Dependence of net investment on net income and gross operating surplus (according to Menges’s model)

The study of macroeconomics is very important for evaluation of overall performance of an economy in terms of national income. The mathematical modelling transforms the theory in a numerical way. Therefore future performance can be predicted.

The work is dedicated to estimation of Menges’s model in relation to its second equation describing linear dependence of net investment on net income and gross operating surplus.

To build models five developed economies were chosen: Netherlands, Norway, Switzerland, United States, Australia.

The data measured in billions of local currency for the period from 1960 till 2013 was gathered from AMECO – the annual macro-economic database of European Commission.

In this paper I have conducted a study of the influence of current value of net income and gross operating surplus on net investment.

The initial form of a model is as follows

(У с = « 0 + « 1 ^х * 1С + « 2 * * 2С + ^ С

{          Е&д = 0

о(гс') = Const

where x 1t - gross national income, x 2t - gross operating surplus, y t - net investment, £_t - disturbance term.

Gross national income is the sum of value added by all resident producers plus any product taxes (less subsidies) not included in the valuation of output plus net receipts of primary income (compensation of employees and property income) from abroad.

Operating surplus is the surplus (or deficit) on production activities before account has been taken of the interest, rents or charges paid or received for the use of assets.

Net investment represents the value of acquisitions of new or existing fixed assets by the business sector, governments and "pure" households (excluding their unincorporated enterprises) less disposals of fixed assets and less consumption of fixed capital.

Therefore y t is an endogenous (dependent) variable while x 1t and x 2t are exogenous (independent) ones.

1.    Correlation analysis

Correlation analysis was made to investigate the level of dependence of endogenous variable on exogenous variables.

Correlaton	Netherlands	Norway	Switzerland	US	Australia
y t and x 1t	0.773	0.913	0.165	0.803	0.982
y t and x 2t	0.775	0.917	0.204	0.790	0.984

Therefore there is a positive relationship of stated variables. The linear relationship between variables is the strongest in Australia and Norway, while there is the weakest relationship (or no linear relationship at all) in Switzerland.

2.    Regression analysis

Estimation of coefficients of the model for every country was made by Excel function called Data analysis. Obtained coefficients are presented in a following table.

	a 0	S a0	t a0	a 1	S a1	t a1	a 2	S a2	t a2
Netherlands	7.42	1.42	5.21	-0.015	0.072	-0.21	0.017	0.18	0.67
Norway	9.56	5.10	1.88	-0.01	0.053	-0.20	0.16	0.12	1.39
Switzerland	9.32	2.3	4.05	-0.14	0.046	-3.07	0.44	0.14	3.21
United States	34.74	36.75	0.95	0.37	0.085	4.39	-0.84	0.22	-3.89
Australia	-0.66	1.94	-0.34	-0.15	0.069	-2.20	0.62	0.16	3.95

Standard error analysis

The standard error analysis showed that all regressors should be excluded from the Netherlands model, in Norway one regressor a1 should be excluded. Free terms are not significant in the United States and Australia.

3. Regression statistics

Regression statistics results are presented below.

Regression Statistics	Netherlands	Norway	Switzerland	US	Australia
Multiple R	0,775	0,917	0,437	0,852	0,986
R-Square	0,601	0,840	0,191	0,727	0,973
Adjusted R Square	0,585	0,834	0,159	0,716	0,972
Standard Error	5,575	24,883	6,014	148,209	8,780
Observations	54	54	54	54	53

Number of observations in Australia is less since there was no data for the

2013 year.

4.    Estimated forms of models and their testing

The Netherlands

Y_t = 7.42 - 0.015X 1 + 0.017X 2 + £_t

• (1.42)    (0.072)     (0.18)   (5.57)

• [5.21]    [-0.21]      [0.67]

• -                R² = 0,6 F = 38.36 F_crit = 3,18

GQ = 12.48 GQ^-1 = 0.08 F crit (gq) = 1.98

DW = 0.5 d_l = 1.49 d_u = 1.64

In the model only 60% of all variations of the dependent variable are explained by the independent variables included in the model and 40% are the result of other sources not included in the model. There are no significant regressors in the model. F-test showed that R2 is not random and the model is specified properly. GQ test presented that residuals are heteroscedastic. And DW test defined positive autocorrelation of residuals. Therefore only the first condition of Gauss-Markov theory is confirmed, it iss impossible to use OLS and estimate coefficients. The Netherlands model is not adequate.

Norway

Y_t = 9.56 - 0.01X 1 + 0.161X 2 + £_t

(5.09)    (0.053)     (0.12)   (24.88)

• [1.87]    [-0.2]      [1.39]

• -         R² = 0,84 F = 134.19 F_crit = 3.18

GQ = 32.91 GQ^-1 = 0.03 F crit ( _GQ ) = 1.98

DW = 0.69 d i = 1.49 d_u = 1.64

• 84% of all variations of the dependent variable are explained by the independent variables included in the model. There are no significant coefficients. Only the first condition of Gauss-Markov theory is confirmed. Therefore it is impossible to use OLS and estimate coefficients. The Norway model is not adequate.

Switzerland

"     Y_t = 9.32 - 0.14X 1 + 0.44X 2 + £_t

• (2.3)    (0.046)     (0.14)   (6.01)

[4.05]    [-3.06]      [3.21]

R2 = 0.19  F = 6.01  Fcrit = 3.18

GQ = 2.78 GQ^-1 = 0.35 F^ it (gq) = 1.98

DW = 0.27 dl = 1.49 du = 1.64

In Switzerland only 19% of all variations of the dependent variable are explained by the independent variables included in the model while all the coefficients are significant. Only the first condition of Gauss-Markov theory is confirmed. But in the way of predicting Net investment the Switzerland model is adequate.

The United States

Y_t = 34.74 + 0.37X 1

-

(36.75) [0.95] R² = 0.73 GQ = 76.36 DW = 0.41

(0.085)

[4.39]

F = 67.77

0.84X 2 + £_t

(0.22)   (148.21)

[-3.89]

F crit = 3.18

GQ^-1 = 0.013 F crit ( _C0 ) = 1.98 d_i = 1.49   d_u = 1.64

In the US 73% of all variations of the dependent variable are explained by the independent variables included in the model and 27% are the result of other sources. The only significant coefficients are a0 and a2. Only the first condition of Gauss-Markov theory is confirmed. But in the way of predicting Net investment the US model is adequate.

Australia n Yt = -0.66 - 0.15X1t + 0.62X2t + st

• (1.94)   (0.069)     (0.16)   (8.78)

[-0.34] [-2.2]      [3.95]

• - R² = 0.97 F = 893.13 F_crit = 3.18

GQ = 60.35 GQ^-1 = 0.017 F_{crit (GQ)} = 2.01

DW = 0.78 d i = 1.48  d_u = 1.63

In Australia 97% of all variations of the dependent variable are explained by the independent variables included in the model. Both regressors are significant while free term is not significant. Only the first condition of Gauss-Markov theory is confirmed. While in relation to predicting Net investment the Australian model works.

Conclusion

Econometric study of the influence of gross operating surplus and gross national income on net investment including construction of the initial and estimated forms of models, F-test, Goldfeld-Quandt test, Durbin-Watson test, showed that the model does not work in the modern environment.