The LOTTE System of Tax Microsimulation Models

3.1 Model design

The Norwegian non-behavioral tax-benefit model LOTTE-Skatt holds a key position in the decision-making system in Norway. The model is extensively used by the Ministry of Finance in preparing the budget, while the other political parties in the Storting (the Norwegian parliament) make particular use of the model to develop their alternative budget proposals after the proposed government budget has been presented. Simulation results are reported back to the opposition parties fairly promptly. Many of these simulations are done by staff at the Ministry of Finance through LOTTE-Aksess. More complicated tax changes and tax simulations for alternative budget proposals are executed by dedicated model operators at Statistics Norway.

Figure 1 provides a graphical illustration of the different components of a standard LOTTE-Skatt tax simulation. A simulation consists of several elements and steps: individual input data (described in Section 3.2), a program that projects data for the year of interest (described in Section 3.3), a set of tax scheme parameters reflecting the tax legislation and a simulation program that applies the tax legislation to the individual data records.¹¹ The results of a tax policy change simulation are compared to results of a reference simulation. For instance, when the policy-makers are preparing the next year’s budget, they compare effects of various tax-law changes to effects of a simulation based on this year’s tax-law, projected to the next budget year.

Standard model output of LOTTE-Skatt includes aggregate tax revenue effects and various descriptions of distributional effects. To illustrate this, we show simulation results for an increase in the net tax rate of the dual income tax scheme: the tax on ordinary income is increased by 1 percentage point, from 22 percent to 23 percent. Table 1 demonstrates how a standard revenue table would look like in this case, whereas Figure 2 provides a graphical depiction of an output table for distributional effects. The income distribution of Figure 2 (horizontal axis) is established by ranking individuals above the age of 16 by individual pre-tax income.¹²

3.2 Data

The primary data source of the model is the Income and wealth statistics for households (Statistics Norway, 2021), which is based on several administrative registers, including detailed income tax return data from the Norwegian Tax Administration. Data from the Norwegian Labour and Welfare Administration (NAV) provide information about family, pension, disability, unemployment and other social security benefits, and data on education level and education support are provided by the Register of Education and the Norwegian State Educational Loan Fund. Limited company ownership of real estate is calculated for each person using data from the Register of Shareholders and from tax returns of limited companies.

The individual person is the primary unit of the model population, but output can be presented in terms of effects on households too. Households are formed based on a unique address register for all dwellings in Norway (see Section 2), connecting individuals by residential unit.

The full data sample include all 5.5 million individuals (of the country), corresponding to 2.2 million households. In order to reduce computational time, we usually use a sample consisting of about 10 percent of all households. However, high-income households (gross income exceeding NOK 10 million) and the wealthiest households (net wealth of more than NOK 100 million) are always included in the sample, to avoid biases in the revenue calculations.¹³ Accordingly, these households get a weight of 1, whereas other households have a 10 percent chance of being selected and therefore get a weight of 10.¹⁴

Households are categorized into five socioeconomic groups depending on the status of the “head of the household”, defined as the person with highest income: i) wage earners (52% of our sample in 2021), ii) self-employed (2%), iii) pensioners (20%), iv) social security recipients (11%), and v) others (14%).

3.3 Projections of tax base and tax scheme

Data must be projected from the year of the data (base year) to the simulation year, typically a three year time span. For example, in the spring of 2023, we prepared a data set for the year 2021 to be employed in simulations with respect to the 2024-budget, made public in early October 2023. The projections (or nowcasting) consists of two steps. First, projections are made for economic variables such as income, income deductions and wealth for each person. Income variables and income deduction variables are categorized with respect to adjustment factors, as different factors are employed for different income variables, such as for wage income, pension income, social security benefits, self-employed income (business income) and capital income (interest income, dividends, and gains).

