Russian Journal of Agricultural and Socio-Economic Sciences, 2013, №5 (17) Май


Russian Journal of Agricultural and Socio-Economic Sciences, 5(17)

A COMPARISON OF BOOTSTRAP AND MONTE CARLO APPROACHES TO TESTING FOR SYMMETRY IN THE HOUCK’S MODEL

Henry de-Graft Acquah, Senior Lecturer
Department of Agricultural Economics and Extension, University of Cape Coast, Ghana E-mail: henrydegraftacquah@yahoo.com

ABSTRACT
The power of the Houck’s model of asymmetry is examined via bootstrap and Monte Carlo techniques. The results of bootstrap and Monte Carlo simulations indicate that the power of the Houck’s test for asymmetry depends on sample size, level of asymmetry and the amount of noise in the data generating process. Furthermore, the simulation results suggest that both bootstrap and Monte Carlo methods are effective in rejecting the false null hypothesis of symmetric adjustment in large samples with small error size and strong levels of asymmetry. However, in small samples, with large error size and subtle levels of asymmetry, the results suggest that asymmetry test based on bootstrap are powerful than those based on the Monte Carlo methods. I conclude that both bootstrap and Monte Carlo algorithms provide useful tools for investigating the power of the test of asymmetry.

KEY WORDS
Monte Carlo Simulation; Bootstrap Methods; Houck’s Model; Power Test; Asymmetry.

     Houck (1977) proposes a methodology to investigate asymmetric adjustments in price transmission processes. This involves specifying asymmetries to affect the direct impact of price increases and decreases and does not take into account adjustments to equilibrium level.
     Some studies (Capps and Sherwell, 2007) have applied this methodology to a series of problems and note the inabilities of the Houck’s model to detect asymmetries in practice. Against this background, Acquah 2010 investigated the power of the Houck’s model via Monte Carlo experimentation and finds that the Houck’s model has low power in rejecting the null of symmetric adjustments. Alternatively, Acquah 2013 using bootstrap simulations demonstrated that the Houck’s model has low power in bootstrap samples.
     Though Acquah (2010, and 2013) sheds light on the low power of the Houck’s model via bootstrap and Monte Carlo simulations, these previous studies fails to provide a comparison of the bootstrap and Monte Carlo methods in the power analysis test. A fundamental question such as, under what conditions will bootstrap and Monte Carlo techniques of testing for asymmetry lead to the same results remains unanswered. Empirically, this study fills a gap in the literature by providing a comparison of asymmetry test based on bootstrap with those based on Monte Carlo methods.
     The purpose of this study is to support the claim that the failure of the Houck’s model to capture asymmetry in practice is due to low power and in so doing provide a comparison of bootstrap and Monte Carlo based test for asymmetry in the Houck’s model.
     The paper is organized as follows. The introductory section is followed by sections on measuring asymmetry, testing for symmetry in the Houck’s model, Monte Carlo experiments and bootstrap methods. This is followed by the results and discussion and the conclusions of the study.
     Measuring Asymmetry. Tweenten and Quance (1969) were the first to develop a model to test for asymmetric price transmission. This approach of testing for asymmetry was later modified by Wolffram (1971).Wolffram’s approach to measuring asymmetry was further modified by Houck (1977). Houck’s contribution which is most widely cited involves developing a more rigorous approach to specifying and testing non reversible linear functions in economic research. Houck’s paper stimulated considerable interest in the study of price asymmetry. For instance Ward (1982) extended Houck’s specification by including lags. Boyd and Brorsen (1998) were the first to employ lags to differentiate between magnitude and speed of transmission. However, the Houck’s model has been found to have low power (Capps and Sherwell, 2007, Acquah, 2010).
     Testing for Asymmetry in the Houck’s Model. Houck (1977) model of testing for asymmetric price transmission can be specified as:


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Russian Journal of Agricultural and Socio-Economic Sciences, 5(17)

