Generate growth-rate                                              (STB-7: sts2)
--------------------

    ^growth^ varname [^, peri^od^(^#|str^) m^a^(^#^) noa^nnual ^l^og ^p^ercent ^s^uffix^(^str^)^]


Description
-----------

^growth^ creates ^G.^varname containing the growth in varname.  For instance, 
"^growth gnp^" creates ^G.gnp^.


Options
-------

^period(^#^)^ specifies the periodicity of the data.  If not specified, the per-
    iodicity set with the ^period^ command or, if not set, 1, is assumed.
    ^period()^ may be specified as a number (interpreted as number of observa-
    tions in the data per "year") or as a word such as "^weekly^", "^quarterly^",
    etc., and may be abbreviated "^w^", "^q^", etc.; see ^help period^.

^ma(^#^)^ specifies that the moving average of growth is to be calculated; ^ma()^
    is specified in ^period()^ units.  Thus, ^ma(1)^ calculates the growth between
    adjacent observations.  ^ma(2)^ calculates the growth between y[t-2] and 
    y[t].  Thus, with ^period(quarterly)^ data, one could obtain moving average
    of yearly growth by specifying ^ma(4)^.

^noannual^ prevents the annualizing normalization of the resulting growth rate.

^log^ calculates the growth rates in log terms.

^percent^ records the growth rates as percent rather than fractions.

^suffix(^str^)^ specifies the base part of the name to be used rather than the 
    existing name.  E.g., "growth gnp, suffix(x)" names the new variable G.x
    rather than G.gnp.


Examples
--------

 . ^growth gnp^

calculates the growth in GNP.  Assuming one has not previously used the ^period^
command, the growth rate is "per-observation" growth.  If one were using quar-
terly data, one might want the quarterly growth rates normalized to an annual
rate.  This would be accomplished by

 . ^growth gnp, period(4)^

or 

 . ^growth gnp, period(quarterly)^

or

 . ^period quarterly^
 . ^growth gnp^

This last form is preferred because you only have to set the period once after
using the data; see ^help period^.

Now pretend we have not given the ^period^ command.

 . ^growth gnp, ma(4)^

would calculate the growth between y[t-4] and y[t], normalized to a per-obser-
vation (quarterly) growth rate.  If we had given the period command, the com-
mand would create ^G.gnp^ containing growth between y[t-4] and y[t] normalized 
to an annual rate (which in this case, means no normalization at all). 




Methods and Formulas
--------------------

Let p be the period of the data (1 for annual, 4 for quarterly, etc.)  If 
^noannual^ is specified, p=1, as it also is if ^period()^ is not specified and 
the ^period^ command has not been given stating that the period is other than 
"annual".

The ma(1) growth rate of y is then (y[t]/y[t-1])^p - 1.  The ma(m) growth rate
is (y[t]/y[t-m])^(p/m) - 1.

The log growth rate is (ln(y[t])-ln(y[t-m]))*(p/m).

The percentage growth rate is obtained by multiplying these fraction growth 
rates by 100.



Author
------
 
Sean Becketti, Federal Reserve Bank of Kansas City.


Also see
--------

    STB:  sts2 (STB-7)
On-line:  ^help^ for ^dropoper^, ^lag^