Chapter 4. Data and Methodology
4.2 Stochastic Frontier Analysis (SFA)
4.2.1 Stochastic Frontier Model
The functional form of a translog production model when the ML method is utilized in SFA can be expressed as:
ln(𝑌𝑖𝑡) = 𝛽0+ ∑ 𝛽1𝑙𝑛𝑋𝑖𝑡+1
2∑𝑛𝑖=1𝛽𝑖𝑖𝑙𝑛𝑋𝑖𝑡2 + ∑𝑛𝑖=1∑𝑛𝑗≠𝑖=1𝛽𝑖𝑗𝑙𝑛𝑋𝑖𝑙𝑛𝑋𝑗 + 𝑣𝑖𝑡− 𝑢𝑖𝑡
𝑛𝑖=1
(6)
where 𝑌𝑖𝑡 denotes output 𝑋𝑖𝑡 = inputs variables
4 Second-order flexible forms.
20
𝛽0, 𝛽𝑖, 𝛽𝑖𝑖= the unknown parameters to be estimated. 𝑣𝑖𝑡= ramdom variables associated with disturbance in production; 𝑢𝑖𝑡=country specific/social economic characteristics. Where the technical inefficiency effects can be specified and defined as:
𝑢𝑖𝑡 = 𝑑0+ 𝑑1𝑧𝑖𝑡+ 𝑑2𝑧𝑖𝑡+ ⋯ (7) where the z’s are social-economic variables which explain inefficiency and 𝑖𝑡= i-th country in the t-th period.
The ML method is similar to the OLS method, with the difference that OLS assumes that all the countries are efficient, and then the random error of the OLS (𝜀𝑖) is equal to the random variables of the ML, that is 𝜀𝑖𝑡 = 𝑣𝑖𝑡.
In the ML method, the error term has two components. According to Coelli et al.
(1998), the first component 𝑣𝑖𝑡 is assumed to be iid N(0,𝜎𝑣2) random error and independent of the second term (𝑢𝑖𝑡). The second term is considered as a non-negative random variable and assumed to be distributed iid N(𝜂𝑖𝑡,𝜎𝑢2) and truncated at zero. Kumbhakar and Lovell (2003) also incorporate a composed error structure with a two-sided symmetric term and a one-sided component. When the assumptions concerning to the distribution of error term are valid, the ML irrespective to the type of model estimated has many desired large sample (i.e asymptotic) properties, which is also the reason why ML is more popular in the analysis of productivity.
21
Because technological advances often affect the economic relationship among variables, especially with production functions, this model includes a time variable or time trend (𝑡𝑖) that accounts for non-neutral technical change, and a time square term to allow for a non-monotonic technical change; this is
ln(𝑌𝑖𝑡) = 𝛽0+ 𝛽𝑡𝑡 +1
2𝛽𝑡𝑡𝑡2 + ∑𝑛𝑖=1𝛽𝑡𝑖𝑡𝑙𝑛𝑋𝑖𝑡+ ∑𝑛𝑖=1𝛽𝑖𝑙𝑛𝑋𝑖𝑡+1
2∑𝑛𝑖=1𝛽𝑖𝑖𝑙𝑛𝑋𝑖𝑡2 +
∑𝑛𝑖=1∑𝑛𝑗=1𝛽𝑖𝑗𝑙𝑛𝑋𝑖𝑙𝑛𝑋𝑗+ 𝑣𝑖𝑡 − 𝑢𝑖𝑡 (8)
where 𝑡 is a time trend representing technical change;
𝛽: the unknown parameters to be estimated;
𝑣𝑖𝑡 : the random error, assumed to be i.i.d and have N(0, 𝜎𝑣2) distribution, independent of the 𝑢𝑖𝑡𝑠.
And 𝑢𝑖𝑡 the technical inefficiency effect.
The EC and TC of each country can be predicted using previous approaches. In this parametric case, the EC in equation (4) of DEA analysis can be compared directly with equation (9).
