How to calculate the standard error of a one-year impact from a two-year impact? I am collecting one-year impacts to conduct a meta-analysis on a certain type of education intervention (high-dosage tutoring). Some papers only report two-year impacts of the intervention and the corresponding standard errors. Is it possible for me to obtain an estimate of the annual impact and its standard error from just the reported two-year impact and its standard error? We are assuming that the distribution of the outcome variable remains the same over the two years of the intervention.
An example: a paper only offers the two-year cumulative impact (let's say $\hat{\beta} = 0.6$ with $SE(\hat{\beta}) = 0.4$) but I want the annual impact. Would an appropriate estimation of the one-year impact be $\hat{\beta/2} = 0.3$ with $SE(\hat{\beta}/2) = 0.2$?
 A: If
${{SE}(\hat{\beta}) = \sqrt{{VAR}(\hat{\beta})}}$
Then
${SE}(\hat{\beta/c}) = \sqrt{{VAR}(\hat{\beta}/c)}= \sqrt{{VAR}(\hat{\beta})/c^2} = \sqrt{{VAR}(\hat{\beta})}/c$
EDIT: 
This part is now obsolete since you've changed your question. For your new question, the answer depends very much on your outcome, and how you assume the "intervention" to affect it.
Dividing by 2 is suitable when you assume the effects of tutoring are additive. I.e. receiving a second year of tutoring has the same absolute effect as receiving the first year.
If you assume the effects to be multiplicative (e.g. each year of tutoring increases the outcome-measure by 10%) then you should choose another transformation of $\hat{\beta}_{2yr}$.
In summary: the ideal choice depends very much on the details of your measure, your assumptions about what the intervention does and most importantly the regression model you're estimating.
A: Your estimate for the mean 1-year beta was correct, however, standard errors are proportional to the square root of the time step. I would therefore expect the 1 year estimate of the standard error to be 0.4 / sqrt(2). 
This intuitively makes sense, too, as you would expect  greater uncertainty around results in a shorter timeframe. 
