Possibility of nonlinear combination of state variables in measurement equations?

Dear Johannes,
First thank you for your previous guidance, I am grateful.
In my PhD thesis, I have modelled an economy with state-owned firm production and privately firm production, however, in real data, i only have aggregate production data, I am wondering that in measurement equation, can I model observed GDP (observable variable Y) as a nonlinear combination of state-owned production (state variable Y_s) and privately production (state variable Y_p), specifically,

Y=(\alpha Y_s^{1/\beta}+(1-\alpha) Y_p^{1/\beta})^{\beta}

where \alpha is the share for state-owned production, (1-\alpha) is the share of privately-owned production. \beta is elasticity of substitution between state-owned production and privately-owned production.
Alternatively, should i connect between observable variable Y and state variable Y_s and state variable Y_p using a simple linear combination:
Y=Y_s+Y_p
Thank you very much and look forward to hearing from you.
Best regards,
Jesse

There is no general answer. Your model should tell you what the consistent aggregation of output is. The simple linear combination means that both outputs are perfect substitutes. The CES one has a more flexible substitution elasticity.