# Эконометрика, вариант 4 (3 задачи)

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Objective 1
According to the two years studied the dependence of retail trade turnover (Y, bn. Rub.) On a number of factors: X1 - inventories at current prices, bln. Rub .; X2 - nominal wages, rub .; X3 - money income, bln. Rub .; X4 - the official rate of the ruble against the US dollar.
Table 1 Initial data
Month Y X1 X2 X3 X4
1 72.9 42.1 988 117.7 6,026
2 67.0 36.7 123.8 1000 6.072
3 69.7 37.9 126.9 1059 6.106
4 70.0 39.1 134.1 1040 6.133
5 69.8 39.6 1047 123.1 6,164
6 69.1 39.6 126.7 1122 6.198
7 70.7 38.8 1110 130.4 6,238
8 80.1 44.9 129.3 1052 7.905
9 105.2 42.9 145.4 1112 16,065
10 102.5 41.5 1123 163.8 16.010
11 108.7 46.9 1164 164.8 17.880
12 134.8 50.6 227.2 1482 20,650
13 116.7 48.3 164.0 1167 22,600
14 117.8 46.7 1199 183.7 22.860
15 128.7 50.4 1385 195.8 24.180
16 129.8 51.9 1423 219.4 24.230
17 133.1 54.2 209.8 1472 24,440
18 136.3 54.6 1626 223.3 24.220
19 139.7 54.4 1618 223.6 24.190
20 151.0 54.9 1608 236.6 24.750
21 154.6 57.0 1684 236.6 25.080
22 160.2 58.1 1716 248.6 26.050
23 163.2 63.1 1785 253.4 26.420
24 191.7 68.0 351.4 1808 27,000
Setting: 1 For a given set of data, build a linear multiple regression model. Evaluate the accuracy and adequacy of the constructed regression equation.
2 Calculate the significant and insignificant factors in the model. Build a regression equation with statistically significant factors. Give an economic interpretation of the model parameters.
3 for the model, check the condition of homoscedasticity residues, using test Goldfeld - Quandt.
4 Check the resulting model for the presence of autocorrelation by the test Durbin - Watson.
5 Check whether adequate assumption of homogeneity of initial data in the sense of regression. Is it possible to combine the two samples (in the first 12 and the rest of the observations) in one and consider a single regression model Y for X.

According to the dynamics of trade turnover (Y, bn. Rub.) And income (X bn. Rub.) Was obtained by the following model with distributed lags:
Yt = 0.55 * Xt + 0.25 * Xt-1 + 0.14 * Xt-2 + 0.09 * Xt-3 + εt.
(0.06) (0.04) (0.04) (0.03)
In parentheses are the values \u200b\u200bfor the standard errors of the regression coefficients.
Meaning of R2 = 0,99.
Task: 1. Examine the results of the regression analysis.
2. Give an interpretation of the model parameters: Define the short-term and long-term multipliers.
3. Determine the mean and the median lag lag.

Objective 3
One of the modifications of the demand and supply is as follows:
Qtd = β1 + β2 * Pt + β3 * It + ε1
Qts = β4 + β5 * Pt + β3 * Pt-1 + ε2
Qtd = Qts
where Qtd - demand for goods in the period t;
Qts - offer goods in period t;
Pt - the price of goods in the period t;
Pt-1 - price of goods in the period t-1;
It - income in the period t.
Task: 1. Check each equation model identifiability, applying the necessary and sufficient condition for identifiability.
2. Record the shape of the model.
3. Determine the method for estimating the structural parameters of each equation.