## 2/10/12

### A 130-year long argument against the Solow growth model

We have already presented strong quantitative arguments against the Solow growth model, which presumes that the rate of change in real GDP per capita must approach some constant level. In developed countries, the annual increments of real GDP per capita have been rather oscillating around constant level since 1955. We use the estimates of real GDP per capita published by the Conference Board’s total economy database.  Since the late 1990s this database has been developed and maintained in conjunction with the Groningen Growth and Development Centre (University of Groningen, The Netherlands). As of the summer of 2007 the database has been transferred from the University of Groningen to The Conference Board and is maintained there. The GGDC also provides historical estimates of real GDP developed by Angus Maddison.  It is instructive to use these historical estimates in order to reject the Solow model by empirical data.
Under our empirical framework [1,2,3], real GDP per capita in developed countries grows as a linear function of time, we call it inertial growth, when population pyramid does not change much in the long run:
G(t) = At + C           (1)
Relationship (1) defines the linear trajectory of the GDP per capita, where C=Gi(t0)=G(t0) and t0 is the starting time. In the regime of inertial growth, the real GDP per capita increases by the constant value A per time unit. The relative rate of growth along the inertial linear growth trend, g(t), is the reciprocal function of G:
g(t) =  A/G(t)                     (2)
Relationship (2) implies that the rate of GDP growth will be asymptotically approaching zero, but the annual increment A will always be constant. This is different from the Solow model where the rate of growth is a positive (nonzero) value. Moreover, the absolute rate of GDP growth is constant and is equal to A [\$/y]. This constant annual increment thus defines the constant “speed” of economic growth in a one-to-one analogy with Newton’s first law. Hence, one can consider the property of constant speed of real economic growth as “inertia of economic growth” or simply “inertia”.
In Figure 1, we present the estimates of annual increments of real GDP per capita in the USA since 1870. At first glance, these data support the Solow model, i.e. annual increments increase with time. However, we know that since 1955 the increment has been oscillating around constant level of \$423 (2011 US dollars) and the accuracy of GDP measurements (actually obtained by reconstruction) before 1950 can hardly be characterized as a high one.  In Figure 2, we display the estimates of annual increment since 1955 as measured by the Bureau of Economic Analysis. There is no linear time trend in the curve and thus the Solow model does not work well.
The period between 1940 and 1955 is characterized by extremely large oscillations. This period corresponds to the Second World War and the development of the concept of Gross Domestic Product (Simon Kuznets introduced this idea in 1934). Therefore, the war and the development of measurement procedure may introduce significant structural breaks in the time series and we remove the years between 1940 and 1955 from our consideration as a mixture of an artificial step in measurements (say, the transition from mph to km/h) and the effects of noneconomic factors in economic evolution.  Figure 3 shows the period between 1871 and 1940 (70 years). Not surprisingly, there is no linear time trend and the overall length of the period when the Solow model is not applicable is now ~130 years.
All in all, the Solow model of economic growth (and all its branches and versions) contradicts hundred and fifty years of observations.   We are going to report the evolution of real GDP per capita in other developed countries.
Figure 1. The estimates of annual increment of real GDP per capita in the USA since 1970.
Figure 2.  Annual increments since 1955 as reported by the BEA. There is practically no linear trend.
Figure 3. The annual increment between 1871 and 1940. The mean value is \$65.