Economic Forecasting with an Agent-Based Model

We develop the first agent-based model (ABM) that can compete with and in the long run significantly outperform benchmark VAR and DSGE models in out-of-sample forecasting of macro variables. Our ABM for a small open economy uses micro and macro data from national sector accounts, input-output tables, government statistics, and census data. The model incorporates all economic activities as classified by the European System of Accounts as heterogeneous agents. The detailed structure of the ABM allows for a breakdown into sector level forecasts. In a recent application, we have used the detailed structure of the ABM to forecast the medium-run macroeconomic effects of lockdown measures taken in Austria to combat the COVID-19 crisis. Other potential applications of the model include stress-testing and predicting the effects of monetary or fiscal macroeconomic policies.

The dominant theory-driven approach to modeling the economy over recent decades has been the dynamic stochastic general equilibrium (DSGE) model. In particular, models following the New Keynesian paradigm, that include financial and real frictions to replicate phenomena observed in empirical data, have become a new standard in macroeconomics (Christiano et al., 2010;Brunnermeier et al., 2013). Together with structural econometric and vector autoregressive (VAR) models of various types and sizes, DSGE models are the workhorse framework of central banks and other institutions engaging in economic forecasting, especially since the advent of Bayesian DSGE models such as Wouters (2003, 2007), exhibiting good forecasting capabilities when compared to simple time series models. One of the main reasons for the evident success of DSGE models is their rigorous micro-foundations rooted in economic theory, which have been complemented by Bayesian parameter estimation techniques to reach a better empirical fit (An and Schorfheide, 2007;Fernandez-Villaverde, 2010;Linde et al., 2016). However, in the light of the financial crisis of 2007-2008 and the subsequent Great Recession, these models have been criticized by several prominent voices within the economic profession, coming from different schools of economic thought. The limits of the DSGE approach at the core of the New Neoclassical Synthesis have been discussed in detail, for example, in (Vines and Wills, 2018). 1 As an alternative, some economists are pushing forward with agent-based models (ABMs)potentially to complement DSGE models-as a new promising direction for economic modelling. 2 Farmer and Foley (2009), in particular, suggest that it might be possible to conduct economic forecasts with a macroeconomic ABM, although they consider this to be ambitious.

Related literature
Since their beginnings in the 1930s, 7 ABMs have found widespread application as an established method in various scientific disciplines (Haldane and Turrell, 2018), for example, military planning, the physical sciences, operational research, biology, ecology, but less so in economics and finance. The use of ABMs in the latter two fields to date remains quite limited in comparison to other disciplines. An early exception is Orcutt (1957), who constructed a first simple economically motivated ABM to obtain aggregate relationships from the interaction of individual heterogeneous units via simulation. Other examples include topics such as racial segregation patterns (Schelling, 1969), financial markets (Arthur et al., 1997), or more recently the housing market (Geanakoplos et al., 2012;Baptista et al., 2016). Since the financial crisis of 2007-2008, ABMs have increasingly been applied to research in macroeconomics. Furthermore, in recent years, several ABMs have been developed that depict entire national economies and are designed to deliver macroeconomic policy analysis. The European Commission (EC) has in part supported this endeavor. One example of a large research project funded by the EC is the Complexity Research Initiative for Systemic Instabilities (CRI-SIS), 8 an open source collaboration between academics, firms, and policymakers (Klimek et al., 2015). Another is EURACE, 9 a large micro-founded macroeconomic model with regional heterogeneity (Cincotti et al., 2010).
See also: http://www.wiwi. uni-bielefeld.de/lehrbereiche/vwl/etace/Eurace_Unibi/ (Last accessed November 30 th , 2018) 10 For another recent overview on macroeconomic ABMs see Fagiolo and Roventini (2017). the framework developed by  in Bielefeld as an offspring of the EURACE project, known as Eurace@Unibi; (4) the EURACE framework maintained by Cincotti et al. (2010) in Genoa; (5) the Java Agent based MacroEconomic Laboratory developed by Seppecher, Salle, and Lavoie (2018); (6) the family of models developed by Dosi et al. (2017) in Pisa, known as the "Keynes meeting Schumpeter" framework; and (7) the LAGOM model developed by Jaeger et. al (2013). What unites all these families of models is their ability to generate endogenous long-term growth and short-to medium-term business cycles. These business cycles are the macroeconomic outcome of the micro-level interaction of heterogeneous agents in the economy as a complex system subject to non-linearities (Dawid and Delli Gatti, 2018). All these models assume bounded rationality for their agents, and thus suppose adaptive expectation in an environment of fundamental uncertainty. Typically, they minimally depict firm, household, and financial (banking) sectors populated by numerous agents of these types (or classes), and agents exhibit additional heterogeneity within one or more of the different classes. All results are obtained by performing extensive Monte Carlo simulations and averaging over simulation outcomes. The great majority of models are calibrated and validated with respect to a (smaller or larger) variety of stylized empirical economic facts (Fagiolo and Roventini, 2017). However, despite their level of sophistication, all these models suffer from one or more impediments: they serve as a theoretical explanatory tool constructed for a hypothetical economy; the choice of the number of agents is arbitrary or left unexplained; time units may have no clear interpretation; validation with respect to stylized empirical facts cannot solve the potential problem of over-parameterization; the choice of parameter values is often not pinned down by clear-cut empirical evidence; and most of these models exhibit an extended transient or burn-in phase that is discarded before analysis.
To address these concerns we develop an ABM that fits microeconomic data of a small open economy and allows out-of-sample forecasting of the aggregate macro variables, such as GDP (including its components), inflation and interest rates. This model is based on micro and macro data from national accounts, input-output tables, government statistics, census data, and business demography data. Model parameters are either taken directly from data or are calculated from national accounting identities. For exogenous processes, such as imports and exports, parameters are estimated. As an empirical validation, we compare the out-of-sample forecast performance of the ABM to that of AR, VAR, and DSGE models.

An agent-based model for a small open economy
In this section we give a short overview of the model; for details, see Appendix A to Appendix C. Following the sectoral accounting conventions of the ESA, Eurostat (2013), the model economy is structured into four mutually exclusive domestic institutional sectors: (1) non-financial corporations (firms); (2) households; (3) the general government; and (4) financial corporations (banks), including (5) the central bank. These four sectors make up the total domestic economy and interact with (6) the rest of the world (RoW) through imports and exports. Each sector is populated by heterogeneous agents, who represent natural persons or legal entities (corporations, government entities, and institutions). We use a scale of 1:1 between model and data, so that each agent in the model represents a natural or legal person in reality. This has the advantage that our ABM is directly linked to microeconomic data and that scaling or fine tuning of parameters and size is not needed; rather, parameters are pinned down by data or calculated from accounting identities. All individual agents have separate balance sheets, depicting assets, liabilities, and ownership structures. The balance sheets of the agents, and the economic flows between them, are set according to data from national accounts.
The firm sector is composed of 64 industry sectors according to the NACE/CPA classification by ESA and the structure of input-output tables. The firm population of each sector is derived from business demography data, while firm sizes follow a power law distribution, which approximately corresponds to the firm size distribution in Austria. Each firm is part of a certain industry and produces industry-specific output by means of labor, capital, and intermediate inputs from other sectors-employing a fixed coefficient (Leontief) production technology with constant coefficients. These productivity and technology coefficients are calculated directly from input-output tables. Firms are subject to fundamental uncertainty regarding their future sales, market prices, the availability of inputs for production, input costs, and cash flow and financing conditions. Based on partial information about their current status quo and its past development, firms have to form expectations to estimate future demand for their products, their future input costs, and their future profit margin. According to these expectations-which are not necessarily realized in the future-firms set prices and quantities. We assume that firms form these expectations using simple autoregressive time series models (AR(1) expectations). These expectations are parameter-free, as agents learn the optimal AR(1) forecast rule that is consistent with two observable statistics, the sample mean and the sample autocorrelation (Hommes and Zhu, 2014). Output is sold to households as consumption goods or investment in dwellings and to other firms as intermediate inputs or investment in capital goods, or it is exported. Firm investment is conducted according to the expected wear and tear on capital. Firms are owned by investors (one investor per firm), who receive part of the profits of the firm as dividend income.
The household sector consists of employed, unemployed, investor, and inactive households, with the respective numbers obtained from census data. Employed households supply labor and earn sector-specific wages. Unemployed households are involuntarily idle, and receive unemployment benefits, which are a fraction of previous wages. Investor households obtain dividend income from firm ownership. Inactive households do not participate in the labor market and receive social benefits provided by the government. Additional social transfers are distributed equally to all households (e.g., child care payments). All households purchase consumption goods and invest in dwellings which they buy from the firm sector. Due to fundamental uncertainty, households also form AR (1) expectations about the future that are not necessarily realized. Specifically, they estimate inflation using an optimal AR(1) model to calculate their expected net disposable income available for consumption.
The main activities of the government sector are consumption on retail markets and the redistribution of income to provide social services and benefits to its citizens. The amount and trend of both government consumption and redistribution are obtained from government statistics. The government collects taxes, distributes social as well as other transfers, and engages in government consumption. Government revenues consist of (1) taxes: on wages (income tax), capital income (income and capital taxes), firm profit income (corporate taxes), household consumption (valueadded tax), other products (sector-specific, paid by industry sectors), firm production (sector-specific), as well as on exports and capital formation; (2) social security contributions by employees and employers; and (3) other net transfers such as property income, investment grants, operating surplus, and proceeds from government sales and services. Government expenditures are composed of (1) final government consumption; (2) interest payments on government debt; (3) social benefits other than social benefits in kind; (4) subsidies; and (5) other current expenditures. A government deficit adds to its stock of debt, thus increasing interest payments in the periods thereafter.
The banking sector obtains deposits from households as well as from firms, and provides loans to firms. Interest rates are set by a fixed markup on the policy rate, which is determined according to a Taylor rule. Credit creation is limited by minimum capital requirements, and loan extension is conditional on a maximum leverage of the firm, reflecting the bank's risk assessment of a potential default by its borrower. Bank profits are calculated as the difference between interest payments received on firm loans and deposit interest paid to holders of bank deposits, as well as write-offs due to credit defaults (bad debt). The central bank sets the policy rate based on implicit inflation and growth targets, provides liquidity to the banking system (advances to the bank), and takes deposits from the bank in the form of reserves deposited at the central bank. Furthermore, the central bank purchases external assets (government bonds) and thus acts as a creditor to the government. To model interactions with the rest of the world, a segment of the firm sector is engaged in import-export activities. As we model a small open economy, whose limited volume of trade does not affect world prices, we obtain trends of exports and imports from exogenous projections based on national accounts.
The parameters of our ABM are summarized in Table 1; for details see Appendix B. For the forecasting exercise in Section 3, parameters were initially calculated and estimated over the sample 1997:Q1 to 2010:Q1 and then, respectively, re-estimated and recalculated, every quarter until 2013:Q4. Here we show, as an example, parameter values for 2010:Q4. Data sources include micro and macro data from national accounts, sector accounts, input-output tables, government statistics, census data, and business demography data; for details, see Appendix B and Table B.6. Model parameters are either taken directly from data or calculated from national accounting identities. Parameters that specify the number of agents are taken directly from census and business demography data. Model parameters concerning productivity and technology coefficients, as well as capital formation and consumption coefficients, are taken directly from input-output tables, or are derived from them. Tax rates and marginal propensities to consume or invest are calculated from national accounting identities. These rates are set such that the financial flows observed in input-output tables, government statistics, and sector accounts are matched. Capital ratios and the inflation target of the monetary authority are set according to the literature. For exogenous processes such as imports and exports, parameters are estimated from national accounts (main aggregates). Technology coefficient of the g th product in the s th industry see Appendix B.1 b CF g Capital formation coefficient of the g th product (firm investment) see Table B.7 b CFH g Household investment coefficient of the g th product see Table B.7 b HH g Consumption coefficient of the g th product of households see Table B.7 c G g Consumption of the g th product of the government in mln. Euro see Table B.7 c E g Exports of the g th product in mln. Euro see Table B.7 c I g Imports of the g th product in mln. Euro see Table B

