THE FACTORS AFFECTING MONTHLY EXPENDITURE OF FTU’S STUDENT

Econometrics Assignment TABLE OF CONTENTS Page I INTRODUCTION II METHODOLOGY DEFINITION 1.1 Income 1.2 Expenditure THEORIES OF CONSUMERS’ BEHAVIOR 3 THE KEYNESIAN CONSUMPTION FUNCTION III ECONOMETRIC MODEL MODEL CONSTRUCTION COEFFICIENTS PREDICTION IV DATA DESCRIPTION V EMPERICAL RESULTS 13 USING THE ABOVE DATA TO ESTIMATE THE REGRESSION MODEL BY OLS METHOD .13 MEANING OF THE REGRESSION COEFFICIENTS 14 TESTING THE SIGNIFICANCE OF THE REGRESSION COEFFICIENTS AND THE RELEVANCE OF THE REGRESSION FUNCTION 14 FIRST CURE: FOR THE REGRESSION MODEL 17 TESTING THE CONFORMITY WITH THE ASSUMPTIONS OF OLS METHOD 21 -1- Econometrics Assignment SECOND CURE: FOR THE HETEROSKEDASTICITY 23 FINAL REGRESSION MODEL .28 VI CONCLUSION 29 VII REFERENCES 30 -2- Econometrics Assignment I INTRODUCTION Vietnam in recent years, along with nearly 200 countries around the world, has been integrating into the trend of globalization and exercising national campaigns towards the overall development in economic, political, social and cultural aspects In this context, human capital is considered one of the key factors for Vietnam’s long-term revolution, and it is university students that make up an indispensable part in the domestic labor force in the future Regarded as one of the most privileged universities in Vietnam, Hanoi Foreign Trade University has long attracted thousands of students from North to South every year Each student, as a matter of fact, has his own family background, distinctive personalities as well as certain level of knowledge and experience Such factors, certainly, have significant impacts on students’ daily life, in which students’ expenditure should be mentioned first of all Therefore, after taking everything into consideration, we decided to choose and study the project: “THE FACTORS AFFECTING MONTHLY EXPENDITURE OF FTU’S STUDENT” Although the government has tried to implement financial aid programs for university learners, we, especially those coming from provincial areas, have still met many difficulties in managing our spending every day It is really not easy to allocate -3- Econometrics Assignment our limited source of money into a range of activities in the most effective way Thus through our project, we would like to provide you with more in-depth understanding about some main factors dominating daily spending of FTU’s students We hope that arguments and statistics in this project will be helpful for you in drawing a reasonable plan of expenditure for the time being II METHODOLOGY In this project, we consider three factors that may affect students’ monthly spending: income, students’ homeland and students’ characteristics Homeland and characteristics are two qualitative variables In general they have certain impacts on the ways students plan their expenditure For instance, a student coming from rural area may consume less than one coming from a big city Similarly, the amount of spending depends on whether the student is generous or thrifty, shopping-lover or shopping-averse Income, by contrast, is a quantitative variable It can be said that income and expenditure are two critical elements of the market economy, as everyone has to consider how to spend their -4- Econometrics Assignment disposable income in the most reasonable way There also exists a close-knit relationship between those two factors, thus we will use microeconomic and macroeconomic theories and models to interpret it DEFINITIONS 1.1 Income There are two main types of income, which can be listed as personal income and disposable income 1.1.1 Personal income (PI) Personal income is the income earned by households and noncorporate businesses Unlike national income, it excludes retained earnings, which is the amount of revenue corporations have earned but have not paid out to stockholders as dividend It also subtracts corporate income taxes and contributions for social insurance (mostly Social Security taxes) In addition, personal income includes interest income, the amount households receive from their holdings of government debt, and transfer payment, the amount they get form government transfer program such as welfare and social security 1.1.2 Disposable income (DI) Disposable personal income is the net income that households and non-corporate businesses earn after fulfilling all their -5- Econometrics Assignment obligations to the government It equals personal income minus personal taxes and certain non-tax payments (such as traffic tickets) DI = PI – personal taxes In the scope of our project, however, our studied subjects are FTU’s students who have no obligation to pay income tax Thus they have entire disposal of what they earn, which means that their personal income also equals their disposable income Besides, students’ earnings generally come from two main sources: family