Estimation problem in econometric model I am trying to estimate the following equation:
$$Y_{i,t+1}=(λβ)X_{i,t}^{'}+(1-λ)Y_{i,t}+\epsilon_{i,t+1}$$
but I don't understand how to find the $\lambda$ estimate especially since $X'$ consists of multiple variables. In this equation, $\lambda$ is a scalar and $\beta$ is a vector. Can anyone point me in the right direction in terms of model type? I am using Stata 12 for this problem and my data is an unbalanced panel. Thanks.
 A: It turns out that I did not understand how to get Stata to do combinations of coefficients. The code that appears to work is:
reg F.MDR MDR EBIT_TA MB DEP_TA lnTA L.FA_TA RD_DUM RD_TA Ind_Median
nlcom  (Lambda: 1 - _b[MDR])(EBIT_TA: _b[EBIT_TA] / (1 - _b[MDR])) ///
(MB: _b[MB] / (1 - _b[MDR])) (DEP_TA: _b[DEP_TA] / (1 - _b[MDR])) ///
(lnTA: _b[lnTA] / (1 - _b[MDR])) (FA_TA: _b[L.FA_TA] / (1 - _b[MDR])) ///
(RD_DUM: _b[RD_DUM] / (1 - _b[MDR])) (RD_TA: _b[RD_TA] / (1 - _b[MDR])) ///
(Ind_Median: _b[Ind_Median] / (1 - _b[MDR])) (Constant: _b[_cons])

where MDR is the Y in the question's equation and $X'$ consists of EBIT_TA MB DEP_TA lnTA L.FA_TA RD_DUM RD_TA Ind_Median. As @richardh says, $\lambda$ is (1- $\beta$ of MDR) and nlcom can be used to recover the actual $\beta$'s on the independent variables.
A: Your own solution looks reasonable, although I would probably call it tedious. Another reasonable approach would have been to use the nonlinear regression or GMM:
    generate lagged_x = L.x
    generate lagged_y = L.y
    nl (y = ( {lambda}*( {b0} + {b1}*lagged_x ) + (1-{labmda})*lagged_y ) )

    gmm ( y - {lambda}*( {b0} + {b1}*L.x ) - (1-{labmda})*L.y ), instruments( L.x L2.x L.y L2.y)

or something of that kind. (Updated to write up the lagged values explicitly for nl which does not support lags.)