𝑇𝐸𝑖𝑡 = 𝐸(exp(−𝑢𝑖𝑡)/𝑒𝑖𝑡) (9)
Where 𝑒𝑖𝑡=𝑣𝑖𝑡− 𝑢𝑖𝑡 can be used to calculate the component of efficiency change. By observing that 𝑑𝑜𝑡(𝑥𝑖𝑡, 𝑞𝑖𝑡)=𝑇𝐸𝑖𝑡 and 𝑑𝑜𝑠(𝑥𝑖𝑠, 𝑞𝑖𝑠)=𝑇𝐸𝑖𝑠 we calculate the efficiency change by dividing the TE in period t by the TE in period s.
We can also define the TE as the ratio resulting between observed production and the production output from the frontier production function.
22 𝑇𝐸𝑖𝑡 = 𝑌𝑖𝑡
exp (𝑋′𝑖𝑡𝛽+𝑣𝑖𝑡) =exp (𝑋′𝑖𝑡𝛽+𝑣𝑖𝑡+𝑢𝑖𝑡)
exp (𝑋′𝑖𝑡𝛽+𝑣𝑖𝑡) = exp(−𝑢𝑖𝑡) (9a)
In the same way, we can estimate TC using the parameter of our ML model. The TC index between periods for each of the countries can be calculated using the following equation:
𝑇𝑒𝑐ℎ𝑛𝑖𝑐𝑎𝑙 𝐶ℎ𝑎𝑛𝑔𝑒 = exp (1
2[𝜕𝑙𝑛𝑞𝑖𝑠
𝜕𝑠 +𝜕𝑙𝑛𝑞𝑖𝑡
𝜕𝑡 ]) (10)
This is, TC is equal to the exponential of the arithmetic mean of the log derivatives of the production function with respect to time using the data for each country in period s and t.
Considering equation (7), the derivative of output respect time can be rewritten as:
𝑇𝑒𝑐ℎ𝑛𝑖𝑐𝑎𝑙 𝐶ℎ𝑎𝑛𝑔𝑒 = 𝑒𝑥𝑝 {1
2[(∑𝑛𝑖=1𝛽𝑡𝑙𝑛𝑋𝑖𝑡+ 𝛽𝑡𝑡∗ 𝑡 + 𝛽𝑡)𝑝𝑒𝑟𝑖𝑜𝑑 𝑠 + (∑𝑛𝑖=1𝛽𝑡𝑙𝑛𝑋𝑖𝑡+ 𝛽𝑡𝑡∗ 𝑡 + 𝛽𝑡)𝑝𝑒𝑟𝑖𝑜𝑑 𝑡]} (10a)
in the i-th country( 𝑖 = 1,2,3, . . ,6) in the t-th period (𝑡 = 1,2,3, . . ,36)
23 4.2.2 Empirical Stochastic Frontier Model
The functional form of translog production model in SFA used in this study is defined as follows:
ln(𝑌𝑖𝑡) = 𝛽0+ 𝛽1ln (𝐿𝑎𝑏𝑜𝑟𝑖𝑡) + 𝛽2ln (𝑀𝑎𝑐ℎ𝑖𝑛𝑎𝑟𝑦𝑖𝑡) + 𝛽3ln (𝐴𝑟𝑒𝑎𝑖𝑡) + 𝛽4ln (𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟𝑖𝑡) + 𝛽5 (𝑇𝑖𝑚𝑒𝑖𝑡) +1
2[𝛽11ln (𝐿𝑎𝑏𝑜𝑟𝑖𝑡2) + 𝛽22ln (𝑀𝑎𝑐ℎ𝑖𝑛𝑎𝑟𝑦𝑖𝑡2) + 𝛽33ln (𝐴𝑟𝑒𝑎𝑖𝑡2) + 𝛽44ln (𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟𝑖𝑡2) + 𝛽55 (𝑇𝑖𝑚𝑒𝑖𝑡2)] + 𝛽12ln (𝐿𝑎𝑏𝑜𝑟𝑖𝑡)*