Ay t = p1Ax⁺ₜ + p1 Ax; + s s ~ N⁽⁰,^J (1)


where Axt and Axt are the positive and negative changes in x. The independent variable xt is generated as independent draws from normal distribution with a constant mean and a variance of one. Asymmetry is introduced by allowing differing speeds of adjustments for the
    A •       A A x ⁺  . A x; ■       .•          . О •         . .    ....
coefficients of t and t in equation (1) and £ is generated as i.i.d. draws from the standard normal distribution with a sample size n. Ayt is obtained using the values for beta, positive and negative changes in xt (i.e. Axtt and Axt; ) and the error term as specified in equation 1. Symmetric price transmission is tested by determining whether the coefficients ( P1 and P1 ) are identical (i.e. H⁰: P¹ “P1 ).
      Monte Carlo Experiments. A Monte Carlo experiment involves the following steps.
Consider the following linear regression:


У “ P 0 + P1 x 1 + P 2 x 2 ⁺ S (2)


      First, draw the exogenous variables of the model from their respective distributions. Second, draw a random sample of the error term in the model from its respective probability distribution function. Assuming values for the true parameters and drawing values of the stochastic element, we can estimate the endogenous variable and calculate the estimate of interest. Fundamentally, in Monte Carlo experiments, we draw from a specified distribution, by a random number generator. In effect, we make assumptions about the distributions and about the true values of parameters.
      The Bootstrap. Bootstrap is a method to derive properties of the sample distribution of estimators. Efron and Tibshirani (1993) notes that bootstrap involves drawing with replacement from the original sample to produce samples of the same size as the original sample referred to as bootstrap sample. It therefore takes the empirical distribution function as the true distribution function. The great advantage compared with Monte Carlo methods is that we neither make an assumption about the distributions nor about the true values of the parameter.
      Parametric Bootstrap. Parametric Bootstrap denotes the process of resampling from the residuals of a parametric regression model. It begins by estimating the model of interest and saving the residuals. It performs a simulation using the estimated parameter values as the true parameter values and the actual values of the explanatory variable as the fixed explanatory variable values. During this simulation study, errors are drawn with replacement from the set of original residuals. This residual based technique is referred to as parametric bootstrapping.




                RESULTS AND DISCUSSION





     In order to investigate the power of the test for asymmetry under various conditions, a series of bootstrap and Monte Carlo comparison of the Houck’s model is carried out based on 10000 replications. In particular, the power of the Houck’s model is examined under conditions of different sample sizes, noise levels and two levels of asymmetry given by

(p₂⁺, p₂;) e (0.5 0,0.25)or(0.75,0.25)


      We incorporate subtle and strong levels of asymmetry in the data generating process. The Houck’s model is evaluated in terms of its ability to reject the incorrect null of symmetric adjustment using an F-test of the restricted versus the unrestricted model. The results in Table 1 and 2 indicate the low power of the conventional F-test in rejecting the incorrect null hypothesis of symmetry.

Table 1 ; Rejection frequencies based on 10000 Monte Carlo Replications


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Sample    ;       (РГ,РГ)
Size       :             
50         ; (0.50, 0.25)
50         ; (0.50, 0.25)
50        i  (0.50, 0.25)
150       ;  (0.50, 0.25)
150       i  (0.50, 0.25)
150       :  (0.50, 0.25)
500       :  (0.50, 0.25)
500       ;  (0.50, 0.25)
500      i   (0.50, 0.25)
50         : (0.75, 0.25)
50         ; (0.75, 0.25)
50        ;  (0.75, 0.25)
150       ;  (0.75, 0.25)
150       ;  (0.75, 0.25)
150       ;  (0.75, 0.25)
500      i   (0.75, 0.25)
500      :   (0.75, 0.25)
500      ;   (0.75, 0.25)
Error        --Size (a) F      
3         1.1981
2         1.4260
1         2.5709
3         1.5301
2         2.2117
1         5.6800
3         1.8699
2         4.9340
1        16.6603
3         1.7428
2         2.6578
1         7.5351
3         2.0589
2         5.7735
1        19.7038
3         7.9174
2        16.5895
1        63.4595
Rej (5%) Rej (1%)
0.0689   0.0157  
0.0924   0.0240  
0.2249   0.0804  
0.1113   0.0323  
0.1878   0.0675  
0.5696   0.3206  
0.1544   0.0508  
0.5122   0.2705  
0.9754   0.9132  
0.1271   0.0384  
0.2305   0.0824  
0.6630   0.4100  
0.1728   0.0554  
0.5732   0.3297  
0.9845   0.9421  
0.7450   0.5194  
0.9757   0.9126  
1.0000   1.0000  

