I have empirically estimated the elasticity of substitution parameter in the following model: $$Y_t=[(A_1L_tK_{t})^{\rho} +(A_2M_{t})^{\rho}]^\frac{1}{\rho} $$
here, $Y_t$ is output, $A_i$ is a factor-augmenting technology index, $K, L$ and $M$ are factors of production and the elasticity of substitution is $\sigma = 1/(1 - \rho)$. I estimated $\rho$ combining the logorithmised form of the above function and its FOC conditions in a system of nonlinear equations.
I am getting $\rho>1$ which gives a negative elasticity of subsitution, $\sigma<0$. I am now struggling to put a plausible interpretation on this result; theoretically, the lower bound for $\sigma$ is 0.
I am guessing that I could still interpret the negative $\sigma$ as an evdience that factors are strong complements. Would this be a correct interpretation?