Forecast performance
To validate the ABM, we conduct a series of forecasting exercises in which we evaluate the out-of-sample forecast performance of the ABM in comparison with standard macroeconomic modeling approaches. 11

Comparison with VAR models
In this section, we compare the out-of-sample forecast performance of the ABM with that of various unconstrained (non-theoretical) VAR models estimated on the same observable macro time series in a traditional out-of-sample root mean squared error (RMSE) 12 forecast exercise. We compare the ABM with three standard VAR models of lag order one to three, estimated using the same eight observable time series. Observable time series include the real GDP, inflation, real government consumption, real exports and real imports of Austria, as well as real GDP and inflation of the euro area (EA), and the Euro Interbank Offered Rate (Euribor). To allow the data to decide on the degree of persistence and cointegration, in the VAR models we enter GDP, government consumption, exports, imports, and GDP of the EA in log levels. For this exercise, the VAR models and the ABM were initially estimated over the sample 1997:Q1 to 2010:Q1. The models were then used to forecast the eight time series from 2010:Q2 to 2016:Q4; the models were re-estimated every quarter. ABM results are obtained as an average over 500 Monte Carlo simulations. Table 2 reports the out-of-sample RMSEs for different forecast horizons of 1, 2, 4, 8, and 12 quarters over the period 2010:Q2 to 2016:Q4. These out-of-sample forecast statistics demonstrate the good forecast performance of the ABM relative to the VAR models of different lag orders. For GDP and inflation, the ABM delivers a similar forecast performance to that of the VAR(1) for short-to medium-term horizons up to two years, and improves on it for longer horizons up to three years. For the other five variables (government consumption, exports, imports, GDP and inflation EA, Euribor), the ABM does better than the different VAR models by a considerable margin for almost all horizons. The forecast performances of the VAR(2) and especially the VAR(3) model clearly deteriorate for longer horizons.

Comparison with DSGE and AR models
In this section, we compare the out-of-sample forecast performance of the ABM to that of a standard DSGE model. As variables for this comparison, we choose the major macroeconomic aggregates: real GDP growth, inflation, and the main components of GDP-real household consumption and real investment. As a DSGE model, we employ a standard DSGE model of Smets and Wouters (2007), which is a widely cited New Keynesian DSGE model for the US economy with sticky prices and wages, adapted to the Austrian economy. For this purpose, we use the twocountry model of Breuss and Rabitsch (2009), which is a New Open Economy Macro model for Austria as part of the European Monetary Union (EMU). 13 The DSGE model is estimated on the following set of 13 variables for the same time period as the ABM (1997:Q1-2010:Q1): log difference of real GDP, real consumption, real investment and the real wage, log hours worked, the log difference of the GDP deflator (six each for Austria and the EA), as well as the three-month Euribor. As standard time series models for comparing the forecast performance of the ABM and DSGE models, we estimate AR models of lag orders one to three on the log levels of real GDP, real household consumption, real investment, and the log difference of the GDP deflator (inflation). Again, all models are initially estimated over the sample 1997:Q1 to 2010:Q1, and the models are then used to forecast the four time series from 2010:Q2 to 2016:Q4, with the models being re-estimated every quarter. ABM results are obtained as an average over 500 Monte Carlo simulations and the DSGE model is estimated using Bayesian methods. 14 Table 3 shows comparisons between the ABM and the DSGE and AR models of different lag orders for forecast horizons of 1, 2, 4, 8, and 12 quarters over the period 2010:Q2 to 2016:Q4. Similar to the forecast exercise above, 11 This out-of-sample prediction performance evaluation is constructed along the lines of Smets and Wouters (2007), who compare a Bayesian DSGE model to unconstrained VAR as well as Bayesian VAR (BVAR) models. 12 The root mean squared error is defined as follows:  the AR(1) overall turns out to perform better than the AR models of lag orders two and three. Regarding forecasts of GDP growth and inflation, the performance of the ABM, DSGE, and AR(1) model is relatively similar, with the DSGE model applying more filtering than the other models. Both the ABM and the DSGE models show their strengths in terms of forecasts of household consumption, and especially investment, as theory-driven economic models. Both these models explicitly incorporate the behavior of different agents in the economy, as well as constraints due to the consistency requirements of national accounting-for example, they take into consideration that household consumption and investment are major components of GDP. While the improvement for household consumption is clearly noticeable-especially for the DSGE model, whose sophisticated assumptions about agents' behavior seem to make the greatest difference for this variable-there is also quite a pronounced improvement for investment. For investment forecasts, both the ABM and the DSGE model clearly do better than the AR(1) model, especially for longer horizons.

Conditional forecasts
As a further validation exercise, we test the conditional forecast performance of the different model classes (ABM, DSGE, and AR models). In this exercise, we generate forecasts from the three models conditional on the paths realized for the following three variables: real exports, real imports, and real government consumption (as government consumption is an exogenous shock in the DSGE model, conditional forecasts in the DSGE models are subject to exogenous paths for exports and imports). The exogenous predictors can be included in the AR model and the ABM in a straightforward way; for details, see Appendix D. Conditional forecasts in the DSGE model are achieved by controlling certain shocks to match the predetermined paths of the exogenous predictors. In particular, we control the consumption preference shocks for Austria and the EA, which are the major drivers for Austrian exports and imports in the two-country setting of the DSGE model; see Appendix F.12 for details. Again, we use the period 1997:Q1-2010:Q1 to initially estimate our models. We then forecast real GDP growth, inflation, and nominal household consumption and investment from 2010:Q2 to 2016:Q4, with the models being re-estimated every quarter. Thus, together with the real exports, real imports, and real government consumption, we account for all main components of GDP. Table 4 shows that the forecast performance of the ABM and AR models improves pronouncedly for GDP growth and household consumption and investment when exogenous predictors are included. Similar to the forecast exercise above, the ARX(1) turns out overall to perform better than the ARX models of lag orders two and three. Again, the performance of the ABM (conditional forecasts) and ARX(1) model is relatively similar for GDP growth and inflation. However, compared to the unconditional case, the ABM as a theory-driven model does not better in forecasting household consumption and investment. The forecast performance of the DSGE model (conditional forecasts) clearly deteriorates for all variables for longer horizons. This is for methodological reasons, that is, the need to control exogenous shocks such that the exogenous paths of the predictors are matched in the DSGE model. This clearly has the most pronounced implications for the forecast of household consumption in the DSGE model, where forecast  Figure 1 shows aggregate GDP growth and inflation (measured by GDP deflator) rates-annually (top) and quarterly (bottom). One can see at first glance that the ABM tracks the data very well for GDP growth (left panels). For annualized (top left) and quarterly (bottom left) model results, almost all data points are within the 90 percent confidence interval (gray shaded area)-except for two outliers (2011:Q1,2012:Q2), where the Austrian growth rate either picked up quite sharply (2011:Q1) or decreased considerably, despite an upward trend before (2012:Q2). It is especially interesting to note how the ABM catches trends in the data somewhat better than the ARX(1) model. In particular, the ABM reacts directly to a fall in exports in 2013:Q1 (see Figure 3)-which reflects a slowdown in economic growth for some of Austria's European trading partners during the European debt crisis-that drags down GDP growth in the ABM. In contrast to this, the ARX(1) model simply extrapolates the past trend into the future. Similar to the ABM, the DSGE in a conditional forecasting setup seems to catch upward and downward trends in the data quite well, but tends to "overreact" by taking the trend too far. This certainly deteriorates the forecast performance of the DSGE, and is most probably connected to the way in which controlling the shocks for the conditional forecasting procedure influences the mechanics of the DSGE model. A similar picture arises when the conditional forecasts for the main macroeconomic aggregates in levels (GDP, household consumption, investment) of the ABM are compared to the other models; see Figures 2 (annual) and 3 (quarterly). Looking at GDP at annual levels (top left in Figure 2) and quarterly levels (top left in Figure 3), it is evident that the ABM closely follows the data, as do the growth rates in Figure 1, and that all data points, except for the two outliers referred to above, are within the confidence interval. The ARX(1) model delivers a comparable forecasting performance, but smooths the trends more than the ABM does. The DSGE model at first consistently underestimates both annual and quarterly GDP levels, and then overestimates the upward trend starting in 2013:Q2. Again, the influence on quarterly GDP of the drop in exports in 2013:Q1, due to overall economic developments in Europe during the European debt crisis ( Figure 3, bottom middle panel), remains visible, and the ABM captures this trend quite well. Both the ABM and the ARX(1) model seem to smooth out the changes in household consumption to approximately match the average trend, with the ABM being somewhat closer to the data. Again, the DSGE model seems to follow the trends in the data quite accurately, but consistently overestimates the level, which might be responsible for the overall poor forecasting performance of the DSGE model for household consumption. As to be expected, the volatility of investment in the data is the highest of all these variables. The ARX(1) smoothes this volatility out on average, and is thus very successful in tracking both annual and quarterly investment data (Figures 2  and 3, top right). The DSGE model, while catching the initial trend in the data, overshoots in its forecast at the end, whereas the ABM consistently underestimates investment levels.

Components of GDP
The previous section has demonstrated that the size and detailed structure of the ABM tend to improve its forecasting performance compared to standard models. Another important advantage of our approach is the possibility of breaking down simulation results in a stock-flow consistent way according to national accounting (ESA). In particular, we are able to report results for all economic activities depicted in this model consistent with national accounting rules, in addition to relating them to the main macroeconomic aggregates. Most importantly, for all simulations and fore- casts, our model preserves the principle of double-entry bookkeeping. This implies that all financial flows within the model are made explicit and are recorded as an outflow of money (use of funds) for one agent in the model in relation to a certain economic activity, and as an inflow of money (source of funds) for another agent. In principle, we can thus consistently report on the economic activity of every single agent at the micro-level. A more informative aggregation is on a meso-level according to the NACE/CPA classification into 64 industries, which encompasses many variables. This multitude of results consists of all components of GDP on a sectoral level: among others, wages, operating surplus, investment, taxes and subsidies of different kinds, intermediate inputs, exports, imports, final consumption of different agents (household, government), employment, and also economic indicators such as productivity coefficients for capital, labor, and intermediate inputs.
Probably the simplest example indicative of this model structure is that it breaks down simulation results into the larger components of GDP. Figure 4 is a graphical representation of the conditional ABM forecasts from Section 3.3 decomposed for these larger components of GDP. The components are shown according to the production, income, and expenditure approaches to determining GDP, which are defined within the framework of our model along ESA lines, as laid out in equation (Appendix E.1). With the fine-grained detail incorporated into our model, we can demonstrate how the development of macroeconomic aggregates such as GDP relates to trends in different industry sectors (production approach), the distribution of national income (income approach), and the composition of final uses in the economy (expenditure approach). Here, the colored fields indicate ABM simulation results for the different components of GDP, while the dashed line refers to the values reported in the data. Our results show that ABM forecasts of these components of GDP, where the ABM does not predict major structural changes for the Austrian economy, correspond closely to the developments in the data.