Second, sample weights are adjusted to account for changes in the number of households assigned to each of the five socioeconomic statuses (see Section 3.2). Other demographic changes from base year to simulation year are not taken into account, which means that, e.g., distributions of age, gender, and geographical location as well as marital, socioeconomic, occupational and employment statuses are assumed to be the same in the simulation year as in the base year. The factors used in the projections are based on different sources of information: data from Statistics Norway, such as the National Accounts, published information from the Norwegian Labour and Welfare Administration, and forecasts from the Ministry of Finance.

Similarly, variables representing the tax legislation for the current year (e.g., maximum and threshold values) are projected to the budget year. The method for uprating the tax scheme includes using estimates of wage growth and consumer price growth. Importantly, there is an established convention guiding the procedure to project the tax system from one year to the next (for example, in the spring of 2023 we established a 2024 tax scheme benchmark based on the 2023 tax law): the tax scheme is uprated to the next year under the condition that the ratio of the tax to the tax base, for a taxpayer with only standard income deductions, is close for the two years.

3.4 Model validation

In general, model simulation results may deviate from the actual taxation, as reflected in the income tax return. Discrepancies emerge because 1) the tax simulations are simplified and because 2) not all parts of the scheme are simulated. As a result model output results typically deviate from what we get from the administrative tax registers, for example in terms of the individual tax burden. Various tests of model performance are regularly executed to get a picture of the magnitude of deviations and to keep track of over time developments.

Table 2 shows a comparison of output from LOTTE-Skatt and output collected from the tax register for 2021. Thus, this illustrates the extent of inaccuracies due to simplified tax simulation procedures. The table shows that total taxes, as simulated by LOTTE-Skatt, is 0.2 percent higher (1.2 billion NOK) than the taxation reported in the registers. Deviations vary from -0.11% to 3.84%, depending on the type of tax. Moreover, deviations caused by not being able to include all components of the tax system in the simulations give additional discrepancies of a similar magnitude, implying that the total deviation is about 0.4 percent.

Furthermore, using the 10 percent sample (see Section 3.2) instead of the full population is also a source to discrepancy. The deviation in total taxes caused by employing the 10 percent sample in the simulations is generally small (less than 0.1 percent), but care has to be taken when studying highly disaggregated simulation output.

3.5 Use of LOTTE-Skatt in academic work

3.5.1 Fixed-income approach

In the following we present two studies that use LOTTE-Skatt in contributions aimed for the international academic literature. First, we refer to Lambert and Thoresen (2009), where the tax-benefit model is used to evaluate the contribution of the tax system to redistribution and tax progressivity over time. Next, in Section 3.5.2, we describe how measures of tax policy behavioral effects can be produced by feeding estimates of behavioral response into a non-behavioral tax-benefit model, illustrated by Jia et al. (2023).

Lambert and Thoresen (2009) evaluate the contribution of the tax system to redistribution and tax progressivity over time (1992–2004) by using a “fixed-income” approach: different tax-laws are applied to the same (fixed) pre-tax income distribution.¹⁵ They present results for several pre-tax income distribution bases – those of 1992, 1998 and 2004. For each of these data sets, individuals were subjected to taxation as per the tax legislation of 1992, 1995, 1998, 2001, and 2004. When tax rules are from a year different from the point of time of the pre-tax income distribution, all tax thresholds are adjusted by wage growth.

Figure 3 shows how the tax policies of the period 1992–2004 are evaluated by the fixed-income approach. Effects are measured in terms of the Blackorby–Donaldson index (BD index) of redistributional effect (Blackorby and Donaldson, 1984), decomposed into vertical and horizontal inequity effects (VR and HI). The BD index is founded on social welfare function reasoning, as it employs the index of Atkinson (1970), ${\displaystyle I(e)}$, as an inequality index, where ${\displaystyle e>0}$ is the (relative) inequality aversion parameter, capturing the concavity of the utility function of an assumed social decision-maker.¹⁶ Furthermore, the decomposition into vertical and horizontal effects is carried out in terms of two concepts of horizontal inequity – the so-called “classical” and the “no reranking” approaches (C and NR). The classical approach to horizontal inequity Atkinson (1970) measurement starts from a perception of the vertical effect as being the average effect of the tax system on the relative income differentials of pre-tax unequals (Musgrave, 1990; Aronson et al., 1994; Jenkins and Lambert, 1999). The “no reranking” procedure arises from the perception that if individuals are reranked by the tax schemes in the transformation from pre-tax income to post-tax income, this amounts to procedural unfairness (Plotnick, 1981; King, 1983; Jenkins, 1994).

