The high-frequency forecasting model (part 2)

 

The same occurs with agriculture and services. Hence, in order to replicate what INEGI does, we could survey the industrial sector, and then compute the aggregate industrial value-added. Fortunately, we do not have to do that, since INEGI already does it. Thus, every month, INEGI computes the approximate value-added of agriculture, industry and services. With this sectoral information, it also computes an aggregate index of production for the whole economy, which is called the general index of economic activity (IGAE). The IGAE represents a little more than 85 percent of the total production of goods and services in the economy, including agriculture, industry and services. In this sense, the IGAE is considered a measure of the monthly GDP.

The existence of the monthly IGAE makes our life much easier, since we can use it as the best single monthly indicator to predict the quarterly GDP by the production-side analysis. The IGAE is published six weeks after the end of each month. For example, by the middle of March we know the observed GDP for January; by the middle of April we know the observed GDP for February, and so on. Hence the first approach (production side) generates the quarterly GDP through two basic equations: the quarterly IGAE based on the monthly IGAE, and the bridge equation. Since the intercept is not statistically significant, the quarterly GDP is almost fully explained by the quarterly IGAE, in terms of percentage changes.

In addition, we also estimate GDP for the three main production divisions: primary, secondary and tertiary. Equations for primary and tertiary GDP (agriculture and services) are estimated as functions of the IGAE, as shown below.

Meanwhile, the equation for secondary GDP (industry) comes from the principal components section as an ARIMA (autoregressive integrated moving-average) equation. In this case, we use the bridge equation linking the quarterly industrial production (IPI%qt) to the three-month average of the monthly indicator (IPIqt) obtained from the ARIMA equation, both variables in percentage changes.

Since these three divisions of GDP (by the production side) are only for distributional purposes, the discrepancy between the total GDP obtained from them and the total from equation (6.3) is called taxes and subsidies.

The second approach computes GDP through the estimation of the quarterly aggregates of domestic demand linked to the corresponding monthly indicators similar to those used by INEGI. Here, we also use the two basic equations: the monthly indicator linked to its quarterly figure and the bridge equation.

The third approach is given by the principal components method. The first step is the selection of a set of strategic indicators known to be strongly related to GDP. These monthly indicators come from industrial activity, expenditure, financial and monetary sectors, labor and trade. Then we extract the main independent sources of variation from this set of 15 monthly indicators, which are called the principal components. These new mutually uncorrelated variables are used as independent variables in the explanation of the quarterly. Hence we regress the quarterly GDP on the three-month average of the principal components.

Finally, in order to compute the nominal value of GDP, we need to have an equation for the price deflator (PGDP). We build this equation using the principal components methodology again. We select a set of ten monthly indicators and extract the main sources of variation. These indicators are different from those used previously for GDP estimation. Then we estimate the equation for the quarterly GDP price deflator as a function of the principal components. We include the dummy for the NAFTA effect.

 

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