Sectoral decomposition
The detailed structure of the ABM allows macroeconomic forecasts to be broken down into varying levels of detail, offering insights into the composition of overall macroeconomic trends. Figure 5 shows ABM forecasts for gross value added (GVA) generated within the industry sectors in comparison with the data for the conditional forecasting setup (see Table B.8 for a detailed list of industry sectors). 15 The projections of the ABM capture the trends in larger sectors particularly well. Most notably, trends in major sectors such as construction and construction works (F), retail trade (G47), accommodation and food services (I), or land transport services (H49) are matched by the ABM in close relation to the data. These sectors tend to follow overall trends in GDP to a large degree, which is one explanation for the good forecasting performance of the ABM for these sectors.
Some of the more pronounced differences are due to sector-specific features such as sizeable export-induced exogenous shocks or an unusually low number of firms in the sector, which can cause sectors to deviate from aggregate macroeconomic trends. This is especially true for smaller sectors, where deviations of ABM forecasts are higher in relative terms. This is especially relevant to products of agriculture, hunting and related services (A01), mining and quarrying (B), air transport services (H51), motion picture, video, and television program services (J59), and telecommunication services (J61), among others. For manufacturing sectors, which are potentially influenced more by trends exogenous to the ABM, such as the structure of Austrian exports, the forecasts are within an acceptable range, which is often also the case for larger sectors. Indicative examples for such sectors are wood and products of wood (C16), fabricated metal products (C25), and machinery and equipment (C28).

Conclusion
We have developed an ABM of a small open economy that fits micro and macro data from national accounts, sector accounts, input-output tables, government statistics, census data, and business demography data. Although the model is very detailed, it is able to compete with standard VAR, AR, and DSGE models in out-of-sample forecasting. An advantage of our detailed ABM is that it allows for a breakdown of the forecasts of aggregate variables in a stock-flow consistent manner to generate forecasts of disaggregated sectoral variables and the main components of GDP.
The ABM is tailor-made for the small open economy of Austria, but the model can easily be adapted to other economies of larger countries such as the UK and the US or to larger regions such as the EU. Such extensions and applications are currently being explored. Our detailed ABM can also be used for stress-testing exercises or for predicting the effect of changes in monetary, fiscal, and other macroeconomic policies.
Our model is the first ABM that can compete in out-of-sample forecasting of macro variables. A grand challenge for future work would be a "big data ABM" research program to develop ABMs for larger economies and regions based on available micro and macro data to eventually monitor the macro economy in real time on supercomputers. Such detailed "big data ABMs" have the potential for improved macro forecasting and more reliable policy scenario analysis.  Each firm i (i = 1, 2, . . . , I = s I s ) produces a principal product g (g = 1, 2, . . . , G) using labor, capital and intermediate inputs from other firms, and is part of an industry or sector s (s = 1, 2, . . . , S ), 16 with a number of I s firms in each industry. Demand for products of firm i is formed on markets for final consumption goods, capital goods as well as material or intermediate input goods.
Firms face fundamental uncertainty regarding the main determinants of their individual success on the market: future sales, market prices, the availability of inputs for the production process (labor, capital, intermediate inputs), wages, cash flow, and their access to external finance, among others, are unknown. This implies that in each period t, (t = 1, ..., T ), the firm has no knowledge about its equilibrium position (P i (t),Q d i (t)) 17 -given by the equilibrium priceP i (t) and equilibrium demandQ d i (t)-at which all its products would be sold and all consumer demand for its products would be satisfied. Therefore, the firm's future input costs, its capacity to produce given input constraints, as well as the corresponding implications for its cash flow and balance sheet are fundamentally uncertain. Firms only have access to partial information: their current status quo-sales, prices, labor, capital and material input costs, cash flow, etc.-and its past development, as well as selected macro time series such as growth, inflation, or index prices. Consequently, each firm has to form expectations about the future that may not correspond to actual realizations.
Every agent active on a market as a consumer-be it a household h or a government entity j intending to consume, or a firm demanding capital or intermediate input goods-searches for the best bargain, i.e., the lowest price, to satisfy its demand for each of products g it requires. The consumption and supply networks in the model are formed in every period of the model according to a search-and-matching process: in each period, consumers visit a number of randomly chosen firms i that sell the good g in order to ascertain the selling prices. The probability of a firm i being chosen is determined by weighted sampling without replacement. This probability is given (1) by the price charged by firm i according to an exponential distribution, where firms charging a lower price are more likely of being picked, and (2) by the relative size of the firm compared to other firms, so that bigger firms have a higher probability to be picked. The total probability of firm i of being selected in this process is then the average of the latter two probabilities: where pr price i (t) is the probability of firm i of being selected by a consumer due to its offering price, pr size i (t) the probability of being chosen due to its size, pr cum i (t) the cumulative average probability to be picked according to both of these factors, and Y i (t) is the production of goods by firm i, see equation (A.12). If the most preferred firm is in short supply, the consumer resorts to the remaining firms, otherwise it satisfies all its demand with the first firm. If an agent does not succeed in satisfying its demand for a specific product g, it saves involuntarily. Thus realized demand is the endogenous outcome of the model algorithm, which depends mainly on the random-visiting element, that is, whether the agent acting as a customer finds firms to fulfill its demands.
Demand Q d i (t) will be determined by consumers only after the firm has set its price and carried out production Y i (t). It is subject to the search-and-matching mechanism specifying the visiting consumers of firm i: if demand from visiting consumers is smaller than supply from firm i, and = S i (t − 1) + Y i (t) if demand from visiting consumers exactly matches supply from firm i, and is the inventory of finished goods. Sales are then the realized demand dependent on the supply available from firm i after the production process has taken place: The difference between production and sales is excess supply which is a reflection of firms' expectation error concerning demand. This difference is stored as inventories, until the next period, where they are supplied on the goods market together with newly produced goods. We do not assume any depreciation of this inventory of finished goods.

Appendix A.1.2. Price Setting and Supply
Given the importance of accurate forecasts, fundamental uncertainty and imperfect information, firms' have the option of choosing forecasting methods that may closely reflect their economic environment, but that fail to be a complete model of the economy inclusive of every detail. One such forecasting model that meets these requirements is an AR model: this is a simple procedure for projecting past trends into the future, while its forecasting capabilities are comparably high. We therefore assume that an individual firm i in our model uses an autoregressive model to form expectations of demand for its products (Q e i (t)) and to determine the selling price P i (t) it will charge. According to these expectations, the firm will set its desired production (Q s i (t)) as well as its selling price. The information set that the firm uses for these two decisions consists of the previous period's demand for its product, the expected rate of real economic growth, the expected rate of inflation, its expected future input costs based on past prices and expected inflation, and a unit target for attaining an operating surplus.
The supply choice of firm i is thus made based on the expected rate of real economic growth (γ e (t)) and the previous period's demand for its product Q d i (t − 1): Expectations regarding economic growth are formed using an autoregressive model with lag one (AR (1)): 18 where α Y (t), β Y (t), and Y (t) are re-estimated every period on the time series of aggregate output of firms i Y i (t ) where t = −T , −T + 1, −T + 2, . . . , 0, 1, 2, . . . , t − 1. To allow the data to decide on the degree of persistence and cointegration, output is entered in log levels and the growth rate is calculated from the percentage change to the previous period: Price setting by the firm evolves according to the expected rate of inflation (π e (t)), the cost-structure faced by the firm ("cost-push inflation"), and the unit target for attaining an operating surplus (where again firm i is part of sector s (i ∈ I s )): Unit net taxes/subsidies products Unit net taxes/subsidies production Target unit operating surplus ∀i ∈ I s whereᾱ i indicates the average productivity of labor, w i are gross wages indexed by the consumer price indexP HH (t), see equation (A.30), and including employers' contribution to social insurance charged at a rate τ SIF ; 1 β i g a sg are unit real expenditures on intermediate input by industry s on good g weighted by the average product price index for good g (P g (t)), see equation (A.28), δ i /κ i are unit real capital costs due to depreciation (δ i is the firm's capital depreciation rate and κ i is the productivity coefficient for capital);P CF (t) is the average price of capital goods as in equation (A.29), τ Y i and τ K i are net tax rates on products and production, respectively, andπ is the operating margin. Expectations on inflation are formed using an autoregressive model of lag order one (AR (1)): where α π (t), β π (t), and π (t) are re-estimated every period on the time series of inflation π(t ) where t = −T , −T + 1, −T + 2, . . . , 0, 1, 2, . . . , t − 1. The inflation rate is calculated from the log difference of the producer price index where the producer price index is defined as .
With our assumption for firm price setting, we simultaneously incorporate firms' current input cost structure as well as their expectations about future cost, inflation and profit developments.
In each period t firm i (which is part of industry s) produces output (Y i (t), in real terms) in form of the principal product g by means of inputs of labor (N i (t), the number of persons employed), intermediate goods/services and raw materials (M i (t), in real terms), as well as capital (K i (t − 1), in real terms). We assume a production function with Leontief technology and separate nests for intermediate goods, labour and capital, respectively-all of which represent upper limits to production: where α i (t) is the productivity of labor of firm i ∈ I s , see equation (A.22), and β i and κ i are productivity coefficients for intermediate inputs and capital, respectively. Production by firm i may not equal desired scale of activity (Q s i (t)). Output could be limited by the amount of available labor force, the quantity of intermediate goods, or the availability of capital needed in the production process. In these cases, the firm has to scale down activity.
In each period the i-th firm has to decide how much to invest (I d i (t), in real terms). Investment allows the firm to adjust the real capital stock K i (t). Capital adjustment, however, is not immediate and time consuming. New capital goods 19 bought at the time t will be part of the capital stock only in the next period t + 1. This makes capital a durable and sticky input.
The desired investment in capital stock in period t is where δ i is the firm's capital depreciation rate. The economic rationale behind this equation is that firms adjust their investment demand to expected wear and tear of capital, and that only capital planned to be used in the production process is expected to depreciate and needs to be replaced by new investment. The latter in turn depends on the future demand estimated by the firm according to past demand and the expected rate of economic growth. We assume a homogenous capital stock for all firms and thus fixed weights b CF g , namely, each firm i-irrespective of the sector s firm i is part of-demands b CF g I d i (t) as its real investment from firms producing good g: . It may be the case that firms cannot obtain the requested investments goods on the capital goods market, or at an unexpectedly high price. The amount of realized investment therefore depends on the search-and-matching process on the capital goods market, see Appendix A.1.1: In the case where firm i cannot realize its investment plan, it will have to scale down future activity, see equation (A.12). The capital stock, as an aggregate over all goods g, evolves according to a depreciation and investment law of motion, where only the amount of capital actually used in the production process depreciates: Appendix A.1.5. Intermediate Inputs Each firm needs intermediate input of goods for production. We assume that firm i holds a stock of input goods M i (t) (in real terms) for each type of good g. From this stock of intermediate input goods, firm i takes out materials for production as needed, and it keeps these goods in positive supply to avoid shortfalls of material input impeding production. Each period the i-th firm has to decide on the desired amount of intermediate goods and raw materials (∆M d ig (t)) that it intends to purchase in order to keep its stock in positive supply. Here also, similar to equation (A.12), firm i is part of industry s and consumes an intermediate input g according to sector-specific technology coefficients (a sg ). We assume a steady use by the firm of its raw materials in production, and hence that the material stock does not depreciate. This is given by Firms thus try to keep their stock of material input goods within a certain relationship to Q s i (t) by accounting for planned material input use in this period. In the intermediate goods market, too, the amount of realized purchases of intermediate goods depends on a search-and-matching process, see Appendix A.1.1: if the firm successfully realized its plan, and < g ∆M d ig (t) if all firms visited could not satisfy its demand.
If firm i does not succeed in acquiring the materials it intended to purchase, it will be limited in its production possibilities. The stock of good g held by firm i evolves according to the material use in the production process necessary to achieve actual production (Y i (t)) and realized new acquisitions of intermediate goods: Appendix A.1.6. Employment Each firm i uses employment N i (t) as labor input for production, which is the number of persons employed. The firm decides on the planned amount of employment N d i (t) in each period according to its desired scale of activity (Q s i (t)) and its average labor productivity (ᾱ i ): Rounding to the nearest integer translates as follows: if the additional labor demand of firm i is less than a half-time position, labor demand is left unchanged. If the additional production needs of firm i exceed a half-time occupation, a new employee is hired. If the operating workforce at the beginning of period t (N i (t − 1)), i.e., the number of persons employed in t − 1, is higher than the desired work force, the firm fires N i (t − 1) − N d i (t) randomly chosen employees (accounting for production constraints due possibly to a shortage of capital). If demand for labor to reach the desired scale of activity is greater than the operating workforce, the firm posts labor vacancies, , 0 , which represent a demand for new labor. Whether vacancies are filled or not depends on the search-and-matching mechanism in the labor market (see Appendix A.2.1), thus if the firm successfully fills all vacancies, and < N d i (t) if there are unfilled vacancies. As employees are either employed full-time, part-time, or work overtime, the actual productivity of labor α i (t) of firm i reflects overtime or part-time employment: where the maximum work effort is 150 percent of a full position. To remunerate increased or decreased work effort as compared to a full-time position, the average wagew i of firm i is adapted accordingly: where w i (t) is the real wage paid by firm i. Nominal wage increases accounting for inflation are considered when money wages are paid out to households as part of their disposable income, see Appendix A.2.4.
Appendix A.1.7. External Finance Firms may need external financial resources to finance current or future expenditures. Thus, each firm i forms an expectation on its future cash flow ∆D e i (t), that is, the expected change of deposits D i (t): , is the profit expected by firm i based on the profit in the previous period; θ is the rate of debt installment on firm i's outstanding loans L i (t − 1), τ FIRM is the corporate tax rate, and θ DIV is the dividend payout ratio.
If the internal financial resources of a firm are not adequate to finance its expenditures, the firm will ask for a bank loan, i.e., new credit ∆L d i (t), to cover its financing gap ) . The availability of credit depends on the capitalization of the banking sector and the arrival of firms to ask for a loan, see Appendix A.4.1 for details. If the firm cannot obtain a loan on the credit market, it might become credit constrained, see equation (A.64). If the firm does not obtain the desired loan, it may become insolvent, see Appendix A.1.9. Appendix A.1.8. Accounting Firm profits Π i (t) are an accounting measure that are defined as revenues from sales plus change in inventories minus expenditures on labor, material, depreciation, interest payments and taxes (all accounted for mark-to-market): Interest payments where r(t) is the interest rate paid on outstanding loans, see equation (A.66).P g (t) is the price index for the principal good g: , P CF (t) is the economy-wide capital formation price index defined as where b CF g is the capital formation coefficient for product g, andP HH (t) is the consumer price index: where b HH g is the household consumption coefficient for product g. Firm net cash flow reflects the amount of liquidity moving in or out of its deposit account: Net taxes/subsidies on products and production where P ig (t) and P CF i (t) are the actual prices paid by firm i for intermediate goods of type g and investment in capital goods, respectively, which both are an outcome of the search an matching process. Furthermore, firm i pays interest on outstanding loans and overdrafts on firm i's deposit account (in case D i (t) < 0) at the same rate r, which includes the bank's markup rate. In the opposite case when the firm holds (positive) deposits with the bank, i.e., D i (t) > 0, the interest rate received is lower and corresponds to the policy rate set by the central bank, see Appendix A.4.
Firm deposits are then previous deposits plus net cash flow: Similarly, overall debt is updated as follows: Finally, firm equity E i (t) evolves as the balancing item on the firm's balance sheet, where all stocks are again accounted for mark-to-market: If a firm is cash-flow insolvent, i.e., D i (t) < 0, and balance-sheet insolvent, i.e., E i (t) < 0, at the same time, it goes bankrupt and is replaced by a firm that newly enters the market. We assume that the real capital stock of the bankrupt firm is left to the entrant firm at zero costs, but that the new firm has to take over a part of the bankrupt firm's liabilities. Therefore, a part of loans taken out by the bankrupt firm is written off so that the remaining liabilities of firm i amount to a fraction ζ b of its real capital stock. After this partial debt cancellation, the remaining liabilities of the bankrupt firm are transferred to the balance sheet of the entrant firm. In the next period (t + 1) liabilities of firm i are initialized with (A.35) and firm deposits with Correspondingly, in the next period (t + 1) equity of the new firm i is initialized according to equation (A.34).

