# [OPE-L:7099] [OPE-L:598] Re: Re: New Evidence on Sectoral Prices and Values

Allin Cottrell (cottrell@ricardo.ecn.wfu.edu)
Thu, 4 Mar 1999 23:25:57 -0500 (EST)

On Wed, 3 Mar 1999, Andrew Kliman wrote:

> It is difficult to say anything about the results Allin
> claims. He doesn't provide nearly enough information about
> his methods...

Let P_i = V_i * exp(u_i), where u_i ~ N(0,0.143)

Typical result from OLS regression of ln(P_i) on ln(V_i) and a constant:

slope coefficient: 0.998596 std. error: 0.0140729

(This result shows very little variation on repeated trials.)

Now let C_i = (0.85 * V_i) + e_i

"Typical" results (though these vary quite widely) from OLS regression of
ln(P_i/C_i) on ln(V_i/C_i) and a constant:

- where e_i ~ N(0,0.02)

slope coefficent: 1.01295 std. error: 0.116752

- where e_i ~ N(0,0.01)

slope coefficient: 0.518361 std.error: 0.379714

- where e_i ~ N(0,0.005)

slope coefficent: 0.26919 std. error: 0.755219

- where e_i ~ N(0,0.003)

slope coefficient: 0.707948 std. error: 0.977812

- where v_i ~ N(0,0.0025)

slope coefficient: -0.24611 std. error: 0.913988

- where e_i ~ N(0,0.0020)

slope coefficient: -1.57142 std. error: 1.89204

> I do suspect that an error has crept in somehow, somewhere. That is
> because it is a simple matter of algebra that, if it were true that
>
> Yj = Xj*exp(Uj)
>
> then it would also be true that
>
> Yj/Zj = (Xj/Zj)*exp(Uj).
>
> Hence, if the labor theory of relative prices were true, the
> regression coefficients would have to have the same "true" values
> whichever equational form was specified and whatever Zj (not equal
> to Xj or Yj) were chosen. That's what the algebra says...

Andrew seems to be operating under the assumption that one can
do "algebra" with stochastic equations by substituting expected
values for all distributions and proceeding as if everything
were degenerate. This would not get him very far on a stats
exam.

Allin Cottrell.