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1
Secrieru V.
Student of International Finance Master Degree Program Financial University under the Government of the Russian Federation
Russian Federation, Moscow MODELING OF THE CONSUMTION FUNCTION OF THE CONJUNCTION MODEL ON THE EXAMPLE OF USA
Abstract This article is devoted to the analysis of consumption in the framework of the market model for the economy on the example of the United States. The time period of 26 years 1991-2016 was chosen for the analysis. The purpose of this work is to verify the applicability of this model in the current market conditions of the United States. In this regard, statistics on the exogenous and endogenous variables of the model were collected, and the least squares method was used to estimate them. The model was tested for the presence of autocorrelation, heteroskedasticity, consistency of estimates.
Key words: USA , econometrics, least squares method, conjuncture model, consumption function, regression analysis.
The US has the most technologically powerful economy in the world, with a per capita GDP of $59,500. US firms are at or near the forefront in technological advances, especially in computers, pharmaceuticals, and medical, aerospace, and military equipment; however, their advantage has narrowed since the end of World War II. Based on a comparison of GDP measured at purchasing power parity conversion rates, the US economy in 2014, having stood as the largest in the world for more than a century, slipped into second place behind China, which has more than tripled the US growth rate for each year of the past four decades.
The main task of the work and data source
In order to analyze weather the consumption function of conjunction model is applicable for such economy as USA we have to take into consideration the latest available data. USA has a very open and quite successful economy now with diversified consumption market. The main task of my research work is to analyze consumption function of the Conjunction model for USA Ecomony. The data for this research was collected World bank data source. As a time period were chosen twenty six years from 1991 till 2016
Model specification
Long-term problems for the US include stagnation of wages for lower-income families, inadequate investment in deteriorating infrastructure, rapidly rising medical and pension costs of an aging population, energy shortages, and sizable current account and budget deficits. This problems can influence the consumption in the country.1
Econometric Conjunction model for USA economy you may see below
1Tregub I.V. Econometrics. Model of real system M.: PSTM. 2016.
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Ct = ao + atYt + a2Ct-X + £t It = bo + b±rt + b2\t-i + n = Co + ciYt + c2Mt + Vt Yt = Ct + It + Gt E(et) = 0;E(^t) = 0:E(pt) = 0 <&(£t) = const; o(^t) = const; <r(pt) = const Where Yt - total income in the period; It - investments in the period; Ct -consumption expenditure in the period; Gt - Government Tax Revenue; rt - Interest Rate; Gt- Government Spending; Mt money supplyIt-1- investments in the period t-1; Ct-1- consumption expenditure in the period t-1
In this model there are four endogenous variables. The first equation is the function of consumption, the second equation is the function of investment, the third equation is the function of the money market, the fourth equation is the identity of income. In this model there are three endogenous variables: Consumption, Investment Money market and Income. money supply, Government Spending are exogenous variables and two lag variables ,It-1- investments in the period t-1; Ct-1 -consumption expenditure in the period t-1
and since the subject of research is Consumption, then we should transform this function to the following one:
Ct = ao + a1^t-1 + a1lt-1 + a1Mt + a1Gt + Bt E(9t) = 0 .
<r(9t) = const
Is should be noted that disturbance terms, which were included in initial form of the model (et and ), are replaced by 9t in reduced form. And before the estimation starts, we assume the first and second conditions of the Gauss-Markov theorem are to be satisfied. During the research these assumptions will be verified.
After the regression analysis is done in Gretl, the estimated behavioral equation is as follows:
!Ct = -65,8 + 1.31 * Ct-1 - 0.5 * It-1 - 0.11 *Mt- 0.5 * Gt + 9t (187.24)(0.12)(0.06) (0.35) [-0.35][10][-1.25] [-1.82] R2adj. = 0.99; F = 2.88 Table 2. Regression analysis output2. The estimated value of the coefficient of determination equals to 0.99, which means that 99% in changes of dependent variable may be explained by changes in independent variables by linear regression model. It is also between 0 and 1, consequently, the test is past.
The meaning of test is to ensure that Fcritica] is less than F. In our case with 25 observation, Fcritical equals to 2,86. F calculated >Fcrit (Fcrit=3,787 and F
calculated= 2207,62). This means inequality Fcritical < F is confirmed. R-Square is not random, and quality of specification and econometric model is high.