Appendix A.2. Households
The household sector consists of a total number of H (h = 1, 2, . . . , H) persons. Every person in the household sector has an activity status, that is, a type of economic activity from which she receives an income. Each person also participates in the consumption market as a consumer with a certain consumption budget. The activity status is categorized into H act economically active and H inact economically inactive persons. Economically active persons are H W workers, and I investors (the number of investors equals the number of firms and is constant, see below). The set of workers consists of H E (t) employed persons and H U (t) unemployed persons that are actively looking for a job. H E (t) and H U (t) are endogenous since we assume that agents may switch between these two sets by being dismissed from their current job or by being hired for a new position. Economically inactive persons include, among others, persons below the age of 15, students, and retirees.

Appendix A.2.1. Activity Status
The h-th worker (h = 1, 2, . . . , H W ) supplies labor to the extent of employment (part-time, full, or including overtime). If worker h works for firm i in period t, she receives wage w h (t) = w i (t).
If unemployed, the person looks for a job on the labor market by visiting firms with open vacancies in random order and applies for a job (the search-and-matching process on the labor market). The unemployed person will accept a job from the first firm with open vacancies that she has the chance to visit. If she does not find a vacancy to fill, that is, when there are no open vacancies left in the economy, she remains unemployed. For simplicity's sake, we do not consider hiring or firing costs for firms, and fired employees become unemployed and start searching for a job in the same period. All unemployed persons receive unemployment benefits, which are a fraction of the labor income that was last received in the period when unemployment starts. In the event that an unemployed person finds a new job, she is remunerated with the wage of firm i that provides the new employment: otherwise, i.e., unemployment continues.
For simplicity's sake, we assume that each firm is owned by one investor, i.e., the number of investors matches that the number of firms overall. Each investor receives income in the form of dividends in the event that the firm she owns makes profits after interest and tax payments. We assume limited liability, i.e., in the case of bankruptcy, the associated losses are borne by the creditor and not the investor household, see Appendix A.1.9.
An economically inactive person h receives social benefits sb inact (t) and does not look for a job: Additionally, each household receives additional social transfers sb other (t) (related to family and children, sickness, etc.) from the government, which we assume to be constant and the same size for all households:

Appendix A.2.2. Consumption
In a bounded rationality setting, consumers' behavior follows a rule of thumb (heuristic) where they plan to consume a fraction of their expected disposable net income including social benefits (Y e h (t)). The consumption budget (net of VAT) of household h (C d h (t)) is thus given by: where ψ ∈ (0, 1) is the propensity to consume out of expected income and τ VAT is a value added tax rate on consumption.
Expected disposable net income inclusive of social transfers is determined according to the household's activity status and the associated income from labor, expected profits or social benefits, as well as tax payments, the consumer index price index of the last period, and expectations of the rate of inflation π e (t) formed using an AR(1) model (see equation (A.9)): if not economically active is the expected profit based on the profit of the previous period of firm i and of the banking sector, respectively; τ INC is the income tax rate, τ SIW is the rate of social insurance contributions to be paid by the employee, θ DIV is the dividend payout ratio, and τ FIRM the corporate tax rate. Consumers then allocate their consumption budget to purchase different goods from firms. The consumption budget of the h-th household to purchase the g-th good is where b HH g is the consumption coefficient for the g th product of households. 20 Once they have determined their consumption budget, consumers visit firms in order to purchase goods according to the search-and-matching mechanism, see Appendix A.1.1 above. Whether the individual firm can accommodate demand depends (apart from aggregate economic conditions) on its production and inventory stock. Thus realized consumption of household h is another outcome of the search-and-matching process: if the consumer successfully realized the consumption plan, and < g C d hg (t) if all firms visited could not satisfy the consumer's demand.

Appendix A.2.3. Household Investment
To depict a simple housing market, households use part of their income to invest in dwellings and other durable investment goods. Similar to equation (A.40) above, we assume household investment occurs according to a fixed rate ψ H on expected disposable net income: where τ CF is the tax rate on investment goods. Investment demand by household h for product g net of taxes (I d hg (t)) is then determined by fixed weights b CFH g : Again, realized sales of investment goods purchased by households are an outcome of the search-and-matching process on the capital goods market: if the household successfully realized the investment plan, and < g I d hg (t) if all firms visited could not satisfy its demand. (A.47) The capital stock of household h then follows: In each period t, all households receive income according to their activity status. Nominal disposable net income Y h (t) (i.e., realized income after taxes but including unemployment benefits and other social transfers) of the h-th household is different from expected income by the realized inflation in period t, which is represented by the current consumer price index, as well as the realized profits by firms and the bank: Savings is the difference between current disposable income Y h (t) and realized consumption expenditure C h (t) plus realized investment in housing I h (t), and is used to accumulate financial wealth: 21 Additionally, the stock of deposits is corrected for interest payments on overdrafts of the household's deposit account (D h (t − 1) < 0), and interest received on deposits held with the bank (D h (t − 1) > 0). 22

Appendix A.3. The general government
In our model, the government takes two functions: as a consumer on the retail market (government consumption), and as a redistributive entity that levies taxes and social contributions to provide social services and benefits to its citizens. We assume that government consumption is exogenous and attributed to individual government entities. Government expenditures, revenues, deficit and public debt, however, are accounted for at the aggregate level (i.e., for the general government).

Appendix A.3.1. Government Consumption
Individual government entities j ( j = 1, 2, . . . , J) participate in the goods market as consumers. These entities represent the central government, state government, local governments and social security funds. Analogous to imports and exports, the real final consumption expenditure of the general government (C G (t)) is assumed to follow an autoregressive process of lag order one (AR (1)): Total nominal government consumption demand is attributed to goods g and is uniformly distributed to the J government entities; the consumption budget of the j-th government entity to purchase the g-th good is thus given as where c G g is the fraction of goods of type g demanded by the government. Realized government consumption is then another outcome of the search-and-matching process on the consumption goods market: if the government successfully realized the consumption plan, and < g C d jg (t) if all firms visited could not satisfy its demand.
Other expenditures of the general government include interest payments, social benefits other than social transfers in kind, and subsidies. Interest payments by the general government are made with a fixed average interest rate r G on loans taken out by the government L G (t − 1). Social transfers by the government consist of social benefits for inactive households ( h∈H inact sb inact (t)) such as pension payments or social exclusion benefits, social benefits for any household h ( h sb other (t)) such as relating to family, sickness or housing, and unemployment benefits for unemployed households ( h∈H U (t) w h (t)). Subsidies are paid to firms with subsidy rates (uniform for each industry, but different across industries) on products and production, and are in incorporated in the net tax rates on products (τ Y i ) and production (τ K i ), respectively. 23

. Government Revenues
Revenues of the general government are generated through taxes, social contributions and other transfers from all sectors.
Net taxes/subsidies on products Net taxes/subsidies on production (A.54) 23 The latter can therefore also have negative values if a sector receives more subsidies on products or production than it has to pay in taxes.

Appendix A.3.3. Government Deficit
The government deficit (or surplus) resulting from its redistributive activities is

. Government Debt
The government debt as a stock variable is determined by the year-to-year deficits/surpluses of the government sector: For reasons of model parsimony, we assume that the government sells its debt contracts to the central bank, which we model as a "clearing house" for capital flows between the national economy and the Rest of the World. Thus, we implicitly assume that the purchase of government bonds is financed by inflows of foreign capital recorded on the liability side of the central bank's balance sheet.

Appendix A.4. The bank
For the sake of simplicity we assume that there is one representative bank. 24 The bank takes deposits from firms and households, extends loans to firms, and receives advances from (or deposits reserves at) the central bank.

