A series of multiplier analysis that illustrate the properties of ADAM are presented below. The calculations are made with the model version ADAM October 2016 using the baseline lang17.


The general features of the model version is presented in another working paper; see tmk15nov16. The model uses national accounts data from November 2016. Employment and working hours are revised in the new data, which, among others, change hourly productivity. Exports and production in the public sector are also revised. The behavioral relations in the present model are re-estimated using the new national accounts data. In general, the estimated elasticities have not changed significantly compared to the predecessor October 2015 model version. Minor changes in the estimated elasticities can be seen in the factor block and housing model.


Changes has also been made to the current model that describes the interaction between public sector, o1, and public services industry, o. For both the o1-sector and the o-industry productivity indices for each factor input has been included and there is now a one-to-one relationship between productivity in o1 and o. Thus a 1 percent rise in productivity of a certain factor in the o1-sector is followed by a 1 percent rise in the corresponding productivity index in the o-industry. A number of papers - for example on estimation, data construction or model analysis - can be found on the homepage


The major change in the present model version is the introduction of supply effects in the export relations. In earlier model versions, exports are described as a function of relative prices and foreign demand. In the present model, exports are in addition related to supply factors, 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 setup in a way such that a user can choose to activate the supply effects through a switch dummy. In general, the difference in the multiplier properties of the new model and the previous model is greatly attributed to the supply effects included in the export relations. Nevertheless, the changes in the estimated elasticities can also create some differences between the two models.


The multiplier analysis 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, lang17, is based on the historical data bank from April 2017 that contains annual historical data up to and including 2016. The baseline is based on a scenario with steady-state growth driven by domestic growth in productivity.


The chosen growth rates reflect historical growth rates in the Danish economy. But demography and labor supply are assumed to be unchanged. So that the number and structure of the population is 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 1.5 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 1.5 percent reflecting the annual productivity growth.


This development in output 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 1.5 percent, like the growth rate of labor productivity. 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 4 percent (close to 100.000 persons).


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 1.5 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 purchase of goods


Labor supply - working hours


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


Private consumption


Indirect tax rates


Hourly wages


Foreign prices


Oil prices


Labor supply - number of workers


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, and an increase in efficiency has also a permanent effect on output.


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, we present some of the experiments listed above in two sections: a section  where each experiment is presented without any consideration for public finances,  and another section where the experiment is accompanied by changes in income tax rates so that the public budget is balanced.


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. Experiment 1-5 affect the volume of aggregate demand directly and the short-term impact on GDP is significant. In experiment 6, 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 experiment 7-9 aggregate demand also expands indirectly through the effect on prices and real income, an the effect on output is also smaller compared to experiment 1-5. Experiment 1-4 and 6-7 present a shock to fiscal policy instrument variables. 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. Experiment 5 and 8-9 shock foreign demand and prices.


Experiment 10-15 present supply shocks. Experiment 10-12 are different but comparable shocks to the labor supply, cf. rbj14512. Experiment 12 concerns labor productivity and can also be compared with experiment 13-14 that shock the efficiency of other production factors. Experiment 15 describes a shock to interest rates.


The final two experiment, number 16 and 17, are somewhat different from the other experiments. They present the effect of a temporary shock to two of the model's central relations, namely private consumption relation and wage relation. Experiment 1 and 10-15 contain a sub-section, where the effect of a budget restriction is presented for public purchase experiment in the former and labor supply shock in the latter.


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.