To illustrates the global average inflation rate from 2015 to 2024. Inflation remained moderate—between 4% and 6%—from 2015 to 2019. A noticeable increase occurred in 2021 and peaked in 2022 at over 11%, driven by post-pandemic supply chain disruptions and energy market volatility. By 2024, inflation is projected to decline significantly, suggesting a return toward pre-pandemic stability.
highlights that high-income countries maintained stable inflation, while upper- and lower-middle-income groups faced notable volatility, especially between 2020 and 2023.
It shows that Sub-Saharan Africa and South Asia experienced the highest and most volatile inflation rates during the period. In contrast, regions like North America and Europe & Central Asia maintained lower and more stable inflation. Most regions saw inflation peaks around 2022, followed by declines into 2024.
We model inflation as a function of time and income group, allowing groups to have different average levels and (optionally) different trends over time.
We estimate the common-slope model: \[ \text{Inflation}_{it} = \beta_0 + \beta_1\,\text{Year}^{(c)}_{it} + \sum_{g\in\{\mathrm{LI},\mathrm{LMI},\mathrm{UMI}\}} \gamma_g\,\mathbf{1}\{\mathrm{IG}_i=g\} + \varepsilon_{it}. \]
Optionally, the interaction model: \[ \text{Inflation}_{it} = \beta_0 + \beta_1\,\text{Year}^{(c)}_{it} + \sum_{g} \gamma_g\,\mathbf{1}\{\mathrm{IG}_i=g\} + \sum_{g} \delta_g\,\text{Year}^{(c)}_{it}\,\mathbf{1}\{\mathrm{IG}_i=g\} + \varepsilon_{it}. \]
Hypotheses (interaction test):
\(H_0:\ \delta_g=0\ \forall g\) (no
group-specific trends)
\(H_1:\ \exists g:\ \delta_g\neq
0\).
## n_year_only n_no_inter n_full
## 1731 1731 1731
##
## # Summaries
##
## Call:
## lm(formula = Inflation ~ Year, data = d_ig)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.02 -5.18 -3.56 -0.71 550.16
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1194.0203 394.2138 -3.029 0.00249 **
## Year 0.5946 0.1952 3.046 0.00236 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.2 on 1729 degrees of freedom
## Multiple R-squared: 0.005337, Adjusted R-squared: 0.004762
## F-statistic: 9.277 on 1 and 1729 DF, p-value: 0.002356
##
##
## Call:
## lm(formula = Inflation ~ Year + `Income Group`, data = d_ig)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.37 -5.03 -1.79 0.64 546.57
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1249.1582 387.3961 -3.224 0.00129 **
## Year 0.6198 0.1918 3.231 0.00126 **
## `Income Group`Low income 13.3531 1.8813 7.098 1.84e-12 ***
## `Income Group`Lower middle income 7.6987 1.4173 5.432 6.37e-08 ***
## `Income Group`Upper middle income 2.4586 1.3891 1.770 0.07691 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.79 on 1726 degrees of freedom
## Multiple R-squared: 0.04158, Adjusted R-squared: 0.03936
## F-statistic: 18.72 on 4 and 1726 DF, p-value: 4.447e-15
##
##
## Call:
## lm(formula = Inflation ~ Year * `Income Group`, data = d_ig)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.35 -4.59 -1.64 0.49 546.05
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.540e+02 6.411e+02 -1.488 0.1369
## Year 4.737e-01 3.175e-01 1.492 0.1358
## `Income Group`Low income 1.105e+03 1.336e+03 0.827 0.4082
## `Income Group`Lower middle income -1.838e+03 1.004e+03 -1.832 0.0672 .
## `Income Group`Upper middle income 1.826e+02 9.774e+02 0.187 0.8518
## Year:`Income Group`Low income -5.407e-01 6.616e-01 -0.817 0.4139
## Year:`Income Group`Lower middle income 9.141e-01 4.970e-01 1.839 0.0660 .
## Year:`Income Group`Upper middle income -8.921e-02 4.840e-01 -0.184 0.8538
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.77 on 1723 degrees of freedom
## Multiple R-squared: 0.04494, Adjusted R-squared: 0.04106
## F-statistic: 11.58 on 7 and 1723 DF, p-value: 1.873e-14
##
##
## # F-tests on nested models
## Analysis of Variance Table
##
## Model 1: Inflation ~ Year
## Model 2: Inflation ~ Year + `Income Group`
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1729 930336
## 2 1726 896433 3 33903 21.759 7.847e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Variance Table
##
## Model 1: Inflation ~ Year + `Income Group`
## Model 2: Inflation ~ Year * `Income Group`
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1726 896433
## 2 1723 893291 3 3142 2.0201 0.1091
The Q-Q plot shows moderate deviation from the normal line, particularly in the tails. This suggests that the residuals are not perfectly normally distributed, which may slightly affect the validity of the ANOVA results. However, given the large sample size (n > 1700), the test is likely robust to this violation.
##
## Model comparison (AIC):
## df AIC
## m_no_interact 6 15742.64
## m_full 9 15742.56