Introduction to the DREAM-model-system

The population projection model is a national demographic projection model which forecasts the Danish population across gender, age and origin (immigrants and descendants from Western and non-Western countries respectively, and the residual population) until the turn of the century. The model is used by Statistics Denmark for the official Danish population projection. The projection is based on estimations of the age-, gender- and origin-dependent frequencies of birth, death and migration.

The mortality projection uses the Lee-Carter mortality forecasting method which is an econometric method that extrapolates decreasing mortality into the future. This allows analyses of the so-called population aging problem. Typical analyses in this part of the DREAM system are altered assumptions about immigration, fertility and mortality.

DREAM’s population projection model

The model is based on transition probabilities calculated from Danish register data, and it thus forecasts education levels by employing historical educational behavior. The model can therefore be used to predict future trends that can be attributed to the behavior of current students (or trends related to the future population composition). Examples of typical analyses include changes in dropout rates and in the age of students beginning a given level of education. The figure below shows the development in the number of people currently in education.

DREAM’s education projection model

The projection of labor market participation rates is based on the assumption that a person of a given age, gender, origin and a given highest completed level of education will have a tendency to choose the same labor market participation in the future as an equivalent person chooses today. By default, these labor market frequencies (share of population with a given labor market participation) are assumed to be constant over time. This basic assumption is then adjusted to reflect current labor market policy. Furthermore, for each level of education an estimated effect of the recent development in labor market participation rates is added. The 2006 welfare reform is also included in the socioeconomic projection. In the reform, the early retirement pay (efterløn) age is indexed to the remaining life expectancy of a 60-year-old. The effect of this regulation on the workforce is shown in the figure below. Examples of analyses in this part of the DREAM system include changes to the rules of early retirement pay and public pensions.

DREAM’s socioeconomic projection model

The DREAM macroeconomic model is a so-called overlapping generations model. This means that there is a representative household for every age group (17-101 years). As an example, the 30-year-old household consists of all 30-year-old males, all 30-year-old females and their children (with regard to consumption, a child has the weight of half an adult). The household demands goods, services, energy and housing and supplies labor to the labor market. With the information from the three pre-models, very well-specified income profiles can be generated for the life of each representative household. From the population projection, the number of people in each household/generation is known. From the socioeconomic projection, the number of people in the workforce and the number of people receiving income transfers are known.

The general wage level in the model is determined by a market macro wage. For each individual generation, the relative wage is determined by the individual productivity which is distributed across gender, age and origin. This productivity is calibrated in the base year using wages generated from register data and distributed across gender, age and origin. Income transfers are based on the current rules and the development in the wage regulation index which follows the general wage level.

Households pay income tax according to a non-linear tax function estimated from register data. The tax function allows for an approximation of the real-world progressive tax system which makes it possible to analyze changes in tax rates and tax brackets.

Households are assumed to pay an age-specific share of wages to labor market pensions and private pensions. Private pensions consist of lifetime annuities (livrente), term annuities (kapitalpension) and private pensions (ratepension). Pensions in DREAM are calculated in a large independent module that takes the correct actuarial regulations into account. This ensures that the model generates a reasonable estimate of the future developments in the Danish pension system, including future tax payments from pension payments. In addition to pensions, households hold savings in housing and in securities (bonds and shares). These last two types of savings are endogenously determined in the macro model.

There are nine production sectors in the model: a large private sector, a construction sector, a public sector, and six energy sectors. The private sectors have quadratic installation costs. This means that a firm’s cost of investing an additional unit is increasing in the investment level. The result is that firms adjust their capital stock gradually, thus avoiding unrealistically large jumps in investment levels.

The public sector is assumed to a have production function in line with the private sectors. Public services are produced with the use of materials, energy, capital, and labor. The public sector is assumed to be service-maximizing: For a given budget, the inputs of materials, energy, capital, and labor are chosen to maximize the level of service. It is assumed that productivity growth in the public sector is equal to productivity growth in the private sectors.

We now have the tools necessary for an assessment of the future revenues and expenditures of the public sector. Public expenditures consist of three basic components: collective public consumption, individual public consumption, and income transfers. These components are modeled separately in DREAM.

Individual public consumption is divided into four categories, equivalent to the division in the national accounts: health care, social care, education, and leisure, culture etc. These four variables are projected based on demographic developments. Based on register data, the cost of a person of a given gender, age and origin is calculated. For social care, education, and leisure, culture etc., it is assumed that the average cost per person increases with the underlying growth rate of the economy. In this lies an assumption that the level of service will rise with the general increase of wealth in the economy. The projection of the costs of health care and care for the elderly is adjusted to follow the development in life expectancy. This is due to the fact that the cost of health care increases substantially in the terminal phase as most expenditures fall in the last years before death. Moreover, it is assumed that the cost of health care services and the part of social care services that is related to care for the elderly, will grow by an additional 0.3 percent the next 25 years. This reflects the observed additional growth of these costs since 1995. In other words, it is assumed that the historical trend in the cost of health care will continue but that the cost will be controlled in the long run.

