# **3 A Critical Overview of Survey-to-Survey Regression Techniques**

In general, SSITs use a log-linear regression to estimate values for the parameter at year t, then use those values to predict values for the previous year _t − n_ if only the independent variables are available. This process is done under the hypothesis that the parameters are stable over the years. Often, this hypothesis is verified by estimating parameters at two non-consecutive years to illustrate that they are similar irrespective of the selected years. The regression usually uses individual or household expenditures as the dependent variable. With the right skew and in order to avoid normality, the variable is transformed into a logarithm and then transformed back to obtain the predicted values.

Regression is the best way to obtain predicted values only if all the assumptions are fulfilled and the selected dependent variables have a higher explanatory power versus the independent one. This last point is summarized in _R_<sup>2Often,articlesdonot</sup> _ad j_<sup>.</sup> report the _R_<sup>2althoughmultipleregressionsarealwaysused.Interactionorspecial</sup> _ad j_<sup>,</sup> transformation of the dependent variables is also common. Unfortunately, failure to report the _R_<sup>2</sup> _ad j_<sup>hinderstheabilitytochecktheaccuracyoftheregression.Giventhe</sup> connection between _R_<sup>2</sup> _ad j_<sup>and</sup><sup>_R_2wecanarguethatthefirstisatleastequaltoor—</sup> more likely — lower than the ones reported (which is often around 0.5 or less). A low _R_<sup>2</sup> can result from a selection that prefers a common set of variables from the two surveys — which is a key requirement for SSITs — over a high explanatory power.

Demographic variables have been identified in both surveys, such as age, sex, household size, or variables related to assets, such as the number of rooms per capita and measures of physical assets such as the asset index, among other variables. However, their choice might present two problems. First, it will be difficult to capture changes in household expenditure using only demographic variables (that change less rapidly). Second, there is often a weak correlation between dependent and independent variables.

As highlighted by Ketkar and Ketkar (1987), household sociodemographic characteristics are as important as determinants of expenditure patterns as price and income. The standard consumer behavior model states that the economic agent maximizes her utility subject only to relative prices and to income constraints. The two theories may both be valid, but if prices and income are excluded from the standard SSITs models, the sociodemographic variables alone may not adequately explain the individual or household consumption patterns. However, these conclusions must be verified for every data set and are impossible to determine a priori.

A low value for _R_<sup>2</sup> arising from insufficient correlated independent variables, combined with a logarithmic transformation, could also generate problems with establishing predictions. The logarithmic transformation compresses the tail of skewed and kurtotic variables, which effectively generate symmetric PDFs and, therefore, cause Gaussianlike errors. But the predicted values could be applied in the tails and, given the low 5