A series of multiplier analyses that illustrate the properties of ADAM are presented below. The calculations are made with the model version ADAM April 2023 – hereafter in short Apr23 – using the baseline Lang23. The model uses national accounts data from november 2023. A number of papers – for example on estimation, data construction or model analysis – can also be found on the homepage


Besides the actual measure for labor supply, the model also provides a cyclically adjusted labor supply enhancing the scope for economic analysis. In the period with historical data, the cyclically adjusted labor-market variables reflect an HP filtering of the actual variables. In the forecast or baseline period, the cyclically adjusted variables are consistent with the long-term equilibrium of the ADAM model.


In addition, significant changes have been implemented in the new model’s core equations, not least in foreign trade, which is now better incorperate trends in reexports and labor supply due to workers crossing borders, cf. tmk081123 for a review of changes in data and model.


The multiplier analyses are based on a baseline. The baseline represents a solution with respect to the endogenous variables given a stylized projection of the exogenous variables. The present baseline, Lang23, is based on the historical data bank from November 2023 that contains annual historical data up to and including 2022. The baseline is based on a scenario with steady-state growth driven by population growth and domestic growth in productivity.


The chosen growth rates reflect historical growth rates in the Danish economy. But demography and labor supply are assumed to grow 0.5 percent per annum. So that the number people grow but structure of the population are assumed to be unchanged. Productivity growth in the Danish economy is assumed to be 1.5 percent per annum. The growth in the market for Danish exports is likewise assumed to be at about 2 percent. Import prices and competitive prices in the export market are assumed to grow by 2 percent annually. In steady-state the domestic prices and costs will grow by 2 percent like foreign prices, and the Danish GDP will grow by 2.0 percent reflecting the annual sum of productivity and population growth.


This development in output per capita is achieved by assigning the growth in productivity to labor and this is reflected by a corresponding increase in real wages of 1.5 percent. The real interest rate is constant and fixed at 2 percent, like the growth rate of output. Thus, the Danish economy can grow in steady-state with unchanged demand structure, unchanged composition of output and income, unchanged economic policy, unchanged tax and public expense burden, and unchanged sectoral composition etc. The replacement rate of unemployment insurance is also unchanged and the equilibrium level of unemployment is approximately 1.5 percent (close to 60.000 persons in 2100).


Overall, it is a baseline of the Danish economy repeating itself into the future roughly as we know it today with a real growth of 2 percent and an inflation rate of 2 percent. In the short term, it is necessary to allow for deviations while variables are adjusting to steady-state but the equilibrium scenario is achieved within a short time frame. For a discussion of the structure and construction of the baseline scenario see chapter 10 in the ADAM book, which is also available for download.


The multiplier experiments are carried out by changing one or a few of the exogenous variables. Then the model is simulated to calculate the effect on the endogenous variables and this creates a new solution called an alternative scenario. The multipliers for the endogenous variables are calculated as the difference between the values in the alternative scenario and the baseline scenario. The multipliers reported in graphs and tables are calculated either as a simple or relative differences depending on the nature of the variables. A word of caution is necessary when reading the text, when a certain endogenous variable is said to increase or decrease following a given shock it should be interpreted as an increase or a decrease compared to the baseline values.


The purpose is to illustrate the properties of ADAM. There is no provision for possible ties between the exogenous variables. This means that one has to be careful in the interpretation of the experiments as real world economic events are rarely confined to changes in one exogenous variable. For example, in the interest rate experiment in section 15 below, the potential effect of interest rate changes on foreign demand are not taken into account, see grh12912 for more.  


It is worth noting the premise that before we introduce a shock to the model, the economy is following a baseline, which ends up in steady-state equilibrium. Economic policy-induced shocks to ADAM may be directed against short-run deviations from the steady-state, i.e. stimulating the economy if the present unemployment is above its long-run equilibrium; or the shocks may try to change the steady-state, for example, increasing the labor supply in order to expand the scope for private and public consumption or increasing energy taxes to reduce the input of energy in output and consumption.


In this paper each of the experiments is presented briefly and the analysis of the multiplier is kept short. A detailed discussion of the key mechanisms in ADAM can be found in chapter 11 in the ADAM book.


The experiments concern the following exogenous variables or groups of variables:



General government employment


Productivity - labor efficiency


General government investment in buildings


Productivity - machinery efficiency


General government investment in machinery


Productivity - efficiency of labor and capital


Foreign demand


Interest rates


Income tax rates


General government purchase of goods


Indirect tax rates


Private consumption


Foreign prices


Hourly wages


Oil prices


Labor supply - number of workers


Labor supply - working hours


All experiments are chosen to be expansionary in order to facilitate comparison. In some of the experiments, the positive effect on economic activity is temporary and in others the effect is permanent. In general, a demand shock in ADAM, e.g. an additional public purchase of goods, affects production and employment in the short run. However, in the long run a pure demand shock has no or little effect on employment and production. A long-term employment effect of zero is a general result for models of a small open economy with fixed exchange rate and a Phillips curve.