Table 2 - Rejection frequencies based on 10000 Bootstrap Replications

Sample    ;                 Error                            
Size       ;   (РГ,РГ)    Size (°-)    F    Rej (5%) Rej (1%)
50        !  (0.50, 0.25)     3     1.8956   0.1395  0.0512  
50         ; (0.50, 0.25)     2     2.1373   0.1664  0.0655  
50        ;  (0.50, 0.25)     1     3.4550   0.2964  0.1431  
150       ;  (0.50, 0.25)     3     2.1569   0.1805  0.0761  
150       :  (0.50, 0.25)     2     2.8612   0.2508  0.1202  
150       ;  (0.50, 0.25)     1     6.3213   0.5546  0.3609  
500      i   (0.50, 0.25)     3     2.4825   0.2240  0.0967  
500      :   (0.50, 0.25)     2     5.6226   0.5025  0.3197  
500       ;  (0.50, 0.25)     1     17.3154  0.9322  0.8489  
50        !  (0.75, 0.25)     3     2.4688   0.2003  0.0865  
50        :  (0.75, 0.25)     2     3.4056   0.2902  0.1466  
50         ; (0.75, 0.25)     1     8.2264   0.6190  0.4390  
150       ;  (0.75, 0.25)     3     2.6982   0.2411  0.1085  
150       i  (0.75, 0.25)     2     6.5265   0.5625  0.3710  
150       ;  (0.75, 0.25)     1     20.9906  0.9595  0.9036  
500      !   (0.75, 0.25)     3     8.5424   0.6936  0.5109  
500      :   (0.75, 0.25)     2     17.3892  0.9390  0.8510  
500       :  (0.75, 0.25)     1     64.7213  1.0000  1.0000  

      Specifically, the Monte Carlo and bootstrap simulations indicate the low power of the conventional F-test in rejecting the null of symmetric adjustment in small sample sizes. For example in small samples with large error size and subtle level of asymmetry, Monte Carlo method achieved a rejection frequency of 7% compared to 14% for bootstrap at the 5% significance level as illustrated in the top parts of Tables 1 and 2. There is some increase in power when the amount of noise in the data generating process (DGP) is decreased systematically. Similarly, when the difference in asymmetric adjustment parameters is increased from 0.25 to 0.50 in the true model, an increase in power is also observed in Houck’s test for asymmetry based on bootstrap and Monte Carlo methods as illustrated in Table 1 and 2. However, it is only when the sample size is increased to 500 that a reasonable results is obtained. For example, both the Bootstrap and Monte Carlo methods achieve a rejection frequency of 100 % with regards to the rejection of the incorrect null hypothesis of symmetric adjustments at the 5% and 1% significance level as illustrated in the bottom parts of Tables 1 and 2.
      In summary, the sample size, difference between the asymmetric adjustment parameters and the amount of noise in the data generating process are important in the power of the test for asymmetry based on bootstrap and Monte Carlo methods. With large sample size or small noise, the Houck’s model display greater power in rejecting the (false) null hypothesis of symmetry.





                CONCLUSION





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Russian Journal of Agricultural and Socio-Economic Sciences, 5(17)

      The power of Houck’s approach of detecting asymmetry has been evaluated using bootstrap and Monte Carlo methods. The results of the bootstrap and Monte Carlo simulations indicates that the power of the Houck’s model depends on various conditions or design characteristics such as sample size, error size and the level of asymmetry. Rejection frequencies increase with increases in sample size, increases with increase in difference between the asymmetric adjustment speeds and increases with a decrease in the amount of noise in the true data generating process used in the application. The power of the test for asymmetry based on Monte Carlo and bootstrap methods are the same (have rejecting frequency of 100%) if the sample size is large with a small error size and strong level of asymmetry. However, in small samples with large error size and subtle level of asymmetry, the test for asymmetry based on bootstrap outperforms the Monte Carlo approach, though both display low power. The low power of the Houck’s model in rejecting the null of symmetric adjustment in the Monte Carlo and bootstrap simulations provides an explanation for the failure of the Houck model to capture asymmetric behaviour in practice. I conclude that both bootstrap and Monte Carlo algorithms provide useful tools for investigating the power of the test of asymmetry.