The most striking feature of Figure 3 is that the two lower panels pick up the temporary tax on dividends in 2001, whereas the upper panel does not. This follows from the small volume of dividend transfers in the 1992 data (less than NOK 2 billion), compared to pre-tax income distributions for 1998 and especially for 2004. These years have much higher taxable dividends, NOK 18 billion and NOK 63 billion, respectively. This is an example of the base dependence problem of the fixed-income approach. On balance, we find that the redistributional effect of the tax system is more or less unaltered from 1992 to 2004 – if anything, we see a small increase in the vertical redistribution over the period (for 1998 and 2004 base years).

4.1 Labor supply responses

4.2 The labor supply model microsimulation module – LOTTE-Arbeid

The “job choice” model is the core of LOTTE-Arbeid. LOTTE-Arbeid work in conjunction with LOTTE-Skatt, in the sense that we transfer estimated parameters of the job choice model to the much larger LOTTE-Skatt data sample. In so doing we make the assumption that individuals of the LOTTE-Skatt data sample behave in the same way as those of the smaller sample used in the econometric estimations of labor supply (the Labour force survey), as long as they have the same observed characteristics. As the labor supply model is designed to provide simulation results for prime-aged wage earners (25–62 years old), we set the labor supply effects of other groups at zero. It is important to note that the model does not include behavioral responses for groups other than prime-aged wage earners, which means that the responses of self-employed individuals are neglected.²⁶

Given the probabilistic nature of the labor supply model (following from the random utility discrete choice framework), we obtain predicted probability distributions for the discrete set of working hour alternatives for individuals, both pre- and post-reform. In particular, we calculate, for any given individual, values of the deterministic part of the utility function for each working hour alternative, using Equation (6), the estimated parameters, and observed characteristics. The corresponding probabilities, ${\displaystyle \phi (h)}$, are obtained by using Equation (5). Based on a predicted probability distribution for a discrete set of working hour alternatives, we obtain estimates of predicted hours of work, taxes paid, pre-tax income and other variables of interest. Furthermore, differences between probability distributions, pre- and post-reform, define labor supply effects of the tax change.

This procedure implies that we ignore the individual-level information on the unobserved error terms, ${\displaystyle \eta (z)}$, as we are mainly interested in aggregate responses. An alternative method is to follow Creedy and Kalb (2005) and Thoresen et al. (2010) and assume that the unobserved error terms are the same before and after the tax change.²⁷

Table 4 presents our estimated labor supply elasticities with respect to the gross wage rate for females and males in couples (both own elasticities and cross elasticities) and for male and female singles, at both the extensive and the intensive margins (for females). In particular, the model predicts that females in couples are more responsive to wage changes than the other groups.²⁸ This is a general finding in the labor supply literature (Whalen and Reichling, 2017; Eckstein et al., 2019; Keane, 2022), and the elasticity estimates are in line with other comparable microsimulation studies; see e.g., Bargain et al. (2014), and de Boer and Jongen (2023).²⁹ Estimation results (not reported here) also show standard income response regularities, with negative labor supply response to increased non-labor income, such as increased child benefit.³⁰ Note also that LOTTE-Arbeid has been extended to allow for state dependence in model framework that describes the timing of labor supply responses, see Jia and Vattø (2021). Results suggest that state dependence bring down the short-term (first-year) response to one-third of the full effect, and the full effect is reached after about five years.

