Estimating Nonlinear Mixed Effects Models That Are Not Nested

[Vafa Behnam]

Hello,


I am trying to fit a nonlinear longitudinal model using the menl command. Specifically, I am trying to fit a CES production function of the form: Y_{ci} = log( (alpha_i * L_{ci}) + ((1-alpha_i) * B_{ci} * K_{ci}) )

(I have omitted the elasticity of substitution as well as the labor augmenting term tp reduce clutter/for exposition -- I have estimated them separately from another equation. But I need to estimate factor shares (alpha_i) and the capital augmenting tech term (B_{ci}))

The two dimensions are not nested within each other.



I have attempted to run the following command:

menl log_out = (1/-1.1426491)*log( ( ({alpha:}) * lab_cost_prod_weight^(-1.1426491)) + ( (1-{alpha:}) * {B:} * capital^(-1.1426491) ) ), define(alpha: U1[ind], xb ) define(B: UU1[ind] UU2[id], xb)


But it states: "crossed effects are not allowed; your random effect specifications define 2 hierarchies"


I feel like it's a bit strange that menl is able to deal with nested structures, but fails to deal with "crossed effects"/non-nested structures, which are very common in economics (i.e. the two dimensions are individual and time). Does anyone have any suggestions? Thank you!




(I have also attempted:

menl log_out = (1/-1.1426491)*log( ( ({alpha:}) * lab_cost_prod_weight^(-1.1426491)) + ( (1-{alpha:}) * {B:} * capital^(-1.1426491) ) ), define(alpha: U2[ind], xb ) define(B: i.id U1[ind], xb)

Here it states: "failed to evaluate linear combination B")

[Joseph Coveney]

You might need to resort to using bayesmh with flat priors. According to the comment here, menl won't allow cross-classified random effects: "The bayesmh syntax is the same as the menl command that fits classical nonlinear mixed-effects models, except that bayesmh additionally supports crossed effects such as UV[id1#id2] . . ."