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Price, private demand and optimal provision of public R&D investment: An application to Italian agriculture, 1960–1995

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Abstract

The current paper presents a model in which public R&D stock is included as a quasi-fixed input in a variable cost function. Its price affects the long run desired level, while its shadow price indicates whether under (over) investment occurs in the short run. Two alternative R&D prices and, thus, two different long-run desired levels, are defined. One concerns the private (farmer) perspective, in which farmers express demand under the assumption of costless R&D. The other considers the societal point of view, in which the objective is the optimal public R&D supply conditioned on its cost. Application of the above model to the Italian agricultural context (1960–1995) suggests a significant difference between these private and social desired R&D levels. The latter are, on average, closer to the observed values, though over-investment has emerged since the mid-eighties.

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Notes

  1. Actually, in the Italian case, the official statistics report private agricultural R&D data only for the own (i.e., self-financed) private agricultural R&D, which is—in fact—less than 5% of public R&D budget (Esposti and Pierani 2003c). On the contrary, R&D spillovers might indeed be relevant but hardly quantifiable, especially over a long time period (Esposti 2002).

  2. In the present paper, we disregard the fact that there may be several different economic, social and political reasons behind public funding of agricultural research rather than the pursuit of the social/private optimum. For a detailed review on this see Barnes (2001).

  3. We assume that the cost function is linearly homogeneous, non-decreasing and concave in W, non-decreasing in Y, non-increasing and convex in X, non-negative, continuous and twice continuously differentiable in all its arguments.

  4. By assuming that R&D is cost-free for private agents (farmers), we implicitly disregard any adjustment/adoption costs related to the introduction of new technologies generated by the public research effort. This issue may be relevant and can make public R&D rather costly from the private perspective as well. These costs can, at least partially, be taken into account using a dynamic specification as in Nadiri and Kim (1996). This may be one possible future extension of the present empirical application.

  5. Feehan and Batina (2003; page 5) state that: “If it is established that the returns to scale are constant in all inputs then the public input must fall into the congestible category. If the returns to scale in the primary inputs are constant then the public input must be a pure public input”.

  6. It must be remembered that, once the financing mechanism of the public good is explicitly included in the analysis, its social optimal provision should more correctly be evaluated within general equilibrium models, as this mechanism (for instance, various forms of taxation) might affect and bias private activities in a different way. This further aspect is beyond the scope of the present study; details can be found in Martinez-Lopez (2004).

  7. See Kumbhakar (2004) for alternative specifications of the exogenous technical change within a dual representation of the technology.

  8. We used the LSQ command of TSP 4.5, whose HETERO option computes consistent standard errors even in the presence of unknown heteroskedasticity.

  9. The use of the GDP deflator as the research IPI is also frequent in the official R&D statistics, as in the Italian case.

  10. The specific research IPI calculated by Mansfield (1984; 1987) grows more than the GDP deflator, and this result is confirmed by other analogous studies (Griliches, 1984; Nadiri and Kim, 1996). Both the deflators by Mansfield and Jaffe-Griliches (on which the Nadiri and Kim study relies) are based on an ad hoc survey on manufacturing firms; dealing with public R&D capital, Nadiri and Mamuneas (1994) use the price deflator of government purchase of goods and services.

  11. As concerns agricultural research, the Italian University system is almost entirely public.

  12. The price indices are derived as follows: the salary deflator of the Ministry of Education is used for W (until 1990, the public University system was in charge of this Ministry); the investment price deflator of agricultural investment (Caiumi et al. 1995) is adopted for S; the GNP deflator is used for E. The input price indices are assumed equal for both U and O. The IPI of the Italian public agricultural R&D is then computed with a Laspeyres formula, as both weights (for the R&D sources and inputs) are not available on an annual basis. So, the price indexes have to be calculated using fixed weights. These fixed weights among research sources and inputs have been taken from ISTAT data and refer to the 1984, 1985, 1986 average. The weights are calculated as follows: \(s_{{j0}} = \frac{{{\sum\nolimits_i {P_{{i0}} X_{{ji0}} } }}}{{{\sum\nolimits_j {{\sum\nolimits_i {P_{{i0}} X_{{ji0}} } }} }}}\) and \(w_{{ji0}} = \frac{{P_{{i0}} X_{{ji0}} }}{{{\sum\nolimits_i {P_{{i0}} X_{{ji0}} } }}}\) where P is the price and X the quantity, respectively.

  13. Comparing real public R&D investments in Italian agriculture deflated with this IPI and with the GDP deflator confirms previous results (Griliches, 1984): the GDP deflator overestimates the real research investment increase. During the period 1960–1995, the R&D stock grew by ten times if the GDP deflator is used, and “only” by six times using the IPI.