As a LOTTE-Arbeid simulation is both more complicated and time-consuming than a conventional LOTTE-Skatt simulation, the use of LOTTE-Arbeid in the Norwegian tax decision-making process is more limited. However, it is used to predict labor supply, revenue, and distributional effects of major reforms. An important output from the model is the information reported in Table 5, providing a rule of thumb for the degree of self-financing for a selection of tax changes. The ratio of self-financing is the ratio between the counteracting effect on revenue of labor supply adjustments due to a tax decrease and the estimated initial non-behavioral (or mechanical) revenue effect.³¹ This table is produced each year and presented in government reports, such as in Finansdepartementet (2023).³²

4.3 Validation of the labor supply model against estimates of the ETI literature

A key question in labor supply microsimulation is the extent to which the labor supply model provides valid results. It is fair to say that implausible structural estimates of taxes on labor supply have contributed to concern about the ability of structural models to generate robust predictions about the effects of policy change (Heckman and Urzúa, 2010; Imbens, 2010). In this perspective, results from (so-called) natural experiments serve as useful information sources for validation of prediction models (Blundell, 2006; Keane, 2010). Here, we demonstrate how simulation results from models like LOTTE-Arbeid can be tested against estimates of the ETI literature. The following is based on Thoresen and Vattø (2015).³³

Some of the best examples of the strength of the structural discrete choice tool for economic planning, such as McFadden’s predictions regarding the use of a new train system in the San Francisco area (BART) (McFadden et al., 1977) and the prediction model developed by Todd and Wolpin (2006) through the PROGRESA project, have acquired their status through careful out-of-sample validations. This highlights that model validation is important and in the following we show how a validation can be done by obtaining estimates of the net-of-tax rate elasticity from a labor supply model simulation on working hours.³⁴

As already denoted, the random utility framework of the discrete choice model involves generating a probability distribution for different working time options. In contrast, response estimates of the ETI literature are derived by marginal optimization, where response estimates reflect (somewhat simplified) the average responses of the “treated”, compared to “the less or not treated”. In order to obtain comparable figures, we therefore let the results of labor supply model simulations enter into a regression similar to that seen in the ETI literature, using the Norwegian tax reform of 2006 as a “natural experiment”. First, we use LOTTE-Arbeid to simulate the pre-reform and post-reform working hours for four groups of wage earners, the same groups as in Table 4, see results in Table 6. Then these results are converted into measures of growth in (simulated) working hours. In the replication of the ETI econometric framework, the variable for the change in the net-of-tax rate is derived from predicted income levels (hourly wage rate multiplied by predicted hours), and instrumented using similar methods to those of the ETI literature, i.e., the change in the net-of-tax rate for constant (predicted) pre-reform labor income.

In Table 7, estimates from the labor supply simulations are compared with the results of a standard ETI evaluation of the reform. We see that the panel data ETI figures for working hours are close to those obtained from the model simulations. In fact, there are no significant differences between the overall average estimates (for working hours); see the last row of Table 7. Furthermore, estimates (for all four groups) are found to be in the range 0.02–0.06. A difference of 0.04, which is the maximum difference (between results of the two methods) observed for working hours in Table 7 (single males), must be described as modest, both compared to the variation in elasticity estimates in the literature (see for example the review in Blundell and MaCurdy (1999)), and from a policy prediction perspective. Thus, it is claimed that the model performs well according to this validation. Of course, this does not mean that the simulation model is approved – it only means that the model has not been rejected by the present test, according to our judgment. It should also be noted that the ETI might potentially capture a broader set of responses, such as the effect of effort (wages), which is exogenously (fixed) in the standard labor supply model.³⁵

5.1 Model design

The purpose of LOTTE-Konsum is to simulate the direct (non-behavioral) distributional effects of changes in commodity taxation. For the same household population as in LOTTE-Skatt, the model contains a procedure for imputing consumption expenditure. A household-specific price index is used to represent the distributional effects of a tax change.

