Introductory Econometrics : Factors Affecting Cereal Production of Bangladesh

7/24/2019 Introductory Econometrics : Factors Affecting Cereal Production of Bangladesh

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Factors Affecting Cereal Production of

Bangladesh

Makina Rahman & Sheikh Samsuzzhan Alam

December, 2015

Faculty of Economics and Management

Master Program in System Engineering and Informatics


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Contents

1 Introduction ........................................................................................................................................... 5

2 Data Description ................................................................................................................................... 6

3 Methodology and Analysis ................................................................................................................... 7

3.1 Single - Equation Model ............................................................................................................... 7

3.1.1 Economic model and econometric model ............................................................................. 7

3.1.2 Multicollinearity Detection ................................................................................................... 8

3.1.3 Parameter estimation using OLS ........................................................................................... 9

3.1.4 Economic verification of the model .................................................................................... 10

3.1.5 Statistical verification ......................................................................................................... 10

3.1.6 Model Application .............................................................................................................. 14

3.2 Simultaneous model .................................................................................................................... 15

3.2.1 Data set ................................................................................................................................ 15

3.2.2 Economic model and econometric model ........................................................................... 16

3.2.2.1 Economicmodel ...................................................................................................................... 16

3.2.3 Model identification ............................................................................................................ 16

3.2.4 Parameter estimation using TSLSM ................................................................................... 17

3.2.5 Economic verification ......................................................................................................... 18

3.2.6 Statistical verification ......................................................................................................... 19

3.2.7 Reduced form of the equation ............................................................................................. 21

3.2.8 Model application ............................................................................................................... 22

4 Conclusions ......................................................................................................................................... 22


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Figure 1: Yearly Cereal Production Per One Thousand Unit (Metric Tons) of Bangladesh ........................ 5

Figure 2: Correlation matrix for Multicollinearity detection ........................................................................ 9

Figure 3: GRETL output for normality of residuals ................................................................................... 11

Figure 4: GRETL output for Autocorrelation test....................................................................................... 12

Figure 5: GRETL output for test of Heteroscedasticity .............................................................................. 13

Figure 6: GRETL output for significance of parameters ............................................................................ 13

Figure 7: Forecasting of Cereal Production for 2014.................................................................................. 14

Figure 8: Data set for two equation model .................................................................................................. 15

Figure 9: GRETL output for TSLM estimation for first equation .............................................................. 17

Figure 10: GRETL output for TSLM estimation for second equation ........................................................ 18

Figure 11: GRETL output for Normality of residuals ................................................................................ 19

Figure 12: GRETL output for test of Autocorrelation of two equation model ........................................... 20

Figure 13: GRETL output for Heteroscedasticity of two equation model .................................................. 21


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1 Introduction

Agriculture is one of the largest producing sectors of the economy for Bangladesh. Which makes

Bangladesh one of the fastest growing country in South - Asia. The performance of this sector has a direct

effect major macroeconomic objects like food reservation, development, employment generation and

poverty alleviation. Focusing on export and self - sufficiency in food Bangladesh produces a large amount

of cereal crops. Cereal crops are also called grain crops. the top 5 cereals in the world ranked on the basis

of production tonnage are maize (corn), rice (paddy), wheat, barley and sorghum. Because of fertile soil

and normally ample water supply , Bangladesh produces significant amount of rice, wheat and corn.

The cereal production is increasing with a very high rate in Bangladesh. So it is very important to analyze

the yearly production and the factors affecting the cereal production for prediction and improvement of

cereal production. This project highlights the production of cereal corps and the factors which has direct

impact on cereal production . Primarily Land under cereal production (hectares) per hundred thousand

unit, Cereal yield (kg per Square Kilometers) , Fertilizer Consumption (Kg Per hectares), GDP Per Capita

(US Dollar) are considered as important factors with respect to different literature for Cereal Production

(Metric tons) per hundred thousand unit. In this project some econometric approach like multiple linear

regression modeling and simultaneous regression modeling is used to determined the most important

variables. Figure 1 shows the annual cereal production per hundred thousand unit in metric tons.