financial support and income from part-time jobs Family financial support is the monthly amount supported by students’ families so that they can fulfill their daily life Income from part-time jobs is what students earn when participating in the labor market, which is tax-free 1.2 Expenditure Expenditure is the sum of money each individual uses for the purchase of goods and services to satisfy their needs For instance, each month students have to pay for some urgent needs such as food, clothing, traveling fees, housing expenses (if students have to rent a house), and so on Those all aim at responding to personal needs of students -6- Econometrics Assignment THEORIES OF CONSUMERS’ BEHAVIOR • We assume that university students always try to maximize their own utility by using a number of certain resources This means that although there are many ways of planning expenditure, students will only follow the choice that is most likely to optimize their satisfaction Moreover, as there always exists a limit to students’ income, they have to consider how to allocate that restricted source for a variety of daily activities In short, this part of our project has two main objectives The first one is to study how students use their income to bring about maximum benefit for themselves And the second one is to explain how income affects expenditure theoretically and realistically • The theories of consumers’ behavior, in microeconomics, begin with three basic assumptions about consumers’ preference Firstly, preferences are complete This means that consumers can rank their baskets of goods based on personal preferences or different levels of utility they may provide Prices of goods have no effects on consumers’ choice in this case Secondly, preferences are transitive If a person prefers good A to good B, and good B to good C, certainly he will prefer good A to good C -7- Econometrics Assignment Thirdly, in case of normal goods, consumers always prefer more to less This is an obvious argument, because everyone feels more satisfied when consuming more goods and services • Generally our project still relies on those basic assumptions, but instead of goods, we aim to study different ways of planning expenditure of FTU’s students Thus in the scope of this project, we will adjust the three assumptions as follows Firstly, students can compare and rank different choices of spending based on their satisfaction Secondly, of a student prefers choice A to choice B, and choice B to choice C, this means that he prefers choice A to choice C Thirdly, students will choose the choice of expenditure that benefits them most THE KEYNESIAN CONSUMPTION FUNCTION In general, the basic form of consumption function is as follows: C = f(Yd) with Yd representing disposable income But as aforementioned, since there is no personal income tax levied on university students, their disposable income also equals their -8- Econometrics Assignment personal income In this case, the consumption function can be rewritten as : C = f(Y) This reflects the relationship between planned expenditure and disposable income Generally students’ spending increases when income increases, but it is assumed to rise less quickly than income The reason is that students tend to divide their earnings into two parts: consumption and savings This means that they not spend all their money on the purchase of goods and services but tend to save a small amount to deal with unexpected incidents in the future, such as illnesses, burglaries, house-moving, etc This is a popular psychological phenomenon of almost every student in Vietnam, especially those coming from provincial areas to big cities to further their study If consumption rises at a lower speed than income does, the ratio consumption/income will decrease as income increases We use a linear function in the form of y = a + bx to build the consumption function In particular, we have the standard Keynesian consumption function as follows: C = f1 (Y ) = C + MPC.Y -9- Econometrics Assignment where C = Students’ expenditure C= Autonomous consumption This is the level of consumption that will take place even if income is zero If an individual's income falls to zero, some of his existing spending can be sustained by using savings This is known as dis-saving spending MPC = Marginal propensity to consume This is the change in consumption divided by the change in income, or in other words, it determines the slope of the consumption function The MPC reflects the effect of an additional VND of disposable income on consumption MPC = - 10 - ∆C ∆Y Econometrics Assignment Schwarz criterion 593.0675 1199 391 criterion 135 Hannan-Quinn 1195 050 After the variable X1 = is omitted, R increases from 0.869396 to 0.975876 ⇒ The variable X1 = will be omitted The regression function has the intercept β1 = c) New regression function (SRF) EXPi = 154.635 