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