Figure 1: Yearly Cereal Production Per One Thousand Unit (Metric Tons) of Bangladesh

0.00

100.00

200.00

300.00

400.00

500.00

600.00

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

Cereal Production (Metric Tons)

Cereal Production (Metric Tons)


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2 Data Description

For this study the main data has been collected from the database provided by The World bank. From the

whole dataset a subset of data has been selected from the year 1998 to 2013. Figure 2 shows the pictorial

representation of the dataset which has been used further analysis. The levels of the headers of the data set

is as follows:

Y1t(Y_1t):Cereal production per hundred thousand unit (Metric tons)

X2t(X_2t): Land under cereal production per hundred thousand unit (Hectares)

X3t(X_3t):Cereal yield (kg per Square Kilometers)

X4t(X_4t):Fertilizer Consumption (Kg Per Hectares)

X5t(X_5t):GDP Per Capita (US Dollar)

Figure 2: Data set for one equation model

Year Y_1t X_2t X_3t X_4t X_5t

1998 315.77 110.2064 2665.305 17170.78 396.17

1999 364.03 116.8097 3116.435 17200.03 398.23

2000 395.03 116.7225 3584.353 17317.88 406.53

2001 380.29 114.856 3511.046 17276.14 403.59

2002 393.41 115.8809 3794.99 18863.92 401.71

2003 400.15 115.0091 3579.315 16026.69 434.05

2004 377.59 109.7827 3439.434 17067.14 462.27

2005 411.47 111.7634 3781.596 19774.87 485.85

2006 420.45 111.7803 4061.367 19319.01 495.85

2007 448.41 111.5209 4220.889 18441.11 543.08

2008 489.47 119.3086 4302.539 20006.41 618.08

2009 497.36 119.0989 4376.013 18885.29 683.61

2010 518.63 120.9395 4588.33 21296.39 760.33

2011 526.29 121.0295 4348.41 27130.69 838.55

2012 528.03 120.1682 4194.06 27883.06 858.93

2013 542.53 124.5103 4357.342 20866.29 954.40


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3 Methodology and Analysis

3.1

Single - Equation Model

In a single equation model the total economic phenomenon is given by a single equation or single

mathematical and statistical model . So the relationship between the Dependent (Endogenous) and

Independent (Exogenous) variable is expressed through a single equation.

3.1.1 Economic model and econometric model

An economic model is a set of assumptions that describes the behavior of an economy, or more general, a

phenomenon. The economic statistics is a descriptive aspect of economics. It does not provide either the

explanations of the development of various variables or measurement of the parameters of the

relationships. Econometrics uses statistical methods for the measurement of economic relationships which

are not meant for controlled experiments conducted inside the laboratories. The econometric methods are

generally developed for the analysis of non-experimental data.

3.1.1.1

Economicmodel

According to the data structure we can assume that, Cereal Production can be influenced by the following

variables:

Land under cereal production per hundred thousand unit (Hectares)

Cereal yield (kg per Square Kilometers)

Fertilizer Consumption (Kg Per Hectares)

GDP Per Capita (US Dollar)

So the Economic model can be written as follows:

3.1.1.2

Econometricmodel

One of the very important role of econometrics is to provide the tools for modeling on the basis of given

data. The regression modeling technique helps a lot in this task. The regression models can be either

linear or non-linear based on which we have linear regression analysis and non-linear regression analysis.


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For our study we will use Multiple Linear Regression Model which is more general form of linear

regression mode. The general form of Multiple Linear Regression is given by:

where, is endogenous variable, are exogenous variables and is random error term.

The assumptions for Multiple Linear Regression model is as follows:

Random error term is independently and identically distributed.

Random error will be normally distributed with mean 0 and constant variance.

No correlation between error terms.

No correlation between Explanatory variables and random terms.

