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4 Empirical Results

This section presents the calculated welfare changes and marginal welfare costs for a simple hypothetical policy change involving an increase in all marginal income tax rates by 5 percentage points. This represents a substantial increase in taxation. Of course, in general the welfare effects depend on the precise nature of the tax structure change, so the results presented here are illustrative of the costs of raising extra revenue in this simple way. The base or pre-change income tax structure is shown in Table 1.

All results were obtained using the NZ Household Economic Survey for 2011/12 and the extended Treasury behavioural microsimulation model, TaxWell-B.[23]

Table 1- Income tax rates
Income band ($ annual) Marginal tax rate (%)
0 to 14,000 10.5
14,001 to 48,000 17.5
48,001 to 70,000 30
70,000 and over 33

4.1 Aggregate results

A summary of aggregate results for four demographic groups, and for all families combined, is given in Table 2. In obtaining these aggregates, the sample weights were used to ‘gross up' the sample to total population values.[24]

Of course it is widely recognised that net income, considered as a welfare metric, does not capture leisure time. The fact that changes in net income ‘overstate' changes in welfare is clearly shown in the final row of the table. The labour supply responses are such that income falls, but the increase in leisure is such that the welfare loss is less than the net income reduction. The differences are larger for single women and single parents, for whom the labour supply responses are relatively large.

The marginal welfare costs reported in Table 2 were obtained using equation (9), and thus measure the aggregate welfare cost per dollar of extra aggregate revenue. These results show large differences among the main demographic groups. The lowest MWC is for single men, at 4 cents per dollar of extra revenue. For single parents the aggregate MWC is very high, at 3.47 dollars per dollar of revenue. The reason for the high welfare cost in this case is that a substantial number of single parents reduce their labour supply by large amounts as a result of the tax rate increases, such that they experience a reduction in the net tax paid. They form a relatively small proportion of total population, and hence the aggregate MWC is much lower, at 12 cents per dollar.

Table 2 - Aggregate income, revenue and welfare effects of tax rate increases ($m a year)
  Couples Single  men Single  women Single parents Total
Net government revenue (with labour response) 3,894 789 502 30 5,215
Net government revenue (labour supply fixed) 4,242 823 678 141 5,884
Aggregate net income change -4,689 -865 -830 -196 -6,580
Equivalent variation (EV) 4,227 821 672 136 5,856
Marginal excess burden 333.0 32.7 170.6 105.3 641.6
Marginal welfare cost 0.09 0.04 0.34 3.47 0.12
% difference between net income change and EV -9.9 -5.0 -19.0 -30.6 -11.0
Proportion of sample 0.46 0.24 0.22 0.08 1.0
Proportion of net revenue (with labour response) 0.75 0.15 0.10 0.00 1.0
Proportion of marginal excess burden 0.52 0.05 0.27 0.16 1.0

A feature of labour supply responses of sole parents can be seen from the budget constraints for two hypothetical cases, shown in Figure 1. The pre- and post-change budget constraints are shown for two different wage rates, $16 and $28 per hour. These show how the marginal income tax rate changes reduce net incomes, particularly in the higher hours ranges. Although a discrete hours modelling approach is used, these constraints illustrate the net incomes over all work hours, showing more clearly the large range of hours for which the budget set is non-convex. An implication of this type of non-convexity is that even very small changes in the tax rates over the relevant range can lead to large changes in labour supply, involving large discrete ‘jumps', in view of the convexity of indifference curves. The relevant range of hours for which the non-convexity applies is clearly much larger for the sole parent with the lower hourly wage rate.[25]

The fact that Taxwell-B uses a discrete hours approach, with a random utility component, means that there is a small probability that some higher hours levels are chosen as a result of the tax change. However, these cases are very small, as shown by the transition matrices shown in Tables 3 and 4, for single women and single parents respectively.

Figure 1 - Budget Constraints for two sole parents with two children

A crucial feature of these transition matrices is that the distributions of work hours following the tax change, conditional on working a particular hours level before the change, are multimodal. Indeed, there are relatively large probabilities of moving from work to non-work. As mentioned above, such moves are associated with net reductions in tax paid. This contributes to the relatively small increase in aggregate net revenue and the high aggregate marginal welfare cost of funds for single women and single parents.

Table 3 - Single women labour supply transitions (row to column)
Labour supply in hours per week
Post-reform
Total %
Pre-reform 0 5 10 15 20 25 30 35 40 45 50
0 100 - - - - - - - - - 0 53.4
5 - 100 - - - - - - - - - 1.5
10 0.4 - 99.6 - - - - - - - - 3.9
15 0.8 - 0 99.2 - - - - - - - 3.1
20 4.6 - - - 95.4 - - - - - - 1.9
25 1.9 - 0.1 - - 98 - - - - - 1.5
30 5.7 0 0.1 0.3 0.1 0.1 93.4 0 0.1 0.1 0.1 4.3
35 3.1 0.1 0.2 0.1 0.2 0.3 0.2 95.7 0.1 0 0.1 5.2
40 5.2 0.1 0.1 0.2 0.3 0.4 0.4 0.4 93 0 0 15.3
45 4.2 0 0.1 0.3 0.4 0.5 0.2 0.4 0.3 93.5 - 4.6
50 5.8 0.2 0.1 0.3 0.3 0.3 0.7 0.6 0.2 0.1 91.4 5.3
Total % 55.3 1.5 3.9 3.1 1.9 1.6 4.2 5.1 14.3 4.3 4.9 100
Table 4 - Single parents labour supply transitions (row to column)
Labour supply in hours per week
Post-reform
Total %
Pre-reform 0 5 10 15 20 25 30 35 40 45 50
0 100 - - - - - - - - - - 62.6
5 2.7 97.3 - - - - - - - - - 3.1
10 6.2 - 93.8 - - - - - - - - 5.3
15 6.4 0.2 0.3 89.4 0.2 1.7 1.6 0.3 - - - 3.3
20 7.7 0.3 0.4 0.1 91.4 - - - - - - 2.4
25 10.9 0.1 0.5 0.2 0.1 88.3 - - - - - 2.8
30 9.7 0.4 0.8 1 0.6 0.1 86.4 0 0.1 0.4 0.7 4
35 11.9 0.3 0.6 0.6 0.7 0.5 0.3 84.6 - 0.2 0.2 3.1
40 10 0.3 0.6 0.6 0.7 1.3 0.7 0.7 85 - 0 8.2
45 1.8 0.2 0.4 0.3 0.2 0.3 0.6 1.3 - 93.1 1.9 1.9
50 8.5 0.4 0.7 0.3 0.7 1.0 0.9 1.2 1.3 0.1 84.8 3.2
Total % 65.6 3.1 5.2 3.1 2.3 2.7 3.6 2.8 7 1.8 2.8 100

Notes

  • [23]This model obtains the required net incomes for each hours level (before and after the tax change) from the Treasury’s non-behavioural model, TaxWell-A. This assumes full take-up of welfare benefits, and ignores cash asset tests and other eligibility requirements for which no data are available. For details of the estimated preference functions and wage equations used in TaxWell-B, see Mercante and Mok (2014a, b).
  • [24]The weights ensure that a range of totals, such as the number of individuals in various age groups, match independently obtained aggregates (referred to as ‘calibration values’).
  • [25]There is of course an additional non-convexity introduced by the existence of fixed cost of working. It is this fixed costs which explains why there are a number of shifts from working to non-working, rather than simply reducing the hours of work.
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