Consumption Function

2

The Consumption FunctionECON 318

Submitted to:Dr. Mohammed Bouaddi

Submitted by:Basma Yassa900121613Sarah Farid900113953Sondos El Kollaly900112000

Submitted on: 23/12/2014

Introduction3Data and Data Source5The General Form of the Model:5First Model Germany7A - Regression Analysis:7B - Testing hypothesis regarding individual estimated coefficients (T test)8C - Testing the overall significance of the whole relation (ANOVA Table)8D - Income-Consumption Graph9Second Model - Italy:10A - Regression Analysis:10B -Testing hypothesis regarding individual estimated coefficients (T test)11C -Testing the overall significance of the whole relation (ANOVA Table)11D Income-Consumption Graph12Third Model - Japan13A - Regression Analysis:13B - Testing hypothesis regarding individual estimated coefficients (T test)14C - Testing the overall significance of the whole relation (ANOVA Table)14D Income-Consumption Graph15Fourth Model - France:16A - Regression Analysis:16B -Testing hypothesis regarding individual estimated coefficients (T test)17C - Testing the overall significance of the whole relation (ANOVA Table)17D Income-Consumption Graph18Fifth Model - Spain19A - Regression Analysis:19B - Testing hypothesis regarding individual estimated coefficients (T test)20C- Testing the overall significance of the whole relation (ANOVA Table)20D IncomeConsumption Graph21Conclusion22Introduction

John Maynard Keynes first mentioned the consumption function in his book "The General Theory of Employment, Interest and Money". The consumption function is used to express consumer expenditure. The components of Keynes' initial version of the consumption function included autonomous consumption which is independent of income (the amount that consumers will consume regardless of their income) and induced consumption which depends on each consumer's level of disposable income which rested on a parameter Keynes described as the marginal propensity to consume. Ever since, the relationship between consumption and income has been of major importance in the minds of economic theorists and researchers. Keynes initial consumption function can be written as:C = a + b(Y-T)where:a represents autonomous consumptionb represents the marginal propensity to consumeY represents total incomeT represents taxes(Y-T) represents disposable incomeKeynes hence claimed that consumption was largely dependent on income, and that the degree of this dependence was the marginal propensity to consume. He assumed the marginal propensity to consume (b), to be between zero and 1.In our project, we aim to test Keynes hypothesis as follows:The aim of this paper is to determine the effects of different explanatory variables on consumption in the German, Italian, Japanese, Spanish and French economies. The variables we have chosen to investigate are income, Interest rate, and consumer price index. A multiple regression has been run to determine the effect of each variable in each country on the level of consumption. The selection of the aforementioned countries was based on the great variation in their respective economies. The OLS estimation and the subsequent test that were run, using E-views 8 software, should show the effect of each variable on consumption in each country considered and should also provide definite answers to whether the model and individual variables are significant or not. We will conclude by comparing the results of each country in order to highlightthe discrepancies between them, and to provide a general conclusion to our research based on the findings for all countries.

Data and Data Source

The data for this project was collected from the World Bank Data Bank. The data collected includes the disposable income (denoted by Yd), consumption expenditure (consumption, denoted by C), the interest deposit rate (interest rate, denoted by R) and the consumer price index (denoted by CPI) for the period from 1975 to 2013. Our model implies that consumption C is a function of inflation CPI, disposable income Yd and interest rate R. To understand the relationship, we have to take into account the Keynesian Consumption Function which states that C (total consumption) is a function of both a (which represents autonomous consumption) and the marginal propensity to consumer (in our case, this is the coefficient of Yd) which should always lie between zero and one if Keynes theory is correct.The General Form of the Model:

C=0+1YD+2R+3CPI+Ui

where:

C: Aggregate consumption

Yd : Disposable Income

R : Effective interest rateCPI: Consumer price index.

O: The constant denotes autonomous consumption, which is the amount of consumption when income, interest rates, and CPI are all equal to zero. In other words, it is the minimum consumption that a person will consume regardless of any other variable.

1: The rate of change in consumption with respect to changes in income holding all other variables constant (the marginal propensity to consume which Keynes assumed to be between zero and one).

2: The rate of change in consumption with respect to a change in interest rate holding all other variables constant (the relationship should be negative since higher interest rates increase the opportunity cost of consumption and would encourage people to save more and consume less).

3: The rate of change in consumption with respect to change in consumer price index holding all other variables constant.

Ui: The error term

First Model Germany A - Regression Analysis:

Dependent Variable: C_GER

Method: Least Squares

Date: 12/11/14 Time: 14:11

Sample: 1975 2013

Included observations: 39

C_GER=C(1)+C(2)*YD_GER+C(3)*R_GER+C(4)*CPI_GER

CoefficientStd. Errort-StatisticProb.

