Combining Yearly and Quarterly Data in Regression Analysis

Data deficiency is often a problem in regression analysis. The problem, for example, may be due to non-availability of data on some variable, missing observations, lack of information due to multicollinearity and measurement errors, etc. Various approaches have been suggested to deal with the problem depending on its precise nature. One such problem we want to focus our attention on is the lack of time disaggregated data in time-series regression analysis. In particular, observations on some variables over a shorter time interval like a quarter may be limited in number while the corresponding observations over a longer time interval like a year are available for a long period of time. The number of quarterly observations may not be sufficient to estimate the desired relationship with acceptable degrees of freedom. On the other hand, estimation with yearly data may require the use of a long time series going way back into the past. The estimates thus obtained may not capture the relationship prevailing at present or in the recent past and, therefore, mislead the researcher. In addition, the use of yearly data may also result in lack of degrees of freedom.