Does a Vector Autoregression Model truly avoid circular function issues? Let's say you have a VAR model that estimates GDP and Unemployment among many other variables using a certain number of lags.  This VAR model can estimate or regress GDP using Unemployment.  And, it can do the reverse too.  It can also do Granger Causality analysis between these two variables to analyze the direction of the causality and Impulse Response Function to measure the intensity of this directional causality.  But, can it truly forecast several periods out both GDP and Unemployment (Hold Out test situation)?
I would think once you run out of lags, this VAR model could not forecast for periods beyond the lags because then it has to rely on estimates of both variables to forecast out the specific variable you want to forecast.  And, at this stage you run into a circular function situation.    
 A: With VAR models you can predict as many steps ahead as you like. When the future horizon increases, you will eventually run out of observed values to base your forecasts on. Then you just substitute the required observed values with their forecasts and iterate forward. Here is an example of VAR(1) (I skip the intercept for brevity):
\begin{aligned}
x_t &= \Phi x_{t-1}+\varepsilon_t \\
\hat x_{t+1|t} &= \Phi x_{t} \quad \text{(have not run out of observed values yet)}\\
\hat x_{t+2|t} &= \Phi \hat x_{t+1} = \Phi^2 x_{t} \quad \text{(have run out of observed values, thus substitute)}\\
\hat x_{t+3|t} &= \Phi \hat x_{t+2} = \cdots = \Phi^3 x_{t} \\
&\cdots \\
\hat x_{t+h|t} &= \Phi \hat x_{t+h-1} = \cdots = \Phi^h x_{t} \\
\end{aligned}
where $x_t$ is a multivariate time series of interest, $\Phi$ is a square matrix of coefficients and $\varepsilon_t$ is a multivariate time series of errors (innovations, shocks).
Update to include some information from the comments:
We are doing the best we can given that we only have current information but not future information. The fact that forecasts are mean reverting reflects an assumption on the data generating process (DGP). As Chris Haug points out, this is a consequence of the linearity of the model, but it is not an approximation. The behavior of the forecasts is actually optimal given the DGP. And as long as VAR is a good approximation of the DGP, I would not expect alternative forecasts to beat the ones by VAR, unless they employ some future information. But in the latter case, a fair comparison would add this information to the VAR model in terms of exogenous variables or the like. 
A: After giving it some thought, I think the straight forward answer is that VAR does not resolve the circular function situation as framed in my question.  And, frankly I don't think any other methodology can.  You can't use A to forecast B at the same time as you use B to forecast A once you go beyond any related lagged variables.  
The key is "at the same time" and "once you go beyond any related lagged variables."
Practitioners often think they can by relying on forecasts once you go beyond the lags.  But, that is not the same thing.  You very soon are relying on the forecast of a forecast to forecast the next period.  You end up with some mean-reverting process whereby you probably would be better off to simply use a simple average as your long term forecast.       
