The following appendix accompanies the main article, “Economic Perspectives on the History of the Computer TimeSharing Industry,” by Martin CampbellKelly and Daniel D. GarciaSwartz, which appears in the JanuaryMarch 2008 issue of IEEE Annals of the History of Computing. The material here was omitted from the main article because of space constraints.
We made an attempt at testing whether the advent of timesharing had an impact on the growth of the core sector of the computer industry, the computer system sector. We studied the pattern of computersystemshipment growth by regressing the figures for (log) annual computer shipments on a linear spline function.^{1} We defined the spline time dimension variables as follows:
X_{t}= t, for t = 1, 2, …, T, and
Y_{t} = max(0, t – a)
In this model, the a parameter is the number that corresponds to the year 1964 in the trend sequence, the year right before the advent of the commercial computer timesharing industry.^{2}
Think of a world where changes in annual computersystem shipments are a function of changes in the average real value of systems shipped and fluctuations in a demand shifter (for example, changes in real GDP). Then, in order to assess whether there have been statistically significant changes in the trend of the growth rates of system shipments over time associated with the advent of the timesharing industry, we can estimate a model of the following form:
log(NCS_{t}) =a+d_{1}X_{t} +d_{2}Y_{t} +g log(P_{t})+h log(GDP_{t}) +w_{t}
In a model like this one, NCS_{t} stands for the number of computersystem shipments at time t, P_{t} stands for the real average value of the systems shipped at time t, and GDP_{t} stands for the real value of GDP at time t. Furthermore, X_{t} and Y_{t} are the spline variables defined above. This model addresses the following question: Was there a statistically significant change in the growth rate of annual computer shipments associated with the advent of the computer timesharing industry, after controlling for changes in other factors that may have had an impact on computershipment growth?
The d_{1} parameter measures the average growth rate of annual shipments between the starting point and 1964, namely in the period without computer timesharing. The d_{2} parameter captures the change in the growth rate of shipments over 1965–1978 relative to the previous period, after controlling for changes in the average system’s real price and changes in demand arising from fluctuations in real GDP. The estimated parameters are reported in Table A.^{3}
Table A. Dynamic least squares regression of the log of annual computersystem shipments on a linear spline function with a knot in 1965 (annual data, 1958–1978), Pvalue calculated on the basis of NeweyWest standard errors.
Variable  Coefficient  Pvalue 
Log of real GDP 


Log of average value shipped  –0.425 

Trend 1958–1964 


Change in trend in 1965  –0.087 

The table reveals the following. The elasticity of annual shipments with respect to real GDP is about 1.5, although not significant at standard levels. The price elasticity of annual shipments is about –0.4 and statistically significant. More interestingly, the conditional (average) growth rate of annual computersystem shipments is about 20 percent in the pretimesharing years. And, last but not least, there seems to be a statistically significant break in the growth rate around 1965—the conditional (average) growth rate of annual shipments declines to about 11 percent (i.e., 0.195–0.087 = 0.108) after that year and through 1978. We obtained similar results with data starting in 1959 and also in 1960. Of course, a model like this one does not prove that timesharing caused the slowdown in the growth of computer systems, but the results are nonetheless consistent with this interpretation.
References and notes