ln(𝑀𝑎𝑐ℎ𝑖𝑛𝑎𝑟𝑦𝑖𝑡) + 𝛽13ln (𝐿𝑎𝑏𝑜𝑟𝑖𝑡)* ln(𝐴𝑟𝑒𝑎𝑖𝑡) + 𝛽14ln (𝐿𝑎𝑏𝑜𝑟𝑖𝑡)*
ln(𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟𝑖𝑡) + 𝛽15ln (𝐿𝑎𝑏𝑜𝑟𝑖𝑡)* 𝑇𝑖𝑚𝑒𝑖𝑡 + 𝛽23ln (𝑀𝑎𝑐ℎ𝑖𝑛𝑎𝑟𝑦𝑖𝑡)* ln(𝐴𝑟𝑒𝑎𝑖𝑡) + 𝛽24ln (𝑀𝑎𝑐ℎ𝑖𝑛𝑎𝑟𝑦𝑖𝑡)* ln(𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟) + 𝛽25ln (𝑀𝑎𝑐ℎ𝑖𝑛𝑎𝑟𝑦𝑖𝑡)* 𝑇𝑖𝑚𝑒 + 𝛽34ln (𝐴𝑟𝑒𝑎𝑖𝑡)*
ln(𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟𝑖𝑡) + 𝛽35ln (𝐴𝑟𝑒𝑎𝑖𝑡)* 𝑇𝑖𝑚𝑒𝑖𝑡 + 𝛽45ln (𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟𝑖𝑡)* 𝑇𝑖𝑚𝑒𝑖𝑡 + 𝑣𝑖𝑡−𝑢𝑖𝑡 , 𝑖 = 1,2,3, . . ,6 , 𝑡 = 1,2,3, . . ,36 (11)
where ln(𝑌𝑖𝑡) denotes the log of primary crops (1000 mt) 5 in country 𝑖 in year 𝑡.
𝛽0, 𝛽𝑖, 𝛽𝑖𝑖: the unknown parameter to be estimated.
The inputs include in the model, namely,
ln(𝐿𝑎𝑏𝑜𝑢𝑟) : log of total employment in agriculture (1000 persons).
ln(𝑀𝑎𝑐ℎ𝑖𝑛𝑎𝑟𝑦) : log of total machinery used in agriculture (1000 units).
ln(𝐿𝑎𝑛𝑑) : log of total land for agriculture (1000 ha) 6 .
ln(𝐹𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟) : log of total fertilizer used in agriculture (1000 mt) .
𝑣𝑖𝑡= random variables associated with disturbance in production, and 𝑢𝑖𝑡=country specific/social economic characteristics.
𝑢𝑖𝑡 can be specified and defined as:
𝑢𝑖𝑡 = 𝛿0+ 𝛿1𝑐𝑜2𝑖𝑡 + 𝛿2ℎ𝑐𝑖𝑡+ 𝛿3𝑖𝑟𝑟𝑖𝑡+ 𝛿4𝑟𝑝𝑖𝑡+ 𝛿𝑙𝑒𝑖𝑡+ 𝛿6ℎℎ𝑖𝑖𝑡 (12)
5 mt stands for metric tons.
6 ha stands for hectares.
24 where
𝑐𝑜2𝑖𝑡= represent the emission of Co2 in agriculture in country 𝑖 in year 𝑡.
ℎ𝑐𝑖𝑡= human capital index in country 𝑖 in year 𝑡.
𝑖𝑟𝑟𝑖𝑡= irrigation area in country 𝑖 in year 𝑡.
𝑟𝑝𝑖𝑡= rural population in country 𝑖 in year 𝑡.
𝑙𝑒𝑖𝑡= life expectancy in country 𝑖 in year 𝑡.
ℎℎ𝑖𝑖𝑡= Herfindahl-Hirschman index (HHI) in country 𝑖 in year 𝑡.
