Question

Problem 2 (25 %)
Use multiple regression to estimate a model for the share of the shadow economy of the
form:
SHADOWi = β0 + β1INCOMEi + β2UNABLEi + εi
i = 1, …, 28
List the assumptions for the regression model, and explain the output provided by Excel.
Provide a nice and easy to read output.
 How is the R2 and the standard error calculated what is the interpretation?
 What signs are found for the estimated coefficients of the included variables and what do
you think should be expected?
 How many of the variables are significant and what is the interpretation of the p-value?
 Finally, inspect the plots of residual. Is white noise observed?
Estimate now a new multiple regression model of the form:
SHADOWi = β0 + β1INCOMEi + β2UNABLEi + β3UNEMPi + εi
i = 1, …, 28
Again set up a nice presentation of your Excel output.
 Compare the two models estimated with regard to R2, the standard error, the significance
of the estimated coefficients, and the plots of residuals
 Which of the two models performs best?


DATA TABLE

	Share of the shadow economy, %	GDP per capita, (1,000) €	Unable to afford life expenses, %	Long term unemployment rate, %	Life satisfaction (1 to 10)	Income quintile share ratio (S80/S20)	Location: W = West, E = East, M = Mediterranian
Country	SHADOW	INCOME	UNABLE	UNEMP	SATISFACTION	RATIO	LOCATION
Belgium	16,8	30,7	25,4	3,4	7,4	3,9	W
Bulgaria	31,9	12,0	68,6	6,8	5,5	6,1	E
Czech Republic	16,0	20,7	42,4	3,0	6,4	3,5	E
Denmark	13,4	32,1	28,2	2,1	8,4	4,5	W
Germany	13,3	31,5	33,4	2,5	7,2	4,3	W
Estonia	28,2	18,2	44,7	5,5	6,3	5,4	E
Ireland	12,7	32,9	31,2	9,1	7,4	5,2	W
Greece	24,0	19,2	40,5	14,4	6,2	6,6	M
Spain	19,2	24,4	42,1	11,1	7,5	7,2	M
France	10,8	27,7	33,0	4,1	7,2	4,5	W
Croatia	29,0	15,7	67,3	10,3	6,8	5,4	E
Italy	21,6	25,6	42,5	5,7	6,9	5,5	M
Cyprus	25,6	23,6	50,5	3,6	7,2	4,7	M
Latvia	26,1	16,4	73,6	7,8	6,2	6,5	E
Lithuania	28,5	18,3	60,4	6,6	6,7	5,3	E
Luxembourg	8,2	67,1	24,8	1,6	7,8	4,1	W
Hungary	22,5	17,0	74,3	4,9	5,8	4,0	E
Malta	25,3	21,9	25,0	3,0	7,2	3,9	M
Netherlands	9,5	32,6	22,0	1,8	7,7	3,6	W
Austria	7,6	33,1	22,2	1,1	7,7	4,2	W
Poland	24,4	17,1	54,1	4,1	7,1	4,9	E
Portugal	19,4	19,4	35,9	7,7	6,8	5,8	M
Romania	29,1	12,8	53,1	3,2	6,7	6,3	E
Slovenia	23,6	21,4	45,7	4,3	7,0	3,4	E
Slovakia	15,5	19,4	36,1	9,4	6,4	3,7	E
Finland	13,3	29,4	27,9	1,6	8,1	3,7	W
Sweden	14,3	32,2	17,6	1,5	8,0	3,7	W
United Kingdom	10,1	26,8	42,9	2,7	7,3	5,4	W
Source: Eurostat
Source: On the black economy: Friedich Schneider (2013): "The Shadow Economy in Europe 2013" Universität Linz, ATKearney and VISA.

Answer 1

List the assumptions for the regression model

1) Normality distributed .

2) Variance constant

3) relationship between two or more variable must be linear .

4) independence .

For Model 1

Model1 is given by

SHADOW=182.8353 -0.30515 *INCOME + 0.207074*UNABLE

model 1 R-square = 0.6705

Adjusted R-square =0.6441

FOr Model 2

Model1 is given by

SHADOW=174.63 -0.2912*INCOME + 0.1997*UNABLE +0.1529*UNEMP

model 1 R-square = 0.6744

Adjusted R-square =0.6337

Comment - Using both the model we say that Model1 is better than model 2 becuse Adjusted R-square is better than model 2.