directions of endogenous coefficients are the opposite in simultaneous equation model

Hi everyone,

I'm running simultaneous equation model (2 equations) but getting a weird result.
My apology that I can't disclose my sample data here since the data set is not a publicly available data.
But below is the equations that I'm running.

(Equation 1) Y_it= β_o+β₁X_it+β₂Z_it+β₃K_it+β₄H_it+u_i+t_t+ϵ_it
(Equation 2) _Xit= β_o+β₁Y_it+β₂Z_it+β₃K_it+β₄G_it+β₅R_it+u_i+t_t+ϵ_it

Code:

The corresponding code would be:

xi: reg3 (eq_1: Y X Z K H i.u i.t) (eq_2: X Y Z K G R i.u i.t)

where i.u and i.t are unit and time fixed effect, respectively

My thought is that I expect I would get the same direction for both β₁ in equation 1 and 2.
But when I run SEM, what I get is for β₁ equation 1 is negative whereas for β₁ equation 2 is positive.
I also checked the correlation between X and Y but it is positive.

I'm not sure it's because something's wrong with my data set or I'm wrongly using SEM.
I appreciate your help in advance.

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