Problems of operationalizing the concept of a cost-of-living index

The micro-data is made anonymous by only making a 98% random sample
of all household files available and by a limitation of the number of variables
for which data is provided.⁴³ The GFSO provided us with the Scientific-Use-
files of the EVS for 1988, 1993, 1998 and 2003. To calculate the COLI after
estimation of the demand systems, we use freely available price data out of
the GFSO consumer price statistics.

5 Estimation

The simplest way to estimate the parameters of a system of equations is
to estimate each equation separately by ordinary least square (OLS) tech-
niques. Here, this is not possible because of two reasons: First, we have
cross-equation parameter restrictions in The AIDS and QUAIDS, which can
only be tested if the equations were estimated simultaneously. Second, we
have to worry about contemporaneous correlation of the error terms that
would violate the OLS assumptions. Contemporaneous correlation of the
error terms occurs if the error terms of the N-budget share equations of one
household were correlated with each other. The probability for the occur-
rence of contemporaneous correlation is in our context very high. The error
terms of each of our budget share equations contains influences such as demo-
graphic composition or income of the household on the budget shares which
are not yet included in the model by exogenous variables. As these influ-
ences typically vary between households but not within the specific budget
share equations of one household, contemporaneous correlation is likely to
occur. Nevertheless we conduct a Lagrange-Multiplier (LM) test, to test our
data on contemporaneous correlation. The null hypothesis of freedom from
contemporaneous correlation has to be rejected for all data sets under consid-
eration. So we have to choose an estimation procedure that accounts for the
effect of contemporaneous correlation and ensures the imposition of cross-
equation parameter restrictions. The nonlinearity of the AIDS and QUAIDS
additionally constrain the potential set of estimators. Following the well
known seemingly unrelated regression approach of [30]Zellner (1962), we use
a feasible generalized nonlinear least square estimator (FGNLS) proposed by
[9]Cameron and Trivedi (2005).

⁴³We are very grateful to the GFSO for the provision of the Scientific-use-files and many
useful advices concerning the data set.

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