Working paper

The Role of R&D in Productivity Growth: The Case of Agriculture in New Zealand: 1927 to 2001 (WP 06/01)

Authors: Julia Hall and Grant M Scobie


Productivity growth is a key determinant of rising living standards. The agricultural sector has been an important contributor to the overall growth of productivity in New Zealand. The average rate of multifactor productivity growth in agriculture from 1926-27 to 2000-01 was 1.8%. We find evidence that this rate has been increasing especially since the reforms of the 1980s. This paper estimates the contribution that R&D has made to agricultural productivity. It develops a theoretical framework based on the stock of knowledge available to producers. This model incorporates foreign stocks of knowledge and the spill-in effect for New Zealand. The estimation allows for extended lag effects of research spending on productivity. We find that foreign knowledge is consistently an important factor in explaining the growth of productivity. It appears that the agricultural sector relies heavily on drawing on the foreign stock of knowledge generated off-shore. The contribution of domestic knowledge generated by New Zealand’s investment in R&D is less clear cut. However, there is typically a significant positive relation between domestic knowledge and the growth of productivity. We find a wide range of estimates of the return to domestic R&D. The results are sensitive to the type of model used and the specification of the variables. Based on our preferred model we estimate that investment in domestic R&D has generated an annual rate of return of 17%. The results underscore the importance of foreign knowledge in a small open economy. The very existence of foreign knowledge may be a necessary condition for achieving productivity growth in a small open economy. However in no way could it be argued that this was sufficient. Having a domestic capability that can receive and process the spill-ins from foreign knowledge is vital to capturing the benefits. The challenge is to be able to isolate those effects from aggregate data for the agricultural sector. In that task we claim only modest success.


The authors are grateful to Tim Helm for a very substantial effort in preparing the data for this study. They also thank Dimitri Magaritis who provided advice and generous help with the modelling. Nathan McLellan and Kam Szeto provided advice on the modelling. Robin Johnson responded to many questions about data sources. Substantial help was derived from very thorough comments by Richard Fabling.


The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the authors. They do not necessarily reflect the views of the New Zealand Treasury. The Treasury takes no responsibility for any errors or omissions in, or for the correctness of, the information contained in these working papers. The paper is presented not as policy, but with a view to inform and stimulate wider debate.

1  Introduction#

… it is essential for scientists, however distasteful the task may be, to prove to the farm community the value of their discoveries in terms of pounds, shillings and pence.

Lord Bledisloe
Address to the Wellington Philosophical Society
26 October 1932

Productivity growth is seen as a key element in both improving the relative income in New Zealand compared to other OECD countries and contributing to achieving higher living standards. Agriculture remains an important sector of the economy and productivity growth in agriculture has been an important contributor to improved performance in the overall productivity growth in New Zealand (Black, Guy and McLellan 2003).

Productivity improvements stem from many sources, but increases in the stock of knowledge are widely acknowledged as one strategy for enhancing productivity growth. Formal investment in R&D is one avenue through which to increase this stock of knowledge. In both the private and public sectors, decisions must be made about allocating resources toward investment in the generation of new knowledge.[1] Public investment in R&D represents a major share of total national R&D expenditure in New Zealand.

In order to determine the appropriate policy settings, a necessary condition is to understand the relationship between investment in R&D and the growth of productivity. The primary objective of this paper is to develop a conceptual model, derive a formal model that can be tested with historical data and thereby generate estimates of the impact of R&D on productivity growth in the agricultural sector. From this we can then estimate the rate of return to investment in R&D.

One of the critical issues in analysing the impact of investment in R&D is the need to recognise the long lags involved. Expenditure on a R&D project today might result in the generation of new knowledge and its adoption into production systems a decade or more from now. Hence investments made in R&D today arguably will not contribute to measured productivity growth until some time in the future. For this reason we have developed time series data for the key variables from 1926-27 to 2000-01.

As a consequence however, it is inevitable that there will have been important changes in the institutional environment. For many years agriculture was heavily taxed in New Zealand as a result of industrial protection policies and labour laws. The economic liberalisation of the 1980s had major implications for the agricultural sector. Furthermore, the arrangements for the conduct and funding of research have evolved through a number of forms, each having implications for the level and allocation of research expenditures.

A second critical feature given emphasis in this study concerns the contribution of knowledge generated offshore to productivity growth in New Zealand. Arguably a great deal of the innovation that takes place in a small open economy such as New Zealand comes not from domestic investment in knowledge, but rather from that which can be “borrowed” from offshore. To accurately assess the contribution of domestic investment in R&D to productivity growth, we need to isolate that part which is attributable to the borrowed knowledge, often referred to as the foreign spill-in.

The paper is organised as follows: Section 2 discusses the importance of the agricultural sector to the economy; Section 3 discusses the methodology and findings of the empirical literature; Section 4 reviews the theory behind and evidence on knowledge spillovers; Section 5 links the stock of knowledge to productivity and sets out our empirical specification; and Section 6 discusses our results.


  • [1]A secondary issue arises about the division of those costs between the public and private sectors. We do not address this issue in this paper.

2  Agricultural R&D and the Contribution to Overall Productivity Growth#

This section first considers the agricultural research intensity compared with Australia, and then reviews the growth performance of New Zealand’s agricultural sector over time and compared with other industries.

2.1  Agricultural R&D#

The institutional arrangements for the public funding of R&D in New Zealand have evolved over the last two decades. Up until the early 1980s, the majority of research funds were allocated to the former Department of Scientific and Industrial Research and the Ministry of Agriculture through the standard process of parliamentary appropriations. After a series of changes the current system of funding emerged in which a significant part of the public sector funding for R&D is channelled through a series of state-owned research institutes. These institutes and universities submit competitive bids to the Foundation for Research, Science and Technology, which through a process of pair review allocates the public funding according to priorities established by the government based on the policy advice of the Ministry of Research, Science and Technology.[2]

Figure 1 shows the level of public spending on agricultural R&D in New Zealand compared to in Australia over the period 1975 to 2001, as a percentage of agricultural GDP. Australia has invested a higher percentage than New Zealand throughout the sample period, with a high in 1983 of 5.9%. Since then the trend has been one of declining public R&D intensity in Australia, although from 2002 to 2003 there was an increase from 2.9% to 3.8%.

New Zealand’s level of public R&D spending as a percentage of agricultural GDP has remained relatively steady over this period, at a level of 1.6% in 1975 and 1.3% in 2001.

Figure 1: Australian and New Zealand public R&D intensities in agriculture


Source: John Mullen (pers. comm.) and Australian Bureau of Statistics.


  • [2]For further details see Jacobsen and Scobie (1999)

2.2  Productivity Growth#

The primary sector continues to play an important role in the New Zealand economy. It directly contributed $8 billion (to the year ended March 2005 in 95/96 prices), or 6.6%, to the country’s real GDP. Of this, the agricultural sector contributed 77% to the primary sector, or approximately $6 billion (95/96 prices) to whole economy real GDP. The primary sector’s recent growth performance is outlined in Table 1 below.

Table 1: Recent Growth Performance: New Zealand: 1988 – 2004.
Sector Annual average growth rates
Whole Economy 2.5%
Primary Sector 2.5%

Made up of:

Agriculture 2.1%
Fishing 1.7%
Forestry and logging 5.0%

Data Source: Statistics New Zealand.

Primary sector average annual growth for the period 1988-2004 has been similar in New Zealand to that in Australia (see Table 2 below). The agricultural sector has also shown a similar growth experience over this period for both countries, with average annual GDP growth of 2.5% in New Zealand and 2.8% in Australia.

In Australia, the primary sector contributed 3.4% of total GDP (to the year ended June 2004 in 2002/03 prices), with the agricultural sector accounting for 93% of the total primary sector.

Table 2: Recent Growth Performance: Australia: 1988 – 2004.
Sector Annual average growth rates
Whole Economy 3.4%
Primary Sector 2.9%

Made up of:

Agriculture 2.8%
Forestry and Fishing 3.6%

Data Source: Australian Bureau of Statistics.

While the overall rate of growth of the primary sector in New Zealand has matched that of the economy as a whole, the productivity performance of the primary sector in New Zealand has been impressive (see Table 3). The primary sector had one of the highest average annual growth rates of labour productivity over the period 1988 to 2004 (with only the Transport and communications and the Electricity, gas and water sectors achieving higher growth).[3] This labour productivity performance was sourced equally from capital deepening and multifactor productivity growth, based on a growth accounting decomposition.

While the primary sector had one of the highest average annual labour productivity growth rates amongst industries in New Zealand (at 3.0%), this was still markedly less than primary sector labour productivity growth in Australia, which averaged 4.1% between 1988 and 2004.

We can also contrast the overall multifactor productivity growth for the primary sector of New Zealand and Australia. In New Zealand, multifactor productivity in the primary sector (comprising agriculture, forestry, hunting and fishing) grew at an annual average rate of 1.5% from 1988 to 2004 (see Table 3). In contrast, the comparable rate of growth in multifactor productivity in the Australian primary sector was 3.8% (Productivity Commission 2005). It is worth noting that this higher multifactor productivity growth in the primary sector was accompanied by a higher public R&D intensity in Australian agriculture (recall Figure 1).

Unfortunately, hours data is not available for the agricultural sector in New Zealand alone. Instead we have constructed a multifactor productivity series using employment numbers back to 1926-27 (see Figure 2). From 1988 to 2001 multifactor productivity in the agricultural sector grew by 1.3%, compared with multifactor productivity growth for the whole business sector of 1.4%. Over our entire sample period, average multifactor productivity growth in the agricultural sector has increased. Between 1927 and 1956, annual MFP growth averaged 1%, increasing to an average of 2.2% between 1957 and 1983. From 1984 onwards MFP growth further increased to an annual average rate of 2.6%.

Table 3: Growth Accounting Decomposition for each Industry: New Zealand: 1988-2004
Sector Labour productivity growth Multifactor productivity growth Weighted capital-labour ratio growth
Agriculture, Forestry, Hunting and Fishing 3.0% 1.5% 1.5%
Mining and Quarrying 0.1% -0.7% 0.7%
Construction -0.6% -0.9% 0.4%
Transport and communications 6.3% 5.5% 0.9%
Business and Property Services 0.1% -0.1% 0.2%
Personal and community services 1.9% 1.6% 0.3%
Manufacturing 1.7% 0.8% 0.9%
Electricity, Gas and Water 5.0% -0.2% 5.2%
Retail and wholesale trade 1.1% 1.0% 0.1%

The growth accounting decomposition is given by: Δln(Y/L)t = ΔlnMFPt + αΔln(K/L)t. Here we have taken the average of each component in this decomposition over the period 1988 to 2004.

Figure 2: Agricultural Multifactor Productivity 1927-2001




  • [3]Table 3 is an updated version of that presented in Black et al (2003).

3  Literature Review and Existing Estimates#

3.1  Methodology#

Since Solow’s (1957) decomposition of economic growth, many empirical studies have tried to determine the importance of various factors which underlie the productivity residual. Investment in R&D has been one of these factors.[4]

The two main approaches that have been used in the empirical literature to assess the importance of R&D to productivity growth are econometric analysis and case studies. The main disadvantage of the case study approach is its lack of representativeness. Since they only tend to concentrate on selected successful projects, it is not possible to draw general conclusions from their findings (for an example of the case study approach see Griliches (1958)).

Most econometric studies use either the production function approach (for example, Guellec and van Pottelsberghe 2001) or the cost function approach (for example, (Rouvinen 2002)). The two approaches are related – it is possible to derive a cost function from a production function, and vice versa – but they use different statistical methods and have different data requirements. Here we use the production function approach due to data availability.

Within the production function framework there are two alternative approaches: estimating the production function directly (i.e. regressing output or value added on conventional inputs plus R&D), or regressing multifactor productivity (MFP) on R&D.

Most of these econometric studies[5] have adopted the general version of the Cobb-Douglas production function, which in addition to the traditional inputs also includes knowledge capital:




where Y is value added, A is a constant, L is labour, C is physical capital, K is the domestic R&D stock and X is the external stock of R&D available (spillover pool).

Usually, equation (1) is taken in logarithms to enable the estimation of the parameters of interest: β and δ, or the elasticity of output with respect to domestic and foreign R&D respectively. This leads to the following linear regression model:




where lower case letters denote logarithms of variables and ut is a random error term.

Alternatively, if constant returns to scale are assumed, then equation (2) can be rewritten in terms of multifactor productivity (MFP) as:

(3)     mfpt = a + βkt + δxt + ut

Thus the elasticity of MFP with respect to the stock of domestic R&D, β, estimated by equation (3), is equal to the elasticity of output with respect to the stock of domestic R&D.

Some studies choose instead to directly estimate the rate of return rather than the elasticity. By taking first differences and disregarding the depreciation of R&D, i.e.,Δk = ΔK/K = RD/K (where RD represents R&D expenditure), and applying the same transformations to the foreign R&D spillover stock, then we have:

(4)    Δmfpt = ρ1(RD/Y)t = ρ2(XD/Y)t + ut - ut-1

where ρ1 =


is the marginal product of the domestic R&D stock, or the rate of return to domestic R&D.[6]




, it can be seen that there is a direct relationship between β and ρ1; either one can be derived from an estimate of the other. That is,





3.2  Empirical Evidence#

The expansive body of empirical literature estimating statistically the part of productivity growth that can be attributed to R&D activities has been surveyed by Wieser (2005).[7] He concludes that on average there is a large and significant impact of R&D on firm performance, although the estimated returns vary considerably: the average estimated rate of return was in the order of 29% for the papers surveyed (for those which were significant),[8] with a lower bound of 7% (Link 1981) and an upper bound of 69% (Sassenou 1988). Wieser also conducted a meta-analysis and found that the estimated returns do not differ significantly between countries, although estimated elasticities appear to differ significantly between countries.[9]

Many of the early empirical studies were conducted for the agricultural sector. Table 4 reproduces Table 1 in Griliches (1992), showing rates of return in the agricultural sector estimated from both case studies and regression studies. The table shows that evidence from the international literature implies a substantial return to R&D in the agricultural sector.

Table 4: Selected Estimates of Returns to R&D in the Agricultural Sector
  Commodity Rates of Return to Public R&D
Griliches (1958) Hybrid Corn 35-40
Hybrid Sorghum 20
Peterson (1967) Poultry 21-25
Schmitz-Seckler (1970) Tomato Harvester 37-46
Griliches (1964) Aggregate 35-40
Evenson (1968) Aggregate 41-50
Knutson-Tweeten (1979) Aggregate 28-47
Huffman-Evenson (1993) Crops 45-62
Livestock 11-83
Aggregate 43-67

A more recent study by Mullen and Cox (1995) estimated that the return from public investment in Australian agricultural R&D between 1953 and 1994 may have been in the order of 15-40%. Cox et al (1997) found support for these earlier findings using non-parametric techniques.

A comprehensive meta-analysis of rates of return to agricultural R&D is found in Alston, Chan-Kang, Marra, Pardey and Wyatt (2000). Their results show that the returns from 1,886 estimates found in 292 studies averaged 100% per year for research, 85% for extension, 48% for studies that estimated the returns to research and extension jointly, and 81% for all the studies combined. The median rates were 48.0% for research, 62.9% for extension, 37.0% for joint research and extension and 44.3% across all studies.

Unfortunately the literature is not replete with estimates of the impact of R&D in New Zealand. As a consequence, much of the policy on public investment in R&D has been made without any explicit estimates of the return that might be expected from that investment.

