3.1 Theoretical Framework

Agricultural productivity has been widely measured worldwide, beginning with the pioneering work of Solow (1957) and Griliches (1963 a-b, 1964). Productivity has been recognized as an essential source of growth that encompasses the output gains attributable to technical change (Pfeiffer, 2003). Development economists have also stated that agricultural productivity is particularly critical to developing countries’ improved economic growth and social conditions (^{Johnson and Mellor, 1961}). In addition, studies have also shown that agricultural productivity is a key factor explaining the dynamics of worldwide trade, by determining changes in the comparative advantages among countries (^{Ball et al., 2010}). Accordingly, agricultural productivity has been the focus of a significant number of studies (Ball, 1985; ^{Fernandez-Cornejo and Shumway, 1997}; ^{Avila et al., 2010}; ^{Evenson & Fuglie, 2010}; Fuglie & Rada, 2013 to name a few).

Three different methodology types are often used to measure agricultural productivity. The first is growth accounting. This technique measures agricultural productivity by following a simple accounting exercise (Solow, 1957): aggregate output growth is estimated as the growth of the value of all outputs; aggregate input growth is measured as a cost share weighted average of the growth in inputs used in production of the various outputs; and productivity growth is identified as the residual difference between these two measures.⁴

The simple exercise makes the growth accounting technique very attractive. However, the technique relies on very strong assumptions: i) competitive markets for both outputs and inputs; ii) constant returns to scale; iii) technical change is Hicks neutral; iv) input-output separability; and v) a Cobb-Douglas production function (^{Antle and Capalbo, 1988}; ^{Diewert, 1992}).^{5 6 7} Many studies have used these techniques and the USDA relies on this methodology for measuring International Agricultural Total Factor Productivity (TFP) Growth (^{Evenson and Fuglie, 2010}; Fuglie, 2010; Fuglie and Rada, 2013; Rada, 2013).

Superlative index methods have been used to relax these assumptions. The most commonly used are the Tornqvist- Theil Index (^{Ball, 1985}; ^{Evenson et al., 1999}; ^{Fan and Zhang, 2002}; ^{Garcia et al., 2012}; Thirtle et al., 2008) and the Fisher Index (^{Cahill and Rich, 2012}; Zhao et al., 2012). These procedures measure the agricultural productivity without estimating a functional structure for the production function for long periods of time. However, these methods are data demanding, and their economic interpretation is not always intuitive (Saikia, 2009). In addition, productivity estimates largely depend on the index number formula (^{Diewert and Nakamura, 2002}).

Another methodology is the frontier technique (^{Farrell, 1957}). These techniques rely on the fact that economic activities may not always be located in their best practice frontiers (i.e. on the Production Possibility Frontier, or PPF) (^{Coelli, Rao and Battesse, 1998}).⁸ Accordingly, agricultural productivity corresponds to the estimation and posterior product of two components: technical change, which captures shifts in the production possibility frontier, and efficiency change, which considers movements exhibited by a firm or economic activity within its production possibility set toward a position closer to that frontier (Sena, 2013). Hence, agricultural productivity measurement largely depends on a robust estimation of the production possibility frontier and the corresponding estimation of these two components using the frontier as an efficiency benchmark.

Two frontier types are primarily utilized for the measurement of agricultural productivity: i) parametric methods, such as Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) (^{Coelli, Rao and Battesse, 1998}), and ii) non-parametric methods, such as the Malmquist Index (^{Caves et al., 1982}). These techniques are very attractive when data is a constraint, because they do not require any price data (Coelli and Rao, 2005; Sena 2003). However, they are susceptible to data quality issues and unusual shadow prices (Coelli and Rao, 2005; Thirtle et al., 2003; Tong et al. 2012).

Econometric techniques are another common approach used to measure agricultural productivity (^{Berndt and Christensen, 1973}). These techniques assume that productivity can be directly measured when assuming a functional approximation of the true production relationship (so-called primal techniques) or indirectly measured from its Dual Cost function (so-called dual techniques), which requires the functional approximation of the cost or profit function. The main advantages are that econometric models allow: i) relaxing certain assumptions required by accounting approaches, such as Hicks neutral technical change or constant returns to scale; ii) estimating rather than assuming certain parameters related to technical changes, such as the elasticity of factor substitution; and iii) estimating confidence intervals around the estimates and testing hypotheses on the estimated parameters. However, these primal econometric models require a production function with input- output separability, as do growth accounting approaches. Primal econometric models also require a large enough data set to ensure sufficient degrees of freedom, address multi-collinearity problems and estimate a large number of parameters with good precision. Nevertheless, these techniques estimate productivity growth with fewer constraining assumptions than required by other approaches. Econometric models have been successfully used by several studies devoted to analyzing agricultural productivity. For example: ^{Cungu and Swinnen, 2003}; ^{Fan, 1991}; Sun et al., 2009.

