Journal of Empirical Economics Vol. 1, No. 1, 2013, 1-10

Trade Openness and Technical Efficiency Change in Ghana’s Agriculture Justice Gameli Djokoto1 Abstract For a small developing country that pursued trade openness policies over three decades, what are the effects of trade openness on technical efficiency in agriculture, a sector that contributes significantly to the economy through employment and GDP? The study estimated the technical efficiency of Ghana’s agriculture, investigated the existence of technical efficiency change and assessed the effect of trade openness on the estimated technical efficiency. Using a Cobb-Douglas production function preferred to translog and fitted to data over 1980 to 2010 with maximum likelihood procedure, there was positive technical efficiency change. That is, technical inefficiency decreased over time. Landholding promoted technical efficiency. Contrary to findings of several studies, this paper showed that trade openness negatively impacted technical efficiency in agriculture in Ghana. Keywords: Stochastic frontier analysis, production function, technical efficiency effects, regression. 1. Introduction Background Trade openness often connotes the relationship between a country and the outside world. This may be through trade, property and funds transfer. Yet, Yanikkaya (2003) had noted that there is no clear definition of what is meant by “openness” or “trade liberalisation”. Indeed, over time, the definition of openness has evolved considerably from one extreme to another. This may be attributable to difficulty in measuring openness. In fact, measures have been employed to examine the effects of trade openness on various phenomena. One category of definition of trade openness is simple trade shares; exports plus imports divided by GDP (Harrison, 1996), export shares and import shares in GDP (Edwards, 1993, Miljkovic and Shaik, 2010). Squalli and Wilson (2011) augmented the trade to GDP measure by weighting it with a country’s share of world trade. Mahadevan (2003) had suggested that globalisation (or trade openness) in agriculture can be best discussed in three components – improvement of productive efficiency by ensuring the convergence of potential and realised output, increase in agricultural exports and value added activities using agricultural produce, and finally, improved access to domestic and international markets that are either tightly regulated or are overly protected. There is evidence of trade openness impacting technical efficiency (Markeihm, 2007). Technical efficiency (TE) measures the difference between the ideal production possibility curve (PPC) (in this case for a country) and the actual level of output (of the country) relative to the PPC. This, Farrell (1957) described as output oriented TE. Changes in the technical efficiency (TEC) indicate a country’s movement towards or away from the PPC, that is, TEC concerns changes to the gap between the actual and potential outputs. Studies provide guidance in estimation of efficiency change and productivity change measures using stochastic frontier (SFA) approaches (Kumbhakar & Lovell, 2000 and Greene, 2004), Problem statement One of the political motives of trade liberalisation is productivity, efficiency gains and prosperity (Markeihm, 2007). Nissanke and Thorbecke, (2006) and Harrison and McMillan, (2007) have acknowledged the joint effect productivity and international trade might have on growth, inequality and poverty alleviation. Proponents of trade openness (Nishimizu and Page, 1991; Helleiner, 1989, 1994) have noted that trade openness promotes competition which in turn propagates pressure for increased efficiencies, product improvement and technical change and factor productivity among other benefits. These benefits are possible through raising profits which stimulate growth, foreign capital investment and inflows of expertise, and enhanced equal access to scarce resources which improve the overall 1

Department of Agribusiness, Central Business School, Central University College, Ghana