Two early studies focussing on the agricultural sector in New Zealand are Dick, Toynbee and Vignaux (1967) and Scobie and Eveleens (1987). Dick et al evaluated the returns to four particular projects and attempted to generate an estimate of the long term aggregate payoff. However their study was based on data for only one decade, arguably not long enough to pick up the full impact of research. Scobie and Eveleens used data from 1926 to 1984 and found that research contributed significantly to the growth of productivity in the agricultural sector. They concluded that this contribution comes over an extended period of 23 years on average, generating a real rate of return of 30 percent per year. However, they were unable to isolate the separate effects of research investment, extension efforts and the contribution from human capital.

Johnson (2000b) used data from 1962 to 1998 to estimate the effect of private and public investment in R&D on total factor productivity in nine sectors of the New Zealand economy. In the case of agriculture he found that private R&D had a significant effect and a rate of return of 68.7%. In contrast, public spending on R&D reduced TFP in agriculture, with the consequence that the rate of return was -6.7% to public spending. In an attempt to allow for foreign spillovers, Johnson found that higher levels of R&D in the Australian business sector reduced the level of TFP in New Zealand agriculture.

In a more recent study Johnson et al. (2005) use panel data over the same nine industries in New Zealand from 1962-2002 and report on average a significant impact on productivity from private R&D, but no effect from public R&D. They also find evidence that private R&D in the Building, Forestry and Other services industries positively affects productivity in the rest of the economy, i.e. it generates positive spillovers.

In short, there is a wide range in the estimates of returns to R&D. This arises in part due to the choice of model. Regrettably, it has been increasingly apparent that the estimates of return found using econometric studies are indeed sensitive to the assumptions and type of model. This conclusion is reinforced by the results of the present study.


  • [4]See for example Guellec and van Pottelsberghe (2004) and Frantzen (2000).
  • [5]For a comprehensive discussion of the econometric measurement of the effects of research see Alston et al (1995).
  • [6]Note that β


    , so that βΔk becomes


  • [7]Note that he only surveys those studies which use microeconomic data at the firm level.
  • [8]Twenty nine of the fifty papers surveyed found significant estimates of the rate of return.
  • [9]The reason for this divergence between rates of return and elasticities is due to the different estimation techniques used - the rates of returns (marginal products) in the sampled studies are measured by estimating the change in TFP that result from a one dollar unit increase in R&D, while the elasticities are measured by estimating the percentage increase in TFP that occurs in response to a one percentage increase in R&D.

4  Spillovers#

Griliches (1979) has identified two types of spillover effects. The first type refers to the effect of research performed in one industry or country improving technology in a second industry or country, and may occur without any economic transaction. The second type of spillover refers to inputs purchased by one industry or country from another industry or country, which embody quality improvements that are not fully appropriated by the selling industry. This is a problem of measuring capital equipment, materials and their prices correctly rather than a case of pure knowledge spillovers. While in principle these two notions are quite distinct, in practice it is very hard to distinguish between them empirically. We do not attempt to adjust our capital and intermediate inputs data for quality in this paper.

Spillovers occur at both the national and international level. National spillovers are composed of two distinct elements: the extent to which firms in the same industry as the firm undertaking the R&D benefit from the R&D (intra-industry spillovers), and from firms in other industries (inter-industry spillovers). Evidence from the empirical literature suggests that spillovers between firms in the same industry are small (Productivity Commission 1995). Direct estimates of their magnitude by Bernstein (1988), Bernstein and Nadiri (1989) and Suzuki (1993) yield estimates in the range of 2 to 15%. Estimates of inter-industry spillovers indicate that they appear to be more significant than intra-industry spillovers, with most estimates lying in the range of zero to 150% (Productivity Commission 1995).

The evidence on international spillovers is more mixed. Mancusi (2004) states that results from different empirical studies seem to suggest that knowledge spillovers are mainly intra-national rather than international in scope.[10] However, the paper finds that international spillovers are always effective in increasing innovation (proxied by patents). Estimates by Coe and Helpman (1995) also suggest that foreign R&D has beneficial effects on domestic productivity, and that these are stronger the more open an economy is to foreign trade. Their estimates indicate that foreign R&D has a larger impact in all of the smaller countries in their sample except Australia, Finland, Spain and New Zealand.[11]

After finding that the correlation between R&D and productivity is weaker in small countries than in the G7 countries, Englander and Gurney (1994) argue that this is consistent with the view that large countries benefit from their own R&D, while small countries benefit largely from R&D done elsewhere.[12]

On the other hand, Engelbrecht (1997) finds that foreign R&D spillovers have a mainly negative impact on TFP in countries with relatively small domestic R&D capital stocks as a proportion of GDP, including New Zealand and Australia.

What are the international channels through which knowledge spills over between countries? Coe and Helpman (1995) argue that the benefits from foreign R&D can be both direct and indirect. The direct benefits consist of learning about new technologies and materials, production processes, or organisational methods. The indirect benefits arise from imports of goods and services that have been developed by trade partners. However, Wieser (2001) states that insufficient data exists to adequately differentiate between disembodied and embodied R&D.

To deal with this, researchers typically assume that all knowledge transferred between countries is embodied R&D or that the usage of knowledge between countries mirrors the usage of commodities between countries (Wieser 2001). For example, Coe and Helpman (1995) define the foreign R&D stock which enters a countries production function as the import-share-weighted average of the domestic R&D stocks of trade partners. This is implicitly assuming that the main channel through which R&D spills over from country to country is through international trade. However, Keller (1998) provides evidence that casts doubt on the effectiveness of trade as a mechanism for knowledge transfer, finding higher coefficients on foreign R&D when using random weights instead of those used by Coe and Helpman. Eaton and Kortum (1999) also show that, except for small countries very near the source of information, trade is not the major conduit for the spread of new technology. By deriving a formal model of technology diffusion, they identify knowledge flows through cross country patenting rather than through the export and import of goods embodying them. Guellec and van Pottelsberghe (2001) argue that by computing technological proximity using patents granted by the United States Patent and Trademark Office and using these weights to form a foreign R&D stock, they are being consistent with the argument by Eaton and Kortum (1999), i.e. they are assuming that technology circulates directly, with no need for exchange of goods as a vector. Patent citations have also become a widely used tool for the purpose of tracing knowledge flows (Mancusi 2004).

Alston (2002) has reviewed the evidence on spillovers within the literature devoted to the agricultural sector. While there are few studies within the agricultural literature which actually take spillovers into account, those that do provide evidence which suggests that interstate and international spillovers from public agricultural R&D account for a significant share of agricultural productivity growth.[13]

Johnson et al (2005) attempt to measure spillovers by including an Australian R&D stock variable in their estimating equations, to proxy the foreign spillover pool. Their results indicate that the Australian R&D stock does not seem to have a direct impact on productivity in New Zealand.[14] However, they concede that this might indicate that the Australian R&D stock is a bad proxy for international R&D, as 35% of the world’s R&D is produced in the US, with Japan the next highest producer (14%) and the rest of the OECD producing 25%.[15] Thus a large portion of international spillovers comes from the US, with a very small proportion produced in Australia (1.4% of the total R&D produced in the OECD). Here we include US patents as a proxy for international R&D spillovers. Using patents ensures that we avoid accounting for outputs of no international consequence. Also, Crawford, Fabling, Grimes and Bonner (2004) find evidence that increased R&D expenditures increases the number of patents. A simple correlation coefficient of 0.91 between US patent numbers and US R&D expenditures from 1953 to 1998 suggests that US patents are a potentially reasonable proxy for R&D and hence the stock of foreign knowledge.

The positive externality generated by international technology flows, will crucially depend on the ability of the destination country to understand and exploit external knowledge. Such ability is a function of past domestic R&D experience, a concept introduced by Cohen and Levinthal (1990) and referred to as “absorptive capacity”. Mancusi (2004) uses self-citations to measure the effect of absorptive capacity, arguing that self citation indicates that a firm who has done some research in the past has then generated a new idea building on the previous research in the same or in a related technology field. She finds that absorptive capacity increases the responsiveness of a country’s innovation to both national and international spillovers. However, its effect differs depending on the position of the country with respect to the world technological frontier: the larger the gap of a country from the technological leaders, the lower is its ability to absorb and exploit external knowledge, but the larger appears its potential to increase this ability.

Griffith et al (2001) also study the relevance of absorptive capacity by analysing the ability of countries to catch up with the more technologically advanced countries. They found that domestic R&D is statistically significant in this catch-up process. Thus R&D stimulates growth directly through innovation and also indirectly through technology transfer. They also identified a role for human capital in stimulating innovation and absorptive capacity. Eaton and Kortum (1999) also show that a country’s level of education plays a significant role in its ability to absorb foreign ideas.

The “absorptive capacity” argument not only means that the country is more able to take advantage of foreign research, it also means that the marginal return to domestic R&D will be higher the more foreign R&D the country has access to. That is, if the stock of available foreign knowledge is increased, increasing domestic research expenditure will be more profitable.[16]


  • [10]See, for example, Jaffe el al (1993), Branstetter (1996), Maurseth and Verspagan (2002).
  • [11]Their sample consists of the G7 countries as well as 15 smaller countries.
  • [12]They do not, however, directly estimate the impact of foreign R&D on domestic productivity.
  • [13]See for example Huffman and Evenson (1993), and Bouchet et al (1989).
  • [14]Johnson (2000b) also used the Australian R&D stock to proxy the foreign spill-in pool, and found a negative relationship between this variable and TFP in the agricultural sector, although a positive relationship in 6 out of the 9 industries sampled, and a positive relationship in the market sector.
  • [15]Data is for 2003, source: OECD, Main Science and Technology Indicators
  • [16]See Evenson, Scobie and Pray (1985) for a discussion.

5  Estimation#

5.1  Basic model/included variables#

The underlying concept to be developed in this section is that output depends on the following:

  1. The level of inputs under the control of the farmer (fertiliser, labour, machinery, buildings, etc).
  2. The influence of uncontrollable variables (weather, pest and disease outbreaks, financial deregulation, terms of trade).
  3. The use that is made of current and past investments in knowledge about how to select, combine and manage the inputs. That knowledge can reflect both domestic and foreign investments in R&D.

Formally, this can be represented by an agricultural production function:





Yt = the volume of agricultural output in year t;

I t = a vector (I1t, 12t, …., Int) of n controllable inputs in year t;

Z t = a vector (Z1t, Z2t, …., Zmt) of uncontrollable variables in year t; and

RDt = R&D in year t, either domestic expenditure (d) or foreign expenditure (f).

The uncontrollable variable we use in our specification is weather, measured as the tenths of days of soil moisture deficit weighted by the four major agricultural activities (dairy, sheep, beef, and crops). The National Institute of Water and Atmospheric Research (2001) found that the agricultural component of GDP is negatively correlated with the strength of the southerly airflow over the country, and that milk fat production is negatively correlated with annual days of soil moisture deficit, regional summer temperature, and regional spring and summer rainfall. Buckle et al (2002) also show that climate is an important contributor to the overall business cycle, and that it appears to have been the dominant source of domestic shocks over the period 1984-2002. However, as Makki et al (1999) point out, weather may not be an important variable in the long-run time series analysis of productivity. It is reasonable to assume that annual weather variation is a random phenomenon, and there may be no long-run relationship with agricultural productivity, although short run variation in output and productivity may reflect seasonal conditions.

The controllable inputs which appear in the vector It include intermediate inputs, capital stock, labour, extension workers, and human capital stock. The capital stock includes livestock, plant, machinery and equipment, land improvements, and the value of all unimproved land. The labour variable is measured as the number of full-time equivalent workers plus working owners. The human capital stock has been calculated as the sum of current and past numbers of students enrolled in agricultural related courses (using a lag length of 15 years). A human capital index was then constructed (equal to 1 in 1949/50) from this human capital stock with a lag of 2 years to capture the lag between enrolment and graduation. Extension workers represent the number of Advisory Services Division staff in the Ministry of Agriculture and Forestry up until privatisation in 1984/85, after which time estimates of this have been drawn from various sources.[17] Extension is seen as impacting directly on agricultural productivity as well as speeding the adoption of new technology. Extension agents disseminate information on crops, livestock, and management practices to farmers and demonstrate new techniques as well as consulting directly with farmers on specific production and management problems.

Technological advances enter the production function in two forms. In the first place improvements are embodied in the inputs themselves, through enhanced design, improved and extended features, new materials, and indeed new inputs. A 1930 tractor or variety of wheat is clearly not the same as a 2001 tractor or wheat variety.

These enhancements arise, in part, from the R&D efforts of firms who supply the machinery, seeds, chemicals, financial, consultancy and marketing services to producers. They are continuously seeking innovations which enhance the quality of their products or services. They expect to recover the costs of this innovative activity through the sale of the item or service.

This raises an inherent problem of measurement. Ideally the vector It refers to the quantity of inputs used, where these are of standard quality. When measuring inputs over a long period their nature is bound to change, and some of the technological advances will be embodied in these data.

The second type of technological advance arises from improved knowledge. This results in more efficient use of the same quantity of inputs through better management decisions. Information about grazing management, the timing of fertiliser or pesticide applications, and tail painting for more accurate heat detection are all examples of technological advances which involve essentially information, rather than physical inputs. In summary, technological change is reflected in part by inputs of enhanced “quality” (captured in the vector, It) and partly through the improved stock of knowledge, which is added to through investments in formal R&D (RDt), and through more informal channels such as on-the-job learning. This study does not isolate the effect on productivity of these informal contributions.

The notion that there is a relationship between investment in research and increments to the stock of knowledge has been used by several authors including Griliches (1979) and Minasian (1969). As Pardey (1986) observes, “it follows naturally from the perception that general science progresses by a sequence of marginal improvements rather than through a series of discrete essentially sporadic breakthroughs”.

At any point in time, producers have available to them a stock of knowledge on which they can draw generated either from domestic sources (RD) or foreign sources (RDf). Both serve as sources of new knowledge but are not perfect substitutes. Organised farm tours to other countries are testimony to the implied demand by producers for access to foreign stocks of knowledge.

While the stock of knowledge may be added to through new investment in R&D, the amount of stock which is actually utilised at any point in time does not necessarily increase one-to-one with the extra R&D expenditure. It is not uncommon to hear scientists bemoaning the lack of use by producers of their findings. Leaving aside the question of whether the findings were relevant in the first place, there are a number of forces which govern the rate at which these increments to the stock of knowledge will be incorporated into production systems.

It is reasonable to suppose that dominant among these forces will be the profitability of the innovation. An advance which does not raise real income (through increasing output, reducing costs, saving time, eliminating unpleasant tasks or lowering variability) will almost certainly fail to be adopted in any widespread or sustained manner.

The cost to the producer of acquiring the innovation will be an important determinant of its profitability, and hence of the rate of utilisation which can be expected. In the case of a new input, or improvements to an existing input, part of the total cost will be the direct monetary price charged for the input. But, in addition, the producers must invest time and effort in learning about the product and its potential applicability to their circumstances. In the case of improved knowledge the entire acquisition costs are made up of these “learning costs”. Factors which lower these costs can be expected to increase the amount of new knowledge actually utilised. Extension services, farming journals, trade publications, the daily paper, radio and television all disseminate information and enhance the acquisition of new knowledge.

