# The Predictive Grey Forecasting Approach for Measuring Tax Collection
## 4 Results and Discussion
### Accuracy of the Forecasting Model
Furthermore, the rising revenue base provides more capacity for investment in the significant expected increase in direct and indirect tax collections, reflecting the economy's formalization and greater tax compliance ([PERSON] and [PERSON] 2023). As the tax base grows, the government can lessen its reliance on borrowing and external funding, resulting in increased financial independence. This increase in revenue may also allow for more targeted fiscal policies, allowing the government to address specific economic difficulties such as unemployment, inflation, and social welfare demands, promoting long-term economic resilience ([PERSON] et al. 2024). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Year** & **2023–24** & **2024–25** & **2025–26** & **2026–27** & **2027–28** & **2028–29** & **2029–30** \\ \hline Direct Tax & 1,683,223 & 1,860,250 & 2,055,896 & 2,272,118 & 2,511,080 & 2,775,175 & 3,067,044 \\ \hline Indirect Tax & 1,427,485 & 1,574,463 & 1,736,576 & 1,915,380 & 2,112,594 & 2,330,114 & 2,570,031 \\ \hline Proportion of Direct Tax & 54.11\% & 54.16\% & 54.21\% & 54.26\% & 54.31\% & 54.36\% & 54.41\% \\ \hline \end{tabular} Source: Authors’ contributions (Idem for all tables).  
\end{table} 
Table 1: Predicted values of tax collection in India (INR in crores). As the actual and predicted values of tax collection rose over the period, Table 2 shows the actual values and predicted values for the period, with error terms indicated by direct (Figure 4) and indirect (Figure 5) tax collection. GM (1,1) predictions are based on the base period, i.e., 2000-01 with zero error and yearly forecasts. From 2000-01 to 2005-06, both direct and indirect taxes had considerable negative errors, indicating lower tax collections than expected. From 2006-07 onwards, the difference between actual and forecast numbers for direct and indirect taxes began to close, with lower errors over time. By 2010-11, the error in direct tax revenues began to fall substantially, eventually approaching zero in 2012-13, when real and forecast numbers were nearly identical. Although the number of indirect tax mistakes decreases over time, greater differences still occur. From 2017-18 to 2021-22, direct tax receipts showed positive errors, suggesting that they exceeded forecasts. This indicates a possible improvement in economic conditions or changes in tax policies. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Year** & \multicolumn{2}{c}{**Actual Values (X\({}^{\text{b}}\)\({}_{\text{k}}\))**} & \multicolumn{2}{c}{**Predicted Values (X\({}^{\text{b}}\)\({}_{\text{k}}\))**} & \multicolumn{2}{c}{**Error E (k)**} \\ \hline  & **Direct Tax** & **Indirect Tax** & **Direct Tax** & **Indirect Tax** & **Direct Tax** & **Indirect Tax** \\ \hline
2000–01 & 68,305 & 119,814 & 68,305 & 119,814 & 0 & 0 \\ \hline
2001–02 & 69,198 & 117,318 & 186,504 & 165,282 & \(-\)117,306 & \(-\)47,964  
However, indirect tax revenues continued to exhibit major inaccuracies, particularly in 2020-21, when there was a significant departure, possibly due to economic disturbances such as the pandemic. The error was reduced, indicating either better forecasting techniques or more stable economic conditions. Notable variations emerged during economic downturns, such as  
Figure 4: Comparison between actual and predicted data on direct tax. Figure 5: Comparison between actual and predicted observations of indirect tax collection in India using the GM (1,1). during the COVID-19 pandemic in the financial year of 2020-21, when the error for direct taxes was particularly large. This most likely reflects the effect of COVID-19 on tax revenue due to the lockdown, which caused the shutdown of manufacturing and other economic activities ([PERSON] et al., 2022). The expected tax collection shows a constant upward trend for both direct and indirect taxes, indicating predictions of economic growth or revisions in tax regulations. In short, we find an increase in the accuracy of tax predictions over time, particularly for direct taxes.