© Research Academy of Social Sciences http://www.rassweb.com

1

J. G. Djokoto resource allocation. In the theory of international trade, the static gains from trade and losses from trade restrictions have been examined thoroughly. Yet, trade theory provides little guideline as to the effects of international trade on growth and technical progress (Yanikkaya, 2003). Miljkovic and Shaik (2010) have noted a negative relationship between TE and trade openness. Iyer et al (2008) have concluded that trade openness has either negative or positive effect on TE. Indeed, it has been observed that trade openness may not have any effect on TE. In the light of the inconclusive effect of trade openness on TE, what is the effect of trade openness on technical efficiency in Ghana’s Agriculture? Objectives The study estimates the technical efficiency of Ghana’s agriculture, investigates the existence of technical efficiency change and assesses the effects of trade openness on the estimated technical efficiencies. Relevance The paper is justified for a couple of reasons. Firstly, despite the importance of productivity in non-farm activities to sustain poverty alleviation, agricultural productivity would be of most direct interest to the majority of the poor (Bardhan, 2006). Secondly, trade actions by the US (Miljkovic and Shaik, 2010) and the EU through farm support and phyto-sanitary rules, the effects of globalisation on Ghana’s agriculture which is dominated by small-holder rural farmers is of utmost relevance. Thirdly, trade policies are considered crucial to the process of industrialisation, with increased exposure to foreign competition acting as a stimulus to technical and economic efficiencies and real growth (Adenutsi, 2008). In the fourth place, economists have long been interested in the theoretical and empirical analysis of technical efficiency (Milner & Weyman-Jones, 2003). And Debreu (1951) offered two principal reasons why inefficiency might be observed, namely (i) market failure, and (ii) non-profit-maximising behaviour arising from institutional structures that differ from private ownership and individual property rights. Finally, for a small developing country pursuing trade openness policies over three decades, the effects on technical efficiency in agriculture, a sector that contribute significantly to the economy through employment and GDP deserves investigation. 2. Literature review Miljkovic and Shaik (2010) addressed the impact of trade openness on technical efficiency in U.S. agricultural sector. The results indicated that a decrease in trade protectionism measured as the share of agricultural imports in agricultural GDP led to an increase in technical efficiency. A change in the share of agricultural exports in agricultural GDP had no impact on technical efficiency. The results, they noted, were partially consistent with the premise of the new trade theory, but also seemed to be driven by the intricacies of the agricultural sector and agricultural policy in the United States and internationally. The results further revealed the double standard of the US. Whilst advocating free trade, yet, has farm support and phyto-sanitary rules, which constituted another form of trade barrier. A strong positive developmental–efficiency relationship and evidence of a positive impact of trade policy openness and health (measured as average life expectancy at birth in years) on aggregate efficiency exists in developing countries (Milner and Weyman–Jones, 2003). The study which covered 85 developing countries over 1980-1989 concluded that country size was also important in explaining aggregate efficiency. Iyer et al (2008) studied 20 OECD countries over 1982-2000 and noted that trade and all foreign investment inflows were found to enhance efficiency. FDI outflows rather exacerbated inefficiency. Lam (2006) also reported openness to trade may reduce inefficiency, but not as much as building-up better domestic governance. The results which were based on a panel of 80 developed and developing countries showed that improving domestic governance may be more essential in promoting economic development for developing economies than simply adopting an open economy strategy without local governance reform. The rest of the paper is composed into three sections. Section 2 presents materials and methods. Section 3 presents results. Discussion of the results is captured in Section 4 with conclusions and some recommendations. 3. Methodolgy Efficiency measurements fall within the broader scope of performance measurements of production. Aigner et al (1977) and Meeusen & van den Broeck (1977) developed SFA approaches to measure technical efficiency. Since then, diverse approaches have been employed to explain the effects of efficiency. There are two stages; estimating the production function and modelling the factors that influence the technical efficiency estimates. These may be attained through a single step procedure and a two-stage procedure. Specifically, the latter involves estimating a production function to collect TE estimates and regressing these on TE effect variables using Tobit procedure. Lall et al, (2000) used this procedure. Fried et al., (1993) provided some reasons for estimating the two-stage procedure as a one-step 2

Journal of Empirical Economics process. First, this procedure provides more efficient estimates than the two-step procedure. Second, in general, it is hard to distinguish between a variables (Xs) that belongs to the first stage (production function) and the second stage (explanatory variables of efficiency Z). Third, if Z and x's are correlated (as is likely), then, estimates of  s and TE are biased (Sotnikov, 1998). i

Stochastic frontier analyses (SFA) are useful in studying efficiency of economic units (See Moreira & Bravo-Ureta (2010) and Lensink & Meesters (2012)). Their use in studying TEC have been exemplified by Tzouvelekas et al (2001) and Helvoigt & Adams (2009). The weakness of imposing a functional form in SFA is obviated by linearising with logarithmic transformation thereby capturing virtually every functional form. Additionally, the opportunity to choose between Cob-Douglas and translog provides ground for an informed decision. Data Envelopment Analysis, though has the advantage of no functional form, suffers upward bias in efficiency estimates. The error term is not composed hence random error is accounted for as part of technical inefficiency. The model used in the study is specified as: y  f ( X )e