4.2.3 Elasticities
Based on the coefficient estimates of MLE, the estimated frontier elasticity of each input can be calculated by using equation (13).
The elasticity is expressed as:
𝜀 =
𝜕ln𝑓(x,t)𝜕ln𝑥𝑚
= 𝛽̂
𝑚+ ∑
𝑛≠𝑚𝛽̂
𝑚𝑛ln𝑥
𝑛+ 𝛽̂
𝑚𝑛ln𝑥
𝑚+ 𝛽̂
𝑡𝑚𝑡
(13)4.3 Data Sources and Variables
To investigate the total factor productivity and its two driving engines: efficiency change and technical change from 1979 to 2014 in Central America, this study uses data from a variety of sources: The Food and Agricultural Organization (FAO), International Labor Organization (ILO), International Fertilizer Association (IFA), the United Nations Economic Commission for Latin America and the Caribbean (ECLAC), World Bank (WB), Penn World Table (PWT), country reports, and author estimations.
25 Country Coverage
This study intends to focus on a homogeneous set of countries located in C.A. These countries are somewhat similar in geographic, climatic, and political characteristics. The countries included in this study are: Guatemala, Honduras, El Salvador, Nicaragua, Costa Rica, and Panamá. Belize was omitted from this study due to the limitation of information.
Time Period
This study exam the TFP for the period 1979-2014. Since information about agriculture prior to 1979 is insufficient in C.A.
4.3.1 Output
Primary Crops
Primary crops are according to (FAO, 2014):
“The crops that come from the land without having any indirect processing, cleaning or quality change. These variables are divided into temporary crop which are both sown and harvested during the same agricultural year (sometimes more than once), and permanent crops which are sown or planted once and not replanted after each annual harvest”. (See list of primary crops in table B in appendix)
26
Guatemala 20003690.6 40% 20003.4 8975.2 7658.4 39039.4 Honduras 7209948.9 15% 7542.5 2395.0 4985.1 12229.1 El Salvador 5962254 12% 5962.3 1374.9 3690.3 8920.8
Nicaragua 5107003.6 10% 5108.7 1723.5 3145.6 9571.7 Costa Rica 8161927.3 16% 8161.9 2648.0 4574.5 12424.8
Panamá 3366367.1 7% 3366.4 332.8 2805.1 4290.9 Source: Food and Agriculture Organization
*Note: weight= production of primary crops in each country
/
total primary crops.4.3.2 Inputs
This analysis included four inputs: labor, machinery, land, and fertilizer. Details information of these inputs is presented in the following.
Land
The variable land is measured as agricultural area. This variable account for arable land, permanents crops, and pastures. However, in this study, the land under permanent meadow and pasture which is land used permanently for a period of five years or more, is not included.
According to the Food and Agriculture Organization Statistic (FAOSTAT, 2014) the definition of arable land and permanent crops are as the following:
“Arable land is defined as the land under temporary crops (multiple-cropped areas are counted only once) which is all land used for crops, not abandoned land resulting from shifting cultivation, and with a less than one-year growing cycle and which must be newly sown or planted for further production after the harvest.
27
Arable land consists of land temporarily fallow (less than five years), temporary meadows for mowing or pasture, and land under market and kitchen gardens”.7
“Permanent crops is defined as the land cultivated with long-term crops which do not have to be replanted for several years (such as coffee), land under trees and shrubs producing flowers (such as roses), and nurseries (except those for forest trees, which should be classified under “forest”).”
Table 4.2 Summary of Land Use for Agriculture, 1979-2014.
