I am trying to estimate a regression with variables of different periodicity. The dependent variable is given monthly, whereas most other independent variables are also given monthly, but some are given yearly and others are given quarterly.
A typical approach to solve this is just to copy the yearly variables $12\times$ and the quarterly ones $4\times$.
But this doesn't seem right, as for example in case of a yearly explanatory variable, only the dependent monthly variable varies over 12 observations, while the yearly variable stays constant.
It seems to me the effect of the yearly variable on the monthly one cannot be measured this way properly, as within a single year, we cannot observe an effect at all. On the other hand, the yearly variables cannot be updated more often than yearly, and e.g. division by 12 doesn't seem to be any better.
So I know of different approaches to disaggregate or to aggregate data from one frequency to another, but my question is more what are the effects on regression analysis? Does it still make sense if I e.g. copy yearly variables by 12 in a monthly setting if I got plenty of years? Also note that I got many observations over time and cross-sectionally (i.e. a panel format), but from my perspective the issue can be illustrated already by looking at one unit over time.
Some data in R to illustrate this:
set.seed(1)
test <- data.frame(growth = rnorm(240),time=c(seq(as.Date("1988/02/01"),as.Date("2008/01/31"), "month")-1),
ylyvar=unlist(sapply(1:20,function(x) rep(sample((x*100)*1000,size = 1),12),simplify = F)),
qlyvar = unlist(sapply(1:80,function(x) rep(sample((x)*1000,size = 1),3),simplify = F)),
depvar1=rnorm(240),
depvar2=rnorm(240))