C(1)-1.50E+102.28E+10-0.6566630.5157

C(2)0.7297190.01452550.238810.0000

C(3)1.53E+093.52E+090.4328330.6678

C(4)1.17E+097.63E+081.5379940.1330

R-squared0.999043Mean dependent var1.48E+12

Adjusted R-squared0.998961S.D. dependent var7.63E+11

S.E. of regression2.46E+10Akaike info criterion50.78787

Sum squared resid2.12E+22Schwarz criterion50.95850

Log likelihood-986.3636Hannan-Quinn criter.50.84909

F-statistic12176.76Durbin-Watson stat1.512471

Prob(F-statistic)0.000000

Interpretation of the model:

0=-1.501010: The constant is the minimum consumption that will be consumed assuming all other variables are equal to zero.

1=MPC=0.729719: The rate of change in the consumption with respect to disposable income holding all other factors constant. This coefficient is called the marginal propensity to consume, and is between zero and one which satisfies Keynesian consumption function.

2=1.35E+09: The rate of change in consumption with respect to interest rate holding all other factors constant.

3=1.17E+09: the rate of change in consumption with respect to CPI holding other variables constant.

The adjusted R-squared is 0.999 (99.9%) which indicates that 99.9% of the variation in consumption can be explained using the regression model which includes the effect of income, interest rate and CPI. Only 1% of the variation in consumption is not explained using the model.

B - Testing hypothesis regarding individual estimated coefficients (T test)

The T-distribution test gives information on the significance level of the parameters. It is carried out by comparing the value of the t-stat with the t-table and then deciding whether to accept or reject H0 based on the information below.We obtain the value of: t-calculated that we obtained from E-Views t-table that we obtained from the t-distribution table and we have a two-tailed test. Significance level is 5 % therefore 0.05/2 = 0.025 in each tail. Degrees of freedom = n-k = 39-4 =35. Critical value = 2.030

If the t-calculated > t-table, then we reject the null hypothesis and the parameter will be significant.Test The Variable t-calculated t-table Decision

Ho:0=0Ha: 00 Constant -0.6566 2.030 Insignificant

Ho:1=0Ha: 10 Income 50.23871 2.030 Significant

Ho:2=0 Ha: 20 Interest Rate 0.432831 2.030 Insignificant H0:3=0 Ha:30 CPI 1.53 2.030 Insignificant

C - Testing the overall significance of the whole relation (ANOVA Table)Ho: 1= 2= 3= 0Ha: 1 2 3 0R2 = 0.999Fcal = 12176.71Ftab = F (3, 35)Significance Level = 0.05Critical value = 2.92

Since Fcal > Ftab, at the 5% significance level we reject H0 which is the whole relationship is insignificant, and accept Ha, that the relationship is significant.

D - Income-Consumption Graph

The graph depicts a very close relationship between consumption and disposable income in Germany, which further supports the Keynesian hypothesis that disposable income is a main driver of consumption.

Second Model - Italy:A - Regression Analysis:

Dependent Variable: C_ITA


Date: 12/11/14 Time: 14:15

Sample (adjusted): 1976 2013

Included observations: 38 after adjustments

C_ITA=C(1)+C(2)*YD_ITA+C(3)*R_ITA+C(4)*CPI_ITA


C(1)-1.67E+108.48E+09-1.9643180.0577

C(2)0.8217840.01618450.776960.0000

C(3)-1.61E+091.07E+09-1.5126550.1396

C(4)-2.66E+083.59E+08-0.7412750.4636








Interpretation:

0=-1.671010: The constant is the minimum consumption that will be consumed assuming all other variables are equal to zero.


2=-1.61E+09: The rate of change in consumption with respect to interest rate holding all other factors constant.

3= -2.66E+08: the rate of change in consumption with respect to CPI holding other variables constant.

The adjusted R-squared is 0.9987 (99.87%) which indicate that 99.87% of the variation in consumption can be explained using the regression model which includes the effect of income, interest rate and CPI. Only 0.13% of the variation in consumption is not explained using the model.