                REFERENCES




[1]    Acquah, H.D. (2013). A Bootstrap Approach to Evaluating the Power of the Houck’s Test for Asymmetry in Journal of Social and Development Sciences, Vol. 4, No. 2 pp 69-73.
[2]    Acquah, H. D. (2010): Testing for Symmetry in the Houck’s Model in Indian Development Review: An International Journal of Development Economics -Vol. 8, No. 1, (January-December, 2010): 105-107.
[3]    Boyd, M. S. and Brorsen, B. W. (1998). Price Asymmetry in the US Pork Marketing Channel, North Central Journal of Agricultural Economics, 10, pp.103- 109.
[4]    Capps, O. and Sherwell, P. (2007). Alternative approaches in detecting asymmetry in farm-retail prices transmission of fluid milk. Journal of Agribusiness, vol 23 (3): 313331.

[5]    Efron, B. & Tibshirani, R. (1993). An Introduction to the Bootstrap, London: Chapman and Hall.
[6]    Houck, J.P. (1977). An Approach to Specifying and Estimating Nonreversible Functions. American Journal of Agricultural Economics, vol 59: 570-572.
[7]    Tweenten, L.G. and Quance, C.L. (1969). Positivistic Measures of aggregate Supply Elasticities: Some new Approaches. American Journal of Agricultural Economics, 51, pp. 342-352.
[8]    Ward, R.W. (1982). Asymmetry in Retail, Wholesale and Shipping Point Pricing for fresh Vegetables. American Journal of Agricultural Economics, 62, pp. 205-212.
[9]    Wolffram, R. (1971). “Positivistic Measures of Aggregate Supply Elasticities - Some New Approaches - Some Critical Notes,” American journal of Agricultural Economics, 53, pp. 356-356.


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                DETERMINANTS OF FARMERS’ DECISION TO ACCESS CREDIT: THE CASE OF ZIMBABWE




Shallone K. Chitungo, Simon Munongo, Lecturers Great Zimbabwe University, Zimbabwe
E-mail: sharone mail@yahoo.com, simonmunongo@gmail.com

ABSTRACT
In developing countries, improvement in productivity through investment in productive ventures, especially in the agricultural sector where majority of the population derive their livelihood is necessary for accelerated economic growth. In this study we look at the determinants of rural households’ decision on credit. The study used random sampling of 2030 farm households from each district and 97 families responded to the questionnaire. The study concluded that the type of crop, household size and gender of household head positively affected the decision by households to borrow while age squared negatively affects decision to borrow.

KEY WORDS
Household; Credit; Productivity; Farmers; Development.

     In developing countries, improvement in productivity through investment in productive ventures, especially in the agricultural sector where majority of the population derive their livelihood is necessary for accelerated economic growth (Awunyo-Vitor 2012). Given the low levels of income in African agricultural production, the accumulation of savings may be difficult. Under such circumstances, access to loans can help poor farmers to undertake investment and increase productivity.
     Agricultural credit has been variously defined by authors. According to Nwaru (2004): Agricultural credit is the present and temporary transfer of purchasing power from a person who owns it to a person who wants it, allowing the later the opportunity to command another person’s capital for agricultural purposes but with confidence in his willingness and ability to repay at a specified future date. It is the monetization of promises and exchanging of cash in the present for a promise to repay in future with or without interest. Without the willingness and ability to repay, the promise to repay at a future date would be futile. Credit can be in cash or in form of agricultural inputs.
     Agricultural household models suggest that farm credit is not only necessitated by the limitations of self-finance, but also by uncertainty pertaining to the level of output and the time lag between inputs and output (Kohansal and Mansoori, 2009). In Masvingo region of Zimbabwe where rainfall is erratic Agriculture is a risky business and output is uncertain thus facilitation of access to credit for the rural poor plays a role in alleviating rural poverty.
     Thus, in order to increase agricultural productivity especially among the rural poor and to assist rural households in maintaining food security, many NGOs and private companies in Zimbabwe and in other developing countries initiated credit programmes including contract farming with the idea that rural smallholder farmers will have access to formal sources of credit and thus improve their welfare (Munongo 2012). Agricultural lending has become a vital function in financial operations as it facilitates the economic growth, agricultural development and improves efficiency. For a farmer to derive benefits from any institutional credit, the size of the loan, the process of granting such loans, timeliness in disbursement and repayment are very important (Nweze, 1991). In Zimbabwe the Bankers Association reported that in 2012 Agriculture received the greater share of loans and combined with the traditional contract farming programmes in most rural communities Agriculture in Zimbabwe receive substantial private funding.
     Few studies which have dealt with the credit problems of limited-resource (small) farms have basically studied their attitudes toward borrowing, without exploring the economic validity of such attitudes (McManus; Otto; Snell, Hopkins, and Barnett; Spitze and Bevins; Spitze and Romans; Wise; Woodworth, Comer, and Edwards). The general consensus that emerges from these studies is that relatively few operators of small farms use credit. This problem is also visible in Masvingo where few rural households take credit and this has

