taxes and transfers. Modeling the pension system as a deferred income results in minor horizontal equity effects of direct taxes and transfers.

Less desirable is horizontal equity (reranking) caused by indirect taxation and subsidies, as well as in-kind transfers. The reranking effect of consumable income is higher than of disposable income, while vertical equity remains unchanged, irrespectively of the market income concept applied. Hence, indirect taxes and transfers do not reduce inequality, but lead to households switching places in the distribution by income. On the contrary, in-kind transfers are associated with a significant vertical equity effect. In the case when market income is modeled according to the assumption of pensions as deferred income, in-kind transfers generate most of the vertical equity effect of the fiscal policy. However, they also cause some horizontal equity effects if households are initially ranked by market income that includes pensions (PDI). On the contrary, the comparison of the household distribution by final income and market income modeled according to PGT approach reveals that in-kind transfers reduce the scale of reranking. This contradiction is rooted in the nature of modeled in-kind transfers. Namely, education transfers are inevitably lower for households with elderly members. Therefore, they make pensioners less wealthy relative to youth. When we compare the final income distribution to the market income distribution prior to pension system effects (PGT), we see that in-kind transfers limit the reranking effect associated with the pension system. Vice versa, the initial ranking of households by market income including pensions (PDI) results in deteriorated relative welfare of pensioners and increasing horizontal equity effects after accounting for in-kind transfers.

**Table 8. Decompositions of inequality changes into vertical and horizontal equity components**

||**Change t**<br>|**o market incom**<br>|**e(PGT)**<br>|**Change t**<br>|**o market incom**<br>|**e(PDI)**<br>|
|---|---|---|---|---|---|---|
||**Disposable**<br>**income**|**Consumable**<br>**income**|**Final**<br>**income**|**Disposable**<br>**income**|**Consumable**<br>**income**|**Final**<br>**income**|
|Gini change with respect to market income|0.139|0.137|0.180|0.025|0.022|0.065|
|Vertical equity (Reynolds-Smolensky Index)|0.200|0.202|0.236|0.031|0.030|0.087|
|Reranking (Atkinson-Plotnick Index of<br>horizontal equity)|0.060|0.065|0.056|0.006|0.008|0.022|

_Note_ . Vertical equity implies reduction of gap in welfare between rich and poor due to fiscal intervention. Horizontal equity implies that fiscal intervention does not influence ranking position of an individual, see Kakwani (1984). _Source_ : own estimates based on CEQ methodology.

The incidence analysis of income changes caused by fiscal interventions shows that benefits are concentrated within the lowest deciles. The bottom two deciles, ranked by market income that does not include pensions (PGT approach), enjoy a substantial average increase of income, which is partly related to the low base of market income (see Figure 14). The positive effect disappears by the 4–5 deciles, while 7–10 deciles suffer income reduction (see Table 9). If market income is modeled within the PDI approach, the positive effect of fiscal interventions holds only for the first deciles (with the exception of in-kind transfers) and its scale is much lower. Consequently, the scale of losses by upper deciles is also lower. Moreover, losses are distributed evenly among relatively wealthy deciles, implying a similar tax burden for upper deciles. The incidence of net effects changes substantially after accounting for in-kind transfers. At the level of final income, the effect from fiscal interventions steadily diminishes from lower deciles to the upper deciles (both compared to the market income modeled by PDI and PGT approach), implying progressivity of in-kind transfers. Moreover, the effect at the level of final income becomes negative only for the wealthiest deciles.

**Table 9. Incidence of net effects from fiscal interventions in relation to market income by deciles**

||**Market**<br>|**income by PGT app**<br>|**roach**<br>|**Market**<br>|**income by PDI app**<br>|**roach**<br>|
|---|---|---|---|---|---|---|
||**Disposable**<br>**Income**|**Consumable**<br>**Income**|**Final**<br>**Income**|**Disposable**<br>**Income**|**Consumable**<br>**Income**|**Final**<br>**Income**|
|1|890.6|805.1|1214.1|18.2|8.0|56.5|
|2|111.4|95.2|169.7|4.9|-3.1|33.8|
|3|37.5|27.7|68.1|1.3|-6.0|23.6|
|4|13.8|5.9|36.2|-1.6|-8.4|18.0|
|5|1.2|-4.9|18.6|-2.4|-8.2|14.0|
|6|-7.1|-13.1|6.8|-3.6|-9.8|10.7|
|7|-12.7|-18.2|-0.8|-4.8|-10.8|8.4|
|8|-14.9|-20.1|-6.1|-5.5|-11.4|4.1|
|9|-17.6|-23.7|-11.4|-6.7|-13.7|-0.1|
|10|-19.5|-23.9|-17.3|-6.9|-12.1|-4.0|
|Total|-3.2|-9.5|9.3|-3.5|-9.8|9.0|

_Source_ : own estimates based on CEQ methodology.

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