We argue that many methodological confusions in
time-series econometrics may be seen as arising out of
ambivalence or confusion about the error terms. Relationships
between macroeconomic time series are inexact, and, inevitably,
the early econometricians found that any estimated relationship
would only fit with errors. Slutsky interpreted these errors
as shocks that constitute the motive force behind business
cycles. Frisch tried to dissect the errors further into
two parts: stimuli, which are analogous to shocks, and
nuisance aberrations. However, he failed to provide a statistical
framework to make this distinction operational. Haavelmo,
and subsequent researchers at the Cowles Commission, saw
errors in equations as providing the statistical foundations
for econometric models and required that they conform to
a priori distributional assumptions specified in structural
models of the general equilibrium type, later known as
simultaneous-equations models. Because theoretical models
were at that time mostly static, the structural modeling
strategy relegated the dynamics in time-series data frequently
to nuisance, atheoretical complications. Revival of the
shock interpretation in theoretical models came about through
the rational expectations movement and development of the
vector autoregression modeling approach. The so-called
London School of Economics dynamic specification approach
decomposes the dynamics of the modeled variable into three
parts: short-run shocks, disequilibrium shocks, and innovative
residuals, with only the first two of these sustaining
an economic interpretation.
Modeling the Covid-19 Epidemic using Time Series Econometrics