B -Testing hypothesis regarding individual estimated coefficients (T test)

The T-distribution test gives information on the significance level of the parameters. It is carried out by comparing the value of the t-stat with the t-table and then deciding whether to accept or reject H0 based on the information below.We obtain the value of: t-calculated that we obtained from E-Views t-tabulated that we obtained from the t-dist. Table and we have a two-tailed test. Significance level is 5 % therefore 0.05/2 = 0.025 in each tail. Degrees of freedom = n-k = 39-4 =35 Critical value = 2.030

If the t-calculated > t-table , then we reject the null hypothesis and the parameter will be significant.Test The Variable t-calculatedt-table Decision

Ho:0=0 Ha: 00 Constant -1.964 2.030 Insignificant

Ho:1=0 Ha: 10 Income 50.7769 2.030 Significant

Ho:2=0 Ha: 20 Interest Rate -1.51265 2.030 Insignificant H0: 3=0 Ha : 30 CPI -0.741275 2.030 Insignificant

C -Testing the overall significance of the whole relation (ANOVA Table)Ho: 1= 2= 3= 0Ha: 1 2 30R2 = 0.9987Fcal = 9365.732Ftab = F (3, 35)Significance Level = 0.05Critical value = 2.92Since Fcal > Ftab, at the 5% significance level we reject H0 which is that the whole relationship is insignificant, and accept Ha, that the relationship is significant.

D Income-Consumption Graph

Once again, the graph shows the strikingly close relationship between consumption and income.

Third Model - Japan

A - Regression Analysis:

Dependent Variable: C_JPN


Date: 12/11/14 Time: 14:18

Sample: 1975 2013


C_JPN=C(1)+C(2)*YD_JPN+C(3)*R_JPN+C(4)*CPI_JPN


C(1)4.58E+114.85E+110.9439420.3517

C(2)0.8390620.05760214.566450.0000

C(3)-4.26E+103.55E+10-1.2006050.2380

C(4)-6.93E+097.85E+09-0.8831000.3832








C_JPNYD_JPNR_JPNCPI_JPN

Mean2.50E+123.37E+123.44920392.32708

Median3.03E+123.98E+123.41539799.71667

Maximum4.82E+125.94E+126.157586103.7083

Minimum3.46E+115.13E+110.22987255.99166

Std. Dev.1.37E+121.70E+121.31495312.84809

Skewness-0.127528-0.392277-0.191206-1.357746

Kurtosis1.8035941.7223442.8844893.813437

Jarque-Bera2.4317183.6528850.25932013.05781

Probability0.2964550.1609850.8783940.001461

Sum9.74E+131.31E+14134.51893600.756

Sum Sq. Dev.7.14E+251.10E+2665.705836272.788

Observations39393939

Interpretation:

0= 4.58E+11: The constant is the minimum consumption that will be consumed assuming all other variables are equal to zero.



3= -6.93E+09: the rate of change in consumption with respect to CPI holding other variables constant.

The adjusted R-squared is 0.975 which means that 97.5% of the variation in consumption is explained by the model using the effect of income and interest rate. That is a decent percentage which suggests that the variables to some extent have a great effect on consumption. However, the other 2.5% of the variation in consumption is not explained using the model.


The T-distribution test gives information on the significance level of the parameters. It is carried out by comparing the value of the t-statistics with the t-table and then deciding whether to accept or reject based on the information below. t-value that we obtained from E-Views t-table that we obtained from the table and we have a two-tailed test. Significance level is 5 % therefore 0.05/2 = 0.025 in each tail. Degrees of freedom = n-k = 39-4 =35. Critical value = 2.030

If the t-calculated > t-tabulated, then we reject the null hypothesis and the parameter will be significant. Test The Variable t-calculated t-tabulated Decision

Constant 0.94 2.030 Insignificant

Income 14.5 2.030 Significant

Interest Rate -1.2 2.030 Insignificant CPI -0.88 2.030 Insignificant

Therefore, from this table we can conclude that Income and Interest Rate have a significant effect on Consumption at 5% level of significance.

C - Testing the overall significance of the whole relation (ANOVA Table)

R2 = 097.5Fvalue = 463.7131Ftable = F (3, 35)Significance Level = 0.05Critical value = 2.29Since Fvalue > Ftable, at the 5% significance level we reject H0 which is the whole relationship is insignificant, and accept Ha, that the relationship is significant.


From this graph we can see that there is a strong relationship between income and consumption. The two lines are moving in the same direction. Both consumption and income increased from 1975 till 1985 then the slope became steeper till1989. The fluctuations of income and consumption that occurred after 1990 happened together at the same years.

Fourth Model - France:

A - Regression Analysis:

Dependent Variable: C_FRA


Date: 12/11/14 Time: 14:20

Sample: 1975 2013


C_FRA=C(1)+C(2)*YD_FRA+C(3)*R_FRA+C(4)*CPI_FRA


C(1)-2.21E+101.59E+10-1.3928470.1725

C(2)0.8202640.01295263.331950.0000

C(3)-6.69E+082.32E+09-0.2885250.7746

C(4)768109115.38E+080.1427420.8873








Interpretation:

0=-2.21E+10: The constant is the minimum consumption that will be consumed assuming all other variables are equal to zero.



3= 76810911: the rate of change in consumption with respect to CPI holding other variables constant.