Country *Weight Mean Std. Dev. Min Max
Guatemala 27% 1975.4 224.2 1726 2564
Honduras 23% 1674.9 201.7 1427 2015
El Salvador 11% 851.4 71.0 727 974
Nicaragua 24% 1755.3 338.8 1240 2320
Costa Rica 7% 512.0 17.7 490 547
Panamá 9% 665.4 60.5 552 757.4
Source: Food and Agriculture Organization
*Note: weight=land used in agriculture in each country
/
total land used agricultural.Machinery
According to (FAO, 2014) variable Machinery refers to:
“Number of agricultural tractors in use, which commonly refers to wheel and crawler or track-laying type tractors (excluding garden tractors) employed in agriculture.”
7 Data for “arable land” are not meant to indicate the amount of land that is potentially cultivable.
28
Source: Food and Agriculture Organization
*Note: weight=machinery used in agriculture in each country
/
total machinery used agriculturalLabor
According to International Labor Organization (ILO, 2014) this variable considers the number of labor specifically working in agriculture. The indicator provides information on persons in working age (15-64) who, during a specified short period, were classified in the following categories: a) paid employment, and b) self-employment.
The economic activity is classified according to the main activity of the establishment in which a person worked during a specific period. It does not depend on the specific duties or functions implied by the job but rather depends on the characteristics of the economic unit in which this person works.
Table 4.4 Summary of Labor in Agriculture, 1979-2014.
*Note: weight=agricultural labor in each country
/
total agricultural labor29 Fertilizer
According to International Fertilizer Organization (IFO), this variable considers the amount of fertilizer used in agriculture by considering the three most important plants nutrients.
These nutrients are nitrogen (N), phosphate (P205), and potash (K20). In C.A. the use of fertilizer is increasing, especially in the last decade. The use of fertilizer is not limited to these three components alone, but these are the most commonly used.
Table 4.5 Summary of Fertilizer in Agriculture, 1979-2014.
Country *Weight Mean Sts. Dev. Min Max
Guatemala 31% 169.2 62.3 68.1 319.5
Honduras 18% 97.9 77.4 15 291.8
El Salvador 13% 72.0 12.1 53.1 97
Nicaragua 8% 43.1 15.8 17.7 76.6
Costa Rica 23% 126.4 36.2 69.9 199
Panamá 6% 33.2 8.0 23.1 60.1
Source: International Fertilizer Organization
*Note: weight=fertilizer used in agriculture in each country
/
total fertilizer used in agricultural.In Figure 4.3 the output and input growth rate are presented. In general, the decade of 1980 was characterized by slow growth and a lot of ups and downs. In addition, we have included in appendix a graph for each input and output growth over the whole period.
30
Source: prepared by author
Figure 4.3 Output and Input growth (1979-2014)
In the case of the production of primary products, it shows a steady growth over the years. However, we can identify the slow growth of this variable during the first years of the study and between 1998 and 2002. This stagnation is explained by the sudden arrival of the hurricane Mitch in 1998 which was one of the worst storms in the last decades and severely destroyed much of the productive infrastructure of the region.
In terms of employment, abrupt changes were experienced in the results of the war in C.A. However, a steady employment growth can be seen after 1990, although some countries such as Panama experienced a slowdown in agricultural employment.
In the case of machinery and fertilizer, both variables presented steady growth, although the fertilizer presented two important breaks in 2002 and 2009. The sudden growth during these two years is attributed to efforts of some governments for compensating the
-60.00 -40.00 -20.00 0.00 20.00 40.00 60.00 80.00 100.00
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
Percentage
Output and Inputs Growth (1979-2014)
Employment Machinary Land Fertilizer Primary Crops
31
effects of climate change that were reflected in the greater prolongation and impact of el niño and la niña phenomena in the region.
Finally in the case of land for agriculture. This variable maintained a steady tendency to growth, however after 2003 this tendency start to decrease. The decreasing use of land for agriculture might be attributed to the expansion of the urban area but also to the abandonment of agricultural activities.
To extend the analysis, we have included in appendix Table C. containing the growth rates of productivity ratios for each of the factors of production used in this study. Taking into account the identity about partial productivities of Hayami and Ruttan (1985)8, and productivity ratios of machinery and fertilizer.