There is no observed consumption data in LOTTE-Konsum – consumption is imputed from micro econometric estimates of Engel functions and macro consumption data. Micro econometric estimates are based on the Consumer expenditure survey (Holmøy and Lillegard, 2014), and macro consumption is constructed by combining data from the national accounts (Bougroug, 2021) with forecasts from the macro model KVARTS (Boug et al., 2023). The first step of this procedure is to establish estimates of total expenditure for each household in the LOTTE-Skatt population. As our point of departure we assume that household ${\displaystyle h}$ has the consumption function,

where ${\displaystyle c_h}$ is total consumption expenditure, ${\displaystyle m_h}$ is the minimum consumption level, ${\displaystyle y_h}$ is disposable household income, and ${\displaystyle \rho }$ is the (common) marginal propensity to consume. By summing across households, we can derive the same expression in macro terms

where ${\displaystyle C=\sum h{c}_h}$, ${\displaystyle M=\sum h{m}_h}$, and ${\displaystyle Y=\sum h{y}_h}$. Given that we set minimum consumption levels and specify how they depend on the composition of household, we can calibrate the ${\displaystyle \rho }$ parameter from the aggregate disposable income and aggregate expenditure in the economy. This enables us to impute the total consumption in each household. Note that the marginal propensity to consume (and save), ${\displaystyle {\displaystyle \rho }}$ is constant. However, as there are minimum consumption levels, low-income households save less of their income than high-income households.

The next step is to distribute the total consumption of each household into different consumer goods. We start with the following Engel function for each good, ${\displaystyle j}$,

where ${\displaystyle c_{hj}}$ and ${\displaystyle m_{hj}}$ are the consumption and minimum consumption, respectively, of good ${\displaystyle j}$, whereas ${\displaystyle {\zeta }_j}$ is the marginal budget share.³⁶ We assume that the minimum consumption of goods depends linearly on the number of children (${\displaystyle a_{1h}}$) and adults (${\displaystyle a_{2h}}$),

Hence, we have an Engel function with demographic variables. By summing across households we get

where ${\displaystyle C_j=\sum h{c}_{hj}}$, ${\displaystyle M_j=\sum h{m}_{hj}}$. Given that we have information on macro budget shares, the Engel elasticities and the effects of adults and children on demand, we can calibrate the constant, ${\displaystyle m_{0j}}$, and assign expenditure per household for each good.³⁷

A well-known problem when imputing consumption for low-income households is that some goods end up with negative consumption (Decoster et al., 2011). For these households, we proceed by setting consumption equal to zero for goods with negative consumption. However, this means that we end up with too high total expenditure for the household. We use an iterative procedure to adjust for this until total household expenditure is back at the initial level. Although we end up with many corner solutions, this ensures that the aggregate household expenditure for different goods in the economy is exactly equal to the macro data estimates.

Furthermore, it should be noted that the imputation of consumption implies that households have homogeneous preferences, given their income and the number of children and adults in the household. For example, this means that alcohol consumption is determined only by income level and household composition, and thus do not vary by other differences in preferences.³⁸

Estimates of the distributional effects of a tax policy change are obtained by assigning to each household a household-specific price index. In practice, this means that based on the imputed budget shares, the Laspeyres formula is used to compute a household-specific price index for each household. The household-specific price index provides a good approximation of a “true cost of living index” for small price changes from the baseline situation for each household. Thus, the effects of a change in a commodity tax (or a commodity price) on the standard of living of each household, and each individual belonging to the household, is defined as total expenditure (possibly adjusted for economies of scale) divided by the household’s price index. Finally, it is worth noting that this approach makes it possible to consider the distributional effects of changes in direct and indirect taxation simultaneously.