3.2 Agricultural Productivity in Colombia

Colombia’s agricultural productivity has been the focus of just a few studies at the national level (^{Atkinson, 1970}; ^{Avila et al., 2010}; Ludena, 2010; Pfeiffer, 2003; USDA, 2015). It has usually been analyzed in the context of multi-national studies (^{Bravo-Ortega and Lederman, 2004}; ^{Coelli and Rao, 2005}; ^{Fuglie, 2015}; ^{Fulginiti and Perrin, 1998}; Trueblood and Coggins, 2003). Relatively little is known about its dynamics over the last several decades.

^{Atkinson (1970}) is the pioneering scholar of Colombia’s agricultural productivity. Using partial productivity indices for the period of 1950-1967, he found that Colombia’s agricultural productivity was uneven across crops and largely dependent on farms’ ability to mechanize their production practices. Also, large farms usually exhibited higher agricultural productivity than small farms, because large farms could afford to pay for better seeds, pesticides and fertilizers.

In more recent studies, growth accounting techniques have been the most common methodology used to measure Colombia’s agricultural productivity. For instance, the USDA (2015) used the technique for 173 countries from 1961-2012. The study estimated that Colombia’s agricultural productivity grew 1.4% on average per year during this period. ^{Avila et al. (2010)} used a Tornqvist-Theil Index to examine Colombia’s agricultural productivity between 1961 and 2001 and estimated that it grew an annual average of 0.7%. However, these studies reached different conclusions and none used budget data from Colombian farmers.⁹

Ludena (2010) used a frontier approach and found that Colombia’s agricultural productivity grew an average of 2.4% during the 1980s, 2.5% during the 1990s, and 0.2% from 2000-2007. Likewise, Pfeiffer (2003) estimated that Colombia’s agricultural productivity grew on average between 0.6-1.9% during the period 1972-2000.¹⁰

Clearly, these studies obtained varying results from various techniques that provided non-robust estimates for Colombia’s agricultural productivity. As the time frames changed, so did productivity and agricultural performance estimates. These studies indicate that Colombia’s agricultural productivity grew slowly and unevenly over the last several decades. We suspect that this is probably because most studies implicitly assume that changes in economic conditions and policy regimes did not impact Colombia’s agricultural productivity. This paper considers this to be a crucial assumption that accounts for these differences. Therefore, we incorporate important changes in the political economy over time into our analyses of Colombia’s agricultural productivity.

4.1 Cobb-Douglas Production Function

The choice of functional form is a primary issue in the econometric estimation of productivity growth and technical change. The Cobb-Douglas functional form is one of the simplest choices available and has been widely used in applied economics research. The Cobb-Douglas is supported by the same theoretical underpinnings as the growth accounting technique. Rather than use observed farmers’ budget data to estimate all parameters, this approach estimates them econometrically by controlling for other factors and substitution possibilities implied by the data. Assuming that agricultural productivity grows on average at a constant rate g, so A _t = A ₀ e ^gt , the Cobb-Douglas representation of aggregate production is:

where Q _t is total agricultural output in period t, A ₀ is agricultural productivity in the initial period, e is the exponential function, K _t is the stock of capital in agriculture in period t, L _t is labor hired by agriculture in period t, Ft is fertilizer used by agriculture in period t, S _t is animal feed employed by agriculture in period t and u _t is the error in measuring output in period t.

Colombia’s agricultural productivity growth over time is measured as the sum of the average growth g and the residuals of the econometric estimation u _t , (which have a mean of zero).¹¹ Crop and livestock productivity growth are also separately estimated in this paper following a similar approach. One of the advantages of a specification such as the Cobb-Douglas function is that it can be estimated using Ordinary Least Squares (OLS) after transforming to the linear version of equation (1) with variables expressed in natural logarithms. Serial autocorrelation across the time dimensional residuals was tested using the Durbin-Watson statistic. When this problem was detected, one-period lagged output was added to the regression as a concomitant variable to incorporate inertia into the aggregate cropping patterns, which likely led to the serially-correlated error.