In addition changes in the structure of an industry will alter the cost of acquiring new information. A farmer with 100 hectares of barley has more incentive to invest time and effort in searching for information about new varieties, than one growing, say, 2 hectares. This would suggest that the trend to larger production units in say dairying, would cet. paribus lead to a higher rate of investment in and absorption of R&D.

Finally, the education and experience of farmers, their “human capital”, affects the cost of acquiring new information. Schultz (1974) has referred to this as the “value of the ability to deal with disequilibria”. The argument is simply that the operating environment is constantly changing -seasonal conditions, prices, costs and technology are never static. Entrepreneurship requires that these changes be continuously monitored, assessed and appropriate actions taken. Those with greater levels of human capital are presumed to be able to perform these tasks more readily.

Introduction of a new technology changes the operating environment; the greater the level of human capital, the more rapidly the new information (R&D) will be assessed and incorporated.

Evenson (1984) likens the structure of scientific and technological activities in agriculture to that of other economic activities. There is much specialisation in research, just as there is among firms producing different consumer goods. The industrial sector involves different stages of production; some firms produce coal, which is used by others for producing steel bars, which are bought by others to produce parts which are sold then to manufacturers of appliances.

In agricultural research there are counterparts which undertake “pre-technology research” (plant genetics, reproductive physiology, entomology) using as inputs the knowledge generated by the general sciences (e.g. chemistry, biology). The outputs of this stage are then used in the development of technology which is in turn screened and adapted for final use.

The preceding discussion leads to the development of a capital theoretic view of the generation and diffusion of knowledge. In other words, the existing stock of knowledge is seen as part of the capital stock of the agricultural sector in the same way that physical capital represents an input into farm production. Like other forms of capital, knowledge must be created through investment, and it is subject to obsolescence.

Thus we have a production function relating output to the stock of knowledge as in Griliches (1979):

(7)    Y = F(It ,Zt ,Kt )

Where Kt represents the current stock of knowledge. We can then continue following Griliches and assume that there exists a relationship between K and W(B) RD, an index of current and past levels of R&D expenditures, where W(B) is a lag function describing the relative contribution of past and current R&D levels to K, and B is the lag operator. Thus:

(8)    K= G [W (B) RD,v]

where v is another set of unmeasured influences on the accumulated level of knowledge and

(9)     W(B)RDt = (w0+ w1B + w2B2 + ....)RD t = w0RDt + w1RDt-1 + w2RDt-2 + ...

Thus output becomes a function of current and past R&D expenditures as set out in equation (6). The fundamental objective of this study is to statistically measure the relation between agricultural output (Yt) and the current and past values of research expenditures, or W(B)RD, while holding constant other factors which influence output.

Griliches defines W(B)RD as a measure of R&D “capital”. One of the major issues in the measurement of such “capital”, he argues, is the fact that the R&D process takes time and that current R&D may not have an effect on measured productivity until several years have elapsed. This forces one to make assumptions about the relevant lag structure W(B). We discuss alternative lag structures in the next section.


  • [17]For more detail about the data refer to Appendix 2.

5.2  Empirical specification#

We attempted to estimate the production function set out in the previous section, but found that intermediate inputs and capital stock were highly correlated with R&D expenditures (correlation coefficients of 0.97 and 0.95 respectively). Thus we constructed a multifactor productivity index as our dependent variable, calculated using a fisher index of GDP (gross output less intermediate inputs) divided by the weighted sum of capital and labour. Thus our final specification was:




where all variables are in logarithms, weather is our soil moisture deficit variable, extension is the number of extension workers, hk is our human capital index, W(B)RD is current and past domestic R&D expenditures, and W(B)RDf is current and past foreign R&D expenditures (here proxied by current and past patent numbers). These main variables are plotted in Figure 3 below.

We also ran this basic model including a dummy variable, equal to zero before 1984 and one from 1984 onwards. This provides a crude test of whether there is a structural break in our data. That is, has the changed institutional settings and economic environment induced by the reforms impacted on MFP in the agricultural sector?

There are many factors which will be omitted from the typical production function set out above, including the learning by doing mentioned in section 5.1, and improved managerial and organisational practices. These omitted factors not only affect productivity growth but also affect the incentives to invest in R&D. Comin (2004) states that some evidence in favour of the potential importance of this omitted variable bias comes from the fact that, after Jones and Williams (1998) included fixed effects in their regression, the effect of R&D on TFP growth almost disappeared. However, due to data limitations it is impossible to correct for this problem.

Another problem which has been discussed in the literature is that of double counting. This occurs because the expenditures on labour and physical capital used in R&D are counted both in the R&D expenditures as well as in the measures of labour and capital, and so should be removed from the measures of labour and capital used in production. Schankerman (1981) demonstrates that the failure to remove this double counting has a downward bias on the estimated R&D coefficients. Within the agricultural sector, this would be a problem only to the extent that research is carried out by farm owners and farm workers themselves. We believe this would have a minimal effect in New Zealand.

Another problem which arises in any economic time series analysis is that of non-stationary variables. Regressions involving non-stationary variables may result in spurious results. Szeto (2001) notes that there are three solutions to the problem of spurious regression. The first approach is to take first differences of the data before estimating. The second approach is to add the lagged value of the dependent variable. Finally one may consider the cointegration approach.[18] We employ both of the latter two approaches in this paper (discussed below).

To employ the cointegration approach, one must first establish whether the variables in the regression are I(1). We tested all of our series for unit roots using the Augmented Dickey-Fuller unit root test. All series appear to be non-stationary, I(1) processes, except for the human capital index, the public R&D stock, the number of soil moisture deficit days, and MFP, the first two found to be stationary with drift and the latter two to be stationary with drift and trend (see Appendix 1 for unit root tests). However, the unit root test of MFP is very sensitive to the lag length chosen – for all lags greater than zero the Augmented Dickey-Fuller test could not reject the null of a unit root in the series. Also, the Phillips-Perron unit root test accepts the null of a unit root for the MFP series. Therefore we can be fairly sure that we are regressing an I(1) variable on (mostly) non-stationary explanatory variables and hence there could be a cointegrating relationship (which is determined by testing the residuals for stationarity).

As discussed in the previous section, the fact that increments to the stock of knowledge may not be utilised the moment they become available means that the relationship between R&D expenditures and output will not be contemporaneous. Thus it is important to capture this in the estimation procedure.

Alston, Craig and Pardey (1998) highlight the importance of lag lengths in estimating the returns to research. Many studies have used relatively short lag lengths. These may well capture the link between investment in research and increments to the stock of knowledge. However, production depends on the flow of services of the entire stock of knowledge rather than recent additions to it. They find that using a model that allows for the impact of research on productivity to last much longer than conventional approaches, the real marginal rate of return to research in the USA was found to be much lower than studies with inappropriate lag lengths.

However, one cannot simply include many lagged values of the R&D expenditures as this runs into problems of multi-collinearity. In order to overcome this problem, it is necessary to impose some structure on the nature of the lags. We have adopted three different approaches to this problem. In the first case we form estimates of the stock of knowledge (or R&D capital) using the Perpetual Inventory Method (PIM). In the second case we use a Koyck transformation and in the final case we impose a polynomial lag structure.[19] Each approach is discussed in turn in the following sections.

Figure 3: Main Variables


Main variables.
  • [18]Non-stationary variables may be used in a levels regression if they prove to be cointegrated.
  • [19]The Perpetual Inventory Method is a model whereby past flows are accumulated into a stock using weights. All three of our approaches can therefore be classified as using the PIM. The difference between what we label the “PIM” models and our Almon models are the weights used in the accumulation: the “PIM” models use geometric weighting. The difference between our “PIM” models and our Koyck Transformation models is the estimation procedure: our “PIM” models assume a depreciation rate and enter the accumulated stock directly into the production function, whereas the Koyck models estimate the weights from the regression model once the transformation has been applied. Thus for simplicity we have labelled the geometrically weighted PIM, with the depreciation rate assumed, as our “PIM” models.

5.2.1  Creating knowledge stocks using the Perpetual Inventory Method#

The Perpetual Inventory Method (PIM) is used to create a stock of capital (in this case knowledge) from a flow of investments based on the following equation:

(11)     Kt = Rt + (1 - δ)Kt-1

where Kt is the R&D stock in year t, Rt is R&D expenditure in year t and δ is the depreciation rate. The initial stock (K0) is calculated as:




where R0 is the value of the R&D expenditure series in the first year available, and g is the average geometric growth rate for the R&D expenditure series between 1927 and 1947.[20]

This results in the following relationship between the stock of knowledge and current and past R&D expenditures, i.e. the specification of W(B)RD:




A limitation of this formulation is the need to specify a depreciation rate. Coe and Helpman (1995) and Johnson et al (2005) assume an annual depreciation rate of 5%.[21] As the estimation of the Koyck model gives an implicit estimate of the rate (see Section 6.1) then we have adopted a rate of 30% for consistency across these models. [22]

The estimating equation now becomes:




We used the Phillips-Loretan method to estimate the long-run relationship between these constructed R&D stocks (stocks of foreign R&D were calculated in the same way using patents data[23]) and MFP. This method is outlined in Razzak and Margaritis (2002), and requires the non-stationary variables to be cointegrated. We tested for cointegration using the methodology developed in Johansen (1991, 1995) and found evidence of one cointegrating equation.

The advantage of using the Phillips-Loretan method is that it adjusts for endogeneity of the explanatory variables by augmenting the regression with leads and lags of the differenced explanatory variables. Griliches (1979) argued that future output and its profitability depend on past R&D, while R&D, in turn, depends on both past output and the expectation about its future. If that is so, any unobserved shock to productivity that raises output could indirectly raise investment in R&D. Under those circumstances, OLS-based estimates of the coefficient on R&D will be biased. Most R&D studies do not adjust for endogeneity and we do not attempt to adjust for this in our other specifications. However, a Granger causality test between the domestic R&D stock and MFP indicates that causality flows from R&D to MFP: the null hypothesis that the R&D stock does not Granger cause MFP was rejected at the 10% level while the null hypothesis that MFP does not Granger cause the R&D stock could not be rejected.

On the other hand, foreign R&D can be expected to be exogenous. As New Zealand is taken to be a small open economy, it takes the foreign stock of knowledge as given. Conditions in New Zealand are assumed not to materially alter the world stock of knowledge

5.2.2  Using a Koyck transformation#

The specification of the lag structure in equation (13) requires the assumption that the depreciation rate is known. As Griliches (1979) notes: “The only thing one might be willing to say is that one would expect…social rates of depreciation to be lower than the private ones”. To overcome the need to specify an assumed rate of depreciation, we also run our model using the Koyck transformation. This transformation allows the estimation of the decay parameter directly from the regression and also overcomes the spurious regression problem by including the lagged dependent variable as an explanatory variable. The lag structure using this transformation is:

(15)    Kt = RDt + λRDt-1 + λ2RDt-2 + ...

And the estimating equation becomes:




The contemporaneous contribution to MFP given by domestic R&D is β4, whereas the contribution from all past and current domestic R&D is given by[24] :




and a similar construction applies in the case of foreign R&D under the assumption that the decay parameter is the same as for domestic R&D (i.e. λ).[25]

5.2.3  An Almon Polynomial Lag Structure#

Both of the above specifications for the lag structure (PIM and the Koyck transformation) assume that the effect of an R&D investment in year t declines at a constant rate as the lag length increases. Griliches (1998) concludes that the usual declining balance or geometric depreciation does not fit very well the likely gestation, blossoming, and eventual obsolescence of knowledge.

Griliches (1979) was the first to argue that the lagged effects of R&D on output could reasonably be expected to follow a bell-shaped distribution. The Almon polynomial lag structure allows us to capture this in empirical estimation. The specification of the lag structure becomes (with constrained endpoints)[26]:




This results in a second-order polynomial distribution of the contributions of R&D to MFP, which we used for both domestic and foreign R&D expenditures. We tested whether the series exhibited a cointegrating relationship by testing the residuals of each model specification for stationarity, and found evidence of cointegration.

In order to adequately capture what are inevitably lengthy lags in the generation and diffusion of knowledge, a lengthy time series is needed. This project uses annual data from 1926-27 to 2000-01. The definitions and sources of the data are set out in Appendix 2.

Yee et al (2002) argue that, unlike research, agricultural extension input can be expected to have an almost immediate impact on agricultural productivity. Therefore we include the current number of extension workers in our model specification.


  • [20]20 years was chosen to compute g following Caselli (2003).
  • [21]Johnson (2000) investigated the effect on estimated rates of return to the R&D stock when the depreciation rate was varied, and found that the rate of return was remarkably constant across different depreciation rates.
  • [22]We explored the effect of other lower rates, but the signs and significance of the coefficients on R&D were less satisfactory. Results using alternative depreciation rates are presented in Appendix 3.
  • [23]For the starting value of the foreign “stock of knowledge” we have simply used the number of patents granted in 1926/27 instead of using equation (11).
  • [24]This is because


    since the expression on the right side is an infinite geometric series whose sum is 1/(1-λ) provided 0
  • [25]We checked the coefficient restrictions on the lags of the weather, extension and human capital variables using the Wald test.
  • [26]See Appendix 2 for more details.

6  Results#

In this section we present the results of estimating the relationship between R&D and productivity for the agricultural sector. We take each of the three formulations in turn. In addition we present the results of using a simplified model following Scobie and Eveleens (1987).

6.1  Using stocks of knowledge#

The results from running the Philips-Loretan model using R&D stocks generated by the PIM are summarised in Table 5.[27] We ran a number of variants of the basic model including and excluding human capital, and with and without the dummy variable to represent structural shifts. In no case was the variable representing human capital significant. In both cases where the structural shifter for post 1984 was included the coefficient was highly significant. When human capital is removed from the model, the coefficient on the domestic R&D stock becomes significant at the 1% level.

The facts that 1) both human capital and domestic R&D are insignificant (or barely so) when both are included in the regression; and 2) each becomes individually significant when the other is omitted, point to the presence of multicollinearity. In fact, the simple bivariate correlation between these two variables is 0.99. Further evidence that multicollinearity is a problem is given by running the same regression in different (arbitrary) time periods. If two explanatory variables are correlated, a different sample will likely produce opposite results. We ran the regression with both variables included (and the dummy excluded) for the period 1927 to 1964 and the same regression from 1964 to 2001, and found that, while the coefficient on human capital was positive in both samples (although insignificant in the earlier period and significant in the latter period), the coefficient on the domestic R&D stock went from being negative and significant in the first period to being positive and significant in the period 1964-2001.[28] Such correlations mean that the corresponding regression coefficients cannot be interpreted because it is impossible to fix or control one variable while changing the other in the presence of this high correlation.

One solution to the problem is to remove those variables which are highly correlated with others (in this case we removed the human capital index) and therefore redundant. However, the drawback of this approach is that no information is obtained on the deleted variable while the importance of those in the equation may be overstated. Hence the significant coefficient on the domestic R&D stock in models 3 and 4 may be picking up some of the contribution of the omitted variable for human capital as well as the R&D effect itself.

If we ignore this and conclude that the elasticity of MFP with respect to domestic R&D is 0.148 (model 3 which is the preferred specification), then this implies a rate of return of 16.7% to the domestic R&D stock (in the long-run), assuming an R&D intensity (defined as the R&D stock divided by GDP) equal to the average over our sample period.[29] This return is lower than that estimated when we include human capital in the equation (model 1), indicating that the estimated coefficient on domestic R&D in Model 3 (our preferred specification) is not picking up the effect of human capital (the omitted variable) as well as the effect of domestic R&D.