Based on the assumptions our sample Regression Line is as follows:

where,

y1t:Cereal production per hundred thousand unit (Metric tons)

x2t: Land under cereal production per hundred thousand unit (Hectares)

x3t:Cereal yield (kg per Square Kilometers)

x4t:Fertilizer Consumption (Kg Per Hectares)

x5t:GDP Per Capita (US Dollar)

3.1.2 Multicollinearity Detection

Multicollinearity is a phenomenon in which two or more predictor variables in a multiple regression

model are highly correlated, meaning that one can be linearly predicted from the others, which produces

redundant information among the independent variables. If paired correlation between two exogenous

variables is greater than or equal to 0.8, then existence of Multicollinearity is considered. The general

method for elimination of Multicollinearity is to remove any one variable which has a lower correlation

with Endogenous variable.


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Figure 2:GRETL output of OLS estimation

3.1.4 Economic verification of the model

Economic verification is based on the verification of our models with respect to economic theories,

wheatear the phenomenon is supported by descriptive economics or not. So form the model we can

measure the sensitivity of the parameters for economic verification. The following model says that:

If the Land under cereal production per hundred thousand unit increase by 1 unit Cereal

production per hundred thousand unit will increase by 2.04unit.

If the Cereal yield increase by 1 unit Cereal production per hundred thousand will increase by

unit 0.06unit.

If the GDP Per Capita increase by 1 unit Cereal production per hundred thousand unit will

increase by unit 0.18 unit.

Which support the economic theory also. So this model successfully verified through economic

verification.

3.1.5 Statistical verification

and adjusted show that, how well a regression model predicts responses for new observations, Whilethe adjusted is a modified version of that has been adjusted for the number of predictors in themodel. and adjusted shows that what percentage of total variation of endogenous variables isexplained by exogenous variables. In case of our model 98%of total variation of Cereal production can


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be explained by Land under cereal production (hectares) per hundred thousand unit, Cereal yield (kg per

Square Kilometers) , GDP Per Capita (US Dollar).

At least three type of statistical verification is needed for any econometric model. The main three test for

a econometric model is normality of residuals, test of Heteroscedasticity and test of Autocorrelation. If

error term does not follow normal distribution then OLS property is not satisfied. On the other hand if

Heteroscedasticity and Autocorrelation exit then estimated parameter will be Linear Unbiased and

consistent but not the best one. Which will create biased covariance matrix and t - test for parameters will

not be valid.

3.1.5.1 TestForNormality:

Test criteria for normal distribution is:

Error terms are normally distributed

Error terms are not normally distributed

Decision Rule : If p - value is less than 0.05 then reject the .

According to the result from GRETL the p - value for our model 0.96 which is much greater than 0.05 so

we can not reject . So error terms are normally distributed.

Figure 3: GRETL output for normality of residuals

3.1.5.2 TestForAutocorrelation:

Test criteria for Autocorrelation is:


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There is no auto correlation in the model

There is auto correlation in the model


According to the result from GRETL on Breusch - Godfrey test the p - value for our model is 0.18 which

is greater than 0.05 so we can not reject . So There is no autocorrelation in the model.

Figure 4: GRETL output for Autocorrelation test

3.1.5.3 TestForHeteroscedasticity:

Test criteria for Heteroscedasticity is:

There is no Heteroscedasticity in the model

There is Heteroscedasticity in the model


According to the result from GRETL on Breusch - Pagan test the p - value for our model is 0.47 which is

greater than 0.05 so we can not reject . So There is no Heteroscedasticity in the model.


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Figure 5: GRETL output for test of Heteroscedasticity

As there is no significant existence on Heteroscedasticity and Autocorrelation in the mode then we canuse t - test to check the significance of the model parameter. According to GRETL output the all variable

are statistically significant. Among themx3tandx5t has the 99% level of significance andx2t has the 95%

level of significance. So we can keep all the proposed variables in our model.

Figure 6: GRETL output for significance of parameters


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3.1.6 Model Application

3.1.6.1 Forecasting:

Forecasting is one of the major application of any econometric model. Always we are interested to know

about the future for some set of exogenous variable. Figure shows the one year forecasting of Cereal

Production in metric tons with the setting of and for year2014 and the predicted value is 577.71.

