The problem

Keynes observed that: As income increases, consumption also increases, but by a smaller amount:

\[C = a + b Y\]

where:

\(C\) – consumption;

\(a\) – autonomous consumption (consumption when income is zero);

\(b\) – marginal propensity to consume (MPC), where \(0< b <1\)

\(Y\) – Income

The data

From Eurostat’s nama_10_gdp table we extract: P3 (Final consumption expenditure) and ‘B1GQ’ (Gross domestic product at market prices) for EU members in 2023 using R’s eurostat package.

The chart

Testing hypothesis on MPC

Estimating with regression method:

m0 <- lm(c ~ gdp, data=gdp)
summary(m0)
## 
## Call:
## lm(formula = c ~ gdp, data = gdp)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -168973   -5886    9763   13857  100933 
## 
## Coefficients:
##                  Estimate    Std. Error t value            Pr(>|t|)    
## (Intercept) -10864.724776  10280.954130  -1.057               0.301    
## gdp              0.756550      0.008935  84.670 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 44480 on 25 degrees of freedom
## Multiple R-squared:  0.9965, Adjusted R-squared:  0.9964 
## F-statistic:  7169 on 1 and 25 DF,  p-value: < 0.00000000000000022

Thus the estimated consumption function for 27 EU members is:

\[ \hat y = 10864.72 + 0.76 \mathrm{GDP}\]

Keynes’ hypothesis was confirmed!