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help for ^denton, dentonmq^                       
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Interpolate a quarterly flow series from annual totals via proportional Denton method
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    ^denton^  varname  [if] [in], ^i^ndicator(varname) ^g^enerate(varname)
    ^dentonmq^  varname  [if] [in], ^i^ndicator(varname) ^g^enerate(varname)

^denton^ is for use with quarterly time-series data; see @help tsset@. ^denton^
may be used on a single time series of a panel which has been ^tsset^ or ^xtset^.


Description
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^denton^ computes the proportional Denton method of interpolation of an
annual flow time series by use of an associated "indicator series", 
imposing the constraints that the interpolated series obeys the annual 
totals. The method is described in IMF Chapter 6, Benchmarking (2001) as 
"relatively simple, robust, and well-suited for large-scale applications."
It may be particularly useful in cases where, due to sizable statistical
discrepancy, quarterly series do not integrate to annual totals. The
indicator series only contribute their pattern to the interpolation; 
thus it is quite feasible to use both quarterly and annual flow series
expressed at an annual rate. The interpolated series will be at a 
quarterly rate. Although the procedure is usually applied to flow
series (such as GDP), it may be applied to stock series if they are
differenced and then integrated via generate..sum(), after adding their
initial value.

^denton^ is a least squares approach, in which the quarterly estimates 
to be derived are the parameters, and the sum of squares involved are 
the first differences of the X/I ratio: the ratio of the interpolated
series (X) to the indicator series (I). The problem is a constrained 
least squares problem which may be written as a Lagrangian expression
in the minimand and the constraints, one of which is defined for each
year's annual observation.

The annual variable to be interpolated must be specified as ^varname^,
and the quarterly indicator series with the ^i^ndicator option. 
Both variables must be defined on a quarterly timeseries calendar. 
Only the fourth-quarter values of the annual series will be referenced 
by ^denton^. Since the proportional Denton method requires that the 
indicator variable is strictly positive, the indicator variable is 
adjusted prior to use if it contains nonpositive values.

You must specify one new variable to be created, with the ^gen^erate
option. That variable will contain the interpolated series within the
defined sample. Its observations over each calendar year will sum to
the annual total given in the X series. That may be verified, as the
routine indicates, by making use of ^tscollap^.

Since the routine utilizes Stata's matrix language, it cannot handle
timeseries with more observations than the current ^matsize^. It may be 
necessary to ^set matsize^ to use a larger number of observations 
(e.g. if it has been set at the default of 40).

^dentonmq^ performs the same procedure for a monthly flow series from
quarterly totals. The quarterly series must be defined on a monthly 
timeseries calendar. Only the third-month values of the quarterly
series will be referenced by ^dentonmq^. 

Example
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        . ^denton aflow, ind(qflow) gen(qinterp)^
        . ^denton aflow if tin(1970q1,1980q4), ind(qflow) gen(qinterp)^
        . ^dentonmq qflow, ind(mflow) gen(minterp)^

Reference
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Quarterly National Accounts Manual: Concepts, Data Sources, and Compilation 
Adriaan M. Bloem, Robert J. Dippelsman, and Nils O. Maehle
International Monetary Fund, 2001.
http://www.imf.org/external/pubs/ft/qna/2000/Textbook/index.htm 


Author
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        Christopher F Baum, Boston College, USA
        baum@@bc.edu


Also see
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On-line:  help for @tsset@, (if installed) @tscollap@