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reduced the pace of growth in rural banking and financial services. Bagi (1983) argues that conventional methods of estimating the demand for credit use information from only those farmers who have actually used credit and neglect the information from farmers who have not borrowed. Such studies cannot account for farmers' initial decisions about whether or not to borrow; consequently, valuable information is wasted. Omitting non borrowers from the sample also distorts the properties of the original sample. Thus in this study we seek to determine the factors that determine the decisions by farmers to enter credit deal by looking at complete data including the factors that causes non participation.
      The demand of credit is influenced by several factors such as personal attributes of the individual, area specific attributes and credit source attributes (Udoh, 2005). These attributes influence individuals differently irrespective of their gender such that what might determine the demand for credit by a particular female farmer might be different from what determines credit demand by another farmer. For instance, in studying informal lenders and formal credit groups in Madagascar, Zeller (1994) indicated that informal lenders and group members obtain information about the wealth, indebtedness and income potential of loan applicants and hence ration loan demands an in-depth view of total household wealth and leverage of the household.
      Nwaru (2004) examined rural credit markets and resource use in arable crop production in Imo State, Nigeria. The study concluded that credit demand was significantly influenced by interest rate, educational level of farmer, amount borrowed previously, farm size and gross savings, while gross income of lender, total cost of lending, source of loan (whether formal or informal), worth of loan application and previous loan repayment significantly influenced credit supply. We wish to carry a similar study in the Masvingo province of Zimbabwe with the view of helping government and the private sector on how they can assist in improving rural household agricultural output and welfare.

THE AGRICULTURAL CREDIT MARKET IN ZIMBABWE

      The smallholder agricultural sector plays an essential role in ensuring food security, economic growth and employment creation. Therefore financing smallholder farmers becomes an important undertaking for poverty reduction in developing countries, especially those in Sub-Saharan Africa (Made 2000). The smallholder sector is characterized by diversified farming of crops and livestock. Specialization of commodities is minimal, for example some smallholder farmers specifically grow sugar cane under irrigation. Food crops are grown right alongside cash crops, for example maize, cotton and vegetables.
      The Agricultural market was liberalised in 1990 at the inception of The Structural Adjustment Programme (ESAP) in Zimbabwe. Trade liberalisation in the Agricultural sector from this period involved reduction of government direct involvement in the production, marketing and distribution of agricultural commodities. There was also removal of agricultural price controls and subsidies. There was also transformation of Agricultural marketing boards into independent entities with governments having limited shareholding. Zimbabwe is also a signatory to the World Trade Organisation which requires opening up of the agricultural sector.
      The major aim of this liberalisation was to create entrepreneurship in smallholder agriculture in the view to increase output and improve food security. The liberalisation thus brought the profit motive in the Zimbabwean Agricultural sector and thus the credit market in agriculture also started to be visible from this period. In Masvingo region this is the period where the production of cash crops such as cotton, paprika, wheat and sugarcane as households sought to enhance their earnings from agriculture.
      The creation of independent agricultural marketing entities also led to the growth of the credit market in Agriculture as most firms introduced contract farming to enhance their business. Some companies engaged in certain agricultural commodities have resorted to financing smallholder farmers for a specific crop. One example is the Cotton Company of Zimbabwe, which operates an input-credit scheme for cotton farmers. Loans are recovered from the proceeds of the next season’s crop. This method of financing has proved to be effective for farmers.


