Consumption function of Germany, 1995-2017 years
Автор: Odzhagverdiyev E.N., Tregub I.V.
Журнал: Международный журнал гуманитарных и естественных наук @intjournal
Рубрика: Экономические науки
Статья в выпуске: 3-2 (30), 2019 года.
Бесплатный доступ
The following work is prepared on the topic of econometric model of consumption function for Germany. The article considers the practical possibility of using the modified Keynesian model for closed economy in order to forecast Germany’s macroeconomic indicators, especially the country’s volume of consumption. This econometric model was evaluated with a least squares regression analysis (OLS).
Germany, tax revenue, government expenditure, interest rate, consumption expenditure, keynes, econometrics
Короткий адрес: https://sciup.org/170186069
IDR: 170186069 | DOI: 10.24411/2500-1000-2019-10667
Текст научной статьи Consumption function of Germany, 1995-2017 years
Econometrics makes it possible to forecast variables with a help of mathematics and statistics. The consumption function, or Keynesian consumption function, is an economic formula that represents the functional relationship between total consumption and gross national income. It was introduced by British economist John Maynard Keynes, who argued the function could be used to track and predict total aggregate consumption expenditures. The classic consumption function suggests consumer spending is wholly determined by income and the changes in income. If true, aggregate savings should increase proportionally as gross domestic product (GDP) grows over time. The idea is to create
a mathematical relationship between disposable income and consumer spending, but only on aggregate levels. The following work is prepared on the topic of econometric model of consumption function for Germany. It includes statistical data for 22 years 1995-2017 and econometric model estimation, forecasting and tests. All the information was taken from OECD (Organization for Economic Co-operation and Development) and The World Bank: tax revenue, government expenditure, consumption expenditure are represented in million US dollars, interest rate is represented in percentage (%). First of all, using the Excel program the table with Germany’s data 1995-2017 year was created:
Table 1. Germany’s data for 1995-2017
|
Consumption expenditure |
Government expenditure (G) |
Interest rate (Rt) |
Tax revenue (Tt) | |
|
1 964 207,72 |
1 037 926,00 |
0,0685 |
687 96 8,00 |
|
1 913 912,14 |
942 785,00 |
0,0622 |
685 271,00 |
|
1 686 962,55 |
945 330,00 |
0,0564 |
693 264,00 |
|
1 689 963,32 |
962 423,00 |
0,0457 |
715 899,00 |
|
1 667 857,45 |
984 831,00 |
0,0449 |
746 630,00 |
|
1 478 214,48 |
947 098,00 |
0,0526 |
767 045,00 |
|
1 480 980,76 |
1 022 525,00 |
0,0480 |
763 140,00 |
|
1 574 025,03 |
1 044 200,00 |
0,0478 |
759 652,00 |
|
1 920 614,00 |
1 061 545,00 |
0,0407 |
768 400,00 |
|
2 138 071,77 |
1 051 570,00 |
0,0404 |
768 843,00 |
|
2 178 270,12 |
1 062 999,00 |
0,0335 |
779 29 6,00 |
|
2 249 698,91 |
1 069 695,00 |
0,0376 |
825 406,00 |
|
2 497 454,15 |
1 076 099,00 |
0,0422 |
876 839,00 |
|
2 745 422,59 |
1 116 223,00 |
0,0398 |
907 008,00 |
|
2 631 631,01 |
1 170 508,00 |
0,0322 |
887 62 6,00 |
|
2 568 866,92 |
1 219 219,00 |
0,0274 |
903 213,00 |
|
2 781 968,98 |
1 208 565,00 |
0,0261 |
965 050,00 |
|
2 643 914,84 |
1 221 782,00 |
0,0150 |
1 003 734,00 |
|
2 796 690,33 |
1 263 000,00 |
0,0157 |
1 039 169,00 |
|
2 861 925,21 |
1 291 848,00 |
0,0116 |
1 078 561,00 |
|
2 459 391,07 |
1 332 634,00 |
0,0050 |
1 127 848,00 |
|
2 532 910,42 |
1 3 86 760,00 |
0,0009 |
1 182 714,00 |
|
2 671 463,70 |
1 439 839,00 |
0,0032 |
1 230 455,00 |
After we created table, we use regression ing this function, we estimated the following analysis to find out R² and F. The regression variables: a1, a0, a2 and a3.
analysis made in Excel by Data Analysis. Us-
After all the tests performed, it appeared that there is correlation in residuals, and they are heteroscedastic. Only one coefficient a1 is significant. However, the model of consump-
tion function is adequate, and the error of forecast is very low.
