Editor’s Note

The following appendix accompanies the main article, “Economic Perspectives on the History of the Computer Time-Sharing Industry,” by Martin Campbell-Kelly and Daniel D. Garcia-Swartz, which appears in the January-March 2008 issue of IEEE Annals of the History of Computing. The material here was omitted from the main article because of space constraints.

A Technical Exploration of the Impact of Time-sharing on the Growth Rate of Computer Shipments

We made an attempt at testing whether the advent of time-sharing had an impact on the growth of the core sector of the computer industry, the computer system sector. We studied the pattern of computer-system-shipment 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 time-sharing industry.²

Think of a world where changes in annual computer-system 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 time-sharing industry, we can estimate a model of the following form:

 

log(NCS_t) =a+d₁X_t +d₂Y_t +g log(P_t)+h log(GDP_t) +w_t

 

In a model like this one, NCS_t stands for the number of computer-system 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 time-sharing industry, after controlling for changes in other factors that may have had an impact on computer-shipment growth?

The d₁ parameter measures the average growth rate of annual shipments between the starting point and 1964, namely in the period without computer time-sharing. The d₂ 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

 

Variable	Coefficient	P-value
Log of real GDP	510	279
Log of average value shipped	–0.425	045
Trend 1958–1964	195	007
Change in trend in 1965	–0.087	002

 

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 computer-system shipments is about 20 percent in the pre-time-sharing 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 time-sharing caused the slowdown in the growth of computer systems, but the results are nonetheless consistent with this interpretation.

References and notes

1. On linear spline functions see, for example, D. Poirier, The Econometrics of Structural Change, North Holland, 1976. For a more recent discussion see W. Greene, Econometric Analysis, Macmillan, 1993, pp. 235ff.
2. For all practical purposes, therefore, the spline variables are (a) a trend that starts at 1 in 1955 and grows by 1 every year until 1978, and (b) a second trend variable that takes on the value zero until 1964, starts at 1 in 1965, and grows by 1 until 1978.
3. In time-series regressions like the ones we estimate here, researchers are generally mindful of at least two issues—serial correlation and stochastic trends. As regards the possibility of serial correlation, we estimated the model with robust standard errors, more specifically Newey-West standard errors with one lag. As far as stochastic trends are concerned, we proceeded in the following way. First, we ran Dickey-Fuller tests on the log of the total-shipments variable. The tests turned out to be sensitive to the inclusion of lags—a test with a trend and no lags dramatically rejected the null hypothesis of a unit root, whereas a test with a trend and one lag did not. Second, we searched for a co-integrating relationship. We ran a regression of the log of the total-shipments variable on the linear-spline time variables and the log of the average real system price. We estimated the regression residuals and then ran Dickey-Fuller tests on the residuals. The tests rejected the null hypothesis of no co-integration with up to two lags. Therefore, we calculated the first difference of the log of the average system price, and a lag and a lead of the first difference, and estimated a dynamic least squares (DOLS) model. All the results reported here were derived from the DOLS model. For more details on these issues see, for example, W. Enders, Applied Econometric Time Series, John Wiley & Sons, 2004.