4.3.3 Exogenous Variables
In this study, we have included 6 exogenous variables that reflect differences in the quality of the inputs used in the production model but also variables outside the production that could explain qualitative differences among the countries of the region. The exogenous variables used in this study reflect variances in the quality of inputs used, infrastructure, environmental quality and social development of countries.
8 𝑃𝑟𝑖𝑚𝑎𝑟𝑦𝐶𝑟𝑜𝑝𝑠/𝐿𝑎𝑏𝑜𝑢𝑟 = (𝐴𝑟𝑒𝑎/𝐿𝑎𝑏𝑜𝑢𝑟)(𝑃𝑟𝑖𝑚𝑎𝑟𝑦𝐶𝑟𝑜𝑝𝑠/𝐿𝑎𝑛𝑑)
32 Carbon Dioxide (CO2)
According to FAO (2014), Carbon Dioxide (CO2) is defined as follows:
“Total emissions produced in the different agricultural emissions sub-domains, such as manure management, manure applied to soils or left on pastures, enteric fermentation, rice cultivation, synthetic fertilizers, cultivation of organic soils, crop residues, burning of crop residues, burning of savanna, and energy use.
Carbon Dioxide provides a picture of agricultural contribution to the total amount of greenhouse gas (GHG) emissions. GHG emissions from agriculture consist of two non-CO2 gases, namely methane (CH4) and nitrous oxide (N2O), produced by crop and livestock production and by management activities”. The unit of measure of this variable is gigagrams.
Table 4.6 Summary of Co2 in agriculture, 1979-2014.
Country *Weight Mean Std. Dev. Min Max Guatemala 22% 5877.8 1358.1 3711.98 8457.79
Honduras 19% 4876.4 597.7 3814.34 5954.95 El Salvador 10% 2724.3 258.2 2166.48 3294.49 Nicaragua 23% 5974.4 1186.4 3967.14 7759.27 Costa Rica 14% 3789.4 634.5 2765.79 4750.31 Panamá 12% 3029.0 249.6 2685.42 3585.04
Source: Food and Agriculture Organization
*Note: weight= emission of Co2 in agriculture in each country
/
total Co2 emissionsHuman Capital (HC)
We use the human capital index of Penn World Tables (PWT), which follow a standard approach in the literature, based on the construction of average years of schooling
33
from Barro and Lee (2013), and an assumed rate of return to education based on the estimations of Mincer equation around the world (Psacharopoulos, 1994).
Table 4.7 Summary of Human Capital, 1979-2014.
This variable is defined as the area equipped with irrigation infrastructure to provide water to the crops. This variable includes areas equipped for partial and full spate irrigation areas,control irrigation, and equipped wetland. The unit of measure is 1000 ha (FAO, 2014).
Table 4.8 Summary of Area equipped for irrigation, 1979-2014.
Source: Food and Agriculture Organization Rural Population (RP)
According to the World Bank (WB), the rural population refers to people living in rural areas. It is calculated as the difference between total population and urban population.
34
*Note: rural population share=rural population in each country
/
total rural populationLife Expectancy (LE)
Life expectancy at birth according to the World Bank (2014) refers to:
“Number of years that a newborn infant would live considering that the patterns of mortality throughout its lifetime were to remain the same”.
35 Herfindahl-Hirschman Index (HHI)
The index is named after economists Orris C. Herfindahl and Albert O. Hirschman and is usually used to measure the market concentration. In this study, we use this index to measure the concentration of primary crops in CA.
𝐻𝐻𝐼 = ∑ 𝑠𝑖2
𝑁
𝑖=1
Where 𝑠𝑖 refers to the share of primary crop of country 𝑖 and N is the total number of countries.
An HHI below 100 indicates a very high diversification in production of primary crops.
An HHI below 1,500 indicates a balanced diversification in production of primary crops.
An HHI between 1,500 to 2,500 indicates a moderate concentration in production of primary crops.