Collective public consumption is assumed to follow GDP in DREAM’s base scenario. In alternative scenarios, collective public consumption is typically assumed to be given by its level in the base scenario.

The last component of public expenditure is income transfers. There are 13 types of income transfers in DREAM: unemployment benefits, student aid benefits, leave benefits, maternity benefits, sickness benefits, activation benefits, cash benefits (kontanthjælp), transitional benefits (overgangsydelse), early retirement pay (efterløn), early retirement pensions (førtidspension), public pensions, civil servants earned pensions, and introductory benefits (introduktionsydelse). The number of people outside the workforce receiving the different income transfers is determined by the socioeconomic projection. Within the workforce, the ratio between employed and unemployed is determined by the macro model. As previously mentioned, the socioeconomic projection incorporates the 2006 welfare reform. This is of crucial importance to the projection of income transfers.

Public revenues derive from various taxes and duties. They are calculated on a relatively detailed level in the macro model. Firms pay corporate tax as well as numerous other duties. Furthermore, public revenues from North Sea oil and gas extraction are included as the macro model contains sectors for extraction of oil and gas. The development in the production of these sectors is determined by the Danish Energy Agency’s prognosis for oil and gas extraction in the North Sea.

Households pay income tax as well as numerous other duties. The long-run character of the model makes it possible to analyze the long-term consequences of e.g. a tax freeze and energy duties.

A central variable in every DREAM simulation is the so-called sustainability indicator. The sustainability indicator measures, as a share of GDP, the permanent improvement to the primary public budget that is necessary in order for the public sector to meet its long-run budget constraint. The sustainability indicator is thus a measure of the size of the changes in economic policy that are necessary in order to ensure that the public sector does not generate a deficit in the long run. It should be noted that the sustainability indicator does not specify which changes in economic policy should be made.

Read DREAM's long term forecast of the Danish economy

As evident in the previous section, the macroeconomic model is used to calculate a large number of variables: GDP, employment, taxes etc. In principle, these variables could be taken from an external model and used to define a base scenario. A base scenario is a projection that provides the best estimate of future developments given a large number of assumptions about the future (including adopted policies). However, a problem arises if one wishes to present an alternative scenario relative to the base scenario. In an alternative scenario, a number of parameters with significance for the behavior of economic agents will typically be changed (e.g. tax regulations or retirement age). This requires a modeling of the long-term behavior of consumers and firms.

It is for this reason that the DREAM system is built around a long-term macroeconomic model, a so-called structural model. The model is a long-run model in the sense that prices and wages are assumed to create equilibrium in all markets in each period. Imperfect competition is assumed in all markets. This creates mark-up prices in the goods market and structural unemployment in the labor market.

Structural unemployment is basically exogenous in DREAM. This can be interpreted in two ways: Firstly, DREAM is a long-run model. When projections are made 20 or 50 years ahead, it is impossible to know whether the economy will be in a boom or a recession at the time in question. Therefore, an average level of economic activity is assumed. Secondly, it is implicitly assumed that policies that can be analyzed in DREAM will not affect structural unemployment. This does not mean that the DREAM group believes it impossible to affect structural unemployment. It simply means that ways to affect structural unemployment do not exist within the relatively conventional theoretical framework in which DREAM operates. If one wishes to analyze situations in which structural unemployment is affected, these effects must be calculated outside the model or alternatively be included in a special version of the model.

Households and firms are assumed to have perfect foresight. In other words, they know all future prices. This assumption is made to ensure consistent behavior over time. The assumption is very unrealistic at first sight. Few people know what will happen in one year, and no one knows what will happen in ten years. The alternative to the assumption, however, is even more unrealistic: If it is assumed that agents do not know what will happen in the future or that they have simple static expectations, the result will be unrealistically inconsistent behavior over time.

The assumption of perfect foresight in a long-run model like DREAM can be seen as an attempt to describe a system in which agents have a clear sense of the way the system functions in the long run. The assumption means that no economic phenomenon exists as a result of agents’ systematic errors. In other words, no economic phenomenon can be explained by people having wrong expectations, only by people not having wrong expectations (i.e. having made an informed, conscious decision).

Most economists accept this premise in the long run as a useful idealization. In the short run, however, the premise is less useful. In the short run, people make systematic errors, probably due to a combination of inattention and lack of time to obtain the necessary information. In addition, several institutional and behavioral explanations of price and wage rigidities exist. This is, however, not modeled in DREAM.

Read a full documentation of the macroeconomic model