A key advantage of the model concept is that it combines several sources of data, both micro and macro. Consumer expenditure surveys are often associated with substantial uncertainty, as samples are often small and contaminated with non-response bias. Also, consumption of more sensitive goods, such as tobacco and alcohol, is probably under-reported (Browning et al., 2014; Crossley and Winter, 2015). Rather than using observed data directly from a consumer expenditure survey, LOTTE-Konsum is employed to establish underlying stable patterns or trends by means of microeconometric studies, as reflected by Engel elasticity estimates. Moreover, since we use macro data to calibrate, the model results match macro estimates of consumption expenditure. All this ensures stability over time, which is an important quality of a model used on an annual basis by policy-makers.

There are currently 30 consumer goods in the model, but this is easily changed, given the specific policy question and availability of econometric estimates.³⁹ This makes the model flexible, which is a clear advantage for policy-makers with a shifting focus on different commodity taxes.

5.2 Output in the decision-making process

In Tables 8 and 9 we provide examples of LOTTE-Konsum output delivered to the Ministry of Finance. Such information is provided prior to the budget process, updated annually based on new versions of the model. Recall that there is no tax revenue module in LOTTE-Konsum – obtaining estimates of revenue effects of tax changes are done by the Ministry of Finance (with other tools).

Table 8 shows the imputed total expenditure in 2023 for different households and for a selection of goods: food, wine, electricity, clothes, and air travel. Whereas electricity and wine consumption for single-member households is only about half that of large households, clothes consumption by large households is about five times as high as in single-member households. In other words, when this information is used in policy-making, it becomes clear that increasing the tax rates on wine and electricity, for example, will negatively affect single-member households relatively more than a higher tax on clothes.

In Table 9 we go one step further and use price indices to assess the distributional effects of changes in the tax rate, corresponding to an increase in the tax burden by NOK 100 per person on average in 2023. This implies that we change the price of, for example, food such that the real consumption expenditure, defined here as the total consumption expenditure per household member divided by a household specific price index, increases by NOK 100 per person on average. Then we rank all individuals according to their total expenditure, and report the increased tax burden for each decile. We exemplify by use of the same commodities as in Table 8: food, wine, electricity, clothes, and air travel, of which distributional patterns differ dependent on budget shares across deciles. Table 9 shows that two necessity goods stand out: food and electricity. The tax burden is much more evenly distributed for these two goods than for air travel or wine, while clothes is somewhere in the middle.

5.3 Self-financing of tax-cuts: LOTTE-Konsum in conjunction with the two other models

We now return to a discussion of self-financing of tax cuts (recall discussions in Section 3.5.2 and Section 4.2), using all three models of the LOTTE system (LOTTE-Skatt, LOTTE-Arbeid, and LOTTE-Konsum). The following is based on Thoresen et al. (2010).⁴⁰

Overall offsetting effects are calculated for the tax cuts brought about by the Norwegian tax reform of 2006: direct (non-behavioral) effects on tax revenue are compared with revenue effects that controls for effects both through labor supply adjustments and increased commodity taxation. LOTTE-Skatt is used to simulate the direct tax revenue effects of the cuts in the personal income tax from 2004 to 2006. LOTTE-Arbeid is used to include the behavioral effects due to increased labor supply and LOTTE-Konsum is used to calculate commodity tax revenue contributions.⁴¹

The overall offsetting effect is defined as the ratio between the sum of the various offsetting effects and the initial mechanical or direct revenue effect estimate (standard tax-benefit model calculation), where the counteracting effects are: (1) effect of labor supply adjustments on revenue from the personal income tax, (2) effect of labor supply adjustments on payroll tax revenue, (3) mechanical effect on the commodity tax revenue due to the increased consumption made possible by higher disposable income (before labor supply effects), and (4) increase in revenue due to the increased consumption associated with the increased labor supply.