An HHI above 2,500 indicates a high concentration in production of primary crops.
We assumed with this approximation that countries with a higher concentration of products tend to be more specialized in the production of this one, thus increasing the
Source: calculated by the author.
36
Chapter 5. Results and Discussion
This chapter presents the results of the DEA, and the SFA used to calculate the production frontier and the TFP components.
5.1 Data Envelopment Analysis (DEA) 5.1.1 TFP and its components
By using the Malmquist productivity index from Data Envelopment Analysis in C.A. Table 5.1 shows, the average annual TFP change, and its components. Although the EC is negative across the entire period, the TFP shows a positive growth mainly driven by TC.
Table 5.1 Annual mean of TFP change and its components, 1980-2014 (DEA).
Year* Efficiency
*Note: the year 1980 refers to the change between 1979 and 1980, and so on.
37
The results in Table 5.2 show the average EC, TC, and TFP change for each country of C.A between 1979 and 2014. In terms of individual countries, Costa Rica has the highest TFP change, which is consistent with the result of (Coelli, J. and Rao, D. 2005). Panamá has the lowest total productivity. Costa Rica shows a 1.6% average growth in TFP which is entirely due to TC.9
Table 5.2 Summary description of TFP change and its components, 1979-2014 (DEA) Country Description Efficiency
Change
Std. Deviation 0.0000 0.2058 0.2058 Honduras
Mean 0.9883 1.0187 1.0066
Max 2.2080 10.2290 10.2290
Min 0.6120 0.3980 0.3980
Std. Deviation 0.2549 1.5776 1.5980 El Salvador
Mean 1.0000 1.0114 1.0114
Max 1.3560 1.7550 1.4490
Min 0.7090 0.6030 0.6030
Std. Deviation 0.1425 0.2002 0.1681 Nicaragua
Average 0.9986 1.0092 1.0076
Max 1.5360 1.3250 1.4040
Min 0.6670 0.6880 0.7050
Std. Deviation 0.1773 0.1599 0.1872 Costa Rica
Mean 1.0000 1.0159 1.0159
Max 1.0000 1.1970 1.1970
Min 1.0000 0.8920 0.8920
Std. Deviation 0.0000 0.0698 0.0698 Panamá
Mean 0.9898 0.9906 0.9806
Max 1.4430 1.4060 1.3940
Min 0.6280 0.8100 0.6360
Std. Deviation 0.1666 0.1130 0.1500 CA
Mean 0.9961 1.0092 1.0053
Max 2.2080 10.2290 10.2290
Min 0.6120 0.3980 0.3980
Std. Deviation 0.1534 0.6575 0.6672
9 (1.0159-1)*100=1.59~1.60%
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Panama, meanwhile, is the only country that shows a negative change of TFP (-1.95%
average), which is due to the negative growth of EC (-1.02%) and the negative growth of TC (-0.94%). These results revealed that efficiency level in C.A. was less than the optimal level.
The TFP growth in the region was around 0.53%. The main source of this growth was TC at 0.92%.
Analysis by period in Table 5.3 reveals that the overall TFP for the region was driven mostly by TC rather than EC.
Table 5.3 TFP change and its components by period.
Year Efficiency Change
Technical Change
TFP Change Period 1980-1989 0.996 1.006 1.002 Period 1990-1999 0.985 1.012 0.997 Period 2000-2009 0.999 1.033 1.032 Period 2010-2014 1.012 0.965 0.976 Period 1990-2014 0.996 1.011 1.007 Period 1980-2014 0.996 1.009 1.005
Because the decade of 1980’s was particularly unstable in the region due to political and civil war, we generated the results of TFP considering only the years after 1989 (Table 5.4).
The results show that TC remains the primary source of TFP for the region despite the years with more instability were omitted. In the case of EC, the results indicate a decline of 0.43%, which was consistent with the analysis including the decade of the 1980's.