(1)

vu

A natural logarithm transformation yields stochastic production frontier model (2). (2)

ln y

 X

t

t

β  v

t

 u

t

where yt denotes the output for the year t (t =1, . . . ,N), Xt is a vector of the production inputs as well as a column of ones, β is a vector of parameters to be estimated. vt and ut are error terms. vt, is identically and independently distributed (iid) as N(0, σ2v) and uncorrelated to ut. The latter is also assumed to be identically and independently truncated in t instead of zero (half-normal distribution when µ = 0) as N (µ, σ2u). SFA is an alternative to OLS. Thus it is important to test whether SFA is appropriate or superior to OLS given the data for the model estimation. In order to accomplish this FRONTIER 4.1c was used to estimate the following parameters: 

(3)

2

2 2    u v



and

  (

2 u

.

2 2  ) u v

Testing the significance of the parameter  is of interest from the point of view of model specification. The parameter which must the range between 0 and 1, measures the share of total variation that is attributed to technical inefficiency. If  = 0, it means that  alternatively be estimated by OLS.

2 v

= 0, then, the SFA is not a good specification, and the model could

The year specific technical efficiency is defined in terms of observed output

y

t

to the corresponding

y

*

using the

available technology. y T .E . 

(4)

t



e

(X   v  u ) t t t

* y t

where

y

t

is the observed output in year t and u

The solution of equation 4 becomes

e

y

* t

(X e

t

is the frontier output in year t. y

t

v ) t t

u  e

so that 0



t

* y t

1.

The above transformation constrains the technical

efficiency of each year to a value between zero and one, and is inversely related to the inefficiency. Equation 5, 3

J. G. Djokoto (5 )

u

t

 Z

was estimated together with equation 1 in FRONTIER 4.1c (Coelli, 1995). The variable set Z; is a vector of variables that are assumed to influence technical efficiency, including the time trend, and  is a vector of parameters to be estimated. Li & Wahl (2004) and Miljkovic and Shaik (2010) provided evidence for the use of a Cobb-Douglas (CD) production function in efficiency modelling. However owing to the restrictive (constant elasticities of substitution) nature of the CD, the translog formulation was tested. All data were extracted from FAOSTAT (http://faostat.fao.org/site/291/default.aspx, January, 20, 2013; 18:00 GMT) except stated otherwise. The natural logarithm forms of all the variables in the production function are employed. The output, agricultural production was defined as net production value of agricultural output at constant 20042006 prices in US dollars. Labour referred to economically active population in agriculture for each year in Ghana. Fertiliser was captured as total fertiliser import less export in current USD assuming zero local production. Agrochemicals (other) included pesticides, herbicides and fungicides. Again assuming zero local production this was computed as import plus production minus exports equals consumption. These computations were necessitated because query of FAOSTAT for consumption of fertiliser and other agrochemicals (OA) for Ghana yielded null set elements. Other agrochemicals were measured in US dollars. All these inputs and output were divided by agricultural land, which is the sum of area under arable land, permanent crops and permanent pastures. This was accomplished after eliminating variables that could cause multicollinearity. The technical efficiency variables included land area cultivated per agriculture employee (proxy for landholding), proportion of males in agricultural labour force (proxy for gender), fixed and mobile telephone lines per 100 people (proxy for infrastructure) and trade openness human development index. Proportion of irrigated land to total agricultural land (specific proxy for agricultural infrastructure), education, health, agricultural GDP per agricultural labour force (proxy for agricultural livelihood), were excluded due to high correlation with the included variables. Data on fixed and mobile lines were obtained from UNDP database. Four measures of trade openness were tested. The first is agricultural M/GDP and the second, agricultural X/GDP. Edwards (1993), Harrison (1996), Alcala and Ciccone (2004), and Miljkovic and Shaik (2010) employed trade openness computed as agricultural exports plus agricultural imports divided by the agricultural GDP ((X+M)/GDP). However, recently, as noted earlier, Squalli & Wilson (2011) established a new measure of trade openness. It is the (X+M)/GDP adjusted by the proportion of a country’s trade relative to the average world trade. This they christened composite trade share (CTS). (6)

