Technical Inefficiency Effects in Agriculture — A Meta-Regression

A number of studies have examined the effect of study characteristics on mean technical efficiency as the dependent variable. This article departs from these earlier studies by using second-stage inefficiency covariates as key exploratory variables and study characteristics as control variables in a meta-regression. Unlike the vote count method of quantitative review, the parameters of the key variables have desirable properties and enable statistical inferences to be drawn. Additionally, the dependent variable employed is mean technical inefficiency. This is demonstrated using data on technical inefficiency of primary studies in Ghanaian agriculture, fitted to fractional regression models. The appropriate functional form of the fractional regression model is discussed with policy implications.


Background
Technical efficiency (TE) refers to how well a system or unit of production performs in the use of resources to produce outputs, given the available technology relative to a standard (frontier) production function (Fried, 2008).This is the ability of a decision-making unit (farm, in this case) to produce maximum output given a set of inputs (Farrell, 1957).The first step in improving efficiency is measurement.Measured relative to the production frontier, TE may be computed as the fraction of the observed output to the frontier output.In this way, the gap between the observed output and the frontier output becomes technical inefficiency.That is; technical inefficiency equals one less the TE measure.

Problem Statement
The traditional challenge in agriculture, which continues to remain a challenge in some parts of the developing world, has been to improve efficiency (Raj, 2011).The need to reduce inefficiency has motivated studies that estimated technical inefficiency and investigated the role of covariates (technical inefficiency effects) on estimated inefficiencies especially in agriculture.These covariates are usually farm and farmer characteristics such as age of farmer, sex, size of household, access to agricultural extension services, access to credit, access to road and other communication infrastructure among others.However, in meta-regressions of technical efficiency studies in agriculture, factors that account for variations in the mean technical efficiencies generated from primary studies did not include any of these principal determinants.For example Thiam et al. (2001), Bravo-Ureta et al. (2009), Ogundari and Brummer (2011), Ogundari (2014), Iliyasu et al. (2014) and Djokoto (2015) explored methodological, products and spatial effects.Bravo-Ureta et al. (2009) in addition to the above, examined the role of national income on mean technical efficiency.The question this paper seeks to address is; what is the effect of technical inefficiency effects on mean technical inefficiency?To address this question, a meta-regression is performed using primary studies on technical inefficiency studies on Ghana.

Theoretical Review
Among other reasons, the availability of several studies necessities meta-analysis which involves the combination of results of several homogenous studies into a unified analysis that provides an overall estimate of interest for further discussion (Sterne, 2009).Nelson and Kennedy (2009) identified six objectives of meta-analysis.The first objective is to provide a "combined" estimate of the effect-size.The second is to explain what determines the study-to-study variation or heterogeneity in effect-sizes.Third, to provide within-sample predicted values of the dependent variable under a particular set of conditions.Fourth, is to make an out of-sample prediction.Fifth, to summarise results of a single empirical study that has produced multiple estimates.Finally, study publication bias.
A general model for carrying out meta-regression is to relate a key (dependent) variable to some characteristics that are believed to explain that variable (Alston et al., 2000).It is of crucial importance that, this dependent variable is measuring the same concept across primary studies (Nelson & Kennedy, 2009).The study characteristics which include study designs, model specifications and econometric techniques, serve as moderator variables in the regression.Other covariates include valuation method, sample size, place and date of publication, data collection or data coverage (Nelson & Kennedy, 2009).In this article, unlike others, the moderators go into the meta-regression model as control variables whilst technical inefficiency covariates are key explanatory variables.

