The aim of the paper is to check the validity of the basic assumption of the model of "K apital, Labour, and Aggregate TFP" that technical change is well characterized as an exogenous ag-gregate stochastic process, growing at a more or less constant rate. At the other extreme, the alternative hypothesis would be: “It’s a jungle out there”. Firms are created to maximize profits, some of them are successful, some others fail. So the shocks are in fact firm-specific and cannot be modeled as an aggregate shock.
Available data at the industry level have been used to test the hypothesis that technical change is well characterized as an aggregate process. We looked for the common factor underlying sectorial TFPs, and we also checked for the common factor underlying regional TFPs. We were able to identify nation-wide sectorial technical shocks. Moreover, sector-specific TFP dynamics prove to be oscillating, rejecting the assumption that TFP growth proceeds at a more or less constant growth rate, be it of the exogenous or the endogenous type.
Hence, we have to focus on at least sector-specific sources of TFP growth. And look for "fac-tors" that could explain observed differences in sectorial TFP growth rates. These may include:
different savings rates, differences in the substitutability between factor inputs, differences in ad-justment costs if any, differences in the "availability" of technological improvements, differences in the market structure...
In this section, we focus on the role of capital accumulation on TFP growth. More precisely, our first candidate to explain why technical improvement does not accrue to each and every sector simultaneously, and why its growth process shows a rather cyclical pattern is that technical change be investment-specific. Unless firms invest in better-quality machines or more highly qualified workers, the ratio of output to inputs will remain unchanged.
We try a simple test of the hypothesis that technical progress is embodied, using sector-level data. We report some key statistics for the 5 fastest-growing sectors and the 5 slowest-growing sectors during 1965-1995. These are: output growth rate, the Solow residual, labour productivity growth rate, capital growth rate, profits growth rate and the capital contribution to output growth in each sector.
5 fastest-growing sectors over 1965-1995 Key variables' growth rates
Y Solow Residual Y/L K Profits K contr.
C4 4,99% 3,16% 5,99% 3,42% 4,95% 1,78%
C5 5,13% 3,07% 4,75% 2,74% 3,47% 1,44%
C7 5,43% 3,28% 4,54% 3,52% 3,47% 1,22%
C8 4,72% 3,63% 5,10% 2,34% 4,23% 1,04%
C13 4,99% 2,31% 4,12% 6,04% 3,34% 1,85%
Mean 5,05% 3,09% 4,90% 3,61% 3,89% 1,47%
5 slowest-growing sectors over 1965-1995 Key variables' growth rates
Y Solow Residual Y/L K Profits K contr.
C1 1,08% 3,24% 5,37% 2,64% 2,30% 0,72%
C2 2,16% -0,64% 3,37% 3,94% 2,23% 2,72%
C9 1,50% 1,87% 3,21% 1,07% -0,59% 0,46%
C11 2,63% 0,58% 2,49% 4,69% 0,61% 1,73%
C12 2,77% 0,91% 2,27% 5,24% 1,91% 1,29%
Mean 2,03% 1,19% 3,34% 3,52% 1,29% 1,38%
From reported statistics, there is no substantive difference in capital contribution to output growth between the fastest-growing sectors and the slowest-growing sectors. On the contrary, the Solow residual "explains" high growth rates of output in the fastest-growing sectors. Hence, one would have to conclude that technical progress does not seem to be embodied in new capital goods insofar as slow-growing sectors have accumulated as much physical capital as the fastest-growing sectors. Upon reflection, though, it is clear that one should not expect to uncover any relationship between aggregate investment data and sectorial TFP growth rates at the industry level. If TFP improvements accrue only to the firms investing in new and more efficient capital, but do not accrue to the firms that invest in capital goods of the same quality, then aggregate investments at the industry level may be huge while at the same time TFP growth is small. This will happen provided that capital accumulation consists mainly of same-quality capital goods.
improvements. Hence, correlation of both variables is expected to be positive and strong. Results by Castiglionesi and Ornaghi (2003) using a panel of Spanish firms during 1990-1999 show that a great fraction of technical change is embodied in new and better-quality capital. Together, the variables they use to measure the effect of investment-specific technical change17 explain 55% of TFP growth.
On the contrary, one may choose to ignore the findings of sections 3, 4 and 5. And, assuming that all capital is of the same quality, use the data to put formally to a test the hypothesis that growth is generated by "broad externalities" as postulated by some of the models of the
"new" endogenous growth literature18. In particular, one should find a strong and positive relationship between aggregate (industry-level) investments and industry-level TFP growth in the presence of "Marshall-Arrow-Romer" type externalities19. In this sense, the absence of any
1 7These are: research expenditures successfully embodied in new capital goods, weighted average age of the capital stock acquired in the market, and technology usage, which is a variable measuring if in period t the firm has adopted at least one new advanced technology among computer automated designs, robotics and numerically controlled machines.
1 8The model in Romer (1986) belongs to this class of models, with knowledge being privately accumulated and contributing not only to production at a particular firm but to production of all firms.
1 9The simplest model assumes the representative firm has production function:
Yh= Khα[AhLh]1−α where
Ah= BKφ, B > 0, φ > 0
B is a shift parameter, and φ measures the elasticity of the technological level to increases in the aggregate capital stock. That is, workers become more efficient as a side-effect of the accumulation of new capital at the aggregate level. The most widely-known version of this model, the AK model, sets φ = 1.
Ahgrows at the same rate as the stock of aggregate physical capital, K.
A˙h
Ah
=K˙ K
In equilibrium, consumption, output and the stock of physical capital all grow at the same constant growth rate.
Hence, this simple model predicts:
dA A =dK
K
That is, technical progress should be higher in those industries whose aggregate stock of physical capital grows faster.
correlation between capital accumulation and TFP growth, using cross-industry evidence, is a further though very preliminary proof that externalities are not the force underlying TFP growth.
There is a large empirical literature on the existence and magnitude of "knowledge spillovers".
We are in the process of carrying out a more careful investigation, in line with this literature, of the "externalities hypothesis", using data disaggregated by sector and region taken from both DPRN and MORES data sets.