The seasonal distribution of fiscal aggregates such as tax and non-tax revenues and expenditures show an extraordinarily high share in the month of March as well as some notable intra-year peak values. This concentration of monthly shares of annual fiscal aggregates arises due to various regulatory and institutional arrangements apart from the seasonal pattern of economic activities. We measure the degree of concentration of fiscal aggregates by adapting the Hirschman-Herfindahl Index (HHI), which has been used in the context of measuring industrial concentration. We cover four major fiscal aggregates, namely Centre’s net tax revenues, Centre’s non-debt receipts excluding net tax revenues, Centre’s revenue expenditure and Centre’s capital expenditures. An index of seasonal unevenness in these fiscal aggregates was defined and studied in Srivastava and Trehan (2018) . Concentration is a dimension of unevenness.

The period of study covers 2000-01 to 2024-25, that is, 300 monthly observations across 25 years. This overall period is divided into five sub-periods referred to as follows: Period 1 (2000-01 to 2004-05), Period 2 (2005-06 to 2009-10), Period 3 (2010-11 to 2014-15), Period 4 (2015-16 to 2019-20) and Period 5 (2020-21 to 2024-25). It may be noted that Periods 1, 4 and 5 were largely under the National Democratic Alliance (NDA) regime, and Periods 2 and 3 were largely under the United Progressive Alliance (UPA) regime. Two major economic shocks occurred in the overall period: 1) in 2008-09 relating to the global economic and financial crisis, and 2) in 2020-21 relating to the Covid crisis. In both these years, fiscal stimulus, introduced mainly through expanded fiscal deficit, was used to mitigate the impacts of economic shocks.

There is an extensive literature pertaining to the use of HHI for situations of concentration of economic activities. The HHI has been employed in multiple contexts. The U.S. Department of Justice (DOJ) and Federal Trade Commission (FTC) have adopted HHI as a primary screening tool for assessing market concentration and potential anti-competitive effects of mergers in their Merger Guidelines. The agencies consider markets with an HHI above 1800 as highly concentrated, and those above 1000 but below 1800 as moderately concentrated ¹ .

The HHI has emerged as a tool in assessing economic diversification, particularly in resource-dependent economies. In the study by Belbali et al. (2024) , the HHI is employed to quantify the concentration of Algeria’s economic activities across sectors from 2019 to 2023, revealing moderate diversification with index values ranging between 0.2 and 0.4. The literature review within the paper highlights the HHI’s widespread application in similar contexts, including studies by Ghedier and Kiheli (2022) , which underscore the persistent dominance of the hydrocarbon sector despite policy efforts aimed at diversification. The HHI’s sensitivity to sectoral imbalances makes it a reliable indicator for evaluating structural economic shifts, as demonstrated by its use in both sectoral and export diversification analyses. Moreover, the paper discusses interpretive thresholds of HHI values, aligning them with degrees of economic concentration, and reinforces the index’s utility in cross-country comparisons and longitudinal assessments of diversification strategies.

Herfindahl index has also been used for the purpose of fiscal analysis primarily to examine the concentration or diversification of fiscal variables, such as tax revenue composition, expenditure allocation, fiscal decentralization, and intergovernmental transfers ( Table 1 ).

Compaoré and Tagem (2022) utilize the index to estimate the impact of aid fragmentation on tax revenue mobilization in developing countries. The study utilizes data on 90 developing countries covering the period from 2000 to 2020 and finds that aid fragmentation has a significant negative impact on recipient countries’ tax revenue ratios, particularly that of corporate income taxes and value-added tax.

In their study on fiscal stress among U.S. state and local governments, Shamsub and Akoto (2004) employ the HHI as a foundational tool to measure local revenue diversification. Recognizing that reliance on a narrow set of revenue sources can exacerbate fiscal vulnerability, the authors adapt the HHI—traditionally used to assess market concentration—to evaluate the balance among four major revenue streams: income taxes, property taxes, sales taxes, and user charges. By calculating the reciprocal of the HHI and normalizing it against the theoretical maximum diversification, they derive a diversification index that quantifies the extent to which local governments spread their revenue collection across multiple sources. This methodological innovation allows the authors to empirically demonstrate that greater revenue diversification is significantly associated with lower fiscal stress, thereby highlighting the utility of the HHI in fiscal policy analysis.