The effects are summarized in Table 10. The offsetting effects are calculated for different assumptions about labor supply responses and marginal propensity to consume (MPC).⁴² If we focus on the benchmark case, with MPC equal to 0.7 and the middle labor supply response estimate, we observe that the offsetting effect due to labor supply response is 0.34, meaning that the initial static revenue loss of the tax reform is reduced by 34 percent because of increased labor supply. Furthermore, the labor supply adjustments imply that payroll tax revenue increases, resulting in an offsetting effect of 12 percent. The direct effect of reduced income tax on revenue from indirect taxes reduces the revenue costs by 12 percent, whereas the additional effect on consumption of increased labor supply reduces the costs by 6 percent. Overall, the authors find that, in the benchmark case, the initial loss of tax revenue is reduced by 64 percent by taking these additional effects into account.⁴³

1.

Dynamic microsimulation often includes modeling year to year changes in socioeconomic factors, such as marriage, divorce, having a child, becoming unemployed, retire, or die – outcomes which are not usually given much attention in static microsimulation analysis.

2.

Other models based on the microsimulation concept and related to those presented here have been developed. For example, both non-behavioral and behavioral models have been established for families with preschool children; see Kornstad and Thoresen (2007) and Thoresen and Vattø (2015) for two labor supply models for this group of families.

3.

Similar to several of the other models referred to above, the source code of the models of the LOTTE system are not “open source”. See https://euromod-web.jrc.ec.europa.eu/download-euromod/ for source code of EUROMOD.

4.

“Skatt” means tax in Norwegian.

5.

“Arbeid” means work or labor in Norwegian.

6.

“Konsum” means consumption in Norwegian.

7.

Today, simulations of post-tax effects of changes in pensions and social transfers are carried out by means of an ad-hoc procedure, where changes in pensions and transfers are simulated by the Norwegian Labour and Welfare Administration and then taxed by LOTTE-Skatt at Statistics Norway.

8.

Norway is one of only a few countries that levy a tax on annual net wealth, see Thoresen et al. (2022).

9.

To be precise, the Ministry of Finance could get access to anonymized data, which in practice would mean removing personally identifiable information. But given the large number of variables in our administrative registers, in a country with a small population, anonymization would involve reducing the number of variables, likely leading to a deficient model.

10.

“Aksess” is access in Norwegian, and the name alludes to improved accessibility.

11.

The model also includes a “typical household” (constructed household) simulation module, which permits simulating effects of tax changes for specific households – for families with 1 or 2 adults (singles or married couples) and 0–3 children, differentiated with respect to types of income (wage income, pension income, business income, and capital income).

12.

Other standard output tables for distributional effects include tables based on other income concepts, such as household income adjusted by equivalence scale.

13.

Exchange rates for euros and U.S. dollars: 1 EUR = 11.4 NOK and 1 USD = 10.6 NOK (2023).

14.

There are alternative sampling procedures to this method – our method can be characterized as scoring well on transparency.

15.

Kasten et al. (1994) use the same technique studying the development of U.S. tax progressivity over the period 1980–1993. In the Norwegian context, this method has also been used to provide information about the tax policies of different governments (of different colors) and their redistributional ambitions (Lian et al., 2013; Lian et al., 2019). Lambert and Thoresen (2009) also discussan alternative method to the fixed-income approach for comparing tax distributional effects over time – the “transplantand-compare” approach of Dardanoni and Lambert (2002). See also Thoresen et al. (2016) for a generaldiscussion on methods of describing tax redistributional effects over time.

16.

Results are shown only for e = 0.75.

17.

A possible reason for choosing this method is that the policy change in question concerns a specific group for which there is no reliable (structural) behavioral simulation model.

18.

A similar method has also been used in Thoresen (2004) and Thoresen et al. (2012).

19.

A marginal tax rate of 47.4 percent follows from national insurance contribution (8 percent), plus tax on ordinary or net income (22 percent), and plus the top rate of the bracket tax scheme (17.4 percent). Bracket tax is the progressive element of tax on wage income of the Norwegian dual income tax system. Note also that this fifth bracket has been part of the scheme since 2022.

20.

Jia et al. (2023) provides further details as to how estimates at both the extensive and intensive margins are obtained.

21.

