Relative Capital Shortage and Potential Output Constraint: A Gap Approach

Abstract

Focusing on core‐infrastructure capital vis‐à‐vis productive capital, we propose a macroeconomic method to estimate their optimal utilisation ratio in production and their relative shortage in any period. The method is based on an adapted two‐gap model, estimated via linear programming, with application to Chile and Mexico over the 1950–2000 period. Core infrastructure appears to support a variable level of productive investment, relative capital shortage alternating and imposing constraints on potential output over time. This suggests an optimal investment trade off, based on a social opportunity cost that derives from the prevailing gap in any period.

Key Words:

• Capital shortage
• potential output
• two‐gap model

Jel Classifications:

• E12
• O11
• O41
• O54
• C61

Notes

1. This model is from time to time resorted to by academics to analyse constrained growth (e.g. Taylor, 2004, 1994, 1991; Bacha, 1990, 1984, 1984; Chisari & Fanelli, 1990; Eyzaguirre, 1989; Fanelli & Frankel 1989; and others). The World Bank has always used it for its growth programming exercises, now called the ‘Revised Minimum Standard Model’ or RMSM (Agenor, 2000; Khan et al., 1990; Michalopoulos, 1987).

2. Linear programming (LP) picks the best combination of values that satisfies the objective function, given the constraints, while ignoring the others (Choudhury & Kirkpatrick, 1994; Chiang, 1984; Dervis, 1982). The parameters φ so generated are the basis of our potential output calculation (via equation (9)). As is well known, LP results cannot be tested with the same statistical sophistication of econometrics, but they can still be submitted to sensitivity analysis, by changing marginally some parameters, so that the stability of the results can be assessed. We did this by changing the depreciation parameter, which showed that our resulting patterns are pretty stable. In addition we assume a one‐year lag for investment to become productive, which is customary (Berg 1984; Marfan & Artiagoitia 1989). Just as with depreciation rates, this purports to be an aggregate average, as some investment will become productive in the same year, while other will do with a lag of two or more years. We tested the results using no lag, 1‐ and 2‐year lag, alternating between series, but there was not significant difference in the results, so we kept the more conventional average of a 1‐year lag. This of course also assumes that the average lag does not significantly change over time. Finally, notice that we customarily called the ratio output‐to‐capital ‘productivity of capital’, but it actually is the level of total output that a unit of capital can sustain, having as given all other resources and productive conditions. This is why infrastructure capital ‘productivity’ β is so high, i.e. by definition, given that the total output level is the same, the smaller the level of the capital stock we focus upon, the larger this ratio will be.

3. To apply the method, the actual statistical series should be long enough to go across a cycle, so as to include both peaks and troughs, but short enough to let the assumption of fixed parameters hold. We satisfy these constraints by estimating the parameters over a 10‐year period, with five overlapping years. That is, we repeat the calculation for 10 sub‐periods, 1951–1960, 1956–1965, 1961–1970, and so on. Furthermore, the basic series are transformed into 3‐year moving averages, allocating each average to the middle year, which would also prevent a rogue year from exerting undue influence on our optimal results. Notice that the 5‐year overlapping allow us to split the results in 5‐year periods. To do so, the original 10‐year calculation can be modified by averaging the 5‐year overlapped result.

4. All our data come directly from Chilean and Mexican official institutions (e.g. Planning Ministry, Central Bank, Public Works Ministry, National Institute of Statistics, INEGI, etc.). For Chile, we also used a compilation by Moguillansky (1999) from the same official sources. For Mexico, Ernesto Piedras kindly supplied the ‘core infrastructure’ data, which was part of his PhD thesis on the subject at the LSE. All series have been deflated, via PPI and GDP deflators, for 1986 and 1970 for Chile and Mexico, respectively. For the stock of core‐infrastructure capital, we use a definition that is confined to transport, sewage and utilities, i.e. water, electricity and gas (Diewert, 1986). Finally, strictly speaking, what we call private capital is actually non‐infrastructure capital, as there is no reliable way of separating private capital from it.

5. Using basic data produced by Hofman (2000) for Chile and Mexico, the actual average correlation of capital and output, over our 10‐year periods, is around 98%. In turn, the actual capital–output ratio exhibits variation coefficients of only around 5%, but had the capital series been corrected for actual capital usage, the stability of capital–output ratios would have further improved in any sub‐period. Alternatively, using the actual capital stock series, we can estimate what would have been the potential output achievable in each sub‐period. This smoothens out output instability, improving both the capital–output correlation and the stability of capital–output ratios, which is the approach adopted in this paper.