Thiam
Increased number of variables in the technical inefficiency estimation model has implications for multicollinearity (Griffin et al., 1987).These may result in increased standard errors and invalidation of hypothesis tests.Since TE is a residual value; the influence of this theoretical position for technical efficiency is unclear.Thiam et al. (2001) did not find any significant effect of the number of variables on MTE.However, Bravo-Ureta et al. (2007), Iliyasu et al. (2014) and Ogundari and Brümmer (2011) found that, high number of terms in TE estimation model induced high TE estimates.
Since large sample size produces more efficient parameter estimates generally, the effect of sample size on MTE estimates may be important.Although Iliyasu et al. (2014) andThiam et al. (2001) have shown that sample size did not distinguish MTEs; Ogundari and Brümmer (2011) and Moreira López and Bravo-Ureta (2009) however, found that, MTE increased with sample size.Ogundari (2014) showed that TE estimation relations of other functional forms (distance functions) and without functional forms showed higher MTE than those with functional forms such as translog and Cobb-Douglas.However, Thiam et al. (2001), Bravo-Ureta et al. (2007) and Illyasu et al. (2014) suggested that MTE estimates obtained from translog production functions tended to record higher MTEs than those from Cobb-Douglas production functions.Ogundari (2014) showed that, for African agriculture, MTEs from parametric estimations such as SFA (Stochastic Frontier Analysis) were higher than non-parametric MTEs.However, Thiam et al. (2001) did not find any evidence for this, implying that the statistical noise embedded in TE estimates of non-parametric models in the studies investigated may have been small.Geographical region may influence MTEs because agricultural output is highly dependent on environmental factors.Taking account of spatial coverage of studies is an attempt to account for climatic and other environmental variations associated with TE studies.Moreira López and Bravo-Ureta (2009) found that, studies conducted in North America and India posted higher MTE than the reference category.On the contrary, Eastern European studies showed decreases in MTE despite the greater attention Europe attracted from frontier researchers (Bravo-Ureta et al., 2007;Moreira Lopez & Bravo-Ureta, 2009).In Africa, countries in Eastern and Central parts showed lower MTEs than those in West Africa (Ogundari, 2014).Studies that focus on southern parts of Nigeria showed higher MTE than those otherwise (Ogundari & Brümmer, 2011).
Different products may have different yield capabilities.Thus, differences in their ability to attain their maximum potential would also exist.Empirically, conclusions have been made on products and product groups.
Studies on production (crops and livestock) showed higher average MTEs than others.Contrasting crops and animals in developing countries, animal production enterprises were more technically efficient than crops enterprises (Bravo-Ureta et al., 2007).Within crops subsector, cash crop production was more efficient than non-cash crop production in Nigeria (Ogundari & Brümmer, 2011).Turning to the African continent as a whole, there was no discernible difference among food crops, cash crops and non-crops enterprises (fish, livestock, poultry etc.).However, grain crops (rice, maize, wheat sorghum etc.) MTEs were significantly lower than MTEs of the other groups (Ogundari, 2014).Ogundari (2014) showed that studies published in peer reviewed destinations showed higher MTEs than those in non-peer reviewed destinations (conference proceedings, working papers, thesis etc.).The statistical significance of the coefficient showed that MTEs from studies in peer reviewed sources differed from those in non-peer reviewed sources.However, Djokoto (2015) reported statistical indifference between the MTE of peer-reviewed publications and non-peer-reviewed publications (Note 1).

Relevance and Organisation of Study
Unlike Thiam et al. ( 2001), Bravo-Ureta et al. ( 2009), Ogundari and Brummer (2011), Ogundari (2014), Iliyasu et al. (2014) and Djokoto (2015) who examined the effect of study characteristics on mean technical efficiency as the dependent variable, this article departs from these earlier studies by using second-stage inefficiency covariates as key explanatory variables (Note 2) and study characteristics as control variables in a meta-regression.Unlike the vote count method of quantitative review (reference), the parameters of the key variables have desirable properties and enable statistical inferences to be drawn.Also, earlier studies used mean technical efficiency as dependent variable, in this article, the dependent variable in the meta-regression is mean technical inefficiency.
The rest of the article is sectioned into three.The collection of studies, extraction of data and analytical tools are described in section two.Section three presents and discusses the results.Section four concludes the article.

Data
Databases and publishers websites such as AgEconsearch, Google scholar, Wiley online library, EmeraldInsight, EBSCOhost, oupjournals online among others were searched for literature.Relevant studies on technical inefficiency in agriculture obtained on Ghana numbered 34 yielding 49 observations up until June 2015 (Table 1).Though studies from non-peer reviewed studies may not be as reliable as peer reviewed ones, these have however been included for some reasons.First, to increase sample size of the analysis.Second, to test for the difference in MTEs from peer reviewed and non-peer reviewed sources in a single country case and third, to control somewhat for possible publication bias.The mean technical inefficiency (MTI) of the studies was extracted.The information on the statistical significance or otherwise of technical inefficiency effects was captured.These were identified and recognised as statistically significant positive or negative; or statistically insignificant.For statistically insignificant coefficients; these were not separated into positive and negative.
Other study characteristics such as year of data collection, numbers of inputs in estimation model and number of observations were extracted.In the case of Data Envelopment Analysis (DEA) studies, the output-oriented MTI was used in order to conform to those of MTIs from SFA and distance function estimations.Others included products of agriculture, region of study and type of data as well as parameterisation.