1.9 multiplied by 0.2.

22.

Of course, as we will return to in Section 5.3, there are other revenue effects involved, as effects working through the payroll tax and commodity taxation.

23.

The “job choice” model choice model emphasizes that individuals face restrictions when they choose jobs and hours of work and therefore, it can be argued, represents a more realistic depiction of the actual choices of heterogeneous individuals than as following from conventional labor supply models, such as the one by van Soest (1995).

24.

That is, ${\displaystyle {\displaystyle P(\eta (z)\le x)=\exp [-\exp (-x)]}}$.

25.

The model is intermittently re-estimated on new waves of the Labour force survey.

26.

A tax simulation model for the self-employed requires a different decision-making model – it is not straightforward to extrapolate the wage earner model estimates to this group.

27.

A third method would be to make independent drawings (based on the distributional assumptions regarding the error term), pre- and post-reform.

28.

Note that leisure is defined here simply as time spent not working in the market; thus it may include parental childcare and other types of household work.

29.

Some studies report higher wage elasticity estimates than we find here; see for for example Keane (2022) for micro evidence and Mertens and Montiel Olea (2018) and Zidar (2019) for macro studies.

30.

See Rees et al. (2023) for an analysis in which LOTTE-Arbeid is used to discuss child benefit design.

31.

See the discussion of such measures in Section 3.5.2. Furthermore, we return to a presentation of results from a journal article discussing such estimates in Section 5.3.

32.

The estimate of the self-financing due to increased deduction rate of the minimum deduction stands out with a negative sign in Table 5. This follows from a negative behavioral revenue effect, as this change makes it more attractive to work fewer hours.

33.

In Thoresen and Vattø (2015) the ETI literature is referred to as the “New Tax Responsiveness literature”.

34.

This is close to Hansen and Liu (2015), who use a regression discontinuity approach to discuss the performance of a discrete choice model of labor supply and welfare participation for single Canadian men. They find model prediction results that are close to the regression discontinuity estimates.

35.

Allowing the wage rate to be determined partly by the effort and job choice decision of the individual is a challenging extension of the standard labor supply model. Creedy and Duncan (2005) and Peichl and Siegloch (2012) account for “general equilibrium” effects of wages in simulations.

36.

The sum of the marginal budget shares over all goods is equal to one.

37.

Note that ${\displaystyle {\zeta }_j}$ can be calibrated by realizing that ${\displaystyle {\zeta }_j=E_j{\psi }_j}$, where ${\displaystyle E_j}$ is the Engel elasticity and ${\displaystyle {\psi }_j}$ is the budget share of good ${\displaystyle j}$. In the same manner we can define adult and child elasticities (person elasticities), i.e., how the demand depends on number of children and adults, and calibrate ${\displaystyle m{1}_j}$ and ${\displaystyle m{2}_j}$ (Aasness and Holtsmark, 1993).

38.

Since we do not model non-observable differences in preferences, nobody will choose to be, for example, abstainers or non-smokers. The only reason for observing zero consumption of a particular good for a particular household is low income.

39.

We need to have the macro consumption level (from national account data) for the good and estimates of the associated Engel and person elasticities, see above.

40.

Whereas the discussion in the U.S., for example, has primarily been on the long-term self-financing effects of tax changes (dynamic scoring), Thoresen et al. (2010) focus on short-term estimates of self-financing.

41.

Note that although LOTTE-Konsum is not used for calculating the effects on tax revenue of tax changes in the Norwegian budget process, we employ the model for revenue calculation here.

42.

Low-response and high-response labor supply alternatives are obtained by using bootstrap techniques to construct confidence intervals for the model parameters. Whereas the main response alternative gives a labor supply offsetting effect of 34 percent, the two alternative response estimates result in offsetting effects of 27 percent (low) and 39 percent (high).

43.

It should be noted that these estimates are obtained from a previous estimation of LOTTE-Arbeid, generating higher responses than seen in estimations with newer data.