CTS



(X  M ) 1 n

(X  M ) *

n  j 1

( X  M )j

GDP

This variable was computed for Ghana’s agriculture over the period. Data on agricultural GDP was obtained from UNSTAT (http://unstats.un.org/unsd/snaama/selbasicFast.asp, January, 20, 2013, 18:20 GMT). 4. Results Appendix 1 contains all the tables. Table 1 and 2 shows respectively, the Cobb-Douglas and translog functional form estimations of stochastic frontier. The statistically significant log likelihood ratio test (LR test) indicated models 1 to 8 are preferred to their OLS counterparts (available on request) pointing to existence of technical inefficiency. Since model 1, 2, 3 and 4 are the respective nested forms of model 5, 6, 7 and 8, an LR test was performed to test for restrictions (Table 3). The null hypothesis of existence of restriction on the production functions could not be rejected. Consequently, models 1 to 4 in table 1 were selected for further consideration. It is important to select one out of the four models for discussion. Model 4 performs best among the others based on sigma squared, gamma and LR test statistics, which together reflect technical inefficiency. At three decimals places, the gamma values are equal; however, model 4 possesses the lowest standard error indicating the strongest level of statistical significance. Finally, model 4 shows the highest log likelihood function. From the foregoing, model 4 is selected for discussion. The marginal elasticities are positive in line with production function property. With exception of fertiliser which is significant at 10%, all other elasticities are statistically significant at 1% level. The strong significance and elastic coefficient of 1.7838 point to an important role of labour in agricultural production in Ghana. The statistically significant constant term of the production function also shows that some variables have been omitted from the equation 4

Journal of Empirical Economics as confirmed by the exclusion of some variables due to multicollinearity. All control variables have positive coefficient, however, only the proxy for land holding is statistically significant at 1%. Therefore, increasing landholdings by 1ha per person will increase technical efficiency by 0.2553. Trade openness measured as CTS is negative and statistically significant at 1%. The negative and greater than 1 coefficient indicates that increases in trade openness ratio by 1 will induce 2.4032 reduction in technical efficiency. 5. Discussion The positive and statistical significance of the landholding proxy indicates that small parcels of land are inappropriate for increasing technical efficiency. The size of landholding coefficient suggest that the threshold that will exceed the managerial capacity of farmers is not yet exceeded. Importantly, since the proxy was measured as area per agricultural employee, more land needs to be allocated per agricultural worker. This may be achieved through land reforms that will minimise land fragmentation. The proportion of males in the agricultural labour force showed a positive but insignificant coefficient statistically. The positive sign is suggestive of male dominance in agriculture however, such dominance does not differentiate efficiency. The positive but miniscule statistically insignificant coefficient of fixed and mobile phone lines in relation to technical efficiency implies that their role is by chance. This is not surprising as agriculture is a rural phenomenon (World Bank 2008) and fixed phone lines were and still are predominantly an urban occurrence. The proliferation of mobile phones is a phenomenon of the new millennium. The insignificant effect is therefore not surprising. It remains to be seen however, how this variable will influence technical efficiency in the next couple of decades. It is instructive to note that the negative sign of trade openness is consistent across all eight models. This consistency suggests a definite and unmistaken detrimental effect of trade openness on TE in Ghana. In the past three decades, Ghana has pursued openness to trade policies. This permitted import of virtually every agricultural commodity into the country. Though allowed, exports did not have such opportunities due to non-trade barriers such as phytosanitary regulations. The result is stiff competition of a level that did not encourage efficiency. Increased output would have resulted in good margins that would permit payment for more efficient resources. As a result, openness to trade measured as CTS was inimical to improved efficiency in the agricultural sector in Ghana. The detrimental effect of trade openness on TE agrees with the findings of Miljkovic and Shaik (2010) who measured trade openness as exports to GDP. However, Lall et al (2000), Milner and Weyman-Jones (2003), Iyer et al (2008) and Hassine et al (2010) published a contrary finding. As noted earlier, trade openness should promote competition which in turn propagates pressure for increased efficiencies, product improvement and technical change and factor productivity among other benefits (Helleiner, 1989, 1994 and Mahadevan, 2003)). However, the contentions of those opposed to the positive effects of openness to trade seemed to have held sway in this case. Owing to the high correlation (not shown) of time with the technical efficiency effect variables, a correlation coefficient of time and TE was rather employed to test for increasing or regressing efficiency over time, that is, TEC (Table 4). The positive, high and statistical significance of the correlation coefficients between time and the TE suggests that there is positive technical efficiency change in Ghanaian agriculture. The mean technical efficiency of Ghana’s agriculture using data from 1980-2010 fitted to a Cobb-Douglas production function is 0.9094. There is room for expansion of agricultural production given the increasing returns to scale. The land area available to each agricultural worker must be increased to realise greater efficiency. A test of hypothesis revealed technical inefficiency exists in Ghana’s agriculture over the period. Technical efficiency change also exists in Ghana’s agriculture. Gender and infrastructure do not statistically influence efficiency. The measure of trade openness proposed by Squalli and Wilson (2011) negatively affected technical efficiency. The trade openness policies pursued over the last three decades must be re-examined in order not to any longer disadvantage, the sector that employs significant numbers of Ghanaians. A re-estimation of this model after a couple of decades may be necessary to see how infrastructure would influence technical efficiency. References Adenutsi, D. E. 2008. Effects of trade openness and foreign direct investment on industrial performance in Ghana. Journal of Business Research 2 (1&2): 71-89. Aigner D., C.A.K. Lovell, and P. Schmidt, 1977. Formulation and estimation of stochastic frontier production function models. Joournal of Econometrics, 6: 21–37. Bardhan, P. 2006. Globalisation and rural poverty. World Development 34: 1393–1404. 5