Suyderhoud (1994) introduces a quantifiable approach to measuring revenue diversification using the HHI, a widely accepted metric for assessing concentration. By adapting the HHI to state-local tax structures, he constructs a diversification index that reflects the extent to which a jurisdiction’s revenue sources are balanced. A score of 1.00 indicates perfect diversification, while 0 signifies complete reliance on a single source. Suyderhoud’s empirical analysis demonstrates that higher diversification, as measured by the HHI-based index, correlates positively with several indicators of fiscal performance, including tax effort, equity, and revenue adequacy. His findings support the notion that revenue diversification, when properly measured, is a valuable policy goal for enhancing fiscal stability and efficiency.

Kotlinska, Nucinska, and Bednarz (2021) employ the HHI to analyze the concentration of educational expenditures and subvention streams among Polish local governments from 2008 to 2019. Their study reveals that while the educational subvention from the central government maintains a relatively uniform distribution—evidenced by low HHI values—the actual educational expenditures, particularly in cities with county rights, exhibit significantly higher concentration levels. This disparity suggests that local financial decisions, especially regarding property investments and subsidies to private educational institutions, disrupt the universal character of the subvention system. By applying the HHI, the authors effectively quantify the extent of fiscal decentralization and highlight the structural imbalances in education financing, offering a robust methodological framework for assessing expenditure concentration in public finance.

In the context of fiscal aggregates, Srivastava and Aggarwal (1979) had utilized the HHI for studying tax revenue centralization in India. They had defined and estimated alternative versions of the HHI. Srivastava and Trehan (2018) had defined an index of seasonal unevenness and used this index for a study of seasonal patterns of fiscal aggregates in India. In the present paper, the HHI is proposed to be used for the phenomenon of the study of seasonal concentration, particularly March bunching and other noticeable peaks.

The Herfindahl-Hirschman Index (HHI) is favorably placed for analyzing seasonality in fiscal aggregates, especially when the goal is to quantify the concentration rather than to model the seasonal cycle ( Chikoto et al., 2016 ). The HHI highlights extreme concentration more strongly than alternatives like the Gini or Theil indices. Since it is based on squared shares, periods with disproportionately large fiscal flows—such as year-end expenditure spikes—receive greater weight, making bunching more visible. Its bounded and intuitive scale, ranging from 1/n (uniform distribution) to 1 (full concentration), also makes it easy to interpret and communicate to policymakers. Unlike other indices, HHI is less sensitive to small fluctuations or negligible monthly flows, reducing the risk of overstating minor seasonality. These features make HHI especially useful when the key concern is whether fiscal flows are concentrated in only a few months and how severe that concentration is.

A distinguishing feature of the HHI is its decomposability ( Srivastava & Aggarwal, 1979 ). This implies that it can be used to estimate the relative contribution of the constituents of the variable under analysis. For instance, in this study, along with the examination of seasonal concentration patterns of revenues and expenditures at the aggregate level, we also examine the relative roles of their sub-components.

In the context of studies of concentration, the HHI ( Hirschman, 1945 ; Herfindahl, 1950 ) is defined as below. For example, if the share of a particular firm in the overall size of all firms if given by $r_i$, then HHI is defined as:

$H={\displaystyle {\sum }_{i=1}^n{r}_i{}^2}$ (1)

where n is the number of firms.

The HHI Index can be adapted for a study of the pattern of monthly shares defined by $r_i$, where

$r_i=\frac{R_i}{{\displaystyle {\sum }_{i=1}^{12}{R}_i}}$(2)

The index is defined as

$C={\displaystyle {\sum }_{i=1}^{12}{r}_i{}^2}$ (3)

where $i=1$ to 12.

The maximum value for this index would arise when one-month accounts for all the shares, that is, $r_1=1$ and $r_2$ to $r_{12}=0$ and in all other months the value of these shares is zero. In this case, the value of $C$ is 1. The minimum value of

this index would arise when there is no concentration, implying that $r_i=\frac{1}{12}$ for all $i$. The value of $C$ in this case is:

$C={\displaystyle {\sum }_{i=1}^{12}{\left(\frac{1}{12}\right)}^2}=\frac{1}{12}$(4)

Thus, $C$ ranges from $\frac{1}{12}$ to 1. We can normalize the index of seasonal concentration as below. That is,

$C^{\ast }=\frac{1}{11}\cdot \left[12{\displaystyle {\sum }_{i=1}^{12}{r}_i{}^2}-1\right]=\frac{1}{11}\cdot \left[12C-1\right]$(5)

The range of $C^{\ast }$ is from zero to 1.