Appendix A.4.1. Provision of Loans
We assume that government regulation imposes a minimum capital requirement on the bank. Thus, the bank can extend loans up to a multiple of its equity base or net worth: where E k (t) is the equity capital (common equity) of the bank, and 0 < ζ < 1 can be interpreted as a minimum capital requirement coefficient. Hence, 1/ζ is the maximum allowable leverage for the bank. However, the bank-like any other agent-has no knowledge of the realized value of either its equity capital or loans extended to the individual firm i, due to fundamental uncertainty prevailing in the model economy. Therefore, the bank has to form expectations both for its equity capital (E e k (t)) and for the sum of all loans extended to firms in the economy ( I i=1 L e i (t)): This assumption of one representative bank is above all due to national accounting conventions. From national annual sector accounts, which determine the logic of financial flows between the aggregate sectors for our model (households, non-financial corporations, financial corporations, government and rest of the world), we obtain balance sheet positions (credit and debts), as well as interest payment flows between firms and the financial sector (banks) on an aggregate level. Since we do not have information on financial relations between individual firms (or industry sectors) and banks for this model, we have no empirically based method to determine credit and debt relations, acquisition and provision of credit, as well as interest payments, between individual firms (or industry sectors) and individual banks. Therefore, we account for credit relations and financial flows between individual firms and banks on an aggregate level for the banking sector, i.e., we assume a representative bank extending credit to individual firms according to the amount of firms' real capital stock, see Appendix C for details, while we account for the value added generated by financial corporations in the real economy according to the logic of IOTs as separate industries within the firm sector.
have not been surpassed. However, it is equal to zero if the bank does not have enough equity capital to provide the loan asked for by firm i: Furthermore, the bank forms a risk assessment of a potential default on the part of firm i before extending a loan to it. This risk assessment is based on the borrower's leverage as measured by its loan-to-value ratio, i.e., the amount of loans over the market value of its capital stock. Thus, the bank will grant a loan to firm i only up to the point where the borrower's leverage (or loan-to-value) ratio after the loan (including overdrafts on deposit accounts), is below ζ LTV , which is a constant. However, due to fundamental uncertainty, also in this case the bank has to form expectations on both the loans to be provided to firm i (L e i (t)), as well as on the value of firm i's capital stock (K e i (t)): Altogether, therefore, the amount of new credit extended to firm i by the bank (∆L i (t)) is limited by the credit demanded by the firm, the bank's risk assessment regarding the default of its potential borrower, and the minimum capital requirements imposed by the regulator: The order of arrival of firms at the bank is assumed to be random. A financially robust (low leverage) firm, which in principle deserves a large chunk of bank loans, may be denied credit if it arrives "too late" (i.e., after other less robust firms).

Appendix A.4.2. Accounting for Profits and Losses
The bank's profits are computed as the difference between revenues from interest payments payable on outstanding loans to firms, including overdrafts on deposit accounts incurred by firms and households (D i,h (t − 1) < 0), and costs due to interest payments on deposits held with the bank by firms and households (D i,h (t − 1) > 0):

29
Electronic copy available at: https://ssrn.com/abstract=3484768 Deposits are remunerated at the policy rater(t), which we assume to be set exogenously by the central bank. The interest rate r for bank credit to firms is then determined by a fixed markup µ over the policy rater(t): Bank equity grows or shrinks according to bank profits or losses, and is given by where I is the set of insolvent borrowers, and we assume that outstanding overdraft of firm i's deposit account as well as a fraction (1 − ζ b )P CF i (t)K i (t) of loans extended to firm i have to be written off from the bank's balance sheet. The residual and balancing item on the bank's balance sheet (D k (t)), 25 after accounting for loans extended, deposits taken in and its equity capital, are (net) central bank reserves held (D k (t) > 0) or advances obtained by the bank from the central bank (D k (t) < 0). 26 Appendix A.5. The Central Bank The central bank (CB) sets the policy rater(t) based on implicit inflation and growth targets, provides liquidity to the banking system (advances to the bank), and takes deposits from the bank in the form of reserves deposited at the central bank. Furthermore, the central bank purchases external assets (government bonds) and thus acts as a creditor to the government.

Appendix A.5.1. Determination of Interest Rates
The policy rate is determined by a generalized Taylor rule (Taylor, 1993). Following Blattner and Margaritov (2010), we use a "growth" rule specification where the output gap does not enter the equation: 27 (A.69) r(t) = max 0, ρr(t − 1) + (1 − ρ) r * + π * + ξ π π EA (t) − π * + ξ γ γ EA (t) , where ρ is a measure for gradual adjustment of the policy rate, r * is the real equilibrium interest rate, π * is the inflation target by CB, ξ π is the weight the CB puts on inflation targeting, and ξ γ the weight placed on economic growth, respectively. Inflation (π EA (t)) and economic growth (γ EA (t)) of the monetary union are assumed to follow an autoregressive process of lag order one (AR (1)): Note that we assuming here a SoE as part of a monetary union with no influence on interest rates. 28 25 Which also includes currency held by the bank. 26 Note that this variable, if it takes a positive value (D k (t) > 0), signifies that the bank holds positive net reserves, i.e., it holds more reserves than advances and is thus a net creditor to the central bank. On the other hand, in the opposite case of D k (t) < 0, this means that the bank has taken out more central bank advances than it holds central bank reserves, i.e., it is a net debtor to the central bank. The possibility of an inequality of advances and reserves, or, for that matter, an inequality of loans and deposits, is due to the fact that we do not explicitly distinguish between deposits and reserves for reasons of model parsimony. Rather, we use the central bank as a "clearing house" for flows of reserves and deposits between the national economic and the RoW, see equation (A.76). 27 Here, we rely on empirical evidence and statements by leading central bankers reported in Blattner and Margaritov (2010) implying that the concept of an output gap does not seem to influence the behavior of the European Central Bank (ECB) to a large extent. 28 For example, Austria as part of the EA contributes only about 3 percent of total GDP of the monetary union.

Appendix A.5.2. Accounting for Profits and Losses
The central bank's profits Π CB (t) are computed as the difference between revenues from interest payments on government debt, as well as revenues (D k (t) < 0) or costs (D k (t) > 0) due to the net position in advances/reserves vis-à-vis the banking system: The central bank's equity E CB (t) evolves according to its profits or losses and its past equity, and is given by The net creditor/debtor position of the national economy to the rest of the world (D RoW (t)) 29 evolves according to the following law of motion Here, for example, a balance of trade surplus (deficit) enters with a negative (positive) sign, since D RoW (t) is on the liability side of the CB's balance sheet. Thus a trade surplus (deficit), i.e., an inflow (outflow) money into (out of) the national economy, would reduce (increase) national liabilities versus the RoW.
Inherent stock-flow consistency relating to the accounting principles incorporated in our model implies that our financial system is closed via the accounting identity that connects the change in the amount of deposits in the banking system 30 to the government deficit (surplus) 31 and to the balance of trade: 32 Appendix A.6. Imports and Exports To depict trade with the RoW, we include a set of agents that are based abroad and trade with the domestic economy. For simplicity's sake, a representative foreign firm for each sector supplies goods on domestic markets for intermediate, capital and consumption goods (imports), while foreign consumers demand products on these domestic markets (exports). As we assume a small open economy (SoE) setting, we suppose exports and imports to be exogenously given.
Appendix A.6.1. Imports Following this approach, the total amount of imports Y I (t) (in real terms) is assumed to follow an autoregressive process of lag order one (AR(1)): 33 (A.77) log(Y I (t)) = α I log(Y I (t − 1)) + β I and a representative foreign firm for each sector imports goods from the RoW and supplies them to domestic markets. Thus the m-th, (m = 1, 2, . . . , S ), foreign firm representing an industry s imports the principal product g: 34 29 If D RoW (t) < 0, the national economy is a net creditor of the RoW, if D RoW (t) > 0, the national economy is a net debtor to the RoW. 30 These changes in the amount of deposits in the banking system directly correspond to changes in net central bank reserves D k (t), which in turn depend the private sector's surplus or deficit in relation to both the government and the RoW. 31 Financial flows relating to a deficit (surplus) on the part of the government sector either accrue to (are paid by) the private sector (households and firms), or have to flow to (in from) the RoW, in the first case increasing (decreasing) deposits, in the second case increasing (decreasing) D ROW . 32 A positive (negative) balance of trade will either increase (decrease) deposits held by the private sector, or reduce (increase) the amount of government debt by e.g. reducing (increasing) the amount of government deficit. 33 As a simplifying assumption, this implies that imports to the domestic economy are not demand-driven, but rather subject to a supply constraint. 34 As for domestic firms, we assume that there is a one-to-one correspondence between the sets of industries s and products g, meaning that the n-th sector produces only the n-th good, and S = G.
where c I g is the fraction of imported goods of type g as part of total imports. The prices for these import goods are assumed to develop in line with the average sectoral domestic price level. The foreign firm thus sells its products at the inflation-adjusted average sectoral domestic price level. Consequently, where m produces the principal product g. This corresponds to the assumption of a fixed relation between the domestic and international price level, i.e., the same inflation rate at home and abroad.
Sales of imports are then the realized demand as an outcome of the search-and-matching process on the goods markets (see Appendix A.1.1): where Q d m (t) is the demand by consumers from foreign firm m.

Exports
The l-th (l = 1, 2, . . . , L) foreign consumer, be it a foreign firm, household, or government entity, participates in the domestic goods market as a consumer. Total sales to these foreign consumers on domestic markets represent exports to the rest of the world. Analogous to imports, real exports (C E (t)) are assumed to follow an autoregressive process of lag order one (AR (1)): Total exports are then attributed to goods g and are uniformly distributed to the L foreign consumers; the demand for exported goods by the l-th foreign consumer to purchase the g-th good is thus given by where c E g is the fraction of exports of goods of type g. Realized consumption by foreign consumers is then an outcome of the search-and-matching process on goods markets (see Appendix A.1.1): if the foreign consumer successfully realized the consumption plan, and < g C d lg (t) if all firms visited could not satisfy its demand.

Appendix B. Parameters for the Austrian economy
Parameters for the model presented in Appendix A are set for the Austrian economy, so that each agent in the model represents a natural person or legal entity, such as a corporation, a government entity or any other institution, in Austria. Austria is a typical example of an advanced small open economy with about 8.8 million inhabitants and more than half a million registered businesses 35 : it is closely integrated into the European economy by extensive trade (the export quota, i.e. the share of exports in GDP, is slightly more than 52 percent, the import quota about 48 percent). Austria's well-developed service sector constitutes about 71 percent of total GDP, while the industry sector takes a smaller share with about 28 percent in GDP and the agricultural sector contributes much less (about 1.5 percent of GDP). Austria has a well-developed social and welfare system, primarily based on social security contributions, as well as taxation of income and consumption. Correspondingly, the ratio of public spending to GDP is about 52 percent, while the overall tax burden, that is, the ratio of total taxes and social security contributions to GDP, reaches 43 percent.
The parameters of the model are summarized in Table B.5. For the forecasting exercise in Section 3, parameters were initially calculated and estimated over the sample 1997:Q1 to 2010:Q1 and then, respectively, re-estimated and recalculated, every quarter until 2013:Q4. Here we show and discuss, as an example, parameter values for 2010:Q4. Data sources include macroeconomic and sectoral data from national accounts, sector accounts, input-output tables, government statistics, census data, and business demography data and are obtained from the Eurostat bulk download facility where it is freely available. 36 The codes under which the respective datasets are available from Eurostat (such as, e.g., naio 10 cp1700) at this download facility are given in brackets in the description below. Eurostat data tables are collected in Table B.6. Model parameters are either taken directly from data or calculated from national accounting identities. For exogenous processes such as government consumption, imports and exports of Austria, as well as real GDP and inflation of the EA, parameters are estimated from quarterly time series from national accounts (main aggregates).

