# Annual Data to quarterly freq which lambda value in HP

Hello,

I am using WorldBank annual GDP data. I wish to transform this data so it can be entered into a dynare model of quarterly frequency. I wish to clarify which lambda values to used in the HP one-sided filter.

## TRANSFORM STEPS

1. gdp_data = (AnnualGDPData)^1/4 <- convert the annual values to quarterly values

2. gdp_data = log(gdp_data)

3. run hpfilter with a lambda = 1600 on gdp_data : not with lambda = 6.25

4. gdp_obs = gdp_data - (trend for step 3)

5. gdp_obs = y <-- here y is the gdp variable of the dynare model

Question:

1. The gdp_obs from step 4 is the same as the cycle component of the HP results, so would this be the gdp gap instead the gdp in the dynare model. If this is the case then I should set
gdp_obs = ygap <-- here ygap is the gdp gap variable of the dynare model instead.

2. Does (AnnualGDPData)^1/4 in step 1 set the value to quarterly frequency enough to justify using a lambda = 1600 instead of 6.25 in Step3 ?
(I am under the belief that I should use 6.25 instead)

3. Is this the correct sequence of steps to transform the data correctly so it can be used in the dynare model at a quarterly frequency?

Thank you,
Richard

You cannot use purely annual data for a quarterly model. If all your data is annual, use a model in annual frequency.

This applies even if you do an annual->quarterly interpolation? Does the lack of noise within each year (i.e. the strict linearity of the interpolated values for that variable) cause problems with the estimation?

As for your interpolation rwhitt, why do you use ln(gdp_t^(1/4))=ln(gdp_t)/4 as your quarterly values instead of something more along the lines of:

1. (gdp_t+1-gdp_t)/4=gdpdiff_t
2. gdp_t_qN=gdp_t+(Ngdpdiff), i.e. gdp_t_q1 = gdp_t+gdpdiff, gdp_t_q2=gdp_t+2gdpdiff, etc.
3. ln(gdp_t_qN)=ln(gdp_t+(N*gdpdiff))

where gdp_t_qN is the interpolated value for quarter N of year t, such that gdp_t_q4=gdp_t+1? I’m not entirely sure about proper data construction for DSGEs, but I’ve always used something more along the lines of what I’ve listed above for my interpolations when it comes to time series econometrics.

If you have only annual data, what is the point of estimating a quarterly model? There is no information available at quarterly frequency in your annual data.

Note also that you should not interpolate your data. See [Data transformation for estimation)