Question

A researcher investigated the determinants of food security in rural Lesotho based on sample of households living in various livelihood zones namely pastoral, agro-pastoral, marginal agriculture, and high potential agriculture. It is assumed that those households engaged in high potential agriculture as livelihood zones are food secure. Therefore, the dependent variable used in the study indicates that $y_1 = 1$ if household is food secure or $y_1 = 0$ otherwise. The explanatory variables are $cash\_inc$ denotes households income from wage employment; $own\_prod$ denotes own food production either by crop or livestock production. The estimated results using logit and probit models are presented below: Logistic Probit Variable Coefs P- $\frac{\partial F(y_1 = 1)}{\partial x_{ik}}$ P- Coefs $\frac{\partial F(y_1 = 1)}{\partial x_{ik}}$ p-value value value p-value Constant -5.081 0.001 --- -0.032 0.003 --- Cash inc 0.054 0.001 0.006 0.000 0.029 0.000 0.006 0.000 Own prod 0.049 0.002 0.005 0.000 0.032 0.001 0.005 0.001 a) Compare the estimated results from the logit and probit model. Interpret the estimated marginal effects. b) Can LPM be an alternative estimator? Why or why not? c) Specify the binary probit model and its assumptions used in the estimation. d) Derive the expression of probability that a household is food secure. [7] [3] No [5] [3] e) Using MLE approach, derive the likelihood function, log-likelihood equation and the first order with respect to parameters of interest. [7]

Name: a researcher investigated the determinants of food security in rural lesotho based on sample of households living in various livelihood zones namely pastoral agro pastoral marginal agricultu 01677
Uploaded: 2023-12-14T17:35:17-08:00
Duration: 2 min 36 s
Channel: Sheryl Ezze
Description: a researcher investigated the determinants of food security in rural lesotho based on sample of households living in various livelihood zones namely pastoral agro pastoral marginal agricultu 01677

          A researcher investigated the determinants of food security in rural Lesotho based on sample of
households living in various livelihood zones namely pastoral, agro-pastoral, marginal agriculture,
and high potential agriculture.
It is assumed that those households engaged in high potential agriculture as livelihood zones are
food secure. Therefore, the dependent variable used in the study indicates that $y_1 = 1$ if household
is food secure or $y_1 = 0$ otherwise.
The explanatory variables are $cash\_inc$ denotes households income from wage employment;
$own\_prod$ denotes own food production either by crop or livestock production.
The estimated results using logit and probit models are presented below:
Logistic
Probit
Variable
Coefs
P-
$\frac{\partial F(y_1 = 1)}{\partial x_{ik}}$
P-
Coefs
$\frac{\partial F(y_1 = 1)}{\partial x_{ik}}$
p-value
value
value
p-value
Constant -5.081
0.001
---
-0.032
0.003
---
Cash inc
0.054
0.001
0.006
0.000
0.029
0.000
0.006
0.000
Own prod 0.049
0.002
0.005
0.000
0.032
0.001
0.005
0.001
a) Compare the estimated results from the logit and probit model. Interpret the estimated
marginal effects.
b) Can LPM be an alternative estimator? Why or why not?
c) Specify the binary probit model and its assumptions used in the estimation.
d) Derive the expression of probability that a household is food secure.
[7]
[3] No
[5]
[3]
e) Using MLE approach, derive the likelihood function, log-likelihood equation and the first
order with respect to parameters of interest.
[7]

a researcher investigated the determinants of food security in rural lesotho based on sample of households living in various livelihood zones namely pastoral agro pastoral marginal agricultu 01677

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