The Cobb-Douglas parameters α, ß, γ and θ can only be interpreted as input cost shares when the following conditions are satisfied: i) perfect competition; ii) firms maximize their profits; iii) perfect information; and iv) constant returns to scale in period t. Constant returns to scale requires the restriction that α + ß + γ + θ = 1 and that all parameters are non-negative. Otherwise, these parameters represent only the marginal effect of each input on agricultural output. In addition, the Cobb-Douglas function is only capable of representing Hicks-neutral technical change.

The rigid structure and underlying assumptions of the Cobb-Douglas specification may not be supported by the Colombian data. Two alternative econometric approaches were also examined, each of which relaxes some of the assumptions discussed above to varying degrees. The Constant Elasticity of Substitution (CES) production function allows the estimation of a constant elasticity of substitution different from one. The CES also allows for the measurement of biased technical change. Dual approaches that specify a cost function allow for further relaxation of the Cobb-Douglas and growth-accounting assumptions. Dual approaches with higher order polynomial forms are the key aspect of this increased flexibility. In this regard, it is not the dual that is important, but the order of the functional form must be polynomial. However, the dual approach facilitates the use of these functional forms because in many of the more interesting cases, such as the translog functional form, it is not self-dual. This implies that it is not possible to solve the profit maximization problem analytically to obtain a closed form system for the direct estimation of the production function (^{Antle and Capalbo 1988}). The dual approach allows the recovery of potentially unknown but well-behaved production technology information by estimating the input demand and output supply functions derived from the Dual Cost function (^{Christensen and Greene, 1976}). Also, this approach enables the measurement of both biased technical change and the potential impact of aggregate scale effects on productivity growth.

4.2 CES Production Function

The CES production functional form was initially designed to analyze the production of economic activity using only two inputs (^{Arrow et al., 1961}). Sato (1967) generalized this production function for n inputs, explaining that it can be estimated assuming two-input nests. In recent decades, debate has focused on how to determine this nested pair of inputs.

This paper followed the approach developed by ^{Klump et al. (2007)} and Leon-Ledesma et al. (2011) to measure Colombia’s agricultural productivity assuming a CES production function. We rely on the following normalized structure of a nested CES production function with four inputs and technical change. The primary inputs (i.e. capital and labor) are allocated to the first nest and the intermediate inputs (i.e. fertilizer and animal feed) to the second nest. Also, to circumvent problems related to the Diamond McFadden Impossibility Theorem (Diamond et al., 1978), the efficiency growth exhibited by each input E _it is restricted to a constant rate γ _i (Klump et al., 2011).

where the elasticity of substitution between capital and labor (i.e. first nest inputs) is η, between fertilizer and feed (i.e. second nest inputs) is ψ, and between nests is σ. Also, α is the distribution parameter between nests, β within the first nest, π within the second, and u _t is the error in measuring this CES production function.

The measurement of Colombia’s agricultural productivity involves a typical profit maximization problem to determine the input demands. Each equation derived from this optimization is normalized and linearized. The profit optimization was solved by assuming that Colombia’s agriculture faces a demand function , its income is Qt = (1+µ)(RtKt +WtLt +fPtFt +sPtSt ) and it exhibits a rent factor , where real returns to capital are denoted by Rt, wage paid for labor by Wt, fertilizer price by fPt, and animal feed price by sPt .¹² This system of equations was estimated using Iterative Feasible Generalized Non-Linear Least Squares (IFGNLS), as recommended by Kreuser et al. (2015). This technique prevents the estimation of inconsistent parameters and an elasticity of substitution biased towards unity, as is often exhibited when this system of equations is estimated as a Seemingly Unrelated Regression model (SUR) (Luoma and Luoto, 2011).

This model estimated the parameters for technical change γi and input elasticities of substitution (σ,η, and ψ) simultaneously and under two scenarios: i) Hicks-Neutral technical change (γk = γL = γf = γs) and ii) biased technical change (γk ≠ γl ≠ γf ≠ γs). Colombia’s agricultural productivity growth was also measured over time as the actual output growth in period t unexplained by the input growth in period t.