CHAi + 0.859465 FFSi + 0.816912 INCi + ei (2) d) Meaning of the regression coefficients: - βˆ1 = means that if an economical student who comes from an rural area has no family financial support and no income, he/she will spend zero every month - βˆ2 = 154.635 means that a generous student will spend 154.635 thousand dong on average more than an economical one, provided that they have the same family financial support and income every month - 28 - Econometrics Assignment - βˆ3 = 0.859465 means that every month if the family financial support of one student increases (or decreases) by one thousand dong, he/she will spend 0.859465 thousand dong more (or less) on average; provided that his/her character and monthly income remain unchanged - βˆ4 = 0.816912 means that every month if the income of one student increases (or decreases) by one thousand dong, he/she will spend 0.816912 thousand dong more (or less) on average; provided that his/her character and monthly family financial support remain unchanged e) Testing the significance of the regression coefficients and the relevance of the regression function: - Slope β : H : β2 = Hypothesis :   H1 : β ≠ Formula: t= βˆ2 − 154.635 − = = 2.049 75.4656 SE ( βˆ2 ) Since | t | = 2.049 > t0.05(78) = 1.66, we reject H0 There is insufficient sample evidence to claim that β = , that is, the slope is significant - Slope β3 : - 29 - Econometrics Assignment H : β3 = Hypothesis :   H1 : β ≠ Formula: t= βˆ3 − 0.859465 − = = 24.41 0.0352129 SE ( βˆ3 ) Since | t | = 24.41 > t0.05(78) = 1.66, we reject H0 There is insufficient sample evidence to claim that β3 = , that is, the slope is significant - Slope β : H : β4 = Hypothesis :   H1 : β ≠ Formula: t= βˆ4 − 0.816912 − = = 19.58 0.0417275 SE ( βˆ4 ) Since | t | = 19.58 > t0.05(78) = 1.66, we reject H0 There is insufficient sample evidence to claim that β5 = , that is, the slope is significant - The relevance of the regression function:  H : R = Hypothesis :   H1 : R > Formula: F= R (n − k ) (0.976464) (83-4) = = 539.755 (1 − R )(k − 1) [1 − (0.976464) ].3 If α = 0.05 , then F0.05 (3,79) = 2.73 - 30 - Econometrics Assignment Since F = 539.755 > F0.05 (3,79) = 2.73 , we reject H0 There is insufficient sample evidence to claim that R = , that is, the regression function is relevant TESTING THE CONFORMITY WITH THE ASSUMPTIONS OF OLS METHOD a) Testing multicollinearity: - Correlation matrix: Correlation coefficients, using the observations - 83 5% critical value (two-tailed) = 0.2159 for n = 83 CHA 1.0000 FFS 0.3252 1.0000 INC 0.0313 0.3549 1.0000 CHA FFS INC From the above matrix, in which there is no r ij ( i = 2, 4; j = 2, ) greater than 0.8, we can claim that multicollinearity does not exist - Variance Inflation Factors (VIF) method: The following result is obtained: Variance Inflation Factors Minimum possible value = 1.0 Values > 10.0 may indicate a collinearity problem CHA 1.150 FFS 1.314 INC 1.177 - 31 - Econometrics Assignment VIF(i) = 1/(1 - R(i)^2), where R(i) is the multiple correlation coefficient between variable j and the other independent variables Properties of matrix X'X: 1-norm = 2.717891e+008 Determinant = 2.5333308e+017 Reciprocal condition number = 6.3086927e-008 From the above analysis, since VIF(i) < 10 ( i = 2, ), we can claim that multicollinearity does not exist - Conclusion: Multicollinearity does not exist b) Testing heteroskedasticity with White’s test:  H : The regression model is homoskedastic Hypothesis :   H1 : The regression model is heteroskedastic White's test for heteroskedasticity OLS, using observations 1-83 Dependent variable: uhat^2 coefficient std error t-ratio p- value CHA -59510.8 135663 -0.4387 0.6622 FFS 38.4485 77.7873 0.4943 0.6226 INC -2.86511 106.989 -0.02678 0.9787 X1_X2 12.6469 81.7329 0.1547 0.8774 X1_X3 111.923 94.6678 1.182 - 32 - Econometrics Assignment 0.2408 sq_FFS 0.9822 X2_X3 0.6886 sq_INC 0.8009 -0.000733091 0.0236958 0.0327011 -0.02242 0.0588971 0.00807122 0.0318929 0.4023 0.2531 Unadjusted R-squared = 0.255030 Test statistic: TR^2 = 21.167482, with p-value = P(Chi-square(7) > 21.167482) = 0.003530 From the above analysis: nR2 = 83 x 0.255030 = 21.167482 > χ 0.05 (k − 1) = χ 0.05 (8 − 1) = 14.0671 p-value = 0.003530 < 0.05 Therefore, we reject H0 There is insufficient sample evidence to claim that the regression model is homoskedastic In other words, there exists heteroskedasticity SECOND CURE: FOR THE HETEROSKEDASTICITY Two variables FFS and INC are the cause of heteroskedasticity We can cure this problem by dividing both sides of the regression function by either FFS or INC a) Dividing both sides of the regression function by FFS: - Constructing new regression function: - 33 - Econometrics Assignment EXPi CHAi FFSi INCi Ui = β2 + β3 + β4 + FFSi FFSi FFSi FFSi FFSi ⇒ newEXPi = β3 + β newCHAi + β newINCi + υi Model 1: OLS, using observations 1-83 (n = 78) Missing or