Appendix B.1. Firms
Parameters that specify the number of firms are taken directly (or derived from) business demography data. Specifically we use data from business demography by legal form (from 2004 onwards, NACE Rev. 2) (bd 9ac l form r2) to set the number of firms in industries (I s ) according to the population of active enterprises in t (V.11910). Business demography tables do not include the agriculture, forestry and fishing sector (A01-A03), or the public administration, defense, and compulsory social security sector (O64). The number of firms in industries A01-A03 is set according to the "Grüner Bericht", 37 and the number of firms in industry O64 (i.e. generic administrative government units) is set at 10, 000. The amount L of foreign firms that import and export goods is not available from business demography data. As a first simplifying assumption, this number is assumed to be 50 percent of domestically producing firms, which approximately corresponds to the share of exports in total value added. For the classification of industries (s) we use the statistical classification of economic activities in the European Community (NACE). Products (g) are classified according to the classification of products by activity (CPA), which is fully aligned with NACE. Several consolidated tables including input-output tables, demographic data and cross-classification tables are compiled for the EA and European Union with a breakdown of 64 activities/products (NACE*64, CPA*64). We, therefore, set the number of industries (S ) and the number of products (G) at 64 (S = 64, G = 64).
Several model parameters concerning the firm agents are directly taken from input-output tables (IOTs), or are derived from them. The input-output framework of the ESA consists of supply and use tables in current prices and the prices of the previous year. Supply and use tables are matrices describing the values of transactions in products for the national economy categorized by product type and industry; see (Eurostat, 2013). We use the symmetric input-output Technology coefficient of the g th product in the s th industry see Appendix B.1 b CF g Capital formation coefficient of the g th product (firm investment) see Table B.7 b CFH g Household investment coefficient of the g th product see Table B.7 b HH g Consumption coefficient of the g th product of households see Table B.7 c G g Consumption of the g th product of the government in mln. Euro see Table B.7 c E g Exports of the g th product in mln. Euro see Table B.7 c I g Imports of the g th product in mln. Euro see Table B  GDP and main components -output, expenditure and income (quarterly time series) namq 10 gdp Symmetric input-output table (IOT) at basic prices (product by product) naio 10 cp1700 Cross-classification of fixed assets by industry and by asset (stocks) nama 10 nfa st Balance sheets for financial assets nasa 10 f bs Non-financial transactions nasa 10 nf tr Business demography by legal form (from 2004 onwards, NACE Rev. 2) bd 9ac l form r2 Government revenue, expenditure and main aggregates gov 10a main Government deficit/surplus, debt and associated data gov 10dd edpt1 Government expenditure by function -COFOG gov 10a exp Population by current activity status, NACE Rev. 2 activity and NUTS 2 region cens 11an r2 Money market interest rates -annual data irt st a Money market interest rates -quarterly data irt st q table at basic prices (product by product) (naio 10 cp1700) to set the technology, consumption and capital formation coefficients (a sg , b HH g , b CF g , c G g , c E g and c I g ). Specifically, we use intermediate consumption (P.2) 38 of 64 (CPA*64) products for the technology coefficient of the g th product in the s th industry a sg . To obtain the technology coefficient, the entries are normalized column-wise. Real estate services (CPA L68) also include imputed rents. Entries of "services of households as employers, undifferentiated goods and services produced by households for own use" (CPA T) and "Services provided by extraterritorial organizations and bodies" (CPA U) contain zeros only and are excluded. The capital formation coefficient of the g th product b CF g is set according to the gross fixed capital formation (P.51G) as given in the symmetric input-output table. The consumption coefficient of the g th product of households b HH g is set according to final consumption expenditure by households (P.3) plus final consumption expenditure by non-profit organizations serving households (NPISH). Again, entries are normalized to obtain capital formation and consumption coefficients. The consumption of the g th product of the government c G g , imports of the g th product c I g and exports of the g th product (c E g ) are taken directly from the symmetric input-output table by using the final consumption expenditure by government (P.3), as well as total exports (P.6) and imports (P.7).
For some parameters we need to combine the logic of annual sectoral accounts and IOTs. The information by institutional sector in the sector accounts and the information by industry or product in the supply and use tables can be linked by cross-classification tables. We use the cross-classification tables and structural business statistics (business demography) to complement symmetric IOTs. Specifically we are using statistics on population by current activity status, NACE Rev. 2 activity and NUTS 2 region (cens 11an r2) to set the average productivity of labor for firm i (ᾱ i ), which is assumed to be equal across firms in each industry s, but different between industries (ᾱ i = α s ∀i ∈ I s ). It is defined by output (P.1) in the industry divided by the number of persons employed in the population of active enterprises in t (V.16910) in the industry. 39 The average wage that employees receive from firm i (w i = w s N s ∀i ∈ I s ) (which is industry-specific) is defined by wages and salaries (D.11) in the industry divided by the number of persons employed in the population of active enterprises in t (V.16910) in the industry. The average productivity of capital 38 The accounting code of the European System of Accounts (ESA) data source is given in brackets. In this coding system, the capital letter D represents a figure from the distributive transactions account, while a P indicates data from the transactions in products and non-produced asset account. The letter B generally stands for a balancing item, i.e. the subtraction of one side of an account from the other. Balancing items carry much of the most vital information in these data. For example, operating surplus/mixed income (B.2A3N) is obtained by subtracting the cost factors compensation of employees and taxes on products from value added. The capital letter F indicates a financial asset/liability for financial balance sheets, e.g. F.2 indicates currency and deposits. The numbers after the letters indicate the type of transaction/balancing item/asset class, in a similar coding system as IO classification with increasing amount of detail in the classification as the amount of digits increases. This means that e.g. D.41 (interest payments) is a sub-category of D4 (property income). 39 In the context of the Labour Force Survey (LFS), an employed person is a person aged 15 and over (or 16 and over in Iceland and Norway) who during the reference week performed work-even if just for one hour a week-for pay, profit or family gain. For further information, see http://ec.europa.eu/eurostat/statistics-explained/index.php/Glossary:Employed_person_-_LFS (Last accessed November 30 th , 2018).  in the i th firm (κ i ) is set using cross-classification of fixed assets by industry and by asset (stocks) (nama 10 nfa st) Crop and animal production, hunting and related service activities A02 Forestry and logging A03 Fishing and aquaculture B Mining and quarrying C10-12 Manufacture of food products, beverages and tobacco products C13-15 Manufacture of textiles, wearing apparel and leather products C16 Manufacture of wood and of products of wood and cork, except furniture; manufacture of articles of straw and plaiting materials C17 Manufacture of paper and paper products C18 Printing and reproduction of recorded media C19 Manufacture of coke and refined petroleum products C20 Manufacture of chemicals and chemical products C21 Manufacture of basic pharmaceutical products and pharmaceutical preparations C22 Manufacture of rubber and plastic products C23 Manufacture of other non-metallic mineral products C24 Manufacture of basic metals C25 Manufacture of fabricated metal products, except machinery and equipment C26 Manufacture of computer, electronic and optical products C27 Manufacture of electrical equipment C28 Manufacture of machinery and equipment n.e.c. C29 Manufacture of motor vehicles, trailers and semi-trailers C30 Manufacture of other transport equipment C31 32 Manufacture of furniture; other manufacturing C33 Repair and installation of machinery and equipment D35 Electricity, gas, steam and air conditioning supply E36 Water collection, treatment and supply E37-39 Sewerage; waste collection, treatment and disposal activities; materials recovery; remediation activities and other waste management services F Construction G45 Wholesale and retail trade and repair of motor vehicles and motorcycles G46 Wholesale trade, except of motor vehicles and motorcycles G47 Retail trade, except of motor vehicles and motorcycles H49 Land transport and transport via pipelines H50 Water transport H51 Air transport H52 Warehousing and support activities for transportation H53 Postal and courier activities I Accommodation and food service activities J58 Publishing activities J59 60 Motion picture, video and television programme production, sound recording and music publishing activities; programming and broadcasting activities J61 Telecommuni-cations J62 63 Computer programming, consultancy and related activities; information service activities K64 Financial service activities, except insurance and pension funding K65 Insurance, reinsurance and pension funding, except compulsory social security K66 Activities auxiliary to financial services and insurance activities L68B Real estate activities excluding imputed rents M69 70 Legal and accounting activities; activities of head offices; management consultancy activities M71 Architectural and engineering activities; technical testing and analysis M72 Scientific research and development M73 Advertising and market research M74 75 Other professional, scientific and technical activities; veterinary activities N77 Rental and leasing activities N78 Employment activities N79 Travel agency, tour operator reservation service and related activities N80-82 Security and investigation activities; services to buildings and landscape activities; office administrative, office support and other business support activities O84 Public administration and defence; compulsory social security P85 Education Q86 Human health activities Q87 88 Social work activities R90-92 Creative, arts and entertainment activities; libraries, archives, museums and other cultural activities; gambling and betting activities R93 Sports activities and amusement and recreation activities S94 Activities of membership organisations S95 Repair of computers and personal and household goods S96 Other personal service activities and is again assumed to be equal across firms by industries (κ i = κ s ∀i ∈ I s ), and different across industries s. It is defined by output (P.1) in the industry divided by total fixed assets (net) (N11N) 40 in the industry multiplied by the desired capacity utilization rate (ω, see the Appendix C.1). An exception is the sector L68 (real estate services), where the stock of household dwellings (K h (0)) is included that has no productive use in the economy regarding the output of goods and services on markets, and thus has to be treated differently. We remove the stock of dwellings from sector L68 and attribute it to the household sector, see Appendix C.2. The productivity of intermediate consumption goods of firm i (β i ) is again the same for each firm in industry s, but differs across industries (β i = β s ∀i ∈ I s ). It is defined by output (P.1) in the industry divided by total intermediate consumption (P.2) of the industry from symmetric input-output tables. The average depreciation of capital in the i th firm (δ i ) is again heterogenous across industries and homogenous across firms by industry (δ i = δ s ∀i ∈ I s ). It is defined by consumption of fixed capital (P.51C1) in the industry divided by total fixed assets (net) (N11N) in the industry multiplied by the desired capacity utilization rate. Firms' dividend payout ratio θ DIV is set to match interest and dividend receipts (D.4 received) plus mixed income (B.2A3N) 41 by the household sector in national accounting data (non-financial transactions (nasa nf tr)) in relation to total net operating surplus and mixed income (B.2A3N) as obtained from IOTs. As these payments also include interest payments to the household sector, the dividend payout ratio can be seen as the total return property rights ownership in non-financial and financial firms by the household sector, and is set accordingly for each individual firm.

Appendix B.2. Households
Parameters that specify the number of households (persons) are taken directly (or derived from) census data. We use the register-based census and the register-based labor market statistics in Austria conducted by Statistik Austria, and supplied via Eurostat. Specifically we are using statistics on population by current activity status, NACE Rev. 2 activity and NUTS 2 region (cens 11an r2) to set the constant number of inactive persons (H inact ). The total number of economically active persons (H act ) is set to the total number of persons employed in the population of active enterprises in t (V16910) plus the total number of unemployed and one investor for each firm. The total number of unemployed (plus the labor reserve) is taken from the European Labour Force Survey (LFS). 42 Households' marginal propensity to consume out of initial disposable income (ψ) is chosen such that consumption out of disposable income (ψY h (0)) equals actual household and NPISH consumption in IOTs (P.3 in sectors S.14, S.15). The parameter ψ H capturing the fraction of household expected disposable income Y h (0) which is invested gross of taxes every period is set according to IOTs. We set ψ H such that investment by the firm sector (in line with our investment function) plus investment by the household sector equals total gross fixed capital formation (P.51G). The household investment coefficients b CFH g are set such that investment in dwellings as obtained from IOTs for Austria provided by Statistik Austria 43 and gross fixed capital by sector from IOTs are mutually consistent. The replacement rate for unemployment benefits θ UB is chosen according to the statutory replacement rate of 55 percent of net income, which amounts to a replacement rate on gross income of θ UB = 0.55(1 − τ INC )(1 − τ SIW ).