For the measurement of crop and livestock productivity, a similar nested CES production function was used. Crop production was modeled to depend on capital, labor and fertilizer, and livestock production was modeled to depend on capital, labor and animal feed. Accordingly, a nested CES production function with only one nest and an extra input was defined for each case. Also, two possible forms for their respective, nested CES production functions were examined: i) when primary inputs are in the nest or ii) when capital-related inputs are in the nest.¹³

4.3 TransLog Cost Model

This approach is simpler than using primal methods when price data is available and (as discussed earlier) functional forms of the production function lack a closed form solution to the profit maximization or cost minimization problems. Dual functions, such as a cost or profit function, are valid alternatives to represent the multi-product function and to define the technical change (^{Antle and Capalbo, 1988}).

The effects of technical change can be quantified through a reduction in cost or an increase in profits, given an output level and a set of input prices.

The following translog functional form was specified for the aggregate cost function for Colombia’s agriculture:

where Ct are the production costs of Colombia’s agriculture in period t, wit is the price of input i in period t, Qt is output in time t, T is a time trend variable that captures technological change and ut is the error in measuring the logarithm of the total cost.

This functional form is a second-order approximation of an arbitrary, twice-continuously differentiable cost function. It exhibits three main strengths: i) flexibility of functional form; ii) does not restrict input substitution possibilities, and iii) scale economies can vary based on output levels (Kant and Nautiyal, 1997; Varian, 1978). The form has been used successfully by other studies in which the production generating dynamic structure was unknown (^{Binswanger, 1974b}; ^{Christensen and Greene, 1976}; ^{Clark and Youngblood, 1992}; Kant and Nautiyal, 1997; Sun et al., 2009).

Estimation involves each input i cost share equation, which can be derived by applying Shepard’s Lemma to equation (3).^{14 Christensen and Greene (1976)} explained these equations add additional degrees of freedom to the estimation and do not constrain the coefficients, because it constitutes a multivariate system of equations of i+1 equations where across-equation parameter restrictions create more rapid growth in system degrees of freedom than in parameters as equations that are added to the system. The derived cost share equations take the following form, where Sit is the cost share in period t for input i and εit is the error in measurement of cost share i in period t:

The measurement of Colombia’s agricultural productivity proceeds by estimating this system of equations as a seemingly unrelated regressions (SUR) because a common approximation error is passed to each cost share equation though their residuals (^{Christensen and Greene, 1976}) and the specification of a second order polynomial when the true cost function may be of even higher order. The estimation of the system involves n-1 of the cost share equations due to the adding up restriction of cost shares and associated singularity of the system error variance-covariance matrix.¹⁵ Estimated parameters are invariant to which equation is omitted so long as the estimation involves maximum likelihood and the parameters of the omitted equation can be retrieved via the homogeneity and adding up restrictions imposed on the model for regularity purposes. Iterative Feasible Generalized Non-Linear Least Squares (IFGNLS) was used to estimate this system of equations because this estimator is equivalent to a Maximum Likelihood estimator (Greene, 2012).

The following restrictions were imposed to ensure that the corresponding production function is well behaved (^{Capalbo, 1988}; Kant and Nautiyal, 1997): i) coefficients are the same in the cost function and cost share equations; ii) certain coefficients are symmetric among equations; iii) ∑i ai = 1; ∑i ßiQ = 0; and iv) ∑i ßij = ∑j ßji = ∑i ∑j ßij = ∑i ßit = 0 to ensure that this cost function is homogeneous of degree 1 in input prices. Also, curvature restrictions were imposed at the point of the approximation of this cost function (^{Diewert and Wales, 1987}; Ryan and Wales, 2000) and price elasticities for all inputs were computed from estimated parameters using the following expression:

where this expression is equivalent to calculating these elasticities using the Allen partial elasticities of substitution (AES) (^{Binswanger, 1974a}). The dual rate of technical change -Ḃt was computed as follows:

where the basic assumption is that costs decrease due to technology improvements. a _t is the constant rate of technical change, a _tt T captures variations in the rate of technical change over time, ∑ _i ß _it lnw _it is the input bias and ß _Qt lnQ _t is the scale bias. Therefore, pure technical change is equal to -(a _t + a _tt T), which corresponds to the rate of reduction in overall costs due to a technical innovation, holding constant the scale effect. Also, scale augmenting technical change is measured by -ßQ _t lnQ _t , which is the rate of reduction in costs due to a technical innovation exhibited along with changes in output. Similarly, biased technical change (IBTC) was computed using the following expression when the production function behind a translog cost function is non-homothetic (^{Antle and Capalbo, 1988}):

where captures the potential biased technical change exhibited by the input i and denotes the scale effect of technical change. These results can be used to test the presence of biased technical change, which can be described in terms of input-saving or using, which indicates the rate of change in cost shares due to technical change, and is a relative concept. That is, input saving means that the ratio of the input relative to others is declining rather than the absolute quantity of use of the input declining, although it is possible for both to occur simultaneously.

