Interpolate a quarterly flow series from annual totals via proportional Denton > method ------------------------------------------------------------------------------- > ------
^denton7^ varname [if] [in], ^i^ndicator(varname) ^g^enerate(varname) ^dentonmq7^ 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 > ^.
Users of Stata 11 or 12 should use the new ^denton^ routine.
Description -----------
^denton7^ 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.
^denton7^ 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 ^denton7^. 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).
^dentonmq7^ 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 ^dentonmq7^.
Example -------
. ^denton7 aflow, ind(qflow) gen(qinterp)^ . ^denton7 aflow if tin(1970q1,1980q4), ind(qflow) gen(qinterp)^ . ^dentonmq7 qflow, ind(mflow) gen(minterp)^
Reference ---------
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 ------
Christopher F Baum, Boston College, USA baum@@bc.edu
Also see --------
On-line: help for @tsset@, (if installed) @tscollap@, @denton@