Model
The meta-regression model is specified as in Equation 1.
Where, SIGNEG j refers to study that reported statistically significant negative coefficients for the jth technical inefficiency effects and captured as 1 and 0 otherwise.The sign of this dummy variable is expected to be negative since the coefficients in the primary studies were negatively signed.SIGPOS j captured studies that reported statistically significant positive coefficients of the jth technical inefficiency effects and recognised as 1 and 0 otherwise.The studies that reported the statistically insignificant coefficient for the jth technical inefficiency effect is recognised as 0. The coefficients captured as SIGPOS j in this article were positively signed in the primary studies.Therefore, a priori the sign for this dummy variable is expected to be positively signed.
The letter i represent observations in the metadata set.
A number of variables known to influence technical inefficiency were included in the model as control variables.Stochastic frontier approach (SFA) = 1 and 0 otherwise; data envelopment analysis (DEA) = 1 and 0 otherwise.The reference variable is distance functions (DF).Although distance functions are similar to SFA, they are distinguished here because they capture multiple outputs whilst the SFA uses single out (or aggregated multiple output).Year of data collection (DATAY) was represented as four digit year (YYYY).The number of production inputs included in the estimation relation was captured as VAR.This was not necessarily equal to the number of terms in the production function.Thus a translog function may not necessarily have more variables than a Cobb-Douglas function.SSIZE captured the number of observations or sample size of the case studies.Studies that used Cobb-Douglas (CD) production functions were represented as 1 and 0 otherwise; translog (TL).The translog functional form used by Ofori-Bah and Asafu-Adjaye (2011) in estimating their distance function is not different from the usual translog function.Hence this was not distinguished.
Ghana was segmented into three; coastal (Central, Greater Accra, Volta and Western Regions) (COSTL), middle (Ashanti, Eastern and Brong-Ahafo Regions) (MID) and north (Northern, Upper East and Upper West Regions) (NORTH).Five observations cut across the coastal and middle sections; therefore, these were grouped together with whole country studies as reference.Following previous studies, products were categorised as crops (CROPS), fish (FISH), and combination of crops and animals.All these were represented as 1 except crops and animal combinations which was the reference product and captured as 0. PR equals 1 if the study is peer reviewed and 0 if the study was not peer reviewed.This variable is used in place of a formal test for publication bias because many studies did not report standard deviations of the technical inefficiency estimates.

Estimation Procedure
Since technical inefficiency is generated as a fraction, fractional regression is employed to estimate Equation 1 (Papke & Wooldridge, 1996;Ramalho et al., 2010).

Model selection
The appropriate specification of each functional form was tested by the use of Ramsey (1969) RESET test and goodness-of-functional form test (GOFF) (Ramalho et al., 2014).Although the RESET test was originally developed for use with linear functions, it is also applicable to any type of index models (Pagan & Vella, 1989;Ramalho et al., 2010Ramalho et al., , 2011;;Cameron & Trivedi, 2013, p. 52).GOFF test note that the model is free of mis-specification if the null hypothesis cannot be rejected (Note 3).It is possible that more than one model would be selected by the RESET and GOFF tests.Therefore, the P test proposed by Davidson and MacKinnon (1981) provides an opportunity for one-on-one tests using the selected models from the first two stages as alternative hypotheses.Unlike RESET and GOFF tests for which failure to reject the null hypothesis selects the model, in the case of the P test, a model is selected if the null hypothesis is rejected.

Descriptive Statistics
Although 49 studies were found, not all of these reported many technical inefficiency effect results (Table 2).Specifically, 3 studies reported the effect of household income on technical inefficiency whilst 49 reported the effect of formal education on technical inefficiency.The number of studies that jointly reported at least 3 technical inefficiency effects was 23 whilst those that reported at least one were 49.Although it was desirable to use more technical inefficiency effects variables, doing so for variables more than one would severely limit degree of freedom for hypothesis testing of the parameters estimates.Therefore, only one; formal education was employed.Although the 49 observations are low compared to other technical efficiency meta-regressions, the resulting 34 degrees of freedom (to be shown shortly) is appreciable.Moreover, the principal contribution of this article is the estimation of technical inefficiency effects in a meta-regression environment, for which the 49 observations are not out of place.

