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CONSUMPTION FUNCTION OF GERMANY, 1995-2017 YEARS E.N. Odzhagverdiyev, student
Supervisor: Tregub I.V., doctor of economic sciences, professor Financial university under the Government of the Russian Federation (Russia, Moscow)
DOI: 10.24411/2500-1000-2019-10667
Abstract. 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).
Keywords: Germany, tax revenue, government expenditure, interest rate, consumption expenditure, Keynes, econometrics.
Econometrics makes it possible to forecast variables with a help of mathematics and statistics. The consumption function, or Keynes-ian 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 687 968,00
1 913 912,14 942 785,00 0,0622 685 271,00
1 686 962,5S 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 779 296,00
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 887 626,00
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 Ю39 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 1 386 760,00 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-
Table 2. Regression analysis
вывод итогов
Регрессионная сммсмш
Множественный В 0,794684238
В-квадрат 0,631523038
Нормированный R-квадрат 0,573342465
Стандартная ошибка 307783,4868
Наблюдения 23
Дисперсионный анализ Fcrit: здз
<ц Si MS F ЗшчшопьР
Регрессия 3 3,08489Etl2 l,0283Etl2 10,85 0,00
Остаток 19 l(79995Etl2 94734368201
Итого 22 4,88485Etl2
кэффщм ты СтаЛртт ошибки Йжипгапшш Р-Знтеш НшашШ
V-яересечение ■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 (Bt) 2503240,781 11193948,6 0,223624466 0,825436385 -20925962,89
Ta* revenue (Tt) 0,275489186 1,906656459 0,144488109 0,886636668 -3,715188646
TcriP 2,09
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:
Ct= a0 + a± (Yt - Tt) + Et It = b0+ bjYt + b2Rt + vt Yt = Ct + It + Gt Yt = a0 + аг * Gt + a2 * 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 < (T(Et) = const, a(vt) = const, a(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<Fcrit and 1/GQ<Fcrit) our residuals are homoscedastic.
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.
Table 3.
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
Y 3 048 525,62
Y- 2 404 314,82
Y+ 3 692 736,42
Y real 2 671 463,7
□ 12,37%
So, estimated value of consumption is quacy and correctness of using modified close to the real value of consumption for Keynesian model for closed economy and year 2017 with approximation error of shows that this model can be used for fore-12,37%. all our tests and analysis show ade- casting.
Библиографический список
1. Кейнс Дж. М. Общая теория занятости, процента и денег / Пер. с англ. проф. Н.Н. Любимова; под ред. д.э.н., проф. Л. П. Куракова. - М.: Гелиос АРВ, 2002.
2. ТрегубИ.В. Эконометрика на английском языке: учебное пособие / И.В. Трегуб. - М.: Русайнс, 2017. - 110 с.
3. Stanford University. Critical Values for the Durbin-Watson Test [Электронный ресурс] Stanford University. - 2019. - Режим доступа: https://web.stanford.edu/~clint/bench/dwcrit.htm, open.
4. World Bank national accounts data [Электронный ресурс] World Bank Open Data. -2019. - Режим доступа: https://data.worldbank.org/, open.
ФУНКЦИЯ ПОТРЕБЛЕНИЯ ГЕРМАНИИ ЗА 1995-2017 ГОДА Э.Н. Оджагвердиев, студент
Научный руководитель: Трегуб И.В., д-р экон. наук, профессор Финансовый университет при Правительстве Российской Федерации (Россия, г. Москва)
Аннотация. Статья посвящена теме тестирования эконометрической модели функции потребления на примере Германии. В данной работе анализируется практическая возможность применения модифицированной модели Кейнса для закрытой экономики для прогнозирования макроэкономических показателей Германии, а именно объема потреблений. Данная эконометрическая модель была оценена с регрессионного анализа методом наименьших квадратов (МНК).
Ключевые слова: Германия, налоговые доходы, государственные расходы, процентная ставка, потребительские расходы, Кейнс, эконометрика.