J. G. Djokoto Coelli T. J. 1995. Estimators and hypothesis tests for a stochastic frontier function: A Monte Carlo analysis. Journal of Productiity Analysis 6(4): 247–268. http://dx.doi.org/10.1007/BF01076978 Debreu, G. 1951. The coefficient of resource utilisation. Econometrica 19: 273–292. Edwards, S., 1993. Openness, trade liberalisation, and growth in developing countries. Journal of Economic. Literature 31: 1358 – 1393. Farrell, M. J. 1957. The measurement of productive efficiency. Journal of the Royal Statistical Society Series A (General), 120 (3): 253-290. Fried, H. O., C. A. K. Lovell, and S. S. Schmidt, (eds.) 1993. The measurement of productive efficiency. Techniques and applications. New York: Oxford University Press. Greene W. H. 2004. Fixed and random effects in stochastic frontier models. Journal of Productivity Analysis, 23 (1): 732. Harrison, A., 1996. Openness and growth: A time series, cross-country analysis for developing countries. Journal of Development Economics. 48: 419 – 447. Harrison, A. and M. McMillan, 2007. On the links between globalisation and poverty. The Journal of Economic Inequality 5: 123–134. Hassine, N.B. and M. Kandill, 2009. Trade liberalisation, agricultural productivity and poverty in the Mediterranean region. European Review of Agricultural Economics 36 (1): 1–29. Hassine, N. B., V. Robichaud, and B. Decaluwé, 2010. Agricultural trade liberalisation, productivity gain and poverty alleviation: A general equilibrium analysis. Cahier de recherche/Working Paper 10-22. Helleiner, G. K. 1989. Transnational corporations and direct foreign investment, in Handbook of Development Economics, II, H. B. Chenery and T. N. Srinivasan (eds.), Elsevier, Amsterdam: 1442-1480. Helleiner, G. K. 1994. Trade policy and industrialization in turbulent times, London: Routledge. Helvoigt, T. L., and D. M. Adams, 2009. A stochastic frontier analysis of technical progress, efficiency change and productivity growth in the Pacific Northwest sawmill industry. Forest Policy and Economics. 11(4): 280-287. Iyer, K. G., A. N. Rambaldi, and K. K. Tang, 2008. Efficiency externalities of trade and alternative forms of foreign investment in OECD countries. Journal of Applied Econometrics 23(6): 749-66. Kumbhakar, S. C., and C.A. K. Lovell, 2000. Stochastic frontier analysis. New York, NY: Cambridge University Press. Lall, P., A. Featherstone, and D. W. Norman, 2000. Productive efficiency and growth policies for the Caribbean. Applied Economics 32 (11): 1483-1493. Lam, C. K. Y. 2006. Estimating cross-country technical efficiency, economic performance and institutions–A stochastic production frontier approach. Paper Prepared for the 29th General Conference of The International Association for Research in Income and Wealth. Joensuu, Finland, August 20 – 26, 2006. Lensink, R., and A. Meesters, 2012. Institutions and bank performance: A stochastic frontier analysis. Oxford Bulletin of Economics and Statistics. Li, Q. and T. I. Wahl, 2004. Efficiency and technological progress in the Chinese agriculture: the role of foreign direct investment. Selected paper presented at the American Agricultural Economics Association Annual Meetings, Denver, CO-August 1-4, 2004. Mahadevan, R. 2003. Productivity growth in Indian agriculture: The role of globalisation and economic reform. AsiaPacific Development Journal 10 (2): 57-72. Meeusen W., & van den Broeck, J., 1977. Efficiency estimation from Cobb-Douglas production functions with composed error. International Economics Review, 18: 435–444. Miljkovic, D., and S. Shaik, 2010. The impact of trade openness on technical efficiency in US agriculture. Agribusiness & Applied Economics Report No. 660. Department of Agribusiness and Applied Economics, Agricultural Experiment Station, North Dakota State University, Fargo, ND 58108-6050. Milner, C and T. Weyman–Jones, 2003. Relative national efficiency and country size: Evidence for developing countries. Review of Development Economics 7 (1): 1–14. 6