In order to facilitate interpretation of the values of $C$ and $C^{\ast }$ for certain benchmark distributional patterns, we have included illustrative values in Table 2 . In simulation 1 it is shown that the maximum value of $C$ and $C^{\ast }$ are 1, whereas the minimum values are 0.083 (1/12) and 0 respectively. In the second half of the table, we compare the equally distributed pattern with a pattern of four even peaks. In the latter case, the value of $C$ is 0.25 and the value of $C^{\ast }$ is 0.182. In general, the magnitude of $C^{\ast }$ tends to be quite low.

Since the values tend to be low, for any individual fiscal aggregate inter year variability can also be studied by rescaling the values of $C^{\ast }$ as follows:

For year t, the value of $C^{\ast }$ may be written as $C_t^{\ast }$. Then we may write $C_t^{\ast \ast }$ as a scaled up transformation of $C_t^{\ast }$ as follows:

$C_t^{\ast \ast }=\frac{C_t^{\ast }-C_{\min }^{\ast }}{C_{\max }^{\ast }-C_{\min }^{\ast }}$(6)

Source (basic data): Author’s estimates.

Utilizing the methodology described above, we have studied patterns of concentration in receipts consisting of net-tax revenue and other non-debt receipts of the central government. For the purpose of analysis, we have divided the sample period covering 2000-01 to 2024-25, into five sub-periods of five years each namely: Period 1 (2000-01 to 2004-05), Period 2 (2005-06 to 2009-10), Period 3 (2010-11 to 2014-15), Period 4 (2015-16 to 2019-20) and Period 5 (2020-21 to 2024-25). It may be noted that Periods 1, 4 and 5 were largely under the NDA regime, and Periods 2 and 3 were largely under the UPA regime.

Case of Net-Tax Revenue

Table 3 highlights that a local peak occurs in the months of June, September, December and March in the case of Centre’s net tax revenues. The average share pertaining to these peak months progressively increases, resulting in the March peak to be much higher than the corresponding June peak.

The phenomenon of March bunching is shown in Chart 1 , although in some periods, September and December peaks are broadly similar. Correspondingly, troughs occur in the monthly shares of April, August, November and February. Clearly, there is significant concentration of collection of net tax revenues in the month of March.

Source (basic data): CGA.

Chart 2. Period-wise average monthly shares: Other receipts.

Source (basic data): CGA.

With the patterns of peaks or concentrations in the case of ‘other receipts’ vis-à-vis net tax revenues being different, these two components, when considered together, would show a lesser degree of concentration as compared to their individual concentration coefficients. Table 6 shows that in the case of ‘other receipts’, second and fourth quarter show a relatively larger share of annual collections. There are some inter-period differences in this pattern. Particularly with respect to Period 5 it is noted that the maximum share is observed in the first quarter. Comparing the relative shares of half yearly collections, we notice that the all-period average in the second half at 55%, is nearly 10% points higher than the first half collections. In the case of other receipts, the peak observed in the earlier half of the fiscal year may also be due to the payment of dividends by the RBI.

Source (basic data): CGA.

Case of Total Non-Debt Receipts

Table 7 and Chart 3 bring together the pattern of monthly shares in total receipts consisting of net tax revenues, and other receipts. In this case, with the contribution of net tax revenues being larger than that of other receipts, broadly the peaking pattern of net tax revenues is replicated with noticeable local peaks in the months of June, September, December and March. The share of March receipts is much larger than the earlier peaks. The all-period average for March is 19.95% which is marginally lower than the corresponding share of net tax revenues in this month at 20.60%.

Source (basic data): CGA.

Source (basic data): CGA.

Source (basic data): CGA.

Chart 6. Period-wise average monthly shares: Revenue expenditure.

Source (basic data): CGA.

Table 11 shows that the fourth quarter share of revenue expenditure is nearly 8% points higher than the first quarter share, whereas the share of second and third quarters are broadly similar. Expenditure shares in the second half of the year are higher than the first half of the year by about 7% points.

Source (basic data): CGA.

