adjusted
Hong Kong year 4.928 0.3353 14.7 1.366e-19 2.144e-17
Slovak Republic year 4.584 0.4834 9.483 3.145e-09 3.428e-07
Kyrgyzstan year 4.06 0.6464 6.281 1.096e-05 0.0008876
Cambodia year 3.647 0.3147 11.59 3.361e-14 4.739e-12
Malaysia year 2.896 0.1732 16.72 5.238e-23 8.8e-21
Lesotho year 2.715 0.1856 14.63 1.631e-19 2.544e-17
Georgia year 2.674 0.3985 6.711 5.005e-06 0.0004355
Singapore year 2.656 0.3627 7.323 2.099e-09 2.33e-07
Vietnam year 2.626 0.2462 10.67 3.972e-13 5.283e-11
Serbia year 2.513 0.4143 6.066 7.802e-06 0.0006476

A simple way of determining if more countries are becoming open is to plot the coefficients.

barplot(open_coefs$estimate, ylab = "Coefficients", xlab = "Countries", main = "Openness Coefficients")

As we can see, the majority of countries have coefficients above zero, meaning they became more open with time.

Other Applications

The same code can be executed for other means, let’s do a quick example with multiple regression, having per capita gdp explained by openness (openc) and government share of gdp (cg).

multiple_growth <- pwt7.1 %>% select(country, openc, cg, cgdp) %>% 
  na.omit() %>%
  nest(-country) %>%
  mutate(model = map(data, ~lm(cgdp ~ openc + cg, data = .)),
         tidied = map(model, tidy)) %>%
  unnest(tidied)

This time we didn’t filter for a specific coefficient or only for significant ones, let’s take a look at the output.

pander(head(multiple_growth, 18))
country term estimate std.error statistic p.value
Afghanistan (Intercept) 255 77.66 3.283 0.00221
Afghanistan openc -5.025 1.093 -4.597 4.632e-05
Afghanistan cg 69.99 10.29 6.803 4.549e-08
Albania (Intercept) 615.3 768.7 0.8004 0.4284
Albania openc 80.04 12.53 6.39 1.661e-07
Albania cg -254 95.63 -2.656 0.0115
Algeria (Intercept) 3775 1943 1.942 0.05799
Algeria openc 24.93 17.73 1.406 0.1661
Algeria cg -169.4 118 -1.435 0.1578
Angola (Intercept) 5213 886 5.884 8.214e-07
Angola openc 0.4503 4.256 0.1058 0.9163
Angola cg -99.51 16.32 -6.097 4.185e-07
Antigua and Barbuda (Intercept) -44051 10384 -4.242 0.0001368
Antigua and Barbuda openc 40.93 26.06 1.57 0.1246
Antigua and Barbuda cg 1225 237 5.169 7.822e-06
Argentina (Intercept) 9681 1165 8.309 1.863e-11
Argentina openc 155.5 22.09 7.039 2.517e-09
Argentina cg -1040 105.2 -9.888 4.707e-14

We won’t go into interpreting any of the results, since the idea was just to show how powerful this code can by in providing quick comparisons.