Figure 7: Forecasting of Cereal Production for 2014

3.1.6.2 MeasurementofElasticity

Elasticity measurement is one of the major application of econometric data. In econometric analysis we

want to see the sensitivity of each parameter which are affecting our economic model. We want to see

that, if we change some percentage on exogenous variables then how the endogenous variable will react.

The elasticity function can be given by,

So for, and for year 2014 and the predicted value . Then the elasticity of cereal production is, ; and . So1% increase in the Land under cereal production per hundred thousand unit will increase the Cereal


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production per hundred thousand unit by 0.43%, 1% increase in the Cereal yield will increase the Cereal

production per hundred thousand unit by 0.5% and 1% increase in the GDP Per Capita increase the Cereal

production per hundred thousand unit by 0.28%.

3.2

Simultaneous model

A simultaneous equation system is one the important types of equation systems that are used to specify

statistical models in economics. If there exist correlation between exogenous variable and error term or

mutual dependency exist between any endogenous and exogenous variable then simultaneous equation

model could be a good solution. The 3 most important sources that produce a correlation between the

error term and an explanatory variable are the following 1) Omission of an important explanatory

variable. 2) Measurement error in an explanatory variable. 3) Reverse causation.

3.2.1 Data set

In our study we can assume mutually dependency between Cereal production per hundred thousand unit

and Cereal yield, which creates two endogenous variables in the equation system. Then Land under

cereal production per hundred thousand unit, Household consumption expenditure and GDP Per Capita

will be considered as exogenous variables in the model.

Y1t(Y_1t):Cereal production per hundred thousand unit (Metric tons)

Y2t(Y_2t): Cereal yield (kg per Square Kilometers)

X1t(X_1t):Land under cereal production per hundred thousand unit (Hectares) X2t(X_2t):GDP Per Capita (Kg Per Hectares)

X3t(X_3t):Household consumption expenditure (US Dollar)

Figure ... shows, the pictorial representation of new arranged data set.

Figure 8: Data set for two equation model


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3.2.2 Economic model and econometric model

3.2.2.1 Economicmodel

According to the data structure we can assume that, Cereal Production can be influenced by the

following variables:

Cereal yield (kg per Square Kilometers)

GDP Per Capita (Kg Per Hectares)

Household consumption expenditure (US Dollar)

Our Cereal yield can be depends on the following variables:

Cereal production per hundred thousand unit (Metric tons)

Land under cereal production per hundred thousand unit (Hectares)

So the Economic model can be written as follows:

3.2.2.2 Econometricmodel

According to the economic model we are able to construct our two equation econometric model as

follows:

where, are endogenous variable, are exogenous variables and are random error terms in thetotal system.

3.2.3

Model identification

The identification is done only for simultaneous models. All equations of an econometric model must

comply with:


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where

is number of exogenous variables which is not included in the particular equation and

is the

number of endogenous variables in the equation. According to identification rule,

For the first equation, K** = 1 and G* = 2, so model exactly identified

For the second equation,K**=2 and G*= 2, so model is over identified. So we can use this model for our

further analysis and application.

3.2.4 Parameter estimation using TSLSM

Parameter estimation through Two Stage Least Square Model (TSLSM) is similar to OLS, but at the first

step one endogenous variable is estimated by instrumental (exogenous) variables and in the second steps

the another endogenous variable is estimated using this estimated value which is from the first step.

Figure shows the GRETL output for first and second equation:

Figure 9: GRETL output for TSLM estimation for first equation

Here we can see that, all variables are significant to the model with at least 90% level of significance.

Figure shows the parameter estimation from the second equation. For this equation , variables are

significant to the model with at least 90% level of significance.