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      Multilateral and bilateral aid has been the most common forms of financing smallholder farmers in the developing world and in Zimbabwe it is also visible. These come as either grants or loans. This form of aid has come about through the recipient governments signing multilateral or bilateral agreements with aid agencies. Through this aid, farmers benefit from large investments, such as dam construction, irrigation facilities, machinery and other equipment. They also benefit from the transfer of technology and other ‘softer’ sides of financing, such as management and organizational skills (Made 2000).
      Central governments have the role of ensuring that there is an equitable allocation of resources for development, especially of marginalized people. Apart from allocating funds from aid agencies, governments in developing countries have made efforts to assist smallholder farmers by financing from their own resources programs such as:
   1. Essential infrastructure for agricultural development, including dams, irrigation, roads and provisions of inputs
   2. Credit has been subsidized, to some extent, for smallholder farmers, whereby the interest rates are lower than those charged for commercial farmers. In the case of Zimbabwe, the credit has been provided through the Agricultural Finance Corporation. This institution provides short term, medium term and long term credit.
   3. In most developing countries, and especially in Sub-Saharan Africa, the government provides research and extension services for smallholder farmers.
   4. Decentralization of functions to regional levels has resulted in the empowerment of the local authorities, including the allocation of resources for development projects However, more often than not, the local authorities lack the necessary capacity to generate more income and finances in order to meet demand from their communities In the end, they still rely on the central government.
   5. In most cases, both central and local governments are constrained in terms of resources and are unable to meet the financing requirements of the majority of smallholder farmers.
      Commercial financial institutions comprise the conventionally accepted financial service sources, such as commercial banks and financial houses. The loans offered by these institutions are charged at market related interest rates and require loan guarantees in the form of immovable assets, shares, savings, land, etc. Due to these conditions, most smallholder farmers are not eligible for the loans, and they are considered a high-risk group in terms of repayment.
      This research will look at the determinants of the household decision to get agricultural credit which includes contract farming and direct loans.




                METHODOLOGY




      Our study will follow the leads of Zapata, Jr* (2006) on credit decision and rationing rules a study of informal lenders in the Philippines. The borrowing process is characterized by the famer’s demand for credit and his/her access to credit. To analyze the outcome of this process, it is important to look at the demand and supply factors separately. This can be conceptualized as a sequential decision process. At stage 1, the entrepreneur decides whether to obtain loan from the formal or the informal lenders. Then at stage 2, the informal lenders decide on the amount of funds to be lent and the level of interest rates to be charged (Zeller, 1994). This study will focus on Stage 1.
      The factors that may affect the entrepreneurs’ propensity to borrow are age, household size, civil status, gender, education and income. These factors will be the explanatory variables that will be used in the econometric model. Age is expected to have a positive relationship with the demand for loan. The productive capacity of the entrepreneur increases with age. Consequently, the demand for productive fund also increases. The quadratic form of the age will be used in this study to allow for the diminishing impact of age. The diminishing impact of age means a decrease in marginal experience gained with age.
      Household size is also expected to affect the decision to borrow by households. An increase in the household size will lead to an increase in the demand for consumption funds. Using the loan for consumption makes the funds unproductive. Therefore, large families and expected to desire high production output hence is expected to borrow. The entrepreneurs

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will try to maximize return by choosing a fund source with “lower” borrowing cost or choosing a less risky programme such as contract farming.
      Married entrepreneurs are also more likely to borrow. Married individuals need to create wealth to pass on to the next generation hence they are expected to borrow to increase their capabilities and remove the funds constraint in production. Educated entrepreneurs are expected to prefer funding for their agricultural activities. It can be assumed that they understand the dynamics of risk and need to fund agriculture and move from mere subsistence production and try to move up to commercial levels. Low-income individuals need to improve their earning capacity. They do not have sufficient asset that can serve as collateral. Therefore, they will be more inclined to get their funds from a source that can be easily accessed and does not require collateral. In most case these will prefer contract farming so that they will provide labour and land and try to work and ensure a surplus above the cost of funding and salvage something for their families.
      Most families in the region receive remittances from their families in town and cities and those in the Diaspora. These households are expected to desire loans for their agricultural activities since this will continue to increase their social status. Agriculture in most rural areas is done communally and households share experiences and compete with each other for better output thus closeness to other households that participates in private sector funding mighty affect the household’s decision to participate.
      The type of crop the household produce also determines the decision to get credit. Households that produce cash crops are expected to borrow since they expect higher future earnings and also the activities of cash crop farming require more inputs and are in most cases labour intensive thus require funding.
      The PROBIT method was used to test the model. This method was chosen since the dependent variables are binary variables that take zero-one value. Since the probability that an event will occur is non-linear, the usual least squares estimation method is not appropriate. The Linear Probability Model (LPM) is characterized by heteroskedastic errors -variance of the error term varies among observations. Another problem with the LPM is that it yields unrealistic values of probability (i.e., less than zero or more than 1), because it assumes linearity between the explanatory variables and the probability. On the other hand, the PROBIT model constrains the probability to the (0,1) interval. It also assumes that the probability that an event will occur is non-linear. The following equation is used to estimate the probability that the entrepreneurs will obtain its loan from the informal moneylenders.
      Entrepreneurs decide whether to borrow from lenders.

