simultaneous equations I have the following relationships
logY ~ logX1 + logX2 + logX3 + logX4 + logX5 
and
X1 ~ Z1 + Z2 + Z3 + Z4 + Z5
X2 ~ Z1 + Z2 + Z3 + Z4 + Z5
X3 ~ Z1 + Z2 + Z3 + Z4 + Z5
where Y and Z1, Z2, Z3, Z4, Z5 are endogenous (Say while the Z's play a role in determining Y, the values of Z's are fixed depending upont he values of Y - Kind of like advertising expense has an impact on sales revenue but at the same time managers determine the advertisement expense on the expected sales revenue). So all the variable are changing simultaneously. Can anyone help me on how I can estimate this relationship? I also have instruments for each of the Z's (lagged variables have been treated as instruments and I have the previous year data for the problem as well. Thank you for all your help and suggestions.
 A: If all the $Z$s are also determined by the $Y$ the system of equations, which you have proposed, cannot be identified. What you need to do is to reduce the equations such that the coefficients can be identified.
I recommend reading:

Wooldridge, Introductory Econometrics, 3d ed. Chapter 16: Simultaneous
  equations

Here, your kind of problems gets explained, and there are some pretty nice examples.
I also recommend reading:
Rummery,Vella,Verbeek (1998) - Estimating the Returns to Education for Australian Youth via Rank-Order Instrumental Variables

and 
Vella,Verbeek (1997) - Using Rank Order As An Instrumental Variable - An Applicaton To The Return To Schooling

Vella and Verbeek (also Rummery) estimate smth. like:
$y_i = x_i\beta + z_i\delta + e_i, \ \ \ \ i = 1,...,N$
Here $x_i$ is a $K$ vector of exogenous variables whereas $z_i$ is assumed to be endogenous. Hence the reduced form equation of $z_i$ is given by:
$z_i = x_i\alpha + v_i$
The advantage of this approach is, that you dont need any exclusion restrictions for the $x_i$, which are necessary to make 2SLS/3SLS work.
I've used this approach to solve a three equation system, i.e., i got three equations and in each of them there are two endogenous regressors which are also the dependend variable in some other equation.
I also applied a plug-in style of approach to deal with potential heteroscedasticity. 
There are some issues which are not presented within this papers but I would be happy to talk to you about that.
A: Perhaps it makes sense to do 4 linear regressions to determine how the $Z$s determine the $X$s i.e. 
$X_1 = \beta'_0 + \beta_1' Z_1 + \beta_2'Z_2 + \beta_3'Z_3 + \beta_4' Z_4$
$X_2 = \beta''_0 + \beta_1'' Z_1 + \beta_2''Z_2 + \beta_3''Z_3 + \beta_4'' Z_4$
$X_3 = \beta'''_0 + \beta_1''' Z_1 + \beta_2'''Z_2 + \beta_3'''Z_3 + \beta_4''' Z_4$
$X_4 = \beta''''_0 + \beta_1'''' Z_1 + \beta_2''''Z_2 + \beta_3''''Z_3 + \beta_4'''' Z_4$
Then $Y = (\beta_0' + \beta_0'' + \beta_0''' + \beta_0'''') + (\beta_1'+\beta_2''+\beta_3'''+\beta_4'''')Z_1 + \ldots$