The coefficient on cumulated patents (our proxy for the foreign stock of knowledge) is highly significant and positive in all four models. This indicates that foreign spill-ins to the agricultural sector are an important source of new knowledge and they are associated with the productivity performance of this sector. The estimated elasticity of MFP with respect to the foreign spill-in stock ranges from 0.25 to 0.35. That is, for a 10% increase in the number of patents granted in the US, MFP in the agricultural sector of New Zealand would increase from between 2.5% to 3.5%.

The coefficients on both weather and extension variables are never significant; except for extension in Model 4. In the case of extension this result is somewhat surprising, as with more extension workers we would expect new knowledge to be disseminated to users faster and therefore for more extension workers to have a positive impact on MFP.

Table 5: Estimates of the model using R&D stocks
Independent variables: Model 1 Model 2 Model 3 Model 4
Weather -0.129 0.136 -0.102 -0.118
Extension -0.190 -0.352 -0.156 -0.466***
Domestic knowledge stock 0.232* -0.097 0.148*** 0.260***
Foreign knowledge stock 0.309** 0.334*** 0.352*** 0.248**
Human capital -0.102 0.148    
Dummy84 0.270***   0.243***  
Adjusted r2 0.930 0.932 0.934 0.931

Note: The asterisks indicate the degree of significance of the estimated coefficient; *** = 1%; ** = 5%; * = 10% and an absence of asterisk indicates the coefficient was only significant at more than 10%.


  • [27]The Lead and lag order of the independent variables is 2.
  • [28]The coefficient on the foreign stock of knowledge also exhibited this trait (negative and significant in one period and positive and significant in the other).  The bivariate correlation between human capital and cumulated patents is 0.95, while the correlation between the domestic R&D stock and cumulated patents is 0.96. Thus there are several variables adding to the multicollinearity problem.
  • [29]See equation (5) as to how we calculate our rates of return using our estimated elasticities.

6.2  Estimates based on the Koyck transformation#

The insignificance of the weather variable in both the PIM and Koyck models could be due to the fact that weather only has a short-run impact on productivity in the agricultural sector, whereas we are estimating long-run relationships. Another possibility for the insignificant results is the use of MFP as the dependent variable – if weather has an equal effect on both outputs and inputs, this effect will be netted out when MFP is used.

Table 6 summarises the results from running the regression model using a Koyck transformation. Again we have run the model including and excluding the human capital and the dummy variable for structural change. As with the PIM models above, the dummy variable is always significant, suggesting that there could be a structural break in the data following the reforms. Again, the coefficient on the domestic R&D variable becomes significant when we exclude the human capital index from the regression.[30] The coefficient on the human capital index is never significant. The foreign spill-in variable is again significant for all six models, with an elasticity ranging from 0.10 to 0.14.

We also ran the Koyck transformation specification using education enrolment numbers instead of our human capital index (which is itself constructed from education enrolment numbers). This way we could also have all current and past enrolment levels included in a similar way to the research variables, if we assume that the decay parameter is the same.

We found that by including human capital in this alternative way, domestic R&D remains significant, although the contemporaneous effect of education on MFP is not significant. This is to be expected since the variable is enrolment numbers so will affect MFP with a lag. Thus it is more informative to look at the sum of the current and past enrolment rates by using equation (14), just as it is more informative to look at this sum for the domestic and foreign research variables.

Looking at these long-run estimates, we can see that foreign research is always significantly different from zero, while domestic research is significant in all but one of the models (it is not significant when human capital is included, but is significant when the dummy is added to the equation, even when human capital is still included). That is, once all of the past effects of research on productivity are taken into account, there is a significantly positive association with productivity. However, education is not significant even when we take into account the past effects on MFP. The elasticity of MFP with respect to domestic R&D, once all lags are accounted for, ranges from 0 to 0.21. The long-run elasticity with respect to foreign research ranges from 0.23 to 0.39. The corresponding implied rate of return to domestic R&D lies in the range 0 to 25%, once all of the effects of the R&D expenditure on subsequent output are taken into account.[31] Note that these Koyck models imply a depreciation rate of between 32% and 44%. Once again the weather variable is never significant and extension is always negative, and significant in 2 of the 6 specifications.

The insignificance of the weather variable in both the PIM and Koyck models could be due to the fact that weather only has a short-run impact on productivity in the agricultural sector, whereas we are estimating long-run relationships. Another possibility for the insignificant results is the use of MFP as the dependent variable – if weather has an equal effect on both outputs and inputs, this effect will be netted out when MFP is used.

Table 6: Results from the estimations based on the Koyck Transformation
Independent variables: Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Lagged productivity 0.677*** 0.681*** 0.565*** 0.586*** 0.667*** 0.565***
Weather 0.017 0.017 0.017 0.018 0.017 0.019
Extension -0.150 -0.220*** -0.128 -0.096 -0.220*** -0.094
Domestic R&D: one period effect 0.030 0.065** 0.090** 0.057** 0.057** 0.047*
Domestic R&D: total  effect a 0.093 0.204*** 0.207** 0.138*** 0.171*** 0.108**
Foreign R&D: one period effect 0.126** 0.092*** 0.098** 0.124*** 0.100*** 0.135***
Foreign R&D: total effect a 0.390*** 0.288*** 0.225*** 0.300*** 0.300*** 0.310***
Human capital 0.092   -0.069      
Dummy84     0.112** 0.088**   0.091**
Education:one period effect         0.015 0.019
Education: total effect a         0.045 0.044
Adjusted R2 0.946 0.946 0.950 0.950 0.946 0.950
Wald (chi-squared) test of Coefficient Restrictions (null hypothesis: restrictions are true)b 1.39 2.25 3.48 0.30 1.94 0.13

Note: The coefficients for domestic R&D are computed using equation (15) and its counterpart for the foreign R&D.

Note: The asterisks indicate the degree of significance of the estimated coefficient; *** = 1%; ** = 5%; * = 10% and an absence of asterisk indicates the coefficient was only significant at more than 10%.

a: Significance levels for these long-run coefficients have been calculated using the delta method.

b: This tests whether the coefficient restrictions on the lagged variables in equation (16) (e.g. the coefficient on the lagged weather variable is equal to the coefficient on the weather variable multiplied by the coefficient on the lagged MFP variable) are true. The Wald statistic measures how close the unrestricted estimates come to satisfying the restrictions under the null hypothesis.

The coefficient on the extension variable is consistently negative. Based on concerns that there may be a serious discontinuity in the data (see Figure 2(b)) we re-estimated model 1 using data for a reduced sample period (1926-27 to 1983-84) which eliminated the period of the apparent break in the data series. However the results were similar to those found with the full sample period.

To some extent, the dummy variable could also be picking up this drop in extension numbers after 1984, as well as the drop in enrolment numbers which occurred around this time (as well as the effect of the reforms on agricultural productivity). In short, these changes were in themselves reflections of the many structural reforms that were taking place in the New Zealand economy, and it is not possible to isolate their separate effects within our models.

Figure 4 plots the dependent variable (the log of MFP) against its predicted values using Model 2 in Table 6. The model was run up to 1990 and then out of sample forecasts were computed. The model is found to perform well in this out of sample forecasting, predicting the variable nature of MFP after 1990, recognising that the model contains the lagged value of productivity as an explanatory variable.

Figure 4: Agricultural Productivity: Actual Versus Values based on estimation up to 1990 with projected values beyond 1990



  • [30]Note that the foreign patents variable is no longer as highly correlated with domestic R&D and human capital (0.688 and 0.689 respectively), indicating that the problem of collinearity only remains between the human capital and domestic R&D variables and thus only to the coefficient estimates of these two variables.
  • [31]This rate of return was calculated by constructing the implied R&D stock using a depreciation rate of 1-λ, and a starting value calculated using the Perpetual Inventory approach (i.e. using equation 12, where δ = 1-λ).  The elasticity was then multiplied by the average GDP to R&D stock over our sample period to get the rate of return.

6.3  Estimates using an Almon lag structure#

Table 7 summarises the results from running equation 10 using second order polynomials for both domestic and foreign research. The lag lengths were chosen by first searching over all lags from 1 to 60 years (except when the dummy was included which meant it was only possible to search up to 55 lags). This involved running up to 3,600 regressions for each model to allow for every possible combination of domestic and foreign lag lengths. The search over lag lengths was conducted without fixing the sample period. The effects of fixing the sample period compared to allowing the sample period to vary according to the lag length is discussed below. The combination of lag lengths which gave the minimum value of the Akaike Information Criterion (AIC) was chosen as the preferred model.

When human capital is excluded, the sum of domestic R&D lags is negative and not significant, but becomes significant when the dummy is included. The sum of the lags of US patent numbers is always positive and significant, affecting New Zealand agricultural productivity even after 59 lags (when the dummy is not included). However, when human capital is included, the number of lags on this foreign research variable which effect MFP shortens to 13, while domestic R&D still affects MFP after 59 lags, compared with only 17 lags when human capital is not included. This indicates that the results are subject to considerable variation depending on the particular specification of the model.

The results are also sensitive to the choice of lag length. For example, if we instead of the AIC we were to chose the optimal lag lengths using the adjusted R-squared of each model, for Model 2 (i.e. excluding human capital and the dummy variable) we obtain a positive and significant number for the lagged contributions of domestic R&D (0.25), with a lag length of 24, as well as a positive and significant number for the sum of the lagged contributions for foreign patent numbers (0.21), although only with a lag length of 1. For model 1 (when we include human capital), human capital is negative and significant (with a coefficient equal to -0.55), and domestic R&D is positive and significant, with contributions over a period of 37 years (and the sum of the lagged contributions equal to 0.97). The sum of the contributions from our foreign spill-in variable becomes negative and significant (-0.83), with a lag length of 15.

We also ran this model by using a first order polynomial for the lags of the education variable (see models 5 and 6 in Table 7).[32] The sum of the contributions from both domestic and foreign research become insignificant when we include human capital in this way, while the sum of the lagged contributions from education is significant in both models.

Table 7: Results from the Regressions using Almon second order distributed lags
  Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Weather 0.279*** 0.269*** 0.156** 0.170*** 0.014 0.011
Extension -0.103 0.003 0.084 0.054 0.0.008 0.024
Domestic R&D -1.942** -1.578 -0.879* -0.913** -2.320 -2.266
No. of lags : domestic 59 17 12 11 46 46
Foreign R&D 4.317** 2.177*** 1.727*** 1.723*** 4.371 4.034
No. of lags: foreign 13 59 54 54 32 32
Human capital 4.010**   0.235      
Education         1.882** 2.017**
No. of lags: education         31 31
Dummy84     0.141 0.170***   -0.040
Adjusted r2 0.857 0.806 0.893 0.897 0.948 0.965

Note: The coefficients for domestic R&D, foreign R&D, and education are computed as the sum of the coefficients on the individual lags.

Note: The asterisks indicate the degree of significance of the estimated coefficient; *** = 1%; ** = 5%; * = 10% and an absence of asterisk indicates the coefficient was only significant at more than 10%.

When estimating models with different lag lengths the sample period varies according to the length of the lag as observations are lost from the start of the series to accommodate the lagged effect. It is therefore possible that differences which might appear to arise from different lag lengths in fact arise from different sample periods.

Table 8 compares the results of regressions using the Almon second order distributed lags when we fix the sample period and when we allow the sample period to vary. We have minimised the search over different lag lengths by restricting both the domestic and foreign research variables to have the same lag length. Again, the number of lag lengths which gave the minimum value of the Akaike Information Criterion (AIC) was chosen as the preferred model.

Table 8 shows that fixing the sample period can have a large effect on the number of lags chosen as the preferred model. In turn, the lag length appears to change the results significantly. For example, in Model 1, when we use a fixed sample period for the regression, a lag length of 18 years is chosen as that which minimises the AIC, resulting in a significantly positive coefficient on foreign R&D and human capital. Alternatively, when we allow the sample period to vary with the lag length, the AIC suggests a lag length of 59 years, with a negative and not significant coefficient on both foreign R&D and human capital. This highlights the sensitivity of results to the lag specification.

Table 8: Comparing the Almon Distributed Lag Models with Fixed and Unconstrained Sample periods.
  Model 1 Model 4 Model 5
  Fixed Sample Unconstrained Sample Fixed Sample Unconstrained Sample Fixed Sample Unconstrained Sample
Weather 0.261*** 0.209** 0.024 0.019 0.294*** 0.294**
Extension -0.067 0.115 0.103 0.009 -0.012 0.045
Domestic R&D -3.071 0.539 1.149* 0.154 5.655 1.785*
No. of lags : domestic 18 59 34 45 24 59
Foreign R&D 3.060** -1.003 -1.651 0.618 -1.610 -0.195
No. of lags: foreign 18 59 34 45 24 59
Human capital 2.712** -0.100        
Education         -4.048* -3.100
No. of lags: education         24 59
Dummy84     -0.008 0.071    
Adjusted r2 0.794 0.762 0.918 0.932 0.800 0.788


  • [32]Only searching over 46 lags due to memory constraints in eviews.

6.4  The separate effects of public and private R&D funding#

In this section we report the results of an attempt to isolate the separate contributions of public and private domestic research using both the PIM and Koyck models. The data for this are set out in Appendix 2.

An OECD report (OECD 2005) found that domestic private R&D and foreign R&D stocks impacted positively on productivity in all of the 16 OECD countries used in their panel estimation. However, domestic public R&D had a positive impact on productivity in only 12 of the 16 OECD countries. Johnson (2000b) looked at the contribution from private and public R&D in 9 industries in New Zealand. He found that private R&D was positively related to changes in TFP in 7 out of the 9 cases, while public R&D was positively related to changes in TFP in 4 out of the 9 cases. In the agricultural sector he found that public R&D was negatively related to changes in TFP. However, in another study by Johnson (2000a), he finds that the return to public R&D in the agricultural sector is positive depending on how the lags on R&D expenditure are dealt with in the estimation. The positive relationship was found when he used Almon distributed lags, while the negative relationship was estimated using the perpetual inventory method to construct a public R&D stock variable.

Tables 9 and 10 summarise our results when we include domestic R&D separately as private and public spending. Once again the dummy variable is significant in both the Koyck and PIM models. The weather variable is again not significant in any of the models and the extension variable continues to be mostly negative and sometimes significant.

In all of the models tested under both approaches, the coefficient for domestic public research is only significant in two specifications (model 5 under the PIM approach and model 7 under the Koyck Transformation are discussed below). The coefficient on domestic private R&D is significant in all 4 specifications of the perpetual inventory stock models, but is never significant in the Koyck models (except for model 8, discussed below). The elasticities with respect to the stock of private domestic R&D (see Table 8) therefore ranges from 0.14 to 0.63, with the implied rate of return ranging from 176% to 771% (assuming a Private R&D to GDP ratio equal to the average over our sample period).

The multicollinearity problem also arises between the public and private R&D expenditure variables, with a correlation coefficient of 0.96.[33] Therefore we may not be picking up the significance of domestic private and public R&D spending due to their high correlation with each other and with other variables in the model (both private and public R&D spending are also highly correlated with human capital). When we remove both human capital and private R&D expenditure from the regression models, domestic public R&D becomes significant in both the Koyck model and the PIM model (see model 5 in Table 9 and model 7 in Table 10). When we remove both human capital and public R&D expenditure from the Koyck regression model, we see a significant coefficient on the private R&D expenditure (see model 8 in Table 10). The corresponding rate of return to domestic public R&D in the Koyck model is 26%, and to domestic private R&D the corresponding rate of return is 32%.