Results of Vote Count
Out of the 49 parameters reported for formal education, 30 of these showed statistical insignificance whilst 13 showed statistically significant positive coefficients.The rest of the 6 showed statistically significantly negative parameters.Following the vote count method used by Ogundari andBrummer (2011), andOgundari (2014), one would conclude that formal education has no statistically significant effect on technical inefficiency.

Model Selection
Table 3 presents results of specification and model selection tests.The RESET test statistics are statistically insignificant.This implies the null hypothesis that the explanatory variables have powers not more than 1 cannot be rejected.Therefore, the models are well specified.With regards to the GOFF tests, the statistical insignificance of all the test statistics of all functional forms suggests all models are well fitted to the respective functional forms.Nevertheless, one model needs to be selected for discussion using the P test results (third panel of Table 3).Using logit, probit and loglog as alternative hypothesis; all the statistics are statistically insignificant.
This implies these functional forms are statistically indistinguishable from one another based on the data used.In the case of cloglog as alternative hypothesis, although the statistics are the highest, only that of loglog as null hypothesis is statistically significant.This implies that first; the cloglog is seemingly preferred to logit and probit functional forms.Second, cloglog is clearly statistically distinguished from the loglog functional form.Thus, the cloglog functional form is selected for discussion.

Discussion of Selected Model
The coefficients of the key variables and their marginal effects are statistically insignificant (Table 4).The statistical insignificance of the coefficients imply, combining evidence, studies that reported statistically significant negative, positive and statistically insignificant coefficients (control) are not statistically distinguished.Specifically, studies that reported statistically insignificant coefficients for the effect of formal education on technical inefficiency are not different from those that reported statistically significant coefficients.Although the conclusions are not different from the vote count method, the approach employed in this article is non-trivial.Additionally, the approach accounts for the influence of other factors and permits estimation of statistical properties of the parameters that informs the conclusion.
The statistically insignificant coefficient notwithstanding, the negative sign of coefficients of EDUSSIGNEG is in line with the negative sign of coefficients of formal education reported by primary studies.This shows seeming enhancing effect of formal education on technical efficiency.Formal education provides beneficiaries with reading and writing skills among others.Apart from offering exposure to practices that will enhance production outcomes, formally educated farmers will be able to read instructions on farm supplies such as fertiliser, pesticides, and poultry and livestock medications among others.Also, formally educated farmers have the opportunity to read extension bulletins.All these will contribute positively to their farm operations thereby resulting in high output, most likely close to expected output, thereby increasing efficiency.The negative sign of the coefficient of EDUSIGPOS is contrary to the statistically significant positive signs reported by primary studies.This is because, the reported positive signs of coefficients showed that formal education exacerbated technical inefficiency.Therefore, combining these should show a positive sign of the coefficient.The contrary finding means that the findings of the primary studies are inconsistent with this, based on combined evidence.Additionally, the coefficients are not statistically significant.Therefore, unlike EDUSIGNEG, there is no conformation of the a priori sign.The coefficients of three out of the twelve coefficients of the control variables are statistically significant.The statistically significant positive coefficient of DEA implies that technical inefficiencies measured using DEA are higher than those measured using SFA and distance functions.The random error in DEA models are sometimes picked up as technical inefficiency.Therefore, this finding is in line with theory.However, Ogundari andBrummer (2011), andThiam et al. (2001) reported the contrary.
Although the coefficient and marginal effects of the DATAY is statistically insignificant, the negative sign of the parameter estimates suggests seeming (decrease) increase in (in)efficiency over time.Since Ogundari and Brummer (2011) found that MTE increased over time for Nigeria and did not increase for African and developing countries (Thiam et al., 2001;Iliyasu et al., 2014;Ogundari, 2014); increasing MTE in some countries such as Ghana and Nigeria among possible others may have been masked by some other poorly performing countries relative to MTE.The sources of this increase needs to be investigated in order to reinforce them for sustained decrease in technical inefficiency.This finding also calls for more individual country studies to identify countries regressing in MTE.The statistically significant parameters for FISH means that technical inefficiency for fish products are similar to those of the reference products.In respect of CROPS, the result of the parameter estimates show that technical inefficiency for crops products are higher than those of fish and combination of crops and animals.Despite the large contribution of crop products to agricultural GDP in Ghana (ISSER, 2014), this subsector shows significant technical inefficiency.This certainly requires attention.Although Ogundari (2014) came to a similar conclusion for African agriculture, for Ghana, this finding calls for identification of the specific crops as well as the sources of these inefficiencies for redress.Achieving decrease in technical inefficiency in crops subsector of agriculture would create significant financial gains not only for the subsector but for the agriculture sector as a whole.
As noted in the review, geographical region may influence mean technical inefficiencies because agricultural output is highly dependent on environmental factors which may differ depending on location.However, the statistically insignificant parameter estimates of the location variables suggests otherwise.This finding does not support differential policy on technical inefficiency based on geography in Ghana.The finding for Ghana is inconsistent with that of Ogundari and Brümmer (2011) in respect of Nigerian agriculture.
The positive and statistically significant coefficient and marginal effects of PR means that the reference, studies that were not peer reviewed; produced lower mean technical inefficiencies than peer reviewed studies.By implication non-peer reviewed publications have been under-estimating mean technical inefficiency for Ghana.The causes of this under-estimation could be identified by comparing technical inefficiencies of studies prior to peer review and after peer review.Further research could examine this.This notwithstanding, policy makers must be mindful of publications that inform their decisions viz-a-viz technical inefficiency.Although the finding of this article is inconsistent with that of Ogundari (2014), a recent quantitative review by Djokoto (2015) in respect to organic agriculture is consistent with the findings of this article.

