David F. Hendry 191700 17501800 1850 19001950 20006789 Log bankruptcies1700 1750 18001850 1900 195020005.07.510.0 Log patents1700 1750 18001850 1900 19502000–9–8–7–6
Log industrial output per capita17001750 1800 18501900 1950 20001.52.02.53.0Log real equity pricesFigure 1.2 Logs of historical UK time series
start of the industrial revolution, Smith (1776, Ch. 1) notes the key develop-
ment of specialists in R&D: “In the progress of society, philosophy or speculation
becomes, like every other employment, the principal or sole trade and occupation
of a particular class of citizens.”
The non-stationarities in Figure 1.1 are blatant, and reflect more than just unit
roots. Major historical events are clear: e.g., real equity prices exploded in the
South Sea Bubble, not regaining such levels again for 200 years, collapsed in
the Napoleonic and both world wars, as well as the first oil crisis, and today are
little above pre-industrial revolution levels. Frankly, it is almost infeasible to build
sensible empirical models of these levels series.
Figure 1.2 records the same four series in logs. Non-stationarity remains clear,
but one can at least imagine ways of sucessfully modeling such data. Figure 1.3
reports their data densities separately in each of (approximately) the three centuries
involved. The shifts in means and variances are marked, even if the presence of
heterogeneity and dependence within each century can distort such histograms.
Nor is the non-stationarity restricted to the levels of the variables, as Figure 1.4
illustrates for the annual changes in the four variables. Variance changes are clear,
which also serves to make the densities of the changes look much more alike, as
seen in Figure 1.5. Differencing alone can be insufficient to induce stationarity.
We will analyze the log transformations of these data in section 1.8.
In the absence of complete theoretical guidance on all relevant and irrelevant
variables, functional forms, exogeneity, dynamics, and non-stationarities, empir-
ical determination is essential. Consequently, the initially postulated models of