Table 9: Estimating the separate effects of public and private domestic R&D: based on the perpetual inventory stock models
Independent variables: Model 1 Model 2 Model 3 Model 4 Model 5
Weather 0.093 -0.107 0.081 -0.070 -0.120
Extension -0.241** -0.404*** 0.058 0.053 -0.473***
Public Stock of Knowledge 0.062 0.125* -0.010 -0.081 0.257***
Private Stock of Knowledge 0.576*** 0.144* 0.631*** 0.207***  
Foreign Stock of Knowledge -0.382* 0.098 -0.433* 0.089 0.273***
Human Capital -0.487***   -0.577***    
Dummy84     0.304*** 0.343***  
Adjusted R2 0.943 0.926 0.940 0.930 0.930

Note: The asterisks indicate the degree of significance of the estimated coefficient; *** = 1%; ** = 5%; * = 10% and an absence of asterisks indicates the coefficient was only significant at more than 10%.

Table 10: Estimating the separate effects of public and private R&D based on the Koyck transformation
Independent variables: Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8
Lagged productivity 0.677*** 0.679*** 0.549*** 0.588*** 0.676*** 0.566*** 0.695*** 0.715***
Weather 0.017 0.017 0.017 0.019 0.017 0.018 0.017 0.015
Extension -0.134 -0.146 -0.112 -0.083 -0.150 -0.093 -0.221*** -0.084
Domestic public R&D: one period effect 0.020 0.026 0.080* 0.044 0.026 0.044 0.061**  
Domestic public R&D: total effect 0.062 0.081 0.177** 0.107 0.080 0.101 0.200***  
Domestic private R&D: one period effects 0.026 0.033 0.038 0.011 0.031 0.002   0.046***
Domestic private R&D: total effect 0.080 0.103 0.084 0.027 0.096 0.005   0.161***
Foreign R&D: one period effect 0.109** 0.096*** 0.077 0.125*** 0.098*** 0.136*** 0.090*** 0.088***
Foreign R&D: total effect 0.337** 0.299*** 0.171 0.303*** 0.302*** 0.313*** 0.295*** 0.309***
Human capital 0.037   -0.127          
Dummy84     0.120** 0.084**   0.091**    
Education: one period effect         0.004 0.019    
Education: total effect         0.012 0.044    
Adjusted R2 0.946 0.947 0.950 0.950 0.946 0.949 0.946 0.947
Wald (chi-squared) test of Coefficient Restrictions (null hypothesis: restrictions are true) 1.06 0.99 3.52 0.20 0.97 0.14 2.47 0.25

Note: The asterisks indicate the degree of significance of the estimated coefficient; *** = 1%; ** = 5%; * = 10% and an absence of asterisks indicates the coefficient was only significant at more than 10%.


  • [33]An OECD report (2005) has also found that non-business R&D and business sector R&D are related: an increase of 1 standard deviation in the share of non-business R&D in GDP was found to raise business sector R&D by over 7%. Thus they concluded that private R&D will already embody many of the effects that come from public sector R&D.

6.5  A simplified Almon estimation#

In this section we present results based on an updated version of the model estimated in Scobie and Eveleens (1987). This model is a simplified version of our Almon models presented above, in that the Almon distributed lag variable is a combination of human capital, extension and domestic R&D, and hence these variables are not entered into the regression equation separately. Foreign R&D is also not included in the model. The variable “Deviations from trend net farm income” is included as an explanatory variable, the argument being that in years of high income, farmers may be expected to increase their purchases of inputs.[34] We have not included this variable in our main specification due to concerns about endogeneity. The model is set out in equation 19 below:




where REH is the variable combining research and extension defined as log[Rt+(Et*HKt)], and transformed by a second degree Almon polynomial lag structure with constrained endpoints, with a total lag length of 22 years, and yd is deviations of net farm income from a fitted trend line. The equation was estimated using the Cochrane-Orcutt correction for autocorrelation, and the results are presented in Table 11 below.

Using an internal rate of return calculation such as that used in Scobie and Eveleens (1987), the fitted second order polynomial implies a rate of return to domestic R&D of 70%.[35] The weather variable is again not significant, while the deviations from trend net farm income appear to have a negative effect on productivity, although the effect is very small. That is, in years of high income, productivity is depressed due to increases in farm spending on inputs.

Table 11: Results from the simplified Almon estimation
Independent variables: Model 1
REH 0.338***
weather 0.025
Deviations from trend net farm income (yd) -8.71e-07**
Adjusted R2 0.76

Note: The coefficient for REH is computed as the sum of the coefficients on the individual lags.

6.6  Testing the absorptive capacity hypothesis#

We tested the absorptive capacity argument by interacting the foreign patents variable with both domestic R&D and human capital. A significantly positive coefficient on either of these interactions would indicate that, for a given amount of foreign R&D, increasing the amount of domestic R&D or human capital enables more effective absorption of this foreign research. Thus domestic R&D or human capital respectively would have both a direct and an indirect effect on MFP. We found neither interaction to be significant in the Koyck models and both interactions to be significantly negative in the Phillips-Loretan models. We do not believe that this constitutes definitive evidence that absorptive capacity is not important. One only has to ask how much foreign knowledge a country could absorb were it to have no domestic scientific capacity, to underscore that absorptive capacity is critical in a small open economy such as New Zealand. Rather it reflects the difficulty of defining suitable proxies and then isolating the effects econometrically from aggregate time series data.

The second interaction that we tested was between human capital and domestic R&D, the argument being that research will be more easily adopted and utilised if the sector has a larger stock of human capital, and thus research will have a larger impact on productivity. This interaction was not significant in the Koyck models and was negative and significant in the Phillips-Loretan models. We also tested the interaction between extension and domestic R&D, as more extension workers arguably allow more effective and quicker dissemination of research to those who will use it; this interaction was found to be significant in the Koyck model when the dummy variable was included in the regression equation, but insignificant when it was not included. In the Phillips-Loretan model this interaction was never significant. These results may be an indication that extension staff facilitate the faster absorption of R&D and thus indirectly have a positive effect on MFP, whereas human capital does not appear to have a role in this absorption process.

We also tested whether the elasticity of domestic R&D has changed over time by including an interaction between the dummy variable and domestic R&D. We found this interaction to be insignificant in both the Koyck and PIM models, perhaps indicating that the effect of domestic R&D on agricultural productivity has not changed over time.


  • [34]The trend line has been calculated using a Hodrick-Prescott filter.
  • [35]In order to calculate an internal rate of return, two different research strategies were used: one holding research expenditure constant at the 2001 level, and the other following the same pattern with the exception that in the first year (2001) research expenditure was assumed to increase by 1%. Using the equation, MFP was then calculated under both strategies, and then GDP was calculated holding inputs constant at their 2001 level, the difference between the GDP levels under the two strategies being the benefit from the increased R&D.

7  Summary and Conclusions#

Productivity growth is important as a long run source of real income growth and higher living standards, as well as contributing to enhancing the competitiveness of New Zealand in world markets. This paper has analysed the long term growth of agricultural productivity in New Zealand. The central question addressed in the paper is the contribution of investment in R&D to that productivity growth.

The primary sector (made up of Agriculture, Forestry, Fishing and Hunting) has been an important contributor to the overall improved productivity growth in the New Zealand economy over the last decade. Furthermore, over the last 80 years the rate of growth of productivity in agriculture has continued to increase.

Investment in R&D is a potentially important factor in expanding the stock of knowledge. This stock of knowledge can be viewed as a capital input into agricultural production, and like any other capital input provides a flow of services to the production processes.

Domestic expenditure in both the public and private sector on agricultural research, adds to what we call a domestic stock of knowledge. However in a small open economy the stock of foreign knowledge that “spills in” also adds to the total stock of knowledge that is available to the sector. Given that New Zealand is a very small player and accounts for but a tiny fraction of global R&D efforts, it is to be expected that access to this foreign stock of knowledge would play an important role. Particular attention was given to this aspect in this study.

It is evident that all the benefits from research done today are not captured and reflected in higher productivity immediately. The outputs of the research investment add to the stock of knowledge and it is that stock which potentially contributes to improving productivity. In other words, research done 10, 20 or even 30 years that added to the stock of knowledge could still be relevant and contributing to today’s output. This raises major challenges in modelling the impact of R&D as we need to allow for long lags. Partly for this reason, this study has been based on annual data from 1926-27 to 2000-01. This provides, at least in theory, the opportunity to allow for extended lagged effects.

At the same time the use of stocks of knowledge raises the question of depreciation. Continuing the analogy with other forms of capital, some knowledge can be expected to “depreciate” – ie lose its ability to contribute to high productivity. We have analysed a range of depreciation rates, settling on 30% based on the performance of the models.

As there is no one accepted method of modelling the lagged effects of R&D this study presents the findings of three different approaches. The first estimates stocks of knowledge (both domestic and foreign) based on the perpetual inventory method which involves assuming a rate of depreciation of knowledge. The second allows for a decay parameter to be estimated rather than imposed, and provides an estimate of the long run effect of R&D (the Koyck transformation). The third approach is based on the argument that initially the contribution of research would be small, but as the knowledge generated diffuses and is incorporated in the production process the impact would grow. However in the long run findings of research done many years ago suffer from obsolescence – they were relevant for the particular technological and economic circumstances of say the 1950s, but much less so in 2005 (the Almon lag).

Table 12 gives a summary of the findings for the rate of return to investment in domestic R&D under the various methods. For each method we tried a range of specifications. These are the basis for the range of estimated rates of return shown in the table.

Table 12: Summary of the annual average rates of return to Domestic R&D: Various methods
Method   Y/K Estimated Rate of Return (%pa)
Stocks of Knowledge   Average over entire sample period 0 to 29%
Average from 1950 to 2001 0 to 8.4%
2001 0 to 5.5%
Koyck Transformation   Average over entire sample period 0 to 25%
Average from 1950 to 2001 0 to 7%
2001 0 to 5%
Almon Lag     Negative
Simplified Almon Lag Internal Rate of Return   70%
Stocks of Knowledge Domestic Public Average over entire sample period 0 to 32%
Average from 1950 to 2001 0 to 9%
2001 0 to 6.3%
Domestic Private Average over entire sample period 176% to 771%
Average from 1950 to 2001 76% to 334%
2001 22% to 97%
Koyck Transformation Domestic Public Average over entire sample period 0 to 26%
Average from 1950 to 2001 0 to 7%
2001 0 to 5%
Domestic Private Average over entire sample period 0 to 354%
Average from 1950 to 2001 0 to 153%
2001 0 to 45%

It will be immediately apparent that there is little or no indication of convergence across the methods. In both the Koyck and PIM models, we were able to find a significant effect from domestic R&D in most specifications. Our “preferred” model based on significant contributions to productivity of both foreign and domestic stocks of knowledge yielded a rate of return of 17% p.a. to investment in domestic R&D. However, when we used Almon distributed lags we found a negative and significant coefficient on domestic R&D. When we attempted to estimate the separate effects of private and public R&D we found that in almost all cases there was no identifiable contribution from the public investment, while the private R&D lead to a wide range of possible rates of return. The key message that can be drawn from these results is that the estimates of the contribution of domestic R&D are very sensitive to the method and specification adopted, and that even with lengthy time series data it is not easy to isolate the effect.

In a variant of the Almon lag approach which essentially mirrors that used by Scobie and Eveleens (1987), we derive a return of 70% to total domestic R&D. This compares with a value of 30% from the earlier study. There has been a marked slowdown in the growth of R&D investment and at the same time the rate of growth in productivity has increased. It is possible this higher estimate reflects the lagged contribution of past investments. However, given the wide variations in our estimates and the fact that many cases showed no significant contribution of domestic R&D, we would caution against selecting any one figure as a reliable estimate of the return to domestic R&D.

In contrast we found that, virtually regardless of the method or specification of the model, the spill-in effect from foreign knowledge was an important factor explaining the growth of agricultural productivity (see Table 13).

Table 13: Summary of the response of agricultural productivity to foreign knowledge: various methods
Method Percentage change in productivity following a 10% rise in foreign knowledge
Stocks of Knowledge 2.5 to 3.5
Koyck Transformation 2.3 to 3.9
Almon Lag 0 to 43.0
Stocks of Knowledge (when separate private and public domestic variables included) -4.3 to 2.7
Koyck Transformation (when separate private and public domestic variables included) 0 to 3.4

It should be noted that we are not able to distinguish between the different types of research included in the agricultural R&D expenditure data. For example, recently there has been some increased emphasis in public spending towards research projects whose objectives include ameliorating the environmental consequences of agriculture. As measured productivity does not directly reflect the investment in R&D related to environmental enhancement, this implies that our results might understate the true contribution of R&D to productivity growth.

It should also be stressed that because of the need to have a lengthy series of data we were limited in the variables we could use as a proxy for the foreign stock of knowledge and have relied on US patent data.

The results underscore the importance of foreign knowledge in a small open economy. In formulating policies for fostering innovation, these findings suggest that particular attention be paid to enhancing linkages with the international scientific community. This could take many forms including scholarships for training and research overseas by New Zealand researchers, involvement of New Zealand in international scientific networks, sponsorship of international symposia in New Zealand, etc.

While not as consistently robust, our findings typically support the argument that the stocks of domestic knowledge are positively associated with productivity growth. The very existence of foreign knowledge may be a necessary condition for achieving productivity growth in a small open economy. However in no way could it be argued that it is sufficient. Having a domestic capability that can receive and process the spill-ins from foreign knowledge is vital to capturing the benefits. The challenge is to be able to isolate those effects from aggregate data for the agricultural sector. In that particular aspect we claim only modest success.

Appendix One: Unit root tests#

The unit root tests used in this study are the Augmented Dickey-Fuller and Phillips-Perron tests. The optimal lag length has been chosen using Schwarz criterion.

All variables were tested first to ascertain whether a trend should be included in the unit root test. If we did not reject the unit root null hypothesis, we took the first difference of the series and reran the test excluding a time trend.

All variables were found to be I(1), except for the human capital index, the soil moisture deficit variable, and the MFP index which were all found to be stationary with drift and trend.

Appendix Table 1: Unit Root tests - levels
Variable: Lag Order t-statistic
MFP Index 0 -3.32*
Total R&D expenditures 0 -2.45
Public R&D expenditures 0 -2.52
Private R&D expenditures 0 -0.80
Wet 4 -3.57**
US Patents 0 1.25
Cumulated US Patents 1 1.42
Human Capital Index 1 -3.03**
Total R&D Stock (using 30% depreciation) 4 -1.13
Public R&D Stock (using 30% depreciation) 4 -3.60**
Private R&D Stock (using 30% depreciation) 1 -0.94
Extension (number of workers) 1 0.80

*= sig. at 10% level, **=sig. at 5% level, ***=sig. at 1% level

Appendix Table 2: Unit Root tests – first differences
Variable: Lag Order t-statistic
Total R&D expenditures 0 -7.82***
Public R&D expenditures 0 -7.96***
Private R&D expenditures 0 -8.63***
US Patents 0 -8.37***
Cumulated US Patents 0 -3.94***
Total R&D Stock (using 30% depreciation) 0 -3.73**
Private R&D Stock (using 30% depreciation) 0 -4.48***
Extension (number of workers) 0 -6.49***

*= sig. at 10% level, **=sig. at 5% level, ***=sig. at 1% level

Appendix Two: Almon Distributed Lag#

This appendix sets out the algebra behind the Almon distributed lag polynomials, both using a first order polynomial (which we use for education lags) and using a second order polynomial (which we use for both domestic and foreign R&D lags).