Conclusions
This article addressed the question: what is the effect of technical inefficiency effects on mean technical inefficiency?In order to address this question in this article, meta-regression of studies of technical inefficiency in Ghanaian agriculture was carried out using technical inefficiency effects variable(s) as explanatory variable in the meta-regression.Previous meta-regressions used study characteristics only, as explanatory variables.In this article, these are used as control variables and the statistical significance or otherwise and the sign of the statistically significant technical inefficiency effects are introduced as key explanatory variable.This approach builds on the vote count method which; whilst being simplistic, fails to provide a measure with statistical properties hence lacks statistical rigour.The computation of statistical properties of the parameters of the key explanatory variable provides greater reliability of the results while controlling for the effect of characteristics of the study.Therefore, this approach has merit over the vote count method although the conclusion of the vote count method using the current metadata and that of the enhanced approach are similar.Owing to data limitations, only one technical inefficiency effect, formal education was included in the meta-regression.Further research with larger metadata should consider equally important socio-economic variables such age of farmer, size of household, access to credit and agricultural extension services among others.

Table 1 .
List of primary studies included in the metadata set

Table 2 .
Summary of reported technical inefficiency effects

Table 3 .
Results of Model selection for one technical inefficiency effect (Formal education) and dependent variable weighted by number of observations from each study Note.***, **, * represents 1%, 5% and 10% levels of significance respectively.

Table 4 .
Results of Estimation of using dependent variable weighted by number of observations from each study Note. ***, **, * represents 1%, 5% and 10% levels of significance respectively.
Ogundari and Brümm), Bravo-Ureta et al. (2007imates of VAR and SSIZE imply that number of variables and sample sizes employed in the primary studies are statistically indistinguishable.This suggests the numbers of sizes of these variables employed in the primary studies are adequate to estimate MTE.The finding for VAR is consistent with that ofThiam et al. (2001)but inconsistent with those of Bravo-Ureta et al. (2007),Iliyasu et al. (2014)andOgundari and Brümmer (2011).The finding for SSIZE agrees with that ofIliyasu et al. (2014) and Thiam et al.  (2001)but disagrees with that ofOgundari and Brümmer (2011)and Moreira López and Bravo-Ureta (2009).Cobb-Douglas and translog are the popular functional forms for estimating SFA models.The results of the parameter estimates reveal that these have not distinguished MTE statistically.By implication, estimating SFA by either Cobb-Douglas or translog makes no difference for the size of the inefficiency estimates, given the data used in this article.Thus, although mean technical inefficiencies measured by DEA models are higher than those of SFA, mean technical inefficiency for Cobb-Douglas and translog models are similar.Thus, for SFA estimations specifically for Ghana, the choice between Cobb-Douglas and translog is immaterial as far as mean technical inefficiency is concerned (Note 4).This finding is inconsistent with those ofThiam et al. (2001), Bravo-Ureta et al. (2007), and Illyasu et al. (2014).