Pr ob(Apply) = F (agesq, ms, edu, hh, sex, income, rem, croptp, closens) ,

where: Apply dummy (1 if individual obtained loans from informal lenders, 0 otherwise); agesq = quadratic form of the entrepreneur’s age; ms = dummy for marital status (1 if married, 0 otherwise); edu = number of years in formal education; hh = household size; sex = dummy (1 if male, 0 otherwise); income = entrepreneur’s income (annual revenue of the enterprise was used as a proxy); rem = dummy (1 if household receives remittances and 0 otherwise); croptp = dummy (1 if household produces a cash crop, 0 otherwise); closens = distance from nearest neighbour who participate in the loans market.




                DATA AND RESULTS




      The data used for this study is from a primary data collection in three districts of Masvingo. These districts are Chiredzi, Zaka and Masvingo rural which have similar weather conditions. During this survey, discussions were held with different stakeholders including farmers, traders and extension staff working directly with farmers. We did a random sampling of 20-30 farm households from each district and 97 families responded to the questionnaire. The survey collected valuable information on several factors including household composition and characteristics, land and non-land farm assets, livestock ownership, household membership in different rural institutions, varieties and area planted, costs of production, yield data for different crop types, indicators of access to infrastructure and


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irrigation facilities, household market participation, household income sources and major consumption expenses.


Table 1 - Descriptive statistics

Variable   mean   Standard deviation : minimum maximum
Aqesq    2679.296 1824.857      :      400     8100   
edu      10.61224 3.46003       :      3       21     
hh       11.28571 5.687751      :      2       34     
income   23656.4  22034.63      ;      800     89000  
Closens  5.94898  3.512489      :      1       32     

Source: Author’s computations.

        Table 2 - Determinants of Propensity to Borrow            
Explanatory variable parameter Standard error ■       probability
       aqesq         -.0005542    .0001502    :        0.000     
         ms          .0097235     .5066646    ■        0.985     
        Edu          .0344881     .0507622    !        0.497     
         Hh          .1219105     .0456555    :        0.008     
        sex          1.374783     .5861633    !        0.019     
       Income        .0000316     .0000242    ■         0.191    
        Rem          .0977715  .1431107       ■         0.494    
       Croptp        1.223288    .08143473    !       0.00133    
      closens        .0350914     .0475879    :         0.461    

Source: Author’s calculations from stata
Probit regression: Number of observations = 97; Wald chi2 (9) = 30.28; Log likelihood = -19.607798; Prob > chi2 = 0.0004ю

       Table 2 above shows the probit results, from the results age squared is negative and significant this shows the diminishing impact of age and as people get older the returns to experience vanish thus they become less productive and their demand for loans falls.
       Household size is positive and significant thus an increase in the size of the family incentivises the household to increase its productivity. In most instances families that are agriculturally productive in rural Zimbabwe are polygamous hence they are big and the richer the family the more chances are that the family head if male will increase the number of wives and children thus the family continues to grow.
       The gender variable is positive and significant thus male headed families are more risky taking than female headed families. This is based on the traditional belief that women in most cases are content with average life styles and male ego pushes male headed families to fight for surplus production for societal respect and status.
       Crop type is also positive and significant thus those who embark on cash crop production borrow since they expect to get good returns. Cash crops grown in the region include sugarcane and cotton which have high returns and also require huge investments thus the need for funding.




                CONCLUSIONS





      The government of Zimbabwe need to intervene with seed and fertilizer subsidies since the most vulnerable families are not keen to participate in the private sector initiatives. Therefore in most case those who are in the middle class are benefiting and majority who are poor are not accessing the loans thus societies in Masvingo remain in need of food aid.




                REFERENCES





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