Estimated form of the model:
Table 2. Regression analysis
|
вывод итогов |
||
|
Регрессионная cmomucmmo |
||
|
Множественный 9 0,794684238 |
||
|
R-квадрат 0,631523038 |
||
|
Нормированный R-квадрат 0,573342465 |
||
|
Стандартная ошибка 307789,4868 |
||
|
Наблюдения 23 |
||
|
Дисперсионный анализ |
Fcrit: 3,13 |
|
|
df |
S |
MS F Значимость F |
|
Регрессия 3 |
3,08489E+12 |
1,02836+12 10,85 0,00 |
|
Остаток 19 |
1,799956+12 |
94734368201 |
|
Итого 22 |
4,884856+12 |
|
|
Коэффициенты |
Стонбартнои ошибки |
t-cmomucmuKO P-Значение Нижние 95% |
|
Y-пересечение -979310,0886 |
1745925,324 |
■0,560911784 0,581413052 4633573,789 |
|
Government expenditure |G| 2,556430469 |
1,878187314 |
1,361115822 0,189403207 -1,374660757 |
|
Interest rate |Rt| 2503240,781 |
11193948,6 |
0,223624466 0,825436385 -20925962,89 |
|
Tax revenue (Tt) 0,275489186 |
1,906656459 |
0,144488109 0,886636668 -3,715188646 |
|
Tcrit:2,09 |
||
( Ct = + аг ( Yt - Tt )+ Et
It = + EiYt + b2Rt + vt
⎪ Yt = + It + Gt
⎪ Yt = + aT ∗ Jt + «2 ∗ T + a3 ∗ R
. Ct = -979310,088 + 2,56 ∗ 1439839 + 2503240,78 ∗ 0,0032 + 0,28 ∗ 1230455 (1745925,32) (1,88) (11193948,60) (1,91) (307789,48)
⎪⎪ [-0,56] [1,36] [0,22] [0,14]
⎪ E ( Et )=0, E ( vt )=0, E ( wt )=0
⎩ a( Et)=const, (J ( Vt)=const,о(wt)=const,
Numbers in the round brackets represent standard deviation of each coefficient. Numbers in square brackets represent t-statistic. To estimate our model, we need to perform several tests. Our next step is R²-test. R² is equal to 0,63 and it shows that 63,3 % of consumption expenditures describe variances of disposable income in the linear regression model. We can say that it’s not a good value, as it is not close to 1. Using data analysis for the two subsamples, we must find the values of the residual sum of squares for both samples. The resulting figures are 67 473 918 236,92 and 90 203 641 312,59. So, we obtain GQ=0,75, and (1/GQ) =1,34. To find Fcrit, we must use the same formula as before and use the degrees of freedom from the two samples. The result will be Fcrit=161,45. So, 161,45>0,75 and 1,34 <161,45 so second gauss markov condition is confirmed (GQ So next we will do Durbin-Watson test. In statistics, the Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation at lag 1 in the residuals (prediction errors) from a regression analysis. We have DW test = 0,018 in which case we have autocorrelation because, if dw >0 but less dl or dw>4-dl or less 4 - autocorrelation in residuals. As a result, we have autocorrelation and we don’t have any information. Having carried out Fisher criterion we found out that our calculated F is greater than critical value and we can say that R2 is not random and quality of specification an econometric model is high. So, our P-value is less than probability of mistake that means that all tests are passed. Table 3. Calculation of values on Keynes model Table 3. Ŷ 3 048 525,62 Y- 2 404 314,82 Y+ 3 692 736,42 Y real 2 671 463,7 ꝺ 12,37%
Список литературы Consumption function of Germany, 1995-2017 years
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