Appendix B.3. The general government
The number of government entities (J) is set to 25 percent of domestically producing firms, which roughly equals the share of government consumption in total value added. This corresponds to a realistic depiction of public entities comprising municipalities, public schools, social insurance carriers, and districts, among others, in Austria according to their participation in the Austrian economy. assets can be recorded in balance sheets at current purchasers' prices reduced for the accumulated consumption of fixed capital; this is known as the written-down replacement cost. The sum of the reduced values of all fixed assets still in use is described as the net capital stock. The gross capital stock includes the values of the accumulated consumption of fixed capital. 41 In the logic of IOTs, the self-employed are attributed to firm sectors. Thus, operating surplus of IO sectors includes mixed income, which directly flows to households in the depiction of our model and is thus treated as dividend income. 42 The number of unemployed and employed persons extracted from the Labour Force Survey (LFS) complies with the ILO definition. According to the ILO definition, unemployed persons are defined as persons who are without work during the reference week, are currently available to work and have either actively been seeking work during the past four weeks or have already found a job to start within the next three months. The LFS also provides information on persons who do not meet the ILO criteria for unemployment but who are willing and available to work within short notice (labor reserve). 43 See https://www.statistik.at/web_en/statistics/Economy/national_accounts/input_output_statistics/index.html (Last accessed November 30 th , 2018) for more information on IOTs provided by Statistik Austria. More detailed IOTs for Austria, which include a breakdown of investment into different investment purposes (dwellings, other buildings and structures, machinery, transport equipment, cultivated assets, and intangible fixed assets), can be purchased. This is the only case where we do not rely on publicly and freely available data from the Eurostat bulk download facility.
Tax and subsidy rates are set such that these rates approximate the actual financial flows observed in national accounting data, i.e. non-financial transactions (nasa 10 nf tr), as well as government revenue, expenditure and main aggregates (gov 10a main). In the context of the model, we define an average tax rate as the aggregate tax flow paid by an institutional sector (firms in CPA classification, households, etc.) divided by the corresponding aggregate monetary flow that serves as the base for the tax and that is received by the same institutional sector (such as income, profit, output, fixed assets, etc.). This average tax rate obtained from macroeconomic aggregates is then applied to every individual unit/person in our model in the corresponding economic context. The income tax rate τ INC on income from both labor and capital is particularly chosen such that tax payments on wages received by employees and taxes on dividends received by investors add up to total income tax payments by the household sector taken from government expenditure data (gov 10a main, D.5REC and D.91REC). 44 For reasons of model parsimony we abstract from the progressivity of the Austrian tax system (e.g. regarding income taxes), and secondly from other tax regulations (deductions, exemptions, etc.) relevant for some agents due to specific features of the Austrian tax code.
Firm profit taxes τ FIRM are specified by the ratio of total corporate tax flows (D.51, paid by sectors S.11 and S.12), which are obtained from national accounting data (non-financial transactions (nasa nf tr)), to total operating surplus and mixed income (sum over all firm sectors), which we directly take from IOTs (B.2A3N). Value added tax rates τ VAT are specified as total value added taxes net of subsidies (D.21X31) from IOTs divided by consumption by households and NPISH (P.3 in sectors S.14 and S.15). Rates for social security contributions both for employers (τ SIF ) and employees (τ SIW ) are levied on gross wage income of households (D.11) as given in IOTs. Employers' social security contributions are taken from IOTs by subtracting total gross wage income (D.11) from total compensation of employees (D.1). Employees' social contributions include actual social security contributions (D.613) as well as social security supplements to be paid by employees (D.614), and are obtained by subtracting employers' social contributions from total social contributions received by the government according to government statistics (gov 10a main, D.61REC). Finally, sector-specific net rates for other taxes and subsidies on products (τ Y i = τ Y s ∀i ∈ I s ) as well as on production (τ K i = τ K s ∀i ∈ I s ) are taken from IOTs: sectoral product tax (D.21X31) and production tax (D.29X39) payments. Tax rates on exports (τ EXPORT ), which are levied on total firms' exports as in IOTs (P.6 total) as a uniform tax rate according to total net export tax flows in IOTs (D.21X31 for final use export, P.6). Taxes on capital formation (τ CF ) payable on firm investments are determined by dividing tax flows on investments as IOTs (D.21X31) by total investments in dwellings (obtained from IOTs provided by Statistik Austria, see footnote 43).

Appendix B.4. The Bank
Banks' capital requirement coefficient (ζ) is set at 3 percent. A capital requirement of 3 percent corresponds to the maximum leverage ratio (tier 1 capital in relation to total exposure) as recommended in the Basel III framework. The rate of debt installment (θ) is set such that firms repay 5 percent of their total outstanding debt every quarter. The risk premium µ paid on firms' outstanding debt is obtained from national accounting data. It is set such that total interest payments in our model financial market, where firm debt constitutes the only financial asset held by the banking sector, matches empirically observed interest payments (D.41) paid by non-financial (S.11) and financial corporations (S.12) in national accounting data (non-financial transactions (nasa nf tr)). Therefore, the risk premium by the banking sector µ is calculated by the difference between the 3-month Euribor interest rate obtained from money market interest rates (irt st a) and the observed interest payments (D.41) divided by the initial amount of firm debt L I , which is obtained from national accounting data, see Appendix C. In order to obtain a quarterly risk premium, µ is converted to a quarterly rate. The bank's maximum loan-to-value (LTV) ratio (ζ LTV ) is set to 60 percent. LTV is one of the most common ratios considered for secured loans, and loans with an LTV ratio below 60 percent are typically considered as low-or medium-risk loans. Finally, the loan-to-value ratio for a new firm replacing a bankrupt firm ζ b is set to be equal to 0.5.

Appendix C. Initial conditions for the Austrian economy
We set initial conditions for the model presented in Appendix A to represent the Austrian economy. All initial conditions in the model are collected in Table C.9. For the forecasting exercise in Section 3, initial conditions were initially calculated and set according to 2010:Q1 and then, respectively, recalculated and reset, every quarter until 2013:Q4. Here we show and discuss, as an example, initial conditions for 2010:Q4.

Appendix C.1. Firms
The distribution of firm sizes in industrial countries is well-known to be highly skewed, with large numbers of small firms coexisting with small numbers of large firms (Ijiri and Simon, 1977;Axtell, 2001). Initial employment of firm i (N i (0) ∀i ∈ I s ) is therefore drawn from a power law distribution with exponent −2 (where i∈I s N i (0) = N s and N i (0) > 0), which approximately corresponds to firm size distribution in Austria. 45 To determine initial production Y i (0) of the i th firm, we use the initial employment by firm N i (0), and compute the corresponding amount of production by the productivity of labour per unit of outputᾱ i : Initial capital of firm i, K i (0), (i is part of industry s) is then obtained by dividing firm i's initial level of production Y i (0) by the productivity of capital κ i and the desired rate of capacity utilization ω.
Thus, it is the share of capital of the i th firm in sector s as measured by production, accounting for the reserve capacity of its capital stock targeted by firm i. The initial stocks of raw materials, consumables, supplies, and spare parts (i.e. intermediate inputs) of the i th firm (M i (0)) are set such that-given the initial level of production by firm i, the productivity of intermediate inputs β i and a buffer stock of material inputs 1/ω-firms hold enough intermediate inputs to be able to provide for expected use of these inputs as well as accounting for their desired buffer stock: Regarding financial and current assets cross-classification tables are not available. Correspondingly, a breakdown of financial and current assets for the 64 economic activities (NACE*64) is not available in macroeconomic data. Thus, we apportion initial debt L i (0) to the i th individual firm by disaggregating total firm debts according to the share of the firms' capital stock K i (0) in the total capital stock i K i (0): where the total amount of firm debt L I is obtained from national accounting data (financial balance sheets (nasa 10 f bs), loans (F.4) of non-financial corporations (S.11), non-consolidated liability position). The total initial liquidity (deposits) of all firms as an aggregate, D I , is set according to national accounting data (financial balance sheets (nasa 10 f bs), non-consolidated deposits (F.2) held by the non-financial corporations sector (S.11)). This aggregate is broken down onto single firms by the share of firm i's operating surplus in the overall operating surplus, where we assume that firm liquidity (deposits) moves in line with its production as a liquid form of working capital used for current expenditures: i is the operating margin. Initial profit of the i th firm is given by the initial operating surplus and the initial income from interest less interest payments: The initial inventories of finished goods S i (t) of firm i is assumed to be equal to zero due to a lack of reliable data sources. The initial price of the i th firm P i (0) is set to one.

Appendix C.2. Households
Initial personal assets (deposits) of the h th household (D h (0)) are obtained from national accounting data (financial balance sheets (nasa 10 f bs), F.2, currency and deposits held by the household and NPISH sectors, S14 S15, non-consolidated asset position), which is disaggregated onto the individual level according to the share of each household's income in total income as a proxy for the household's wealth: where D H are the initial personal assets (deposits) of the household sector and Y h (0) is determined according to equation (A.49). Initial capital (dwellings) of the h th household (K h (0)) is set to match dwellings (N111N) as obtained from balance sheets for non-financial assets (nama 10 nfa st) and is again disaggregated onto the individual level according to the share of each household's income in total income as a proxy for the household's wealth: where K H is the initial capital (dwellings) of the household sector. The initial wage of the h th household (w h (0)) is equal to the initial wage paid by firm i (w i ), if i is the employer of household h; or it is equal to the initial unemployment benefits w UB , if the household is unemployed. Initial unemployment benefits are set by dividing the total flow of unemployment payments (GF.1005), as obtained from the Eurostat data set government expenditure by funcion (gov 10a exp), by the amount of unemployed persons (wstatus=UNE), which is determined according to the statistics on population by current activity status, NACE Rev. 2 activity and NUTS 2 region (cens 11an r2). Thus, w h (0) is determined as follows: Transfers other than consumption, savings, taxes and subsidies 46 are netted out for the government and household sectors, and treated as a net transfer from the government to the household sector. Government transfers to households in the form of social benefits (D.62) are attributed to the different household (consumer) types according to their employment status. The data are taken from national accounting statistics on general government expenditures by function (COFOG classification, Eurostat table gov 10a exp), which are used to allocate the total flow of the different social benefits (sb inact (0), sb other (0)) from the government to persons to whom this transfer applies. To break the overall economic flows of social benefits down onto an individual household level, we follow the following procedure: all social benefits are given in equal proportion to the different household types such that the sum of individual flows adds up to total macroeconomic flows.
Appendix C.3. The general government Initial government debt (L G (0)) is set according to the Austrian government's (sector S.13) consolidated gross debt (GD) as obtained from the Eurostat data set government deficit/surplus, debt and associated data (gov 10dd edpt1).

Appendix C.4. The Bank
Initial bank's equity (E k (0)) is obtained from national accounting data (financial balance sheets (nasa 10 f bs), F.5 and BF.90, non-consolidated equity and financial net worth of monetary financial institutions other than the central bank (S122 S123)). Initial bank's profits are given by the initial income from interest less interest payments: where initial advances from the central bank (D k (0)) are set according to equation (A.68).

Appendix C.5. The Central Bank
Initial central bank's equity (E CB (0)) is the residual on the central bank's passive side, obtained by deducting initial bank reserves held (D k (0)) and the initial net creditor/debtor position with the rest of the world (D RoW (0)) from the central bank's assets (initial government debt (L G (0))). Thus, the initial central bank's equity (E CB (0)) is set according to equation (A.76) where the initial balance of trade with the rest of the world (D RoW (0)) is assumed to be zero and the initial bank reserves held (D k (0)) are set according to equation (A.68).