Finally, agricultural productivity growth (TḞP) in this model is measured using equation (8):

where is the shift estimated for the cost function due to technical change and is equal to (^{Capalbo, 1988}). This approach was also used to individually estimate crop and livestock productivity.

4.4 Structural Change Periods

Historical evidence suggests that Colombia’s agriculture faced substantial and distinct structural changes over time (see Table 1). Accordingly, six periods of changing economic conditions and policy regimes were analyzed in an effort to determine whether or not Colombia’s agricultural productivity and technical change were affected. These periods were identified by conducting a historical analysis of Colombia’s agriculture from 1975-2013. Each period was defined based on: i) macroeconomic issues; ii) political changes; iii) economic policy changes (e.g. trade policy); and iv) socioeconomic issues, such as violence.¹⁶ These impacts on agricultural productivity were estimated by including six period specific time trend variables in the Cobb-Douglas regressions. Also, a comparison of the predicted output with and without technical progress was made for the CES and Translog Cost functions.

5.1 Output

The value of agricultural production corresponds to the total gross production value released annually by FAOSTAT (FAO, 2015).¹⁸ In the case of Colombia, this figure encompasses the value of production for 85 crops and livestock commodities.¹⁹ These data were used as they were released annually (per calendar year) and in 2005 international dollars. FAOSTAT releases these data in this currency unit in order to facilitate comparisons across countries. The aim is to avoid the need to use exchange rates by assigning a single global price to each commodity.

For crops, the data correspond to the crop category as reported by FAOSTAT. This includes data for 74 crops produced in Colombia, sold in the market, and consumed by consumers. These figures were multiplied by producer prices and converted to 2005 international dollars (FAO, 2015). For livestock, the data source is FAOSTAT as well and corresponds to its livestock category, including the production of eleven animal products (cattle meat, poultry meat, pork meat, milk, etc.) multiplied by producer prices.

5.2 Inputs

6.1 Colombia’s Agricultural productivity

These results show that Colombia’s agricultural productivity grew on average 0.6-1.4% from 1975 to 2013 (see Table 6). In particular, the CES and Translog Cost techniques predict that it grew on average around 1.3-1.4% per year, respectively, which is similar to the USDA’s prediction (1.4%). The Cobb-Douglas technique predicts that Colombia’s agricultural productivity only grew by 0.6% per year.

These predictions of Colombia’s agricultural productivity were estimated using aggregate data. Although all looked very similar, some key differences were identified. Accordingly, we estimated Colombia’s agricultural productivity using disaggregated data for crop and livestock productivity. This approach renders more consistent predictions for Colombia’s agricultural productivity and removes any difference across techniques generated by the use of aggregate data. Hence, we estimated Colombia’s agricultural productivity as a weighted average of the estimates of crop and livestock productivity, using the shares of crop and livestock production values as weights in total agricultural production value.

This exercise shows that the initial estimates for Colombia’s agricultural productivity using aggregate data maybe slightly overestimated or underestimated. Using Cobb-Douglas techniques, the initial prediction was that productivity has grown by 0.6%; however, it grew by 0.8% per year when computed as the weighted sum of crop and livestock productivity. Likewise, using Translog Cost model, the prediction was that the productivity average growth was around 1.4% per year, but it grew by 0.9% per year when estimated as the weighted sum of crop and livestock estimates. Only the CES technique provided similar estimates regardless of approach. This exercise reaffirmed our initial estimates using aggregate data, showing that Colombia’s agricultural productivity exhibited very low growth from 1975-2013. Also, it suggests that productivity grew in a narrower range, between 0.8% and 1.3%, once a more nuanced crop and livestock productivity performance was considered. These weighted average estimates for Colombia’s agricultural productivity are used in the rest of our analysis.