Case of Capital Expenditures

March bunching in the case of capital expenditure is noticeably higher than that of revenue expenditures. However, this March bunching has come down in Periods 4 and 5, implying that in more recent years, the monthly spread of capital expenditures has improved in the sense of becoming more evenly spread across the year, compared to Periods 1 to 3. This pattern is also depicted in Chart 7 , Table 12 .

Source (basic data): CGA.

Source (basic data): CGA.

Chart 8. Period-wise average monthly shares: Total expenditure.

Source (basic data): CGA

Source (basic data): CGA

Estimation of Concentration Indices: Total Expenditures and Its Components

Chart 9 shows that concentration is lowest for revenue expenditure in most years except in 2020-21, the year affected by Covid. The Covid period was characterized by a large fiscal stimulus accompanied by lockdowns in all countries. The primary spending entity in the economy was the central government. In this year, these factors led to a distortion in the historical expenditure patterns vis-à-vis those observed in other normal years. In the post-Covid years, there is a visible change towards restoring the earlier pattern. However, the adjustments are not complete yet.

$C={\displaystyle \sum {\left(\frac{R_i}{RR}\right)}^2}=\frac{1}{R{R}^2}{\displaystyle \sum R_i^2}$ (7)

Substituting $R_i$ with $\left(R_{1i}+R_{2i}\right)$

$C=\frac{1}{R{R}^2}{\displaystyle \sum {\left(R_{1i}+R_{2i}\right)}^2}=\frac{1}{R{R}^2}{\displaystyle \sum \left(R_{1i}^2+R_{2i}^2+2\cdot R_{1i}\cdot R_{2i}\right)}$ (8)

$C=\frac{1}{R{R}^2}{\displaystyle \sum \left[\frac{R{R}_1^2}{R{R}_1^2}{R}_{1i}^2+\frac{R{R}_2^2}{R{R}_2^2}{R}_{2i}^2+2\cdot R_{1i}\cdot R_{2i}\right]}$ (9)

This can be solved to

$C=W_1{C}_1+W_2{C}_2+\frac{2}{R{R}^2}\cdot {\displaystyle \sum \left(R_{1i}\cdot R_{2i}\right)}$ (10)

where $W_1=\frac{{\displaystyle \sum R_1^2}}{{\left({\displaystyle \sum R}\right)}^2}$ and $W_2=\frac{{\displaystyle \sum R_2^2}}{{\left({\displaystyle \sum R}\right)}^2}$

Table 16 shows the relative contribution in the overall concentration index pertaining to total receipts of the two main components on the receipts side namely net tax revenues and other (non-debt) receipts. It is shown that the contribution of C₁ pertaining to net tax revenues to the overall concentration index has been larger and has also been rising over time, although there is some inter-year volatility. In contrast, the contribution of the concentration index of other (non-debt) receipts has been lower. The joint interaction term also explains the variation in the overall concentration index. This has also fallen over time. In Period 1 it averaged 43.2%, falling to 22.2% in Period 5.

Source (basic data): CGA.

In the case of expenditures, the overall concentration index is dominated by the concentration index of revenue expenditures. The relative contribution of the concentration index of revenue expenditure has also increased over time. It reached a peak in Period 3 and has since fallen marginally.

This study has focused on examining seasonal concentration in central government finances. It would be useful to undertake a similar analysis at the state level individually and for all states considered together in order to highlight the seasonal pressures on government borrowing by the combined government of central and state governments.

In the context of fiscal management, an even spread of fiscal aggregates across the year may be considered desirable. Fiscal intervention represents injections into and withdrawals from the aggregate demand in the system. Any imbalances between receipts and expenditures will have to be financed by borrowing, which carries its own costs. If the patterns of concentration in receipts and expenditures are different, the need to rely on borrowing to fill the gap between expenditures and receipts would be higher. In fact, the borrowing costs could be reduced by bringing seasonal expenditure patterns more in alignment with the seasonal revenue patterns. Administratively, seasonality of expenditure is under relatively greater control of the government than the revenue patterns, which depend on administrative provisions as well as market responses. There are no significant economic reasons why receipts and expenditures should be characterized by a high degree of concentration or unevenness. Some of the noted phenomenon of March bunching and other local peaks in the context of India, particularly with respect to central finances, are due relatively to the formulation of the fiscal year ending in March and certain administrative and institutional arrangements.

