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>Iterated least squares</H1
><P
>A second form of loop structure is designed
primarily for carrying out iterated least squares. Greene
(2000, ch. 11) shows how this method can be used to estimate
nonlinear models.</P
><P
>To open this sort of loop you need to specify a
<SPAN
CLASS="emphasis"
><I
CLASS="emphasis"
>condition</I
></SPAN
> rather than an unconditional
number of times to iterate. This should take the form of the
keyword <TT
CLASS="command"
>while</TT
> followed by an inequality:
the left-hand term should be the name of a variable that is
already defined; the right-hand side may be either a numerical
constant or the name of another predefined variable. For
example,</P
><P
> <TT
CLASS="command"
> loop while essdiff > .00001
</TT
>
</P
><P
>Execution of the commands within the loop (i.e. until
<TT
CLASS="command"
>endloop</TT
> is encountered) will continue so long
as the specified condition evaluates as true.</P
><P
>I assume that if you specify a <SPAN
CLASS="QUOTE"
>"number of
times"</SPAN
> loop you are probably doing a Monte Carlo
analysis, and hence you're not interested in the results from
each individual iteration but rather the moments of certain
variables over the ensemble of iterations. On the other hand,
if you specify a <SPAN
CLASS="QUOTE"
>"while"</SPAN
> loop you're probably doing
something like iterated least squares, and so you'd like to see
the final result — as well, perhaps, as the value of some
variable(s) (e.g. the error sum of squares from a regression)
from each time round the loop. The behavior of the
<TT
CLASS="command"
>print</TT
> and <TT
CLASS="command"
>ols</TT
> commands are
tailored to this assumption. In a <SPAN
CLASS="QUOTE"
>"while"</SPAN
> loop
<TT
CLASS="command"
>print</TT
> behaves as usual; thus you get a
printout of the specified variable(s) from each iteration. The
<TT
CLASS="command"
>ols</TT
> command prints out the results from the
final estimation.</P
><P
><A
HREF="x1082.html#greene-consump"
>Example 7-2</A
> uses a <SPAN
CLASS="QUOTE"
>"while"</SPAN
>
loop to replicate the estimation of a nonlinear consumption
function of the form
<SPAN
CLASS="inlinemediaobject"
><IMG
SRC="figures/greeneC.png"
ALIGN="center"></SPAN
>
as presented in Greene (2000, Example 11.3). This
script is included in the <TT
CLASS="application"
>gretl</TT
>
distribution under the name <TT
CLASS="filename"
>greene11_3.inp</TT
>;
you can find it in <TT
CLASS="application"
>gretl</TT
> under the
menu item <SPAN
CLASS="QUOTE"
>"File, Open command file, practice file,
Greene..."</SPAN
>.</P
><DIV
CLASS="example"
><A
NAME="greene-consump"
></A
><P
><B
>Example 7-2. Nonlinear consumption function</B
></P
><PRE
CLASS="programlisting"
> open greene11_3.gdt
(* run initial OLS *)
ols C 0 Y
genr essbak = $ess
genr essdiff = 1
genr b0 = coeff(Y)
genr gamma0 = 1
(* form the linearized variables *)
genr C0 = C + gamma0 * b0 * Y^gamma0 * log(Y)
genr x1 = Y^gamma0
genr x2 = b0 * Y^gamma0 * log(Y)
(* iterate OLS till the error sum of squares converges *)
loop while essdiff > .00001
ols C0 0 x1 x2 -o
genr b0 = coeff(x1)
genr gamma0 = coeff(x2)
genr C0 = C + gamma0 * b0 * Y^gamma0 * log(Y)
genr x1 = Y^gamma0 genr x2 = b0 * Y^gamma0 * log(Y)
genr ess = $ess genr
essdiff = abs(ess - essbak)/essbak
genr essbak = ess
endloop
(* print parameter estimates using their "proper names" *)
genr alpha = coeff(0)
genr beta = coeff(x1)
genr gamma = coeff(x2)
print alpha beta gamma</PRE
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