Excerpt from Statistical Aggregation Analysis, Characterizing Macro Functions: With Cross Section Data
Although econometricians have been estimating time series macro functions over average data for decades, it is rare to find studies which take into account the "averaged" character of the data. Even in the simplest consumption function regression of average consumption on average income, one is only capturing the statistical relation between two summary statistics of the underlying consumption income distribution. Unless saving behavior is virtually identical across individuals or the structure of the income distribution is extremely limited, an average consumption-average income regression will not completely describe the true economic structure relating average consumption to the income distribution. In the same sense, any macro function relating average data is likely to ignore many important distributional influences.
To completely characterize the true population structure underlying a macro function, one must specify precisely the micro process that connects the individual component distribution over time. As will be reviewed shortly, work in aggregation theory has produced several micro model-distribution schemes which justify certain macro function formulations. But to just state such a justification is not enough, as in general any violation of the underlying assumptions will significantly alter the true form of the macro function. Moreover, all of the approaches provided by aggregation theory either involve linearity assumptions at the micro level, or very strict distribution assumptions, such as requiring a normal distribution for the population of micro variables.
The import of this discussion is that one really needs to utilize micro data to study any macro function justification which is to be taken seriously.
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