Edit: Context: I am estimating persistence analog Heckman (1981) based on firm level data. The endogenous variable is the distribution amount of profits directed to the owners. To estimate persistence, I plan to regress the endogenous variable against its past realization. To circumvent the initial conditions problem, I plan on using the Wooldridge method ("Simple solution to the initial conditions problem", 2005). So far, I dummied the endogenous variable and I thus apply a dynamic random effects discrete choice model.
I am using Stata 13 to estimate a simple probit model. I use panel data of secondary nature. The data is conducted via an annual survey. Unfortunately, the endogenous variable of interest is conducted for the past three years respectively. That is, each year the survey taker is asked to indicate the sum of the endogenous variable for the past two years and the current year.
Let's have an example. The picture below shows the data structure. The first row depicts the periods, the second the endogenous variable and its annual value. The following rows beneath show the past individual annual values and the three year sum - that is the observed value. So we have 12 observed periods in this example. Period
t0 contains the sum of periods
t-1; t-2; t-3 - in this case
3 + 6 + 7 = 16. For period
t1 the survey taker discloses 16 yet again - though this time as the sum of periods
t-2; t-3; t-0 and thus
6 + 7 + 3 = 16 . Each observed value thus consists of the sum of the two previous years and the current year. The picture below tries to show that via the "red" and "blue" shadows.
The problem being, I only see the three year sum - that is the "diagonal, bold values". I do not have the annual data. Given the outset of my research question, having the annual data would however be highly beneficial. Two questions arise:
(1) Is there any smart way how I can untangle the lump sum data? (2) If not, what can I do?