incomplete observations dropped: Dependent variable: newEXP newFFS newCHA newINC Coeffici Std t-ratio p-value ent Error 0.79607 0.05180 15.365 2.141907) = 0.829182 From the above analysis: nR2 = 45 x 0.047598 = 2.141907 < χ 0.05 (5) = 11.0705 p-value = 0.829182 > 0.05 Therefore, we can conclude that heteroskedasticity does not exist - Testing (4) on multicollinearity: + Correlation matrix: Correlation coefficients, using the observations - 83 (missing values were skipped) 5% critical value (two-tailed) = 0.2159 for n = 83 newCH A newFF S 1.0000 0.5674 newCH A 1.0000 newFF S From the above matrix, in which there is no r ij greater than 0.8, we can claim that multicollinearity does not exist + Variance Inflation Factors (VIF) method: The following result is obtained: Variance Inflation Factors - 38 - Econometrics Assignment Minimum possible value = 1.0 Values > 10.0 may indicate a collinearity problem newCHA 1.475 newFFS 1.475 VIF(i) = 1/(1 - R(i)^2), where R(i) is the multiple correlation coefficient between variable j and the other independent variables Properties of matrix X'X: 1-norm = 223.38933 Determinant = 0.042566825 Reciprocal condition number = 5.7550166e-008 From the above analysis, since VIF(i) < 10, we can claim that multicollinearity does not exist + Conclusion: Multicollinearity does not exist - Testing the relevance of the regression function (4)  H : R = Hypothesis :   H1 : R > Formula: R (n − k ) (0.941516) (45-3) F= = = 163.944 (1 − R )(k − 1) [1 − (0.941516) ].2 If α = 0.05 , then F0.05 (2, 42) = 3.23 Since F = 163.944 > F0.05 (2, 42) = 3.23 , we reject H0 There is insufficient sample evidence to claim that R = , that is, the regression function is relevant FINAL REGRESSION MODEL - 39 - Econometrics Assignment From all of the above analysis and results, we obtain the following final regression model: - Population regression function: (PRF): newEXPi = 0.707631 + 269.765newCHAi + 0.928624newFFSi + U i (Ui: disturbance term) - Sample regression function: (SRF) newEXPi = 0.707631 + 269.765 newCHAi + 0.928624 newFFSi + υi (υi : new residual) in which: EXP i + newEXPi = INC i CHA i + newCHAi = INC i FFS i + newFFSi = INC i INC i + newINCi = INC i ei + υi = INC i VI CONCLUSION - 40 - Econometrics Assignment From the above analysis and results, some conclusions are obtained as follows: • The variables newCHA and newFFS have impact on newEXP However, both newCHA and newFFS depend on CHA, FFS and INC; and newEXP depends on EXP Thus, generally EXP depends on CHA, FFS and INC In other words, a student’s monthly expenditure depends on his/her character, monthly family financial support and monthly income • The brief steps of constructing the appropriate model: - First, there exists inappropriate variables in the original regression function This problem is cured by omitting two variables: X1 = and HOM - Second, the above-derived function has heteroskedasticity problem This can be cured by dividing both sides of the function by either of these two variables: FFS and INC - Third, we try dividing both sides of the function by FFS The results show that heteroskedasticity has not been cured Then again we divide both sides of the function by INC This time we obtain the final regression function - Eventually, the final regression model is significant and appropriate and meet all the assumptions of OLS R2 = 0.941516 - 41 - Econometrics Assignment means that the regression function can explain about 94.15% the student’s monthly expenditure in reality • Limitation: When curing heteroskedasticity problem, we have difficulty in dividing both sides of the function by any independent variables This results from the fact that some of the observations for the variables FFS and INC may have value zero (xi = 0) However, Gretl has automatically omitted these incomplete observations and done analysis in a quite accurate way To some extent, the problems have been cured and we get the most suitable regression model VII REFERENCES • Introduction to Econometrics, Brief Edition – James H Stock and Mark W Watson • Econometrics – Nguyen Quang Dong • Principles of Macroeconomics, 3rd edition – N Gregory Mankiw • Macroeconomics – Dr Duong Tan Diep • http://tutor2u.net/economics/content/consumption/consum ption_theory.htm - 42 - ... everything into consideration, we decided to choose and study the project: ? ?THE FACTORS AFFECTING MONTHLY EXPENDITURE OF FTU’S STUDENT? ?? Although the government has tried to implement financial aid programs... instead of goods, we aim to study different ways of planning expenditure of FTU’s students Thus in the scope of this project, we will adjust the three assumptions as follows Firstly, students... This is the change in consumption divided by the change in income, or in other words, it determines the slope of the consumption function The MPC reflects the effect of an additional VND of disposable