If we start with equation (9) such that




Then if we assume a second order polynomial, we can replace wi with




Or if we assume a first order polynomial, then




So we now have








respectively. That is, we have reduced the number of parameters to be estimated down to 3, in the case of the second order polynomial, or 2 parameters in the case of the first order polynomial.

While we did not constrain the endpoints for the first order polynomial (the lags of the education variable), we did constrain both endpoints of the second order polynomials (domestic and foreign research) such that




So we now have



which further reduced the number of parameters to be estimated to 1 (for each variable).

Appendix Three: Results using Different Depreciation Rates#

This appendix discusses the results of the PIM model when we use different depreciation rates. Appendix Table 14 sets out the results using a 5% depreciation rate, while Appendix Table 15 shows the results from using 15% depreciation.

Using a depreciation rate of 5% for both domestic and foreign R&D, the domestic knowledge stock is significant in all 4 specifications, with a rate of return ranging from 9.5% to 15.3%. The foreign stock, however, is significant in only 2 of the 4 specifications. The dummy variable is never significant, nor is the human capital index.

When we instead use a depreciation rate of 15%, both the domestic and foreign stock of knowledge are significant in all 4 specifications. The rate of return to domestic R&D ranges from 14.3% to 24.1%. The human capital index and dummy variables are again not significant.

Table 14: Using 5% depreciation rate.
Independent variables: Model 1 Model 2 Model 3 Model 4
Weather -0.050 -0.076 -0.064 -0.058
Extension -0.429*** -0.387*** -0.407*** -0.358***
Domestic knowledge stock 0.341*** 0.234** 0.231*** 0.212***
Foreign knowledge stock 0.228 0.318* 0.234 0.342*
Human capital -0.142 -0.021    
Dummy84 0.028   0.002  
Adjusted r2 0.928 0.936 0.932 0.938

Table 15: Using 15% depreciation rate.
Independent variables: Model 1 Model 2 Model 3 Model 4
Weather -0.089 -0.099 -0.098 -0.084
Extension -0.295* -0.378*** -0.236 -0.413***
Domestic knowledge stock 0.336*** 0.199* 0.172*** 0.235***
Foreign knowledge stock 0.309*** 0.334*** 0.349*** 0.283***
Human capital 0.198 0.019    
Dummy84 0.177   0.146  
Adjusted r2 0.929 0.934 0.932 0.936

Appendix Four: Description of the Data#

This appendix describes the dataset we have constructed and lists the sources.

Gross Output (1949/50$)#

Gross Farming Income divided by the Farm Output Price Index.

Gross Farming Income

1926/27 to 1966/67: Hussey and Philpott (1969). Table 1 Gross Income, Expenditure and Net Income “Gross Farm Income”.

1967/68 to 1970/71: Nickel and Gibson (1983).

1971/72 to 1976/77: INFOS series SNAA.SAA4Z (Gross Output – total) less INFOS series SNAA.S1J4Z (Gross Output – Other Horticultural Products), SNAA.S1K4Z (Gross Output – Agricultural Services), and SNAA.S1L4Z (Gross Output – Other Products N.E.C).

1977/78 to 1985/86: INFOS series SNBA.SKHAA4 (Gross Output - total) less INFOS series SNBA.SLJ4 (Gross Output – other horticultural products), SNBA.SLK4 (Gross Output – Agricultural Services), and SNBA.SLL4 (Gross Output – other products N.E.C).

1986/87 to 2000/01: INFOS series SNCA.S1NP10AAT4 (Gross Output – total) less INFOS series SNCA.S7NP10JT4 (Gross Output – other horticultural products), SNCA.S7NP10KT4 (Gross Output – agricultural services), and SNCA.S7NP10LT4 (Gross Output – other products N.E.C).

Farm Output Price Index

1926/27 to 1965/66: Hussey and Philpott (1969). Table 3 Prices Received and Prices Paid “Price index of farm outputs”.

1966/67 to 1977/78: Calculated from Ellison (1977) Table 1 Output per unit of Aggregate Input “Index of Gross Output (base 1949/50=100).

1978/79 to 1994/95: Calculated from INFOS series SNBA.SNZ (Volume of Production Index 1978=1000)

1995/96 to 2002/03: INFOS series PPIQ.SUX01 (Producer Price Index – Outputs)

Appendix Table 3: Output data.
Year Gross Farming Income (nominal, $m) Farm Output Price Index Gross Output (1949/50$m)
1926–27 105.2 51.8 203.0888
1927–28 120.8 53.7 224.9534
1928–29 137.2 58.8 233.3333
1929–30 122.2 49.9 244.8898
1930–31 87 35.1 247.8632
1931–32 75.8 30.6 247.7124
1932–33 76 26.8 283.5821
1933–34 99.2 33.9 292.6254
1934–35 93.2 32.9 283.2827
1935–36 118 39.5 298.7342
1936–37 149.2 48.6 306.9959
1937–38 142.2 46.3 307.1274
1938–39 140.2 47.5 295.1579
1939–40 150 48.8 307.377
1940–41 169.9 50 339.8
1941–42 167.6 51.1 327.9843
1942–43 169.6 53.7 315.8287
1943–44 173.4 55.3 313.5624
1944–45 205.2 60.4 339.7351
1945–46 192.2 60.8 316.1184
1946–47 222.6 67.9 327.8351
1947–48 271.4 80.6 336.7246
1948–49 293.4 84.2 348.4561
1949–50 366.2 100 366.2
1950–51 582.6 155.4 374.9035
1951–52 436.5 116.4 375
1952–53 522.2 133 392.6316
1953–54 544.6 138.7 392.646
1954–55 562.1 140.1 401.2134
1955–56 554.4 135.1 410.3627
1956–57 614 147.5 416.2712
1957–58 592.7 132.9 445.9744
1958–59 564.2 121.7 463.599
1959–60 623.5 132.8 469.503
1960–61 613.9 125.2 490.3355
1961–62 595 119.2 499.1611
1962–63 654 124.5 525.3012
1963–64 763.6 140.5 543.4875
1964–65 792.1 141.9 558.21
1965–66 850.5 144 590.625
1966–67 824.5 137.1398 601.2113
1967–68 817.9 129.2162 632.97
1968–69 885.6 135.2921 654.5836
1969–70 893.8 132.961 672.2274
1970–71 934.9 131.4013 711.4848
1971–72 1358 184.4642 736.1861
1972–73 1759 232.1194 757.7997
1973–74 1908 246.0528 775.4434
1974–75 1469 193.8507 757.7997
1975–76 1972 255.4687 771.9147
1976–77 2561 315.716 811.1721
1977–78 2516 323.3559 778.09
1978–79 2929 368.3313 795.208
1979–80 4055 470.3501 862.1237
1980–81 4175 478.6533 872.2389
1981–82 4563 517.5958 881.576
1982–83 4625 508.0378 910.3653
1983–84 5455 585.2051 932.1518
1984–85 6623 669.6986 988.9524
1985–86 6109 611.4702 999.0676
1986–87 6068 609.2644 995.9552
1987–88 6611 625.6588 1056.646
1988–89 7202 701.212 1027.079
1989–90 8078 783.5345 1030.969
1990–91 7408 695.4529 1065.205
1991–92 8043 747.4223 1076.098
1992–93 8618 806.1019 1069.096
1993–94 9304 785.643 1184.253
1994–95 8944 754.2529 1185.809
1995–96 8705 783.2005 1111.465
1996–97 9187 797.7744 1151.579
1997–98 9753 785.5962 1241.478
1998–99 9586 778.8083 1230.855
1999–00 10368 843.892 1228.593
2000–01 13246 1000.812 1323.526
2001–02 15416 1149 1342.217
2002–03   1006  
2003–04   965  

Intermediate Consumption (1949/50$)#

Intermediate Consumption (excluding Livestock Purchases and depreciation) deflated by the Farm Input Price Index.#

Nominal Intermediate Consumption

1926/27 to 1966/67: Hussey and Philpott (1969). Table 1 Gross Income, Expenditure and Net Income, “Total Non-Factor Expenses” less “Depreciation” (Buildings and Structures and Plant and Machinery).

1967/68 to 1970/71: Ellison (1977) Table A5 Real Working Expenses “Total Non-Factor Expenses” less depreciation (average percentage of total intermediate consumption from previous 4 years multiplied by Total Non-Factor Expenses from Ellison).

1971/72 to 1973/74: INFOS series SNAA.SAA4G less the average percentage of livestock purchases to total Intermediate Consumption from 1974/75 to 2000/01, multiplied by total Intermediate consumption in each year.

1974/75 to 1977/78: INFOS series SNAA.SAA4G less INFOS series SNAA.S14G.

1978/79 to 1985/86: INFOS series SNBA.SKGAA4 less INFOS series SNBA.SMA4.

1986/87 to 2000/01: INFOS series SNCA.S1NP20AAT4 less INFOS series SNCA.S7NP20AT4.

Farm Input Price Index

1926-1966/67: Hussey and Philpott (1969) Table 3 Prices Received and Prices Paid “Price Index of Farm Inputs”.

1967/68 to 1974/75: Hussey and Philpott price index updated using Ellison (1977) Table A5 Real Working Expenses “Price Index”.

1975/76 to 1981/82: Updated using INFOS series FPIA.S39 (Farm Costs price index).

1982/83 to 2003/04: Updated using INFOS series FPIQ.SI9Y (Farm Expenses, excluding livestock, price index).

Value Added (1949/50$)#

Calculated as Real Gross Output minus Real Intermediate Consumption.

Appendix Table 4: Intermediate Consumption and GDP data.
Year Nominal Intermediate Consumption ($m) Farm Input Price Index (1949/50=100) Real Intermediate Consumption (1949/50$m) Real GDP (1949/50$m)
1926–27 29 53 56 147
1927–28 30 54 56 169
1928–29 32 55 58 176
1929–30 33 55 59 185
1930–31 32 54 58 190
1931–32 29 50 57 190
1932–33 28 46 61 222
1933–34 28 45 63 230
1934–35 28 45 63 220
1935–36 29 46 64 235
1936–37 32 51 64 243
1937–38 37 57 65 242
1938–39 38 59 64 231
1939–40 44 60 73 234
1940–41 53 60 87 252
1941–42 55 64 87 241
1942–43 63 69 92 224
1943–44 72 73 100 214
1944–45 81 73 111 229
1945–46 74 78 96 221
1946–47 69 83 83 245
1947–48 90 89 101 236
1948–49 97 99 98 250
1949–50 129 100 129 238
1950–51 205 108 189 186
1951–52 149 127 117 258
1952–53 209 132 158 235
1953–54 198 134 148 245
1954–55 202 140 144 257
1955–56 195 144 136 275
1956–57 211 145 145 271
1957–58 176 152 116 330
1958–59 177 153 116 348
1959–60 197 155 127 342
1960–61 168 159 106 385
1961–62 179 162 111 388
1962–63 210 163 128 397
1963–64 257 164 157 387
1964–65 274 166 165 394
1965–66 310 173 179 411
1966–67 285 179 160 442
1967–68 298 178 168 465
1968–69 351 191 184 471
1969–70 339 198 171 501
1970–71 360 209 173 539
1971–72 619 220 281 455
1972–73 742 233 319 439
1973–74 837 264 317 459
1974–75 679 294 231 527
1975–76 792 325 244 528
1976–77 1002 381 263 548
1977–78 1079 430 251 527
1978–79 1247 476 262 533
1979–80 1599 582 275 587
1980–81 1830 713 257 616
1981–82 2170 853 254 627
1982–83 2427 855 284 626
1983–84 2710 872 311 621
1984–85 3267 973 336 653
1985–86 3147 1080 291 708
1986–87 3179 1130 281 715
1987–88 3171 1183 268 789
1988–89 3603 1237 291 736
1989–90 4003 1308 306 725
1990–91 4005 1334 300 765
1991–92 4187 1345 311 765
1992–93 4913 1374 358 712
1993–94 5082 1383 368 817
1994–95 4996 1390 359 826
1995–96 4969 1394 357 755
1996–97 4887 1405 348 804
1997–98 5086 1424 357 884
1998–99 5369 1438 373 858
1999–00 5696 1465 389 840
2000–01 6434 1553 414 909
2001–02   1622    
2002–03   1657    
2003–04   1684    

Capital Stock (1949/50$)#

Sum of Livestock, Plant, machinery and Equipment, Improvements, and the value of all unimproved Agricultural land (valued by Hussey and Philpott (1969) as 1949/50$329.9m).#


1926/27 to 1966/67: Hussey and Philpott (1969) Table 15 Value of Livestock (in constant prices).

1967/68 to 1970/71: Ellison (1977) Table A1 Real Value of Livestock

1971/72 to 1983/84: NZOYB Chapter: Farming section: Livestock. Value of livestock in 1949/50$ estimated as No. of Sheep @ $5 + Cattle @ $30 + Pigs @ $6.

1984/85 to 2003/04: INFOS series AGRA.SACMZZZ (Total Cattle), AGRA.SADDZZZ (Total Pigs), AGRA.SAEJZZZ (Total Sheep), AGRA.SAFMZZZ (Total Goats), and AGRA.SAGXZZZ (Total Deer). Value of livestock in 1949/50$ estimated as Sheep @ $5 + Cattle @ $30 + Pigs @ $6 + Deer @ $20 + Goats @ $3.


1926/27 to 1966/67: Hussey and Philpott (1969) Table 16 Real Value of Depreciated Plant and Machinery.

1967/68 to 1970/71: Ellison (1977) Table A2 Real Value of Depreciated Plant and Machinery

1971/72 to 1983/84: “Agricultural Statistics” Capital Expenditure on Tractors and Farm Machinery. NZOYB – Import Price Index (non-electrical machinery). Capital Expenditure deflated by Import Price Index to give Gross Fixed Capital Formation. Capital Stock calculated from 1970/71 figure using the perpetual inventory method with 9% depreciation.

1971/72 to 1983/84: “Agricultural Statistics” Number of Farm Trucks. Real depreciated value of Farm Trucks calculated by multiplying the number of Farm Trucks by $570 (their real depreciated unit value in 1949/50 prices). These figures added to Plant / Machinery Capital Stock as calculated above.

1984/85 to 1998/99: Statistics New Zealand Gross Fixed Capital Formation and Productive Capital Stock series, by Industry and Asset Type. INFOS series OTPA.SIA1LY1 and OTPA.SIA1MD1 (import price indices for (non-electrical) machinery and for transport equipment). GFKF deflated by the import price index (and CPI where import price index unavailable) to give GFKF in 1949/50$, then Capital Stock calculated using the perpetual inventory model with 9% and 19% depreciation for Plant / Machine and for Transport Equipment respectively. Separate series for Plant / Machine Capital Stock and for Transport Equipment Capital Stock were calculated – the initial values for each were estimated from the 1983/84 Plant / Machine / Transport Capital Stock value by examining the relative size of each from the Statistics New Zealand Productive Capital Stock series.

1999/00 to 2003/04: As above, except GFKF for Agriculture estimated from GFKF – All Industries (INFOS series SNCA.S3NP51AN1140 and SNCA.S3NP51AN1150), using the percentage of all-Industries GFKF for each asset type attributable to Agriculture in the final 5 years of the Statistics New Zealand GFKF series.