Table 6 Average Agricultural Productivity Growth in Colombia from 1975-2013 

These estimates show that livestock productivity was the driver of Colombia’s agricultural productivity from 1975 to 2013. All techniques predict that livestock productivity grew at an average rate between 1.6% and 2.2%, probably due to: i) more efficient production practices in the pork and poultry sectors; ii) higher investments in new herds and technology (mainly dual-purpose cattle) in the late 1990s; and iii) innovations for the feeding and management of livestock, genetic improvements and the purchase of highly productive species in the milk sector (^{Kalmanovitz and López, 2003}; MADR, 2005; Mojica and Paredes, 2005). It is not inconsequential that the poultry and pork sectors of Colombia were dominated by completely vertically-integrated, large-scale producers. These entities have brought modern production systems, improved feeding strategies and advanced the breeding and veterinarian expertise of the animal sector.

Colombia’s crop sectors, with the exception of sugar cane and rice, were dominated by small-scale production, a lack of access to improved technology and potential market power by multinational buyers. The latter is especially true for Colombia’s most famous crop, coffee, for which the benefits of advances in world demand have mostly accrued for multinational processors and retailers, and thus have not led to productivity gains in agricultural production. Also, investments made to replace rust-susceptible coffee trees with rust-resistant trees have required agricultural inputs such as labor and nursery stock, which will not yield significant or immediate productivity gains. These latter investments began to generate productivity enhancements in 2016-2017 (USDA, 2017).

Predictably, the estimates of crop productivity are unclear for this period. Assuming a Cobb- Douglas production function and using the Translog Cost approach, the prediction is that Colombia’s crop productivity’s average growth was zero. However, when assuming a CES production function, crop productivity grew on average by 0.8% per year, which is still low.

Historical evidence suggests that crop productivity would have been low during the period 1975- 2013. Colombian farmers experienced difficult conditions during this period due to: i) agricultural budget cuts during the 1980s Latin American debt crisis; ii) profitability crisis after Colombia executed the second wave of Structural Adjustment reforms in the early 1990s; iii) extreme weather conditions (i.e. severe droughts and severe floods); iv) misallocation of resources for agricultural promotion; v) decreased investment due to armed conflict; vi) lack of public resources for promoting Colombia’s agricultural competitiveness and vii) segmented and restricted funding of Colombian farmers (^{Cuevas et al., 2003}; ^{Jaramillo, 1998}; ^{Junguito, 1994}; Junguito et al., 2014; ^{Kalmanovitz and López, 2003}; Reina et al., 2011). Also, this evidence suggests that only a few crops exhibited higher levels of productivity during this period (e.g., sugar cane, flower, banana, cereals and vegetables) (^{Arbeláez, 1993}; ^{Becerra, 2009}; COMPITE, 2008; Jaramillo, 1998; Montero and Casas, 2012; Ramirez and Garcia, 2006).

In order to reaffirm these findings, we tested the consistency of these annual estimates of Colombia’s agricultural productivity growth across techniques. First, we conducted a graphical analysis of Colombia’s estimated agricultural productivity trends. This figure clearly shows that all techniques predict similar patterns of Colombia’s agricultural productivity during the period 1975-2013 (see Figure 1). Furthermore, this analysis indicates that these estimates exhibit practically the same turning points; the only difference is the magnitude of certain periods of growth or depletion (see Figure 1).

Figure 1 Colombian Agricultural Productivity Growth Predicted by Technique. 

Second, we calculated a correlation matrix using the annual predictions of Colombia’s agricultural productivity for each technique from 1975-2013. Overall, this correlation varied between 70% to 95%. The highest correlation is between the agricultural productivity predicted by assuming a CES production function and the Translog Cost approach (+94%), whereas the lowest correlation is between the agricultural productivity predicted by assuming a Cobb-Douglas production function and the Translog Cost approach (73%) (see Table 7). These results reaffirm that there is a high consistency across all estimates and techniques used in this study. Also, all techniques broadly predicted similar results for Colombia’s agricultural productivity over time.

6.2 Components of Colombia’s Agricultural Growth

Given the high consistency of these estimates for Colombia’s agricultural productivity, our subsequent analysis focused on examining the possible drivers of Colombia’s agricultural growth during the period 1979-2013: agricultural productivity growth or input accumulation growth. To this end, we considered the six periods previously defined, during which: i) Colombia’s agriculture exhibited similar economic conditions and ii) agricultural policy regimes did not drastically change (see Table 1).