In order to check the significance of coefficients, Student's T-test should be used. The inequality |t| < tcrit , where t is the value of t-statistics had to be tested. It is calculated in Excel, using the formula: Tcrit = T.inv.2t (probability; deg_freedom), where probability is equal to 5%/1%/10% and and deg_freedom - is residual.3
By using different percentage, we can say that some independent variables that are insignificant. Unfortunately the results are unsatisfied . the only significant criteria is lag of consumer spending (C(t-1)).
Table 1 T crit test
Tcrit 2.612 1.978 1.656
1% 5% 10%
Intercept msign insign insign
C(t-1) sign sign sign
I(t-1) insign insign insign
M insign insign sign
G insign insign insign
Using these assumptions, the GQ-test can be conducted. Goldfeld-Quandt test checks the second assumption of Gauss-Markov theorem about homoscedasticity of random disturbances in regression analyses. In other words, this test works under the assumption that the error variance is equal for all observations, which is to say that error term is homoscedastic. When this is true, the variance of one part of the sample must be the same as the variance of another part of the sample independent on how the sample is sorted. If this is not the case we must conclude that the data at hand is heteroscedastic. Its Formula:
GQ = ESS1/ESS2, where ESS is explained sum of squares.4 In order to get ESS1 and ESS2 , we should calculate the absolute value of all independent variables in initial table to sort them by given value, and then divide tables into equal parts. As it was said, it will help to check the variance of one part of the sample with another part. It is necessary to conduct the regression analysis of both parts to see are they the same .This will be true if both values GQ and 1/GQ will be less than Fcrit. In our case this test is faild because 1/GQ is higher than Fcrit. The conclusion: second assumption of Gauss-Markov theorem about homoscedasticity is failed there is heteroscedasticity.
3Трегуб И.В. Эконометрика на английском языке: учебное пособие / И.В. Трегуб. — Москва: Русайнс, 2017. — 110 с.
4Tregub I.V. International diversification. М.: PSTM. 2015.
GQ= 0.006945 < Fcrit
1/GQ= 143.9959 > Fcrit
Fcrit 4.387374
DW-test checks a particular case of third assumption of the Gauss-Markov theorem about the absence of autocorrelation (a relationship between values separated from each other by a given time lag) between residuals in the model. We can calculate Darbin-Watson statistics using values of the residuals et.5
There are 25 observations in each model, and 5 endogenous variables (including intersection) hence intervals may be the following:_
25 observations 5Xs DW= 1.816409883
0 dL dU 2 4-du 4-dl 4
0 1.03811 1.76655 2 2.23345 2.96189 4
R N G N L
Table 7.1 DW-test
Possible outcomes: N- No information about autocorrelation: G- Good result
- no autocorrelation, 3rd GM condition confirmed. We can use ordinary least squares; R- Right part - bad result, they are negatively autocorrelative; Left part -bad result, they are positively autocorrelative, third assumption of the Gauss-Markov theorem is disturbed
In our case there are Good result - no autocorrelation, 3rd GM condition confirmed. We can use ordinary least squares
Conclusion
Acording to results which we het after regression analysis of statistical data of the consumption function based on conjunction model is not applicable for USA economy. The reason is low significants of coeficients based on T test and heteroscedasticity of data which is represented by Goldfeld-Quandt test checks the second assumption of Gauss-Markov theorem about homoscedasticity.
In my opinion there are more factors which should be considered in order to create applicable consumption function model. Also the heteroscedasticity can be eliminated by the Greatl software. That will be the topic for further analysis.
References
1. Трегуб И.В. Эконометрика на английском языке: учебное пособие / И.В. Трегуб. — Москва: Русайнс, 2017. — 110 с.
2. Трегуб И.В. Эконометрические исследования. Практическиепримеры. Econometric studies. Practical examples / И.В. Трегуб - Москва: Лань, 2017. - 49
- 50.
3. Tregub I.V. Econometrics. Model of real system М.: PSTM. 2016.
4. Tregub I.V. International diversification. М.: PSTM. 2015.
5. World Bank Open Data, https://data.worldbank.org/
5 Трегуб И.В. Эконометрические исследования. Практическиепримеры. Econometric studies. Practical examples / И.В. Трегуб - Москва: Лань, 2017. - 49 - 50.
