# Are intermediate inputs really fixed?

Marc Jim M. Mariano, George Verikios, Kenneth W. Clements

In the traditional input-output (I-O) model, output is perfectly elastic and determined directly by demand and the use of inputs without considering prices, leading to a formula that calculates industry outputs. In this model, the relationships between inputs and outputs are fixed, meaning that industries cannot adjust their input use based on price changes. On the other hand, computable general equilibrium (CGE) models allow for changes in how products are substituted based on their prices, although they typically assume fixed input relationships for producing goods. This paper examines whether it’s justified to assume fixed relationships for inputs in production.

The literature relevant to our questions is reasonably sparse. As far as we are aware the stability of input-output coefficients was first addressed by Sevaldson (1970, 1974). Sevaldson examined a time series of I-O tables for Norway and found that while I-O coefficients varied over time this was not due to cost-minimising behaviour. Sevaldson concluded that variability in I-O coefficients was likely due to changes in technology, product mix, product specifications, or errors in statistical reporting, measurement, and deflation. It is likely that this work was partly responsible for the typical assumption of a Leontief production function in combining intermediate inputs in CGE models. The only other significant work in this area that we are aware of is McKibbin and Wilcoxen (1999). They estimate intermediate and value-added elasticities of substitution using as time series of US input-output tables. They find that the elasticities diverge substantially from one (i.e., Cobb-Douglas technology). Although McKibbin and Wilcoxen (1999) estimate non-zero elasticities of substitution for US industries their findings did not inspire similar investigations in the CGE literature.

Give the sparsity of the literature in this area, the purpose of the present study is to test the assumption of fixed proportions in combining intermediate inputs. The challenge is the availability of a time series of I-O tables. This condition is now satisfied for Australia. The Australian Bureau of Statistics (ABS) publish a new I-O table each year and there is now a time series spanning several decades. In this paper, we use this rich source of information to provide evidence on intermediate substitutability. First, we examine the properties of the I-O tables in some detail and then provide summary measures of the movements over time of the I-O coefficients in the form of Divisia index numbers. Second, we test input substitutability using the CES production function to provide preliminary estimates of the elasticity of substitution (sigma). Third, we apply the SURE approach to estimate sigma. The two sets of estimates are found to be not too different. Lastly, we establish the importance of the value of delta within a CGE environment by simulating the effects of significant changes in energy prices. The simulation results when sigma = 0 are substantially different to those with our new estimates of this elasticity. The new sigma results appear more plausible.

Full article: Are input-output coefficients really fixed? (tandfonline.com)