The adjusted R-squared is 0.999 which indicates that 99.9% of the variation in consumption can be explained by the model using the effect of Income and Interest rate. On the other hand, 0.01% of the variation in consumption is not explained using the model.

B -Testing hypothesis regarding individual estimated coefficients (T test)

The T-distribution test gives information on the significance level of the parameters. It is done by comparing the t-value with the t-table and then deciding whether to accept or reject based on the information below. t-value that we obtained from E-Views t-table that we obtained from the table and we have a two-tailed test. Significance level is 5 % therefore 0.05/2 = 0.025 in each tail. Degrees of freedom = n-k = 39-4 =35. Critical value = 2.030


Constant -1.392847 2.030 Insignificant


Interest Rate -0.288525 2.030 Insignificant 0.14 2.030 Insignificant

C - Testing the overall significance of the whole relation (ANOVA Table)

R2 = 0.999Fcal = 12843.00Ftab = F (3, 35)Significance Level = 0.05Critical value = 2.29Since Fvalue > Ftable, at the 5% significance level we reject H0 which means that the relationship is significant.


In the graph, we can see a similar relationship between income and consumption. They both fluctuate together. The peak of income and consumption for France was in 2008. This means that during this period of time income has probably increased due to lower rates of unemployment so there are now more consumers in the market. This could also mean that wages have increased in 2008 so people had more disposable income to spend on goods and services.

Fifth Model - SpainA - Regression Analysis:

Dependent Variable: C_ESP


Date: 12/11/14 Time: 14:22

Sample: 1975 2013


C_ESP=C(1)+C(2)*YD_ESP+C(3)*R_ESP+C(4)*CPI_ESP


C(1)-1.97E+095.69E+09-0.3456880.7316

C(2)0.7836630.01358057.706150.0000

C(3)8.47E+087.20E+081.1769140.2472

C(4)-1.01E+082.08E+08-0.4840810.6313








Interpretation:

0=-1.97E+09: The constant is the minimum consumption that will be consumed assuming all other variables are equal to zero.


2=8.47E+08: The rate of change in consumption with respect to interest rate holding all other factors constant.

3=-1.01E+08: the rate of change in consumption with respect to CPI holding other variables constant.

The adjusted R-squared is 0.998718 which indicates that 98.9% of the variation in consumption can be explained using the regression model using the effect of income and interest rate. Only .02% of the variation in consumption is not explained using the model.


The T-distribution test gives information on the significance level of the parameters. It is carried out by comparing the value of the t-stat with the t-tabulated and then deciding whether to accept or reject based on the information below.We obtain the value of: t-calculated that we obtained from E-Views t-tabulated that we obtained from the t-dist. Table and we have a two-tailed test. Significance level is 5 % therefore 0.05/2 = 0.025 in each tail. Degrees of freedom = n-k = 39-4 =35. Critical value = 2.030


Constant -0.345688 2.030 Insignificant


Interest Rate 1.176914 2.030 Insignificant CPI -0.4840 2.030 Insignificant

Therefore, from this table we can conclude that income has a significant effect on Consumption, while Interest rate has an insignificant effect on the consumption at 5% level of significance.

C- Testing the overall significance of the whole relation (ANOVA Table)

R2 = 0.998Fcal = 9088.007Ftab = F (3, 35)Significance Level = 0.05 Critical value = 2.09Since Fcal > Ftab, at the 5% significance level we reject H0 which is the whole relationship is insignificant, and accept Ha, that the relationship is significant.

D IncomeConsumption Graph

Conclusion

Our findings are summarized in the following table:Germany Italy JapanSpainFrance

CoefficientsConstantInsig.Insig.Insig.Insig.Insig.

IncomeSig. Sig.Sig.Sig.Sig.

Interest rateCPIInsig.Insig.Insig.Insig.Insig.Insig.Insig.Insig.Insig.Insig.

R-Squared0.9990.9980.970.9980.99

F-statistic121769365.7463.7908812843

All the models show that the variable with the most significant impact on consumption is income. This is supportive to Keynes hypothesis because while the other variables do affect consumption, their effect is significantly weaker than that of the effect of income. It is also apparent that all the estimated models are good fits with very low percentages of error variance out of the total variance in the model as we can see from the very high R-Squared statistics. This means that the models are very good in representing the source of variation in consumption across the 5 countries. The F-tests also support this.The coefficient for income (denoted by B1) was found to be between 0.72 and 0.85 in all countries meaning that all countries consume about 72% to 85% of the income they make and this is what Keynes described as the marginal propensity to consume. Our findings confirm his hypothesis, which is that the marginal propensity to consume will always be between zero and one.

2

Documents

Consumption Function