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Table 5.4 Summary description of TFP change and its components, 1990-2014 (DEA) Country Description Efficiency
Change
Std. Deviation 0.0000 0.2388 0.2388
Honduras
Mean 0.9837 0.9965 0.9800
Max 2.2080 1.6020 2.3180
Min 0.6120 0.5530 0.5270
Std. Deviation 0.3032 0.1912 0.3706
El Salvador
Mean 1.0000 1.0190 1.0190
Max 1.3560 1.7550 1.2610
Min 0.7090 0.6030 0.6660
Std. Deviation 0.1568 0.1971 0.1403
Nicaragua
Mean 1.0073 1.0089 1.0162
Max 1.4340 1.3250 1.3760
Min 0.7020 0.6880 0.7050
Std. Deviation 0.1495 0.1813 0.1902
Costa Rica
Mean 1.0000 1.0252 1.0252
Max 1.0000 1.1970 1.1970
Min 1.0000 0.8920 0.8920
Std. Deviation 0.0000 0.0770 0.0770
Panamá
Mean 0.9858 1.0069 0.9928
Max 1.4430 1.4060 1.3940
Min 0.6280 0.8370 0.6360
Std. Deviation 0.1981 0.1150 0.1635
Central America
Mean 0.9961 1.0106 1.0067
Max 2.2080 1.9430 2.3180
Min 0.6120 0.4270 0.4270
Std. Deviation 0.1695 0.1726 0.2137
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Table 5.5 Summary description of technical efficiency, 1979-2014 (DEA) Technical
Efficiency Guatemala Honduras
El
In addition to the previous results, Table 5.5 shows the value of technical efficiency (TE) reached by each country. Along the overall period, the TE was 0.912, with a minimum value of 0.396 and a maximum value of 1 represented by the countries on the frontier. A lower value of efficiency means that countries are less efficient and higher values means that countries are more efficient or closer to the frontier. The mean value of 0.912 indicates that countries can reduce the use or consumption of all inputs by 0.88% without reducing their primary crops.
Figure 5.1 Cumulative TFP and its components (DEA) 0.60
1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013
Cummulative Growth
Year
Total factor productivity, efficiency change and technical change in CA, 1980-2014 (DEA)
Tfpch
Effch
Techch
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In Figure 5.1 it is easy to identify that TC (or frontier shift) is the major source of TFP growth for C.A. The cumulative TFP at the end of the period were 1.20, while EC and TC were 0.87 and 1.38 respectively. A detailed observation shows that efficiency change (or catch –up) was also an important source of TFP growth for several years. In addition, in Table 5.6 we analyze the TFP and its components to find if there were any associate tendency among decades. With respect to productivity and efficiency, no association among countries or decades was found. However, from the analysis of EC, we can see that the frontier is defined for Guatemala and Costa Rica throughout the period. Although the average EC for El Salvador is almost 1, this country not always considered to be on the production frontier.
Table 5.6 Summary description of TFP change and its components by decade, 1980-2014 Description/Country Guatemala Honduras El
Salvador
The years after 1990 are considered the years of relative stabilization and commercial opening.
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5.1.2 Country Analysis of TFP change and its components
In this subsection, we investigate the TFP, TC, and EC for each individual country in C.A by using DEA.
Guatemala’s TFP change and components
Guatemala is considered one of the countries which was located in the production frontier along the period of study. This implies that the value of the EC is equal to 1 and so that the change of TFP is due to TC. This country, like other countries in C.A., experienced important economic and social changes as a result of internal conflicts between the government and insurgent groups. The most vulnerable groups were the indigenous people, who were predominantly working or living in the agricultural sector. Normally speaking, it
Guatemala is considered one of the countries which was located in the production frontier along the period of study. This implies that the value of the EC is equal to 1 and so that the change of TFP is due to TC. This country, like other countries in C.A., experienced important economic and social changes as a result of internal conflicts between the government and insurgent groups. The most vulnerable groups were the indigenous people, who were predominantly working or living in the agricultural sector. Normally speaking, it