[R] 2SLS / TSLS / SEM non-linear

[hck]

Dear Arne

Generally I would have the following equations X_i = IV3_i + IV4_i * Y_i
applying for every company (i). In a first step, I am interested in
estimating the relationship between X and Y: Y_i = a + b * X_i + u to
ultimatly estimate X_i by substituting the Y_i and solving for X_i to be
able to estimate the X_i by just IV3_i, IV4_i, and the a and b.

Now, let's construct values from a sample of listed companies. In the
capital market, I can observe IV3_i, IV4_i, and X_i. With these I calculate
Y_i: Y_i = IV1_i + IV2_i * X_i (note: IV3 and IV4 are just a transformation
of IV1 and IV2). Of course, I could rewrite this equation as Y_i = c + d *
IV1_i + e * IV2_i * X_i + v. For a couple of observations, I have now
combinations of X_i and Y_i to get the a and b coefficient by estimating Y_i
= a + b * X_i + u.

I hope the structure is more clear to you now.
Let me know. I am looking very much forward to your answer.
Best
HC





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