In this paper, we have defined and estimated an index of seasonal concentration using the HHI. We have suggested a normalization for this index as well as a scheme of decomposition. Our main findings are indicated below:

1) March bunching and seasonal concentration is higher in the case of receipts as compared to expenditures.

2) In the case of net tax revenues, March concentration is the highest. But there are noticeable local peaks in the months of June, September and December.

3) In the case of other non-debt receipts, the magnitudes of concentration indices are even higher than that of net-tax revenues. However, the impact of this higher magnitude of concentration is less in the overall index of concentration of total receipts because of the lower weight of other non-debt receipts.

4) Looking at inter-period profile of concentration indices, the highest concentration for the series of overall total (non-debt) receipts is observed in Period 3. For individual series, in the case of net tax revenues, it is in Period 3. However, for other receipts, the highest concentration is in Period 4. Thus, fiscal management appears to be successfully geared towards management of concentration in the years 2010-11 to 2014-15.

5) On a trend basis, with respect to the overall series of non-debt receipts, the concentration index appears to have fallen after reaching a peak around 2014-15. With respect to individual years, peak concentration is observed in 2014-15, which fell in the subsequent years to reach a trough in 2019-20, after which concentration increased again.

Overall, it is observed that there was improvement in fiscal management in terms of reducing the magnitude of seasonal concentration before the onset of Covid. But these magnitudes became larger in subsequent years. There is a need to now reduce the magnitude of concentration in fiscal aggregates so that the need for additional intra-year borrowing may be minimized.

Views or perspectives in this article are solely those of the authors and do not necessarily reflect the views, policies, or positions of any organization, employer, or affiliated group.

$C={\displaystyle \sum {\left(\frac{R_i}{RR}\right)}^2}=\frac{1}{R{R}^2}{\displaystyle \sum R_i^2}$

Substituting $R_i$ with $\left(R_{1i}+R_{2i}\right)$

$C=\frac{1}{R{R}^2}{\displaystyle \sum {\left(R_{1i}+R_{2i}\right)}^2}=\frac{1}{R{R}^2}{\displaystyle \sum \left(R_{1i}^2+R_{2i}^2+2\cdot R_{1i}\cdot R_{2i}\right)}$

$C=\frac{1}{R{R}^2}{\displaystyle \sum \left[\frac{R{R}_1^2}{R{R}_1^2}{R}_{1i}^2+\frac{R{R}_2^2}{R{R}_2^2}{R}_{2i}^2+2\cdot R_{1i}\cdot R_{2i}\right]}$

$C=\frac{1}{R{R}^2}\cdot {\displaystyle \sum \frac{R{R}_1^2}{R{R}_1^2}{R}_{1i}^2}+\frac{1}{R{R}^2}\cdot {\displaystyle \sum \frac{R{R}_2^2}{R{R}_2^2}{R}_{2i}^2}+\frac{2}{R{R}^2}\cdot {\displaystyle \sum \left(R_{1i}\cdot R_{2i}\right)}$

$C=\frac{R{R}_1^2}{R{R}^2}\cdot {\displaystyle \sum \frac{R_{1i}^2}{R{R}_1^2}}+\frac{R{R}_2^2}{R{R}^2}\cdot {\displaystyle \sum \frac{R_{2i}^2}{R{R}_2^2}}+\frac{2}{R{R}^2}\cdot {\displaystyle \sum \left(R_{1i}\cdot R_{2i}\right)}$

$C=W_1{C}_1+W_2{C}_2+\frac{2}{R{R}^2}\cdot {\displaystyle \sum \left(R_{1i}\cdot R_{2i}\right)}$

where $W_1=\frac{{\displaystyle \sum R_1^2}}{{\left({\displaystyle \sum R}\right)}^2}$ and $W_2=\frac{{\displaystyle \sum R_2^2}}{{\left({\displaystyle \sum R}\right)}^2}$.

¹ https://www.justice.gov/atr/herfindahl-hirschman-index#:~:text=The%20agencies%20generally%20consider%20markets,Guidelines%20%C2%A7%202.1%20(2023) ; Merger Guidelines, US Department of Justice and the Federal Trade Commission, https://www.ftc.gov/system/files/ftc_gov/pdf/2023_merger_guidelines_final_12.18.2023.pdf.