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Figure 10: GRETL output for TSLM estimation for second equation

From the GRETL output our two equation model is as follows:

3.2.5 Economic verification

Form the model we can measure the sensitivity of the parameters for economic verification. Thefollowing model says that:

If the Cereal yield increase by 1 unit Cereal production per hundred thousand unit will increase

by 0.1unit.

If the GDP Per Capita increases by 1 unit Cereal production per hundred thousand will increase

by unit 0.35 unit.

If the House hold consumption increase by 1 unit Cereal production per hundred thousand unit

will decrease by unit 0.71 unit.

If the Cereal production per hundred thousand unit increase by 1 unit Cereal yield will increase

by 8.54 unit.

We can see that, the all condition is economically satisfied. So we are able to use this model for further

analysis.


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3.2.6 Statistical verification

Both of our regression equations produces a high amount of Adjusted value where, 97% of totalvariation is explained by explanatory variable in first equation and 87% total variation is explained by the

explanatory variable in the second equation.

3.2.6.1 TestForNormality:

Test criteria for normal distribution is:

Error terms are normally distributed

Error terms are not normally distributed

Decision Rule : If p - value is less than 0.05 then reject the

.

According to the result from GRETL the p - value for our model 0.66 and 0.88 which is much greater

than 0.05 so we can not reject . So error terms are normally distributed.

Figure 11: GRETL output for Normality of residuals

3.2.6.2 TestForAutocorrelation:

Test criteria for Autocorrelation is:

There is no auto correlation in the model


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There is auto correlation in the model


According to the result from GRETL on Breusch - Godfrey test the p - value for our model is 0.6 and 0.35

which is greater than 0.05 so we can not reject . So There is no autocorrelation in the model.

Figure 12: GRETL output for test of Autocorrelation of two equation model

3.2.6.3

TestForHeteroscedasticity:

Test criteria for Heteroscedasticity is:

There is no Heteroscedasticityin the model


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There is Heteroscedasticityin the model


According to the result from GRETL on Pesran - Taylor test the p - value for our model is 0.26 and 0.39

which is greater than 0.05 so we can not reject . So There is no Heteroscedasticityin the model. So wecan conclude that, results from t - test from the model are not biased.

Figure 13: GRETL output for Heteroscedasticity of two equation model

3.2.7 Reduced form of the equation


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The reduced form of the equation is,

3.2.8 Model application

In this section we can calculate some elasticity for endogenous variable form the reduced for of our

equation, for and we are able to find the value of and as prediction for 2014.

We are also able to calculate some valid elasticity. For example, in case of the elasticity of is , so 1 % increase of GDP Per Capita (US Dollar) will increase Cereal production per

hundred thousand unit (Metric tons) by 3.76 %. For the elasticity of is , so 1 %increase of GDP Per Capita (US Dollar) will increase Cereal yield (kg per Square Kilometers) by 3.81 %.

4 Conclusions

After analyzing the explanatory variable it is clear that Land under cereal production (hectares) per

hundred thousand unit, Cereal yield (kg per Square Kilometers) and GDP Per Capita (US Dollar) has

significant impact on Cereal Production per hundred thousand unit (Metric tons). The both one equation

model and two equation shows that the production for next year will increase with a significant amount.Elasticity analysis from one equation model shows that, cereal production is more sensitive to cereal yield

than other variable. But two equation model shows that Cereal Production is more sensitive to GDP Per

Capita than other variable.

BIBLIOGRAPHY

1. Land Under Cereal Production. The World Bank.[nline]. 2015

URL:http://data.worldbank.org/indicator/AG.LND.CREL.HA

2.

Damodar N.Basic Econometrics: 4th

Edition.2014. Page no: 717 - 7303. Bangladesh Agricultural.Nations Encyclopedia. 2015.
http://data.worldbank.org/indicator/AG.LND.CREL.HAhttp://data.worldbank.org/indicator/AG.LND.CREL.HAhttp://data.worldbank.org/indicator/AG.LND.CREL.HAhttp://data.worldbank.org/indicator/AG.LND.CREL.HA

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Introductory Econometrics : Factors Affecting Cereal Production of Bangladesh