How Could I Find The Growth Rate of Gdp

How could I find the growth rate of GDP

You can also use the lag() fuction from dplyr. It gives the previous values in a vector. Here is an example

data <- data.frame(year = c(2003:2013),
                   gdp = c(7696034.9, 8690254.3, 9424601.9, 10520792.8,
                           11399472.2, 12256863.6, 12072541.6, 13266857.9,
                           14527336.9, 15599270.7, 16078959.8))
library(dplyr)
growth_rate <- function(x)(x/lag(x)-1)*100 
data$growth_rate <- growth_rate(data$gdp) 

How do I create a an annualized growth rate for GDP column in my dataframe?

You can use shift to access the previous row and vectorial operations for subtraction, division, power, multiplication:

df['Annualized_Growth_Rate'] = df['GDP'].div(df['GDP'].shift()).pow(4).sub(1).mul(100)

Output:

   Index  GDP  Annualized_Growth_Rate
0      0  100                     NaN
1      1  101                4.060401
2      2  103                8.159184
3      3  107               16.462528

How to compute the growth rate of a variable for a varying time horizon in a panel?

Are you looking for something like this?

library(dplyr)

data <- data.frame(
  state = rep(c('Aguascalientes', 'Jalisco'), each = 10),
  year = 2011:2020,
  population = 91:100,
  gdp = 100:109
)

data
#>             state year population gdp
#> 1  Aguascalientes 2011         91 100
#> 2  Aguascalientes 2012         92 101
#> 3  Aguascalientes 2013         93 102
#> 4  Aguascalientes 2014         94 103
#> 5  Aguascalientes 2015         95 104
#> 6  Aguascalientes 2016         96 105
#> 7  Aguascalientes 2017         97 106
#> 8  Aguascalientes 2018         98 107
#> 9  Aguascalientes 2019         99 108
#> 10 Aguascalientes 2020        100 109
#> 11        Jalisco 2011         91 100
#> 12        Jalisco 2012         92 101
#> 13        Jalisco 2013         93 102
#> 14        Jalisco 2014         94 103
#> 15        Jalisco 2015         95 104
#> 16        Jalisco 2016         96 105
#> 17        Jalisco 2017         97 106
#> 18        Jalisco 2018         98 107
#> 19        Jalisco 2019         99 108
#> 20        Jalisco 2020        100 109

data %>%
  group_by(state) %>%
  mutate(
    across(c(gdp, population), ~(.[year == 2020] - .) / ., .names = '{col}_%change')
  )
#> # A tibble: 20 x 6
#> # Groups:   state [2]
#>    state           year population   gdp `gdp_%change` `population_%change`
#>    <chr>          <int>      <int> <int>         <dbl>                <dbl>
#>  1 Aguascalientes  2011         91   100       0.09                  0.0989
#>  2 Aguascalientes  2012         92   101       0.0792                0.0870
#>  3 Aguascalientes  2013         93   102       0.0686                0.0753
#>  4 Aguascalientes  2014         94   103       0.0583                0.0638
#>  5 Aguascalientes  2015         95   104       0.0481                0.0526
#>  6 Aguascalientes  2016         96   105       0.0381                0.0417
#>  7 Aguascalientes  2017         97   106       0.0283                0.0309
#>  8 Aguascalientes  2018         98   107       0.0187                0.0204
#>  9 Aguascalientes  2019         99   108       0.00926               0.0101
#> 10 Aguascalientes  2020        100   109       0                     0     
#> 11 Jalisco         2011         91   100       0.09                  0.0989
#> 12 Jalisco         2012         92   101       0.0792                0.0870
#> 13 Jalisco         2013         93   102       0.0686                0.0753
#> 14 Jalisco         2014         94   103       0.0583                0.0638
#> 15 Jalisco         2015         95   104       0.0481                0.0526
#> 16 Jalisco         2016         96   105       0.0381                0.0417
#> 17 Jalisco         2017         97   106       0.0283                0.0309
#> 18 Jalisco         2018         98   107       0.0187                0.0204
#> 19 Jalisco         2019         99   108       0.00926               0.0101
#> 20 Jalisco         2020        100   109       0                     0

^{Created on 2022-03-28 by the reprex package (v2.0.1)}

How to create a function and a loop to calculate growth rates of variables in a data frame in R

You can use data.table too. data.table is a very powerful data manipulation package. You can get started here.

library("data.table")
as.data.table(testdata)[, lapply(.SD, function(x)x/shift(x) - 1), .SDcols = 2:4]

           gdp    cpi_index   rpi_index
1:          NA           NA          NA
2: 0.006427064 0.0072281257 0.009296686
3: 0.007166400 0.0030245056 0.004805767
4: 0.004061822 0.0061020008 0.006377043
5: 0.006772674 0.0009282349 0.005544554
6: 0.007517419 0.0070574736 0.008270973
7: 0.006551699 0.0004058093 0.003515625
8: 0.005457465 0.0009439040 0.001946283

How to use growth rates with apply function instead of a loop in R

You do not need any apply() function in this case. This is just a simple geometric progression:

# simulate some data
country <- data.frame(year = 2000:2017, 
                      GDP = rep(100, 18), 
                      Population = rep(1000, 18))

country[19:23,1] <- seq(2018, by=1, length.out = 5) 

# define gdp and pop parameters
hypo_gdp = 5
hypo_pop = 2

# define common ratios
b1 <- (1 + hypo_gdp/100)
b2 <- (1 + hypo_pop/100)

# calculate values for years 2018-2022
country[19:23,2] =  country$GDP[18]* b1 ^ (1:5)
country[19:23,3] =  country$Population[18]* b2 ^ (1:5)
tail(country)
#    year      GDP Population
# 18 2017 100.0000   1000.000
# 19 2018 105.0000   1020.000
# 20 2019 110.2500   1040.400
# 21 2020 115.7625   1061.208
# 22 2021 121.5506   1082.432
# 23 2022 127.6282   1104.081

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