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help for denton
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Interpolate a time-series from low-frequency totals via proportional Denton met
> hod

denton varlist using(string) [if exp] [in range], interp(string)
from(string) generate(string) [stock old]

denton is for use with time-series data.  You must tsset your data before using
denton; see tsset. denton may be used on a single time series of a panel which
has been tsset or xtset.

Description

denton computes the proportional Denton method of interpolation of a
low-frequency time series by use of an associated higher-frequency indicator
series, imposing the constraints that the interpolated series obeys the
original low-frequency series totals. The method is described in IMF Chapter 6,
Benchmarking (2001) as "relatively simple, robust, and well-suited for
large-scale applications."

denton requires that the low-frequency variable be an annual or quarterly time
series, while the indicator variable may be of quarterly or monthly frequency.
Although the procedure is usually applied to flow series (such as GDP), it may
be applied to stock series applying the stock option, where both the
low-frequency and indicator variables are stock series.  The method 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. In this
instance the interpolated series will be at a quarterly rate.

denton is a least squares approach, in which the high-frequency 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 low-frequncy observation.

The low-frequency variable to be interpolated is specified as varname. The
using clause specifies the filename of the Stata data (.dta) file to be
created, containing the new series. This must be a new file.

Options

interp(), a required option, specifies the name of the high-frequency indicator
variable. As 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.

from(), a required option, specifies the name of the Stata dataset containing
the indicator variable. This dataset must be tsset as a single time-series.

generate(), a required option, specifies the name of the new variable which
will contain the interpolated series within the defined sample.  The file
created (as specified in from()) will store the interpolated series along
with the X (low-frequency) series and the new time variable.  The new
variable's observations over each calendar year will sum to the
low-frequency total given in the X series.  That may be verified, as the
routine indicates, by making use of tscollap.

stock may be used to specify that both of the time-series to be used are stock
series.  In that case both the low-frequency and indicator series are
differenced, the interpolated variable is created, and then integrated via
sum(), after adding the initial value.  Because of differencing, the new
variable is not interpolated for the first low-frequency period.

old may be used to specify that the new file is saved in Stata 11 format if
denton is run under Stata 12+.

Example

. denton aflow using ydta.dta, interp(qflow) from(qdta.dta)
generate(qinterp)
. denton aflow using ydta.dta if tin(1970, 1980), interp(qflow)
from(qdta.dta) generate(qinterp)
. denton aflow using ydta.dta, interp(qflow) from(qdta.dta)
generate(qinterp) stock old

References

Bloem, A., Dippelsman, R., and Maehle, N., Quarterly National Accounts Manual:
Concepts, Data Sources, and Compilation.  International Monetary Fund,
2001. http://www.imf.org/external/pubs/ft/qna/2000/Textbook/index.htm

Authors

Christopher F Baum, Boston College, USA
baum@bc.edu
Sylvia Hristakeva, Boston College, USA
hristakeva@gmail.com

Also see

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