Journal of Empirical Economics Moreira, V. H., and B. E. Bravo-Ureta, 2010. Technical efficiency and metatechnology ratios for dairy farms in three southern cone countries: a stochastic meta-frontier model. Journal of Productivity Analysis 33(1): 33-45. Nissanke, M. and E. Thorbecke, 2006. Channels and policy debate in the globalisation– Inequality–poverty nexus. World Development 34, 1338–1360. Nishimizu, M. and J. M. Page, Jr. 1991. Trade policy, market orientation, and productivity change in industry, in Trade Theory and Economic Reform, J. de Mello and A. Sapir (eds.), Oxford: Basil Blackwell: 246-264. Sotnikov, S. 1998. Evaluating the effects of price and trade liberalisation on the technical efficiency of agricultural production in a transition economy: the case of Russia. European Review of Agricultural Economics 25(3): 412-431. Squalli, J. and I. K. Wilson, 2011. A new measure of trade openness. The World Economy. 34 (10): 1745–1770. Tzouvelekas, V., C. J. Pantzios, and C. Fotopoulos, 2001. Economic efficiency in organic farming: evidence from cotton farms in Viotia, Greece. Journal of Agriculture and Applied .Economics 33(1): 35-48. World Bank. 2008. Annual Report. Washington D.C. New York. World Bank. 2011. Retrieved on July 31, 2011 from: http://data.worldbank.org/topic/agricultural-and-ruraldevelopment. Yanikkaya, H. 2003. Trade openness and economic growth: a cross-country empirical investigation. Journal of Development Economics 72(1): 57-89.

7

J. G. Djokoto Appendix 1: Table 1: Stochastic Frontier Analysis Estimation of Cobb-Douglas Production Functional Form Dependent variable: output per unit area Model 1

Model 2

Model 3

Model 4

7.8263***

7.6742***

Production function 1

7.8565***

C

(0.0837)

L/H

F/H

P/H

2

7.8791*** (1.0574)

(0.1111)

(0.0879)

1.9307***

1.9522**

1.9107***

1.7838***

(0.0703)

(0.8013)

(0.0932)

(0.0750)

0.0118

0.0045

0.0088

0.0157*

(0.0222)

(0.1045)

(0.0152)

(0.0084)

0.0056

0.0110

0.0124

0.0169***

(0.0144)

(0.0166)

(0.0132)

(0.0057)

Technical efficiency effects C

H/L

PMILF

FML

X/GDP

-0.4148

0.1017

-0.2591

-0.6968

(0.5445)

(1.8287)

(0.5511)

(0.5444)

0.1424

0.0898

0.1624*

0.2553***

(0.0676)

0.3995)

(0.0801)

(0.0665)

0.3413

-0.2966

-0.0054

0.0604

(0.8864)

(0.8830)

(0.8899)

(0.8795)

-0.0036**

-0.0044

-0.0036

0.0006

(0.0023)

(0.0032)

(0.0027)

(0.0026)

-0.5178** (0.2188) -0.4112

M/GDP

(0.6708) -0.3339**

(X+M)/GDP

(0.1243) -2.4032***

CTS

(0.6876) 0.0081

0.0128

0.0132

0.0088***

(0.0022)

(0.0036)

(0.0041)

(0.0023)

0.9999***

0.9999***

0.9991***

0.9999***

(0.0012)

(0.0008)

(0.0064)

(0.0006)

24.1089***

22.9930***

20.5480***

26.9624***

53.7428

53.1848

51.9624

55.1695

Mean TE

0.9120

0.9142

0.9143

0.9094

Returns to scale

1.9481

1.9677

1.0319

1.8164

Sigma squared

Gamma LR test

3

Log likelihood function

1

2

Notes: -*,**,*** are statistical significance at 10%, 5% and 1% respectively. -Numbers in brackets are standard errors. 3-Tests for existence of technical inefficiency.