In contrast, a supply shock, such as an increase in the labor force, has a permanent effect on employment and output, while an increase in efficiency has a permanent effect on output. An increase in the labor force will increase unemployment and hence reduce wages. This will improve the domestic economy's competitiveness, and exports and output will therefore have a permanent positive effect compared to the baseline. This in turn, will also increase employment with as much as the unemployment initially increased with the introduced shock to the labor force. An increase in the efficiency on the other hand, will reduce the demand for employees and hence reduce the wages. This also improves the competitiveness, and thus increases exports and output permanently. However, the employment effect is zero in the long run because the employment will rise again due to the increased exports and output.


In the first half of the analysis, the shocks expand aggregate demand. In most cases policy instruments are used to stimulate domestic demand, and in other cases foreign variables and interest rates change. Experiments 1-4 affect the volume of aggregate demand directly and the short-term impact on GDP is significant. In experiment 5, demand increases indirectly due to the increase in disposable income and the short-term impact on GDP is somewhat smaller than the previous cases. In experiments 6-8 aggregate demand also expands indirectly through the effect on prices and real income, and the effect on output is also smaller compared to the experiments where aggregated demand is expanded directly. Experiments 1-3, 5-6 and 15 present a shock to fiscal policy instrument variables, where experiment 15 induces a demand shock by expanding general government purchases. In all cases the shock is calibrated to have a direct impact of the equivalent of 0.1 percent of GDP on public budget in the first year. Experiments 4 and 7-8 shock foreign demand and prices.


Experiments 9-14 present supply shocks. Experiments 9-11 are different but comparable shocks to the labor supply, cf. rbj14512. Experiment 11 concerns labor productivity and can also be compared with experiments 12-13 that shock the efficiency of other production factors. Experiment 14 describes a shock to interest rates. Experiments 9-14 also include versions with supply effects on exports, i.e. exports expand if domestic output grows in real terms without changes in the terms of trade; cf. the papers dsi08aug16, dsi11nov16 and dsi01mar17. This is in line with the traditional gravity equations where trade flows are related to domestic output (a measure for supply effects) and foreign output (a measure for demand effects). The export equations are set up in a way such that a user can choose to activate the supply effects through the switch dummy, dfyfu. The switch dummy is set to 0 by default, and supply effects on exports is turned on by setting dfyfu equal to 1.


The final three experiments, number 15-17, are somewhat different from the other experiments, as the shocks are only temporary. Experiments 16 and 17 present the effect of a temporary shock to two of the model's central relations, namely private consumption relation and wage relation.


The standard version of ADAM has no fiscal reaction function which would automatically ensure the sustainability of public finances. Without a reaction function the government budget balance can become permanently negative or positive depending on the experiment. Accordingly, some of the experiments listed above, are presented in multiple versions based on whether the government budget balance is taken into account. When considering the public finances, income tax rates are adjusted to keep the public budget balanced. In addition, public consumption can be endogenized by setting the dummy variable dco to 1. The experiments where the alternative with a balanced budget is available, are experiments 9-15, where effects of shocks to labor supply, productivity, interest rate and government purchase  are analysed. In experiment 15, where the effect of a budget restriction is presented for a public purchase expenditure experiment, the tax on capital is also adjusted the first year.


For each experiment, a total of eight figures are presented to illustrate the effect on key endogenous variables. Variables have been divided into supply and use, labor market, saving balance, wage and prices, taxes and income, real income and wealth and private investment variables, in addition to a group of different ratios and asset price variables. For the central variables of the labor market, the multipliers are calculated as the difference between the baseline and alternative scenario, measured in 1000 people. Multipliers for saving balance variables are calculated as the absolute difference in the percentage share of GDP. The multipliers of different ratios and asset prices, are calculated as the difference between baseline and alternative scenario as measured in percentage points. For the remaining groups of variables, the multipliers are given as the percentage change from the baseline to the alternative scenario.


Finally, we should note that comparison with models from other countries may be difficult, for example due to different budget restrictions. Special Danish conditions (e.g. regulatory mechanisms in taxes and transfers etc) incorporated in ADAM produce distinct multipliers and make comparison with other countries difficult. As mentioned, the interest rate and exchange rates are exogenous in ADAM because the Danish economy is modeled as a credible shadow member of the euro zone. Note also that expectations in ADAM are adaptive or constant, i.e. constant inflationary expectations reflecting the constant exchange rate.