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Methodological procedure for estimating Brazilian quarterly GDP series.

Article Excerpt
Abstract This paper presents a methodology for estimating the Brazilian GDP quarterly series in the period between 1960-1996. Firstly, an Engle-Granger's static equation is estimated using GDP yearly data and GDP-related variables. The estimated coefficients from this regression are then used to obtain a first estimation of the quarterly GDP, with unavoidable measurement errors. The subsequent step is entirely based on benchmarking models estimated within a state space framework and consists in improving the preliminary GDP estimation in order to both eliminate as much as possible the measurement error and that the sum of the quarterly values matches the annual GDP.

Keywords Benchmarking * Engle-Granger's equation * Kalman's filter * State space models * GDP

JEL C32 * C51 * C52 * E01

Classification Numbers C10

Introduction

This paper describes and applies a methodology for estimating the quarterly Brazilian GDP from 1960 to 1996. The methodology is based on the initial estimation of the quarterly GDP, obtained through an Engle and Granger (1991) static equation using GDP annual data and GDP-related variables, namely: automobile and cement production, industrial consumption of electricity in the Rio de Janeiro-Sao Paulo axis, and the national treasury tax revenue. The estimated coefficients of this regression are then used to build a quarterly equation between GDP and those variables.

This equation produces a first quarterly GDP estimation, henceforth, referred to as dirty GDP--due to unavoidable measurement errors. The next step consists of improving the estimation, ridding it as much as possible from measurement errors and making it consistent with the annual GDP calculated by the Brazilian Institute of Geography and Statistics (IBGE), an official agency; to clarify, the sum of the quarterly estimations must be equal to the year total.

The process of harmonizing quarterly and annual estimations is called benchmarking, constantly used by official data agencies. In this paper, the benchmarking procedure adopted is anchored on the state space modeling, in which a time series is broken into unobserved and directly interpretable components (cf. Harvey 1990; Durbin and Koopman 2004).

The paper is organized as follows: the next section briefly discusses the benchmarking process and reviews the literature on the subject. In the following, we describe the quarterly GDP estimation methodology. Then we introduce and discuss the estimated models' results, and finally we present our conclusions. The appendix describes the construction of the series used and shows the results of the unit root tests employed.

Benchmarking

A common problem with official statistics is the adjustment of monthly and quarterly observations obtained through surveys or sampling and therefore subject to errors. The adjustment is made with annual data from censuses or more detailed surveys, hypothetically presumed to be free of sampling errors. The annual total is called the benchmark; the process of harmonizing estimations with the year total is called benchmarking.

More specifically, benchmarking--or harmonization--consists of conveniently matching two measurement sources of the same time series, usually obtained from distinct frequencies. The lowest frequency series--the benchmark series--is assumed as having a more reliable registry. Benchmarking is the process of trying to adjust the highest frequency series to the benchmark one. This is done by breaking down the series into its structural elements--trend, seasonality, cycle, irregularity and measurement error--and from the sum of those elements excluding the error.

There are two major methodologies to apply benchmarking to a time series: a purely numeric approach and a statistic modeling one. The numerical approach differs from the statistic modeling by not specifying a statistical model to the studied series. The numerical approach encompasses the family of methods based on the minimization of a squared sum proposed by Denton (1971)--following the principle of movement preservation--Bassie (1958), and Ginsburgh (1973). An application of such procedure can be found in Di Fonzo and Marini (2003). The statistic modeling method, in turn,...

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