8

Journal of Empirical Economics Table 2: Stochastic Frontier Analysis Estimation of Translog Production Functional Form Dependent variable: output per unit area Model 5 Model 6 Model 7 Model 8 Production function 12.9534***1 13.1188*** 12.8124*** 13.1642*** C (0.4979)2 (0.5295) (0.5219) (0.4626) 9.9545*** 10.2923*** 9.8486*** 10.3421*** L/H (0.7601) (0.7948) (0.7930) (0.7063) 0.8450** 0.7759*** 1.0166*** 0.65705** F/H (0.4106) (0.2686) (0.3562) (0.3654) P/H 0.5L/H2 0.5F/H2 0.5P/H2 L/H(F/H) L/H(P/H) F/H(PH)

C H/L PMILF FML X/GDP M/GDP (X+M)/GDP

-1.3684*** (0.3106) 6.2134*** (0.6224) 0.1588*** (0.0491) 0.1947*** (0.5795)

-1.1761*** (0.3707) 6.5345*** (0.6473) 0.1496*** (0.0526) 0.1580** (0.0665)

-1.2686*** (0.2420) 6.2155*** (0.6191) 0.1648*** (0.0435) 0.1809*** (0.0431)

0.7384** (0.2897)

0.6905** (0.3269)

0.8791*** (0.2115)

-1.1540*** -1.0078*** -1.0863*** (0.2377) (0.2871) (0.1890) -0.1507*** -0.1357** -0.1651*** (0.0515) (0.0581) (0.04254) Technical efficiency effects 0.5371 0.6335 0.3578 (0.7485) (0.6700) (0.6361) -0.0841 -0.0483 -0.0266 (0.1432) (0.2025) (0.1296) -0.1927 -0.2547 -0.2457 (0.9054) (0.97726) (0.9034) -0.0015 -0.0024 -0.0022 (0.0027) (0.0028) (0.0025) -0.5516 (0.3343) -0.2092 (0.2143) -0.0015** (0.1160)

-1.03948*** (0.3437) 6.5536*** (0.5705) 0.1607*** (0.0442) 0.1400** (0.0625) 0.6041** (0.2781) -0.8966*** (0.2640) -0.1291*** (0.0472) 0.2652 (0.5444) 0.0226 (0.0952) -0.3757 (0.8856) 0.00006* (0.0029)

-1.6083* (0.7876)

CTS

0.0091 0.00769*** (0.0019) (0.0023) 0.9999 0.9999*** 0.9999*** 0.9999*** Gamma (0.0004) (0.0005) (0.0004) (0.00005) Mean TE 0.9348 0.9362 0.9370 0.9348 LR 56.0661 55.6443 55.7195 55.5412 1 2 Notes: -*,**,*** are statistical significance at 10%, 5% and 1% respectively. -Numbers in brackets are standard errors. 3 -Tests for existence of technical inefficiency. 9 Sigma squared

0.0085 (0.0024)

0.0076 (0.0032)

J. G. Djokoto Table 3: Hypothesis testing to choose between Cobb-Douglas and Translog functional forms Null Hypothesis There is restriction in the production function for X/GDP models There is restriction in the production function for M/GDP models There is restriction in the production function for (X+M)/GDP models There is restriction in the production function for CTS models

Restricted LR

Unrestricted LR

LR Test statistic

Decision

53.7428

56.0661

4.6466

Accept

53.1814

55.6443

4.9190

Accept

51.9624

55.7195

7.5142

Accept

55.1695

55.5412

0.7434

Accept

Table 4: Correlation matrix of time against technical efficiency TE (CTS) (%) Time (years) 0.726***1 -*** represents statistical significance at 1% (2 tailed)

1

10