Using the predictions of Colombia’s agricultural productivity by technique, we found that Colombia’s agricultural production growth exceeded 2% per year whenever agricultural productivity growth increased (e.g. in the late 1980s and in recent years; see Figures 2, 3 and 4). These estimates suggest that Colombia’s agriculture only grew by 1.8% per year from 1979 to 1983 due to an agricultural productivity growth close to 0%, largely explained by the negative impact of the Latin American Debt crisis on Colombian agriculture (^{Kalmanovitz & López, 2003}). From 1984-1989, the agricultural output value increased its average growth to 3.5% per year, the effect of higher agricultural productivity, which grew around 2.2-2.7% per year due to the following favorable conditions: i) agricultural policy focused on promoting private investment, adjusting the price system, raising farmer’s margins, limiting agricultural imports, etc.; ii) higher commodity prices; and iii) productivity innovations carried out by farmers to overcome the early 1980s crisis (^{Guterman, 2007}; IMF, 2015; ^{Kalmanovitz & López, 2003}; Reina et al., 2011). During the period 1990-1997, Colombia’s agriculture exhibited a slowdown and grew on average by 2.1% per year. Annual productivity grew on average only by 0.7-1.4%, seemingly due to the severe profitability crisis exhibited by Colombia’s agriculture during this period. From 1998-2002, Colombia’s agricultural output slightly reduced its growth to 1.9% per year because: i) agricultural productivity stagnated to 0.9-1.6% growth per year; and ii) farmers diminished their input accumulation, probably due to the macroeconomic crisis and worsening armed conflict during this period. Over 2003 to 2009, Colombia’s agriculture continued stagnating, growing at the pace of the 1990s due to a slower agricultural productivity growth (-0.4-1%) caused by: i) lack of political agreement on how resources should be allocated to support agriculture; ii) poor transportation infrastructure; and iii) lack of innovation and technological development to improve agricultural productivity (Reina et al., 2011). Finally, we found that Colombia’s agriculture raised its average growth to 2.4% per year from 2010-2013, due to an increased agricultural productivity growth of 0.9-1.4% per year. In other words, Colombia’s agricultural growth has been less sensitive to input accumulation and more sensitive to productivity trends, policy regimes and economic circumstances.

Figure 2 Agricultural Growth Components - Assuming a Cobb-Douglas Production Function. 

Figure 3 Agricultural Growth Components - Assuming a CES Production Function. 

Figure 4 Agricultural Growth Components - Using Translog Cost Techniques. 

6.3 Biased Technical Change

All estimates show that Colombia’s agriculture exhibited biased technical change during the period 1975-2013 (see Table 10). The CES results show that technical change was capital augmenting using data for the entirety of Colombia’s agriculture. The technical change exhibited by capital grew on average by 4.1% per year over this period, whereas the technical change exhibited by other inputs was not statistically significant (see Table 3). We also found that the technical change in crop production was capital augmenting. The difference across the technical change coefficients estimated for each input was tested because some were statistically significant. There is a statistically significant difference between the technical change exhibited by capital and labor as well as the technical change coefficients exhibited by fertilizer and labor (see Table 8). However, there is no statistical difference between the technical change coefficients found for capital and fertilizer. Likewise, we found that livestock production was animal feed augmenting. We also tested these differences across coefficients, and there is a statistically significant difference between the technical change exhibited by animal feed relative to the technical change exhibited by capital and labor (see Table 9). Also, we found that there is no statistically significant difference between the technical changes exhibited by capital and labor in livestock production.

Table 8 Test of Differences among Technical Change Estimates Exhibited by Inputs in Crop Production 

P - values in parentheses

*This is a symmetric matrix.

*** p<0.01, ** p<0.05, * p<0.1

Table 9 Test of Differences among Technical Change Estimates Exhibited by Inputs in Livestock Production 

P - values in parentheses

*This is a symmetric matrix.

*** p<0.01, ** p<0.05, * p<0.1

Translog Cost estimates reaffirm these results for crops, showing that crop production was capital saving. However, the cost model results suggest that livestock production was labor saving.³¹ The statistical difference across these technical change indices was not tested, because multicollinearity is a latent problem when a Trans-Log cost function is assumed (^{Christensen and Greene, 1976}). Thus, the standard errors for all parameters may be larger and this test would yield untrustworthy results. Consequently, this analysis only involved a comparison of the magnitudes across these indices.

In any case, the CES and Translog Cost results indicate that changes in the input efficiency of Colombia’s agriculture varied across agricultural activities during 1975-2013. Also, technical change tended to improve the marginal productivity of capital in crop production, and marginal productivity of animal feed and labor in livestock production more so than the marginal productivity exhibited by other inputs.

Table 10 Biased Technical Change by Agricultural Activity in Colombia