As pointed in the comments, it's better to provide reproducible examples mimicking your data. What you want to do is a join  after some data manipulation (merge the first two qtr into a class, same for the two last).
library(dplyr)
df <- data.frame(states=rep(c("AL","AR","FL","GA","LA","MS","NC","OK","SC","TN","TX"), times = 4),
                 qtr=rep(c(1,2,3,4), times = 11))
df <- df %>% arrange(states, qtr) # pure cosmetics
df <- df %>% mutate(sem=ifelse(qtr <= 2, 1, 2),    # merge the first two and the last two
                    key=paste0(states, "_", sem))  # create a joining key
head(df)
states qtr sem  key
1     AL   1   1 AL_1
2     AL   2   1 AL_1
3     AL   3   2 AL_2
4     AL   4   2 AL_2
5     AR   1   1 AR_1
6     AR   2   1 AR_1
# recreate an external source
ext <- df %>% select(states, sem) %>% distinct()
set.seed(123) # for the sake of reproductibility
ext$unemp <- runif(nrow(ext)/2) # simulate some unemp rates
# you probably have something that looks like this:
head(ext)
states sem     unemp
1     AL   1 0.2875775
2     AL   2 0.7883051
3     AR   1 0.4089769
4     AR   2 0.8830174
5     FL   1 0.9404673
6     FL   2 0.0455565
# recreate a key column
ext <- mutate(ext, key=paste0(states, "_", sem))
# have a look at it
head(ext)
states sem     unemp  key
1     AL   1 0.2875775 AL_1
2     AL   2 0.7883051 AL_2
3     AR   1 0.4089769 AR_1
4     AR   2 0.8830174 AR_2
5     FL   1 0.9404673 FL_1
6     FL   2 0.0455565 FL_2
# left join and drop redundant columns
df2 <- left_join(df, ext, "key") %>% 
  transmute(states=states.x, qtr, unemp)
head(df2)
states qtr     unemp
1     AL   1 0.2875775
2     AL   2 0.2875775
3     AL   3 0.7883051
4     AL   4 0.7883051
5     AR   1 0.4089769
6     AR   2 0.4089769
Is that what you were looking for?