  14. See Esposti (2002) for a specific analysis of this issue in the case of Italian agriculture.

  15. Inflation and interest rates are taken from the AGRIFIT data base.

  16. Parameter estimates are not reported here; however they are available upon request.

  17. Given that results do not show marked variations over time, for the sake of space we discuss only sample mean estimates. The value of P R does not affect short run elasticities but only long run results. These long run elasticities for both P R=0 and P R>0 are not reported here but are available upon request. In estimation, analytical derivatives and approximated standard errors are obtained through the TSP commands DIFFER and ANALYZ, respectively.

  18. Namely, \({\partial V_{i} } \mathord{\left/ {\vphantom {{\partial V_{i} } {\partial X_{k} }}} \right. \kern-\nulldelimiterspace} {\partial X_{k} }{\text{ = - }}{\partial Z_{k} } \mathord{\left/ {\vphantom {{\partial Z_{k} } {\partial W_{i} }}} \right. \kern-\nulldelimiterspace} {\partial W_{i} }\), which can be re-phrased in terms of elasticities as: \(\varepsilon _{{ik}} = - {\left( {{\omega ^{*}_{i} } \mathord{\left/ {\vphantom {{\omega ^{*}_{i} } {\omega ^{*}_{k} }}} \right. \kern-\nulldelimiterspace} {\omega ^{*}_{k} }} \right)}\;\varphi _{{ki}}\), where \(\omega ^{{\text{*}}}_{{\text{i}}}\) and \(\omega ^{{\text{*}}}_{{\text{k}}}\) are the input shares on shadow cost C*, and φ ki gives the impact of W i on the quasi rent of stock k.

  19. This is the exogenous technical change measured as the reduction rate of the short run cost, i.e. ∂lnG/∂t and is reported in Table 2 as the weighted sum of the variable input growth rates.

  20. In the short run, the MIRR is simply computed as \({\sum\limits_{n = 0}^{L_{R} } {\frac{{w_{n} Z_{{R,t - L_{R} }} \,\,}}{{{\left( {1 + MIRR} \right)}^{n} }}\, = \,1} }\) where L R is the maximum length admitted for the investment to be effective and w n is the age/efficiency function of the research investment over the L R period (both are taken from Esposti and Pierani 2003a).

  21. In the long run, the R&D marginal value corresponds to its long run marginal productivity; therefore the MIRR can be computed as \({\sum\limits_{n = 0}^{L_{R} } {\frac{{w_{n} Y^{*}_{{t - n}} \varepsilon _{{YR,t - n}} }}{{X^{*} _{{R,t - L}} {\left( {1 + MIRR} \right)}^{n} }} = \,1} }\) where \(\varepsilon _{{YRt - n}} = {\partial \ln Y^{*} } \mathord{\left/ {\vphantom {{\partial \ln Y^{*} } {\partial \ln X_{{R,t - n}} }}} \right. \kern-\nulldelimiterspace} {\partial \ln X_{{R,t - n}} }\). However, given that, when P R=0 the marginal productivity of R&D must be zero in the long run \({\partial Y^{*} } \mathord{\left/ {\vphantom {{\partial Y^{*} } {\partial X_{{R,t - n}} }}} \right. \kern-\nulldelimiterspace} {\partial X_{{R,t - n}} }\), in this case the long-run MIRR is indeed meaningless in economic terms. Thus, we only refer to the long run MIRR under the P R>0 hypothesis.

  22. The calculation of IRR is based on a 20-year maximum length of the research effects; therefore, the 1976–1995 period is considered.

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Authors and Affiliations

  1. Department of Economics, Polytechnic University of Marche, Piazzale Martelli 8, Ancona, 60121, Italy

    Roberto Esposti

  2. Department of Economics, University of Siena, Piazza S. Francesco 7, Siena, 53100, Italy

    Pierpaolo Pierani

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  1. Roberto Esposti
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  2. Pierpaolo Pierani
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Correspondence to Roberto Esposti.

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The authors are listed alphabetically and authorship may be attributed as follows: sections 2, 4 to Esposti, sections 1, 2, 5 to Pierani. we wish to thank an anonymous referee for several comments and suggestions on an early version of the paper. The usual disclaimers apply.

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Esposti, R., Pierani, P. Price, private demand and optimal provision of public R&D investment: An application to Italian agriculture, 1960–1995. Empirical Economics 31, 699–715 (2006). https://doi.org/10.1007/s00181-005-0036-3

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