1926/27 to 1960/61: Hussey and Philpott (1969) Table 17 Deflated value of improvements in 1949/50 prices.

1961/62 to 1970/71: Ellison (1977) Table A3 Real value of improvements.

1971/72 to 1998/99: Statistics New Zealand GFKF by Industry and Asset Type series. Sum of the real values of GFKF in Residential Buildings, Non-residential Buildings, Other Construction, and Land Improvements. Improvements Capital Stock calculated using the perpetual inventory method with a 1.7% depreciation rate (from Philpott (1992), based on an average 60 year life for Improvements). Price Indices for these 4 asset types from Hussey and Philpott (1969) and Ellison (1977): Improvements price index, and from INFOS series FPIA.S41 (Farm Buildings), FPIA.S44 (Land Development), CEPQ.S2BF (Farm Buildings), CEPQ.S2GA (Residential buildings), CEPQ.S2GC (Other construction), CEPQ.S2GD (Land Improvements). The price indices for each constructed from combinations of the above series and the series FPIQ.SI9Y (general Farm Expenses) where an appropriate index is not available.

1999/00 to 2003/04: As above, except GFKF for Agriculture estimated from GFKF – All Industries (INFOS series SNCA.S3NP51AN1110, SNCA.S3NP51AN1120, SNCA.S3NP51AN1130, and SNCA.S3NP51AN1180), using the % of all-Industries GFKF for each asset type attributable to Agriculture in the final 5 years of the StatsNZ GFKF series.

Appendix Table 5: Capital Stock data.
Year Livestock (1949/50$,000) PLANT, MACHINERY, AND TRANSPORT (1949/50$,000) REAL VALUE OF IMPROVEMENTS (1949/50$,000) TOTAL CAPITAL STOCK (includes Unimproved Land value), 1949/50$,000
1926–27 230,934 46,300 417,339 1,024,473
1927–28 229,096 49,236 430,641 1,038,873
1928–29 237,404 50,941 443,283 1,061,528
1929–30 251,970 53,203 455,588 1,090,661
1930–31 270,238 58,045 466,292 1,124,475
1931–32 273,080 60,961 474,780 1,138,721
1932–33 267,554 59,964 483,212 1,140,630
1933–34 266,936 59,538 487,111 1,143,485
1934–35 275,086 59,938 490,901 1,155,825
1935–36 277,610 60,879 493,475 1,161,864
1936–37 281,886 63,799 495,577 1,171,162
1937–38 291,860 69,499 496,595 1,187,854
1938–39 300,418 74,433 496,853 1,201,604
1939–40 299,380 78,346 496,880 1,204,506
1940–41 294,404 78,901 497,244 1,200,449
1941–42 299,516 80,371 498,143 1,207,930
1942–43 303,400 80,775 501,109 1,215,184
1943–44 300,640 77,937 504,463 1,212,940
1944–45 302,620 79,506 510,819 1,222,845
1945–46 311,164 84,795 511,161 1,237,020
1946–47 309,942 85,107 514,237 1,239,186
1947–48 305,698 87,059 518,912 1,241,569
1948–49 307,192 90,824 524,275 1,252,191
1949–50 309,176 95,030 535,629 1,269,735
1950–51 321,078 102,819 556,448 1,310,245
1951–52 329,116 111,614 590,782 1,361,412
1952–53 334,756 121,647 637,188 1,423,491
1953–54 348,108 128,941 689,416 1,496,365
1954–55 366,294 136,977 745,703 1,578,874
1955–56 376,278 144,198 800,676 1,651,052
1956–57 385,478 147,664 856,037 1,719,079
1957–58 392,244 150,172 886,123 1,758,439
1958–59 410,464 153,617 921,228 1,815,209
1959–60 417,732 152,453 954,821 1,854,906
1960–61 419,388 154,985 991,709 1,895,982
1961–62 439,618 157,082 1,032,044 1,958,644
1962–63 446,992 157,795 1,078,930 2,013,617
1963–64 456,278 158,045 1,144,787 2,089,010
1964–65 461,976 160,406 1,175,353 2,127,635
1965–66 477,076 161,860 1,200,885 2,169,721
1966–67 507,250 170,035 1,199,980 2,207,165
1967–68 536,172 172,897 1,275,759 2,314,728
1968–69 553,470 174,494 1,312,051 2,369,915
1969–70 561,151 175,324 1,366,364 2,432,739
1970–71 568,167 174,890 1,404,901 2,477,858
1971–72 562,830 175,463 1,405,745 2,473,938
1972–73 566,261 178,452 1,413,609 2,488,222
1973–74 553,000 185,748 1,426,122 2,494,770
1974–75 561,526 187,668 1,430,740 2,509,834
1975–76 557,904 189,429 1,434,195 2,511,428
1976–77 555,060 196,124 1,438,956 2,520,040
1977–78 560,564 196,973 1,442,545 2,529,982
1978–79 566,183 197,770 1,449,713 2,543,566
1979–80 560,948 202,446 1,460,739 2,554,033
1980–81 590,401 208,783 1,477,153 2,606,237
1981–82 593,006 216,739 1,496,049 2,635,694
1982–83 591,309 220,847 1,508,797 2,650,853
1983–84 582,679 227,420 1,520,257 2,660,256
1984–85 590,460 225,624 1,528,784 2,674,768
1985–86 587,308 209,099 1,526,947 2,653,253
1986–87 598,342 196,787 1,513,996 2,639,024
1987–88 576,911 184,934 1,499,752 2,591,497
1988–89 583,242 178,743 1,486,655 2,578,540
1989–90 559,433 181,449 1,477,370 2,548,152
1990–91 555,363 181,734 1,465,553 2,532,550
1991–92 546,220 183,937 1,454,568 2,514,625
1992–93 533,942 190,683 1,444,085 2,498,610
1993–94 525,734 200,205 1,437,262 2,493,101
1994–95 541,951 206,885 1,429,409 2,508,144
1995–96 549,179 208,781 1,426,750 2,514,611
1996–97 534,559 210,734 1,421,200 2,496,392
1997–98 535,677 210,109 1,414,695 2,490,380
1998–99 523,751 206,864 1,409,794 2,470,308
1999–00 533,502 209,046 1,406,994 2,479,442
2000–01 528,314 214,246 1,404,207 2,476,668
2001–02 524,909 223,861 1,404,542 2,483,213
2002–03 522,886 231,962 1,406,211 2,490,960
2003–04 533,405 242,913 1,409,446 2,515,664

Labour Force#

The “Full-time equivalent labour force” is the series we have used in the estimation.#

Total Labour Force

1926/27 to 1966/67: Hussey and Philpott (1969) Table 9 Estimates of Farm Labour Force - “All Farm Labour”.

1967/68 to 1974/75: Ellison (1977): Table A6 Index of Aggregate Inputs – “Labour”.

1975/76 to 1979/80: NZOYB: Section Farming, Table Farm Employment Survey, unpaid family subtracted from total workers on farms.

1980/81 to 1995/96: INFOS series AGRA.SAMAZZZ, AGRA.SAMBZZZ, AGRA.SAMCZZZ, AGRA.SAMDZZZ. The sum of Full-time, Part-time, Casual, and Working Owners.

1996/97 to 2003/04: INFOS series HLFA.SJB3UA (Total persons employed – Agriculture, Forestry, Fishing), and series SNCA.S2ND10AAT4, SNCA.S2ND10ABT4, and SNCA.S2ND10ACT4 (Compensation of Employees in Agriculture, Forestry and Fishing respectively). The percentage of COE in the combined Agriculture, Forestry, Fishing group attributable to Agriculture was multiplied by the Total persons employed.

Working Owners

1926/27 to 1966/67: Hussey and Philpott (1969) Table 9 Estimates of Farm Labour Force - “All Farm Labour” minus “Paid Farm Workers”.

1967/68 to 1979/80: Estimated as a percentage of Total Labour Force. The trend over the adjacent periods is of a steady increase in the percentage of Working Owners in the Total Labour Force. Therefore Working Owners as a percentage of the Total Labour Force was interpolated on a straight line between the 1966/67 figure of 61% and the 1980/81 figure of 71%, and the percentage in each year was multiplied by the Total Labour Force figure for that year.

1980/81 to 1995/96: INFOS series AGRA.SAMDZZZ – Working Owners.

1996/97 to 2003/04: Estimated as 60.9% of the Total Labour Force (in 1995/96 Working Owners made up 60.9% of the Total Labour Force).

Total Employees

1926/27 to 1966/67: Hussey and Philpott (1969) Table 9 Estimates of Farm Labour Force - “Paid Farm Workers”.

1967/68 to 1979/80: Total Labour Force minus Working Owners.

1980/81 to 1995/96: Sum of Full-time, Part-time, and Casual employees (INFOS series).

1996/97 to 2003/04: Total Labour Force minus Working Owners.

Full-time Employees

1926/27 to 1954/55: Hussey and Philpott (1969) Table 9 Estimates of Farm Labour Force - “Permanent Males” minus Working Owners (“Permanent Males” series ends in 1954/55).

1955/56 to 1979/80: Estimated as a percentage of Total Employees. Full-time Employees as a percentage of Total Employees was interpolated on a straight line between the 1954/55 and 1980/81 figures of 77% and 58% respectively, and the percentage in each year was multiplied by the Total Employees figure for that year.

1980/81 to 1995/96: INFOS series AGRA.SAMAZZZ – Full-time Employees.

1996/97 to 2003/04: Estimated as 58.1% of Total Employees (in 1995/96 Full-Time Employees made up 58.1% of Total Employees).

Part-time / Casual Employees

1926/27 to 2003/04: Total Employees minus Full-time Employees.

“Full-time Equivalent” number of Employees

1926/27 to 2003/04: Part-time / Casual Employees divided by two, plus Full-time Employees.

“Full-time Equivalent” Labour Force

1926/27 to 2003/04: Full-time Equivalent Employees plus Working Owners.

Appendix Table 6: Labour Force data.
Year Number of Working Owners Total Number of Employees Number of Full-time Employees Number of Part-time / Casual Employees FTE Total Labour Force (Working Owners + FTE employees)
1926–27 62,800 79,200 37,800 41,400 121,300
1927–28 63,600 84,400 41,300 43,100 126,450
1928–29 64,600 83,400 46,600 36,800 129,600
1929–30 65,600 85,400 52,000 33,400 134,300
1930–31 66,400 88,600 52,600 36,000 137,000
1931–32 67,300 91,700 55,700 36,000 141,000
1932–33 68,300 92,700 56,700 36,000 143,000
1933–34 69,300 92,700 56,700 36,000 144,000
1934–35 71,300 91,700 54,700 37,000 144,500
1935–36 70,300 92,700 54,700 38,000 144,000
1936–37 69,300 91,700 53,700 38,000 142,000
1937–38 68,300 90,700 52,700 38,000 140,000
1938–39 65,300 91,700 53,700 38,000 138,000
1939–40 66,400 87,600 50,600 37,000 135,500
1940–41 66,000 74,000 36,000 38,000 121,000
1941–42 65,600 59,400 21,400 38,000 106,000
1942–43 64,500 60,500 22,500 38,000 106,000
1943–44 64,400 62,600 24,600 38,000 108,000
1944–45 63,300 66,700 28,700 38,000 111,000
1945–46 64,500 72,500 43,500 29,000 122,500
1946–47 65,700 69,300 47,200 22,100 123,950
1947–48 66,900 67,300 42,500 24,800 121,800
1948–49 68,000 65,700 41,200 24,500 121,450
1949–50 69,200 64,300 41,100 23,200 121,900
1950–51 70,400 62,600 41,000 21,600 122,200
1951–52 71,600 60,700 40,900 19,800 122,400
1952–53 71,600 60,000 42,000 18,000 122,600
1953–54 71,600 59,100 43,900 15,200 123,100
1954–55 71,600 58,800 45,100 13,700 123,550
1955–56 71,600 58,600 44,527 14,073 123,163
1956–57 71,600 57,700 43,430 14,270 122,165
1957–58 71,600 56,500 42,123 14,377 120,911
1958–59 71,600 55,600 41,054 14,546 119,927
1959–60 71,600 54,000 39,486 14,514 118,343
1960–61 71,600 52,500 38,014 14,486 116,857
1961–62 71,600 51,300 36,778 14,522 115,639
1962–63 71,600 50,100 35,559 14,541 114,430
1963–64 71,600 48,800 34,288 14,512 113,144
1964–65 71,600 47,700 33,174 14,526 112,037
1965–66 71,600 47,200 32,488 14,712 111,444
1966–67 71,600 46,500 31,674 14,826 110,687
1967–68 72,787 45,813 30,878 14,935 111,132
1968–69 73,266 44,634 29,764 14,870 110,465
1969–70 73,673 43,427 28,649 14,779 109,711
1970–71 74,066 42,234 27,559 14,675 108,963
1971–72 74,577 41,123 26,540 14,583 108,409
1972–73 75,078 40,022 25,543 14,479 107,861
1973–74 76,692 39,508 24,933 14,575 108,912
1974–75 78,323 38,977 24,319 14,658 109,971
1975–76 82,922 39,847 24,577 15,271 115,134
1976–77 88,089 40,857 24,907 15,950 120,971
1977–78 93,393 41,791 25,178 16,614 126,877
1978–79 90,982 39,258 23,371 15,887 122,296
1979–80 94,968 39,493 23,228 16,265 126,328
1980–81 91,321 36,584 21,238 15,346 120,232
1981–82 96,051 39,897 23,374 16,523 127,687
1982–83 93,398 42,815 23,709 19,106 126,660
1983–84 86,981 41,967 22,787 19,180 119,358
1984–85 88,748 40,601 21,886 18,715 119,992
1985–86 86,653 38,974 20,650 18,324 116,465
1986–87 87,311 39,631 19,608 20,023 116,931
1987–88 85,045 36,952 20,866 16,086 113,954
1988–89 83,921 34,544 19,533 15,011 110,960
1989–90 87,203 36,888 21,404 15,484 116,349
1990–91 86,389 40,180 23,310 16,870 118,134
1991–92 84,515 36,982 20,459 16,523 113,236
1992–93 69,092 51,474 31,519 19,955 110,589
1993–94 64,247 44,714 30,745 13,969 101,977
1994–95 73,991 46,174 30,568 15,606 112,362
1995–96 73,547 47,284 27,490 19,794 110,934
1996–97 69,409 44,563 25,891 18,672 104,636
1997–98 68,627 44,061 25,599 18,462 103,457
1998–99 73,167 46,976 27,293 19,683 110,301
1999–00 76,231 48,943 28,436 20,507 114,921
2000–01 73,713 47,326 27,497 19,830 111,125
2001–02 78,046 50,108 29,113 20,995 117,656
2002–03 77,001 49,437 28,723 20,714 116,081
2003–04 74,056 47,546 27,624 19,922 111,641

R&D – expenditure#

Total Agricultural R+D expenditure (1949/50$)#

1926/27 to 1971/72: From Scobie and Eveleens (1987). Sum of Government expenditure, Funds to research associations, and Expenditure in Universities and other. Calculated from data in McBride (1966), and various NRAC, DSIR, and MAF reports.

1972/73 to 2001/02: From Robin Johnson dataset (most of which is in Johnson (2000)). Total R+D, Agriculture.

Nominal R+D deflated to 1949/50$ using INFOS series CPIA.SE9AJ

Private Agricultural R+D expenditure (1949/50$)#

1926/27 to 1971/72 except 1926/27, 1927/28, and 1940/41 to 1944/45: From Scobie and Eveleens (1987). Private R+D is estimated to be approximately equal to the grants paid by DSIR to research associations – that is, that there is a 50:50 split between the contribution to research associations from producers and the government.

1926/27 to 1927/28: Estimated as 11.6% of Total R+D (the 1928/29 proportion).

1940/41 to 1944/45: Interpolated on a straight line basis between 1939/40 and 1945/46 values.

From 1926/27 to 1971/72 the data should be taken as a proxy for private R&D spending as they do not include expenditure by private firms. The research associations funded research beyond the farm gate in the processing sector which has the effect of enhancing the demand for the raw farm products.

1972/73 to 2001/02: From Robin Johnson dataset (most of which is in Johnson (2000)). Private R+D, Agriculture.

Nominal R+D deflated to 1949/50$ using INFOS series CPIA.SE9AJ

Public Agricultural R+D expenditure (1949/50$)#

Total R+D minus Private R+D

Nominal R+D deflated to 1949/50$ using INFOS series CPIA.SE9AJ

US Patents#

Data obtained from the United States Patent and Trademark Office. Total of Utility Patents (inventions) granted, Design Patents granted, and Plant Patents granted.

Appendix Table 7: R&D data.
Year Real Private R&D, 1949/50$,000 Real Public R&D, 1949/50$,000 Real Total Domestic R&D, 1949/50$,000 Total USPTO Patents Granted
1926–27 11 85 97 44,105
1927–28 12 90 102 45,514
1928–29 14 110 124 48,174
1929–30 19 147 166 47,938
1930–31 16 138 154 54,698
1931–32 22 113 135 56,448
1932–33 21 152 173 51,218
1933–34 18 144 162 47,372
1934–35 21 161 182 44,529
1935–36 22 174 196 44,388
1936–37 30 228 258 42,875
1937–38 35 326 361 43,130
1938–39 55 482 536 48,711
1939–40 49 423 472 48,467
1940–41 44 668 713 47,656
1941–42 40 750 790 42,242
1942–43 36 455 490 33,330
1943–44 32 522 554 31,007
1944–45 29 614 643 29,235
1945–46 25 720 745 24,640
1946–47 42 1,030 1,072 22,293
1947–48 56 1,265 1,321 27,973
1948–49 58 1,384 1,442 39,675
1949–50 67 1,664 1,731 47,847
1950–51 49 1,562 1,611 48,548
1951–52 53 1,621 1,674 46,676
1952–53 56 1,495 1,551 43,259
1953–54 62 1,478 1,541 36,446
1954–55 68 1,574 1,643 33,248
1955–56 79 1,678 1,757 49,894
1956–57 101 1,832 1,933 45,236
1957–58 85 1,898 1,984 50,835
1958–59 91 1,893 1,984 55,278
1959–60 95 1,982 2,078 49,828
1960–61 98 2,232 2,330 50,964
1961–62 160 2,393 2,552 58,082
1962–63 181 2,462 2,643 48,773
1963–64 210 2,564 2,774 50,189
1964–65 233 2,977 3,210 66,401
1965–66 313 3,357 3,670 71,707
1966–67 351 3,628 3,979 68,902
1967–68 265 3,683 3,948 62,527
1968–69 284 3,813 4,098 70,997
1969–70 351 3,825 4,176 67,695
1970–71 347 4,232 4,579 81,544
1971–72 448 4,849 5,296 77,910
1972–73 568 6,664 7,232 78,308
1973–74 604 7,653 8,257 80,843
1974–75 662 8,303 8,965 76,432
1975–76 658 7,992 8,649 74,966
1976–77 613 7,268 7,881 69,371
1977–78 636 7,275 7,910 70,150
1978–79 724 8,238 8,962 52,104
1979–80 720 6,758 7,477 65,885
1980–81 751 7,187 7,939 70,699
1981–82 835 7,851 8,686 63,005
1982–83 832 7,612 8,444 61,620
1983–84 882 7,806 8,688 72,350
1984–85 895 7,584 8,478 76,969
1985–86 878 8,193 9,071 76,602
1986–87 913 7,380 8,293 89,140
1987–88 900 7,339 8,239 84,028
1988–89 894 7,660 8,554 102,216
1989–90 908 7,811 8,719 98,707
1990–91 840 7,864 8,705 106,435
1991–92 903 7,854 8,757 107,034
1992–93 1,222 8,240 9,461 109,414
1993–94 1,018 7,910 8,928 113,270
1994–95 1,230 8,790 10,021 113,518
1995–96 1,520 10,155 11,676 121,417
1996–97 1,665 11,184 12,849 123,791
1997–98 1,802 11,909 13,711 162,849
1998–99 1,819 11,350 13,169 168,638
1999–00 1,865 11,475 13,340 175,456
2000–01 1,997 11,636 13,633 183,492
2001–02 2,229 12,280 14,509 183,917
2002–03       186,596

Agricultural Extension and Education#

1926/27 to 1983/84: From Scobie and Eveleens (1987). Data from NZOYB, students enrolled in Massey and Lincoln Agricultural Colleges (to 1940/41), students enrolled in degrees, diplomas, and certificates in Agricultural, Horticultural, Technology, Food Science, and Vet Science programmes (from 1941/42).

1984/85 to 1987/88: NZOYB, students enrolled in degrees, diplomas, and certificates in Agricultural, Horticultural, Technology, Food Science, and Vet Science programmes.

1988/89 to 1989/90: “Education Statistics of New Zealand”, degrees, diplomas, and undergraduate university certificates in various Agricultural and Horticultural fields of study.

1990/91: NZOYB, estimated as the percentage change in Total university enrolments (all fields and levels) from the previous year, with this percentage applied to the 1989/90 Agriculture figure.

1991/92 – 1997/98: “Education Statistics of New Zealand”, sum of National diploma or degree and Postgraduate university categories, for students enrolled in the Agriculture, Forestry, and Fishing field of study. This figure was reduced by 5.4% to remove Forestry / Fishing students (5.4% was the average proportion from 1981/82 to 1986/87).

1998/99 – 2000/01: Ministry of Education website (or “Education Statistics of New Zealand”), degrees, diplomas, and postgraduate university for various Agricultural and Horticultural fields of study.

2001/02: NZOYB, diplomas, degrees, and postgraduate university for Agriculture and Environmental Studies category.

2002/03: Ministry of Education website (or “Education Statistics of New Zealand”), university enrolments for Agriculture and Environmental Studies.

Human Capital Index (HKI)#

Human Capital is estimated as the sum of the Education variable for the current year and previous 15 years (As in Scobie and Eveleens 1987), i.e.

HKIt = EDUt + EDUt-1 + … + EDUt-15

For the first 14 years of the data series it was assumed that the number of students enrolled pre- 1926/27 was the same as the 1926/27 figure.

The Human Capital Index is constructed with a lag of 2 years, and based in 1949/50. As the education variable is constructed of the number of persons enrolled in the various institutions, there will be a lag before these people graduate and are introduced to the work force. Up until this introduction point they do not add anything to the stock of human capital. It has been assumed that on average this lag would be 2 years. That is, HKIt = HKt-2 / HK1947/48

Extension (number of workers)

1926/27 to 1983/84: From Scobie and Eveleens (1987). Represents the number of Advisory Services Division staff in MAF, figures from ASD Head Office.

1984/85 onwards: Following privatisation of the ASD, figures for the number of extension workers / consultants operating are difficult to find. Estimates were found in several sources, and the missing year data was interpolated between adjacent data points on a straight line basis.

1986/87: Journeaux, Stephens, and Johnson (1997), Section “Historical Developments” – estimate of 670 ASD staff.

1990/91: Scrimgeour, Gibson, and O’Neill (1991), Section 2.1 “The number of extension workers in NZ”, conservative estimate that the extension worker: farm holding ratio is about 1:330. With approximately 81,000 farm holdings (INFOS AGRA.SAAAZZZ) this implies about 250 extension workers.

1991/92: Bloome (1993), Section “Commercialisation”, estimate that since 1985 the number of professional staff had fallen by over 50%, implying a figure of around 320.

1995/96: Journeaux, Stephens, and Johnson (1997), Section “The total extension sector” – estimate the number of full-time extension workers/ consultants at 425.

1998/99: from NZ Institute of Primary Industry Management (NZIPIM, professional association for agricultural / horticultural, and forestry/ fishing, consultants, accountants, and bankers). Membership numbers in each year were reduced by 40%, a rough estimate intended to remove bankers / finance, and forestry / fishing, while including some extension workers who are not members of NZIPIM. NZIPIM estimates that around 45% of members are consultants while 40% are bankers/finance.

Other Regression Variables#


Calculated as tenths of days of Soil Moisture Deficit.

1926/27 to 1983/84: From Scobie and Eveleens (1987). Based on data from Met Office of regional SMD. A NZ average calculated by weighting regions by stock units (1 cow = 8 SU, 1 sheep = 1 SU, 1 beef = 6 SU, 1 acre crop = 10 SU) using regional livestock and crop data.

1984/85 to 2003/04. Soil Moisture Deficit data by region from MAF. Calculated using regional livestock data and the same stock units as previously (with cropland excluded).

Deviations from Trend Net Farm Income

Net Farm Income:

1926/27 – 1966/67: Hussey and Philpott (1969), Table 1 “Net Farm Income”

1967/68 – 1971/72: Ellison (1977), Table: Non-factor Expenses, “Net Farm Income”

1972/72 – 1983/84: From Scobie and Eveleens (1987), data from NZOYB, calculated as Personal income from farming (Section: Production accounts, Agriculture, “Operating Surplus”) plus Income of farm companies (Chapter: Incomes and income tax, Table: Incomes of companies, Total of Agriculture and livestock production) minus Rates and land taxes (Chapter: Local government finance: receipts, sum of catchment boards, county councils, land drainage boards and road boards).

1984/85 – 1995/96: INFOS series SNBA.SKBAA4 (Net operating surplus) minus SNBA.SKDAA4 (Indirect taxes)

1996/97 – 2000/01: The % changes in Net operating surplus (Gross operating surplus, SNCA.S2NB02AAT4, minus Consumption of fixed capital, SNCA.S3NK10AAT4) were applied to the final term (1995/96) in the SNBA.SKBAA4 (Net operating surplus) series. The definition of Consumption of Fixed Capital was altered as part of changes to the National Accounts, meaning that the post-1996/97 Net operating surplus data is of a different magnitude to the pre-1996/97 data. The new and old Net operating surplus series are highly correlated, however, so applying % changes to the final term of the old series allows us to create data consistent with the old definition to a high degree of accuracy. From this constructed Net Operating surplus series was subtracted Indirect taxes to give Net farm income (INFOS SNCA.S2ND24AAT4).

Nominal Net farm income data was deflated to 1949/50$ using INFOS series CPIA.SE9AJ

“YD” (deviation from HP trend line):

Over the 75 year period for which data is available, Net farm income seems to exhibit a long-term trend not particularly close to a straight line – therefore we used a Hodrick-Prescott trend line. Since planning horizons of farmers are unlikely to be more than a few years, a straight line trend may not capture very well the phenomenon of extra input purchases in good years. YD was calculated as the deviation from the HP trend line.

Appendix Table 8: Other Regression Variables.
Year Education (no. of students) Human Capital Index Extension workers Tenths of Days of Soil Moisture Deficit Deviations from Net Farm Income
1926–27 56 0.11 115 331 4,530
1927–28 94 0.11 128 446 19,203
1928–29 90 0.11 140 273 34,082
1929–30 276 0.12 152 484 10,563
1930–31 242 0.12 160 470 -37,254
1931–32 259 0.15 157 451 -36,565
1932–33 279 0.17 149 531 -36,248
1933–34 338 0.20 154 330 8,811
1934–35 287 0.22 155 526 -7,192
1935–36 251 0.26 160 228 22,199
1936–37 228 0.29 157 165 46,239
1937–38 488 0.31 179 363 8,660
1938–39 330 0.33 205 670 -2,475
1939–40 330 0.39 224 345 -6,589
1940–41 302 0.42 223 369 5,341
1941–42 112 0.46 220 474 -4,265
1942–43 296 0.49 177 514 -22,249
1943–44 800 0.49 198 360 -39,862
1944–45 1,249 0.52 208 118 -21,818
1945–46 1,549 0.61 248 507 -46,797
1946–47 583 0.76 273 439 -17,484
1947–48 584 0.92 341 540 -6,509
1948–49 598 0.96 364 380 -7,404
1949–50 579 1.00 478 408 19,928
1950–51 528 1.04 506 172 121,421
1951–52 466 1.07 505 359 6,336
1952–53 505 1.10 472 157 4,861
1953–54 499 1.13 488 355 15,981
1954–55 519 1.16 500 387 9,792
1955–56 584 1.16 510 398 -1,280
1956–57 722 1.19 495 265 13,129
1957–58 817 1.22 515 208 14,602
1958–59 885 1.27 518 211 -20,393
1959–60 877 1.36 575 318 -433
1960–61 812 1.43 575 192 4,493
1961–62 917 1.44 590 341 -23,914
1962–63 1,051 1.39 617 287 -12,188
1963–64 946 1.31 654 414 13,199
1964–65 1,427 1.37 517 170 5,339
1965–66 1,434 1.41 516 170 3,849
1966–67 1,469 1.52 506 232 -11,376
1967–68 1,990 1.62 496 319 -26,901
1968–69 2,233 1.74 486 312 -35,427
1969–70 2,269 1.93 537 361 -35,062
1970–71 2,381 2.15 512 357 -48,999
1971–72 2,433 2.37 557 296 -35,641
1972–73 2,280 2.60 572 574 79,791
1973–74 2,053 2.83 591 396 60,184
1974–75 2,537 3.03 586 272 -36,358
1975–76 2,867 3.18 614 324 -7,298
1976–77 2,888 3.39 594 263 34,738
1977–78 3,059 3.63 584 535 -7,456
1978–79 2,842 3.89 620 261 31,425
1979–80 3,100 4.16 604 91 73,235
1980–81 3,771 4.39 623 341 4,063
1981–82 3,901 4.65 639 348 4,044
1982–83 4,030 4.95 654 449 -8,636
1983–84 3,688 5.26 684 169 15,886
1984–85 4,017 5.58 679 371 23,422
1985–86 3,849 5.79 675 261 -11,034
1986–87 3,232 6.01 670 308 -33,900
1987–88 2,690 6.21 565 352 -8,251
1988–89 2,656 6.31 460 507 -2,109
1989–90 2,126 6.35 355 333 2,090
1990–91 1,946 6.39 250 333 -31,356
1991–92 2,581 6.40 320 367 -7,430
1992–93 2,255 6.33 346 296 -20,138
1993–94 2,295 6.29 373 386 -349
1994–95 2,491 6.21 399 414 -14,831
1995–96 1,523 6.12 425 277 -19,747
1996–97 2,247 6.07 422 308 -16,793
1997–98 3,094 5.88 418 460 -30,293
1998–99 2,953 5.69 415 417 -39,413
1999–00 2,776 5.59 413 332 -20,120
2000–01 2,775 5.45 430 399 48,220
2001–02 3,053 5.34 423 250  
2002–03 2,243 5.18 432 449  
2003–04     429 299  


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