Appendix D. Conditional forecasts with the agent-based model
We generate forecasts conditional on exogenous paths for imports, exports and government consumption, corresponding to a small open economy setting and exogenous policy decisions. In this setup, we assume that imports and exports, as well as government consumption, are exogenously given from data. Thus, in this setup we replace equations (A.77), (A.81), and (A.51) and set imports, exports and government consumption according to observed data.
Furthermore, in this setup we assume that agents' forecasts take into account expectations on imports, exports and government consumption. Thus, we replace equations (A.6) and (A.9), and assume expectations on economic growth and inflation to be formed using an autoregressive model with exogenous predictors and lag order one (ARX (1)). Thus, in this setup expectations on economic growth are formed according to an ARX(1) rule: where α Y (t), γ I (t), γ E (t), γ G (t), β Y (t), and Y (t) are re-estimated every period on the time series of aggregate output of firms i Y i (t ) and the exogenous predictors imports Y I (t ), exports C E (t ) as well as government consumption C G (t ), where t = −T , −T + 1, −T + 2, . . . , 0, 1, 2, . . . , t − 1. To allow the data to decide on the degree of persistence and cointegration, output, imports and exports as well as government consumption are entered in log levels.

Appendix E. Macroeconomic variables
Appendix E.1. Gross domestic product GDP in our model can be defined by the production, expenditure and income approaches: Taxes on products Total sales of goods and services − g,s,i∈I sP Household consumption Gross fixed capital formation

Changes in inventories
Taxes on products Gross operating surplus and mixed income Net taxes on production (Income approach)

Appendix E.2. Inflation
Inflation, which is measured by the GVA deflator, is the economy-wide average price of all goods and services produced and sold: where P i (t) and Y i (t) are price and production of firm i, respectively.

Appendix E.3. Household Consumption
Household consumption is the sum of the realized consumption of all individual households, i.e. h (1+τ VAT )C h (t).

Appendix E.4. Investment
Total fixed investment in the model is the sum of realized investment by individual firms plus the sum of realized investment by individual households, that is, Appendix E.5. Government Consumption Government consumption is the sum of the realized consumption of all government entities, i.e. H h=1 C h (t).
Appendix E.6. Exports Export is the sum of the realized consumption of all foreign consumers, i.e. l (1 + τ EXPORT )C l (t).
Appendix E.7. Imports Import is defined as the total sales of all goods and services produces by foreign firms, i.e. m P m (t)Q m (t)).

Appendix F. DSGE model used for out-of-sample-prediction
Appendix F.1. DSGE model: Short description The DSGE model used for out-of-sample forecasting is a two-country New Keynesian New Open Economy macro model of the Austrian economy (home) and the EA (foreign), constructed tightly along the lines of Smets and Wouters (2007). 47 It is a modified version of the two-country DSGE model as put forth in Breuss and Rabitsch (2009). Specifically, this model was modified to achieve comparability with the Smets and Wouters (2007) model through the rescaling of several shocks and estimating the model to growth rates, both of which stabilized the Bayesian estimation procedure.
The two-country economy is normalized to one, where the size of the home economy equals n, the size of the foreign economy equals (1 − n). Firms in each region produce goods using capital and labor according to a Cobb-Douglas production function. Each of the two countries specializes in the production of one region-specific good, i.e., there are both domestic and foreign tradable goods. These domestic and foreign tradable goods come in several varieties, over which producers have some degree of power in price setting. Investment is assumed to be a constant elasticity of substitution (CES) index over domestic and foreign investment goods. Financial markets are assumed to be complete, that is, a full set of Arrow-Debreu securities is assumed to exist. Households receive utility from consumption and disutility from working. They also own the economy's capital stock, which they rent to firms as means of production, and supply a variety of differentiated labor services, over which they have some degree of power in wage setting. Furthermore, household consumption is assumed to be a CES index over domestic and foreign consumption goods, which is possibly different from the CES investment index. In line with recent literature on DSGE models, a number of both real and nominal frictions is assumed. First, costs for capital adjustment and habit formation are imposed. Second, some degree of stickiness for both prices set by firms and wages demanded by households is assumed according to Calvo (Calvo, 1983) staggered price and wage setting mechanisms. Both prices and wages are partially indexed, that is, they are to some degree inflation-adjusted in the event that price or wage changes are not possible. The DSGE model is estimated using Bayesian methods on a quarterly basis and on the same data set as the time series models. Below, the model equations for the home economy are set out, assuming that the foreign economy is described by an analogous set of equations unless this is explicitly stated otherwise. All foreign variables are denoted with an asterisk ( * ).

Appendix F.2. Consumption Appendix F.2.1. Households' intertemporal optimization
The domestic economy is assumed to be populated by a continuum of household agents over the interval [0,n), foreign household agents are populated over (n,1]. Each household is indicated by the index j. Household j intends to maximize her discounted expected lifetime utility, which is assumed to be separable in consumption and leisure. Household j derives utility from consumption C t ( j) in relation to a habit level H t , and disutility from providing a differentiated type of labor L t ( j): where β is the discount factor, σ c is the coefficient of relative risk aversion (the inverse of the intertemporal elasticity of substitution), and σ l is the inverse of the elasticity of work effort with respect to the real wage.
The habit level H t is assumed to be proportional to aggregate past consumption: The (domestic) household budget constraint is determined by total household income from different sources, and by nominal expenditures for consumption (P t C t ( j)) and investment (P X household j are wages received (W hh,nom t (h, j)L t ( j)dh), income from rental of capital to firms for production purposes (R k,nom t u t ( j)K t−1 ), dividend payments from firm ownership ( 1 n n 0 Div(h, j)dh), and net government transfers T t ( j). Under the assumption of complete markets, each individual household has access to a full set of state-contingent (Arrow-Debreu) securities. In the following, we denote the price of one unit of domestic currency available in period t + 1 contingent on the state of nature at t + 1 being s t+1 by Q(s t+1 |s t ). Assuming complete markets, Q(s t+1 |s t ) is the same for all individual households. If now B H,t ( j, s t+1 ) represents the claim to B H,t units of domestic currency at time t + 1 for the state of nature s t+1 , which a household j can buy at time t and carry over into time t + 1. Q * (s t+1 |s t ) and B F,t ( j, s t+1 ) are defined analogously in terms of foreign currency. Nominal interest rates can thus be expressed by R t = 1/( s t+1 Q(s t+1 |s t )) and R * t = 1/( s t+1 Q * (s t+1 |s t )). Now let S t denote the nominal exchange rate of domestic currency per unit of foreign currency.
The household budget constraint, which is subject to a risk shock ε b t , is thus given by: where R k,nom t is the nominal return rate to physical capital, u t ( j) is the capital utilization rate as chosen by the household agent, and K t−1 is previous period's physical capital stock.
Since households choose the utilization rate of capital, the amount of effective capital that households rent to firms is: Furthermore, a u t ( j)K t−1 ( j) are costs for the utilization of capital that depend on the real return rate on capital, the utilization rate of capital and a fixed parameter φ a as follows: where r k denotes the real rate of return on capital in steady state (r k = R k,nom P ). The law of motion for capital reads as follows: where δ is the depreciation rate of physical capital, and is a function that transforms investment into physical capital stock including adjustment costs for investment, where, similar to the utilization of capital above, investment above the steady state growth rate γ bears additional costs. Furthermore, φ K represents a fixed parameter for investment adjustment costs, γ is the trend growth rate in the steady state of the exogenous productivity factor, and ε X of the household budget constraint by Λ t ( j), and the household constraint regarding the capital law of motion by Q t ( j), one can derive the respective first order conditions listed as follows.
Consumption C j t : Labor supply L j t : Domestic and foreign Arrow-Debreu securities holdings, B j H,t and B j F,t : where S t denotes the nominal exchange rate of domestic currency per unit of foreign currency. Investment X j t : Capacity utilization u j t : R k,nom

.2. Households' intratemporal optimization
Consumption. Each consumer j's overall consumption, C t ( j), is composed of a bundle of domestic and foreign consumption goods indexed by H and F, which are subject to a constant elasticity of substitution (CES): where denotes the elasticity of substitution between the bundles of domestic and foreign goods, and γ c is the share parameter in the CES consumption function. Domestic (foreign) consumption C H,t C F,t again are CES bundles over many varieties of domestic (foreign) goods (c t (h, j), c t ( f, j)), according to a constant elasticity of substitution θ: In each period, the consumer allocates her consumption of domestic varieties by minimizing expenditure: . By inserting equation (F.13) and minimizing with respect to c t (h, j), one obtains the optimal demand function as follows: One can derive the optimal domestic CES price index P H,t by inserting the demand function for the h good, equation (F.15), into the CES consumption bundle, equation (F.13), to obtain: Solving the analogous problem for the consumption of varieties of foreign goods, yields the optimal demand functions and price indices for varieties of foreign goods: (F.18) Using equation (F.12), and minimizing with respect to C H,t ( j) and C F,t ( j), one can derive optimal demand functions for bundles of home and foreign goods: By inserting the input demand functions, equations (F.19) and (F.20), into the aggregate CES bundle of home and foreign goods, equation (F.12), one obtains the optimal price index P t as: Investment by household j (X t ( j)) is modelled in a fashion similar to that of consumption, that is, as CES indices over domestic and foreign (varieties of) investment goods x t (h, j), with the same elasticity of substitution , but a different share parameter γ x . Investment demand functions and prices are thus given by:

.3. Government purchases
Public consumption of government agent j, G t ( j), is modelled in a fashion similar to that for private consumption, that is, as CES indices over domestic and foreign varieties of goods. Analogously to above, one can derive demand functions and prices for the government as follows: Appendix F.3. Intermediate labor union sector and wage setting Following Smets and Wouters (2007), households supply their homogenous labor to an intermediate labor union, which differentiates the labor services from labor varieties of type l and sets wages in a Calvo fashion, selling the labor varieties of type l to labor packers. Labor used by the intermediate goods producer of variety h, L t (h)-henceforth for reasons of simplicity referred to as L t -is then a Dixit-Stiglitz composite of varieties of labor l: where λ w is the elasticity of substitution among differentiated labor types. There are labor packers who buy the labor from the unions, package L t (or L t (h) to be precise), and resell it to intermediate goods producing firms. Labor packers maximize profits in a perfectly competitive environment. From the optimization problem of labor packers  F.29) or, in more precise notation: 48 Labor unions take the households' marginal rate of substitution as the cost of the labor services in their negotiations with labor packers. The (nominal) household's marginal rate of substitution is given by equation (F.6), rearranging this equation yields the nominal wage level for households that unions take to wage negotiations W hh,nom t : The markup above the marginal disutility of labor is distributed back to households. In setting the wage rate for labor of type l, the union is subject to nominal rigiditiesà la Calvo. In particular, the union can reset the wage in the current period with probability 1 − ξ w . Where the wage rate cannot be reset, the wage rate W nom t (l) increases with the deterministic GDP trend growth rate γ, a weighted average of the steady state inflation, π, and last period's inflation, π t−1 . The wage setting problem of the labor union is then described as: Here, Ind w t,k denotes the rule for wage indexation, which is given by: (F.34) and where ι w is a parameter governing the degree of this wage indexation. Solving this maximization problem, one arrives at the following markup equation for the optimal nominal wage W o,nom t : Households' wages that could not be chosen optimally due to the Calvo pricing mechanism (those which could not adapt their wages according to the Calvo probability of rigid wages ξ w ), are subject to a standard wage indexing related to the development of the general price level in the economy and the trend GDP growth rate. The wage index of these households evolves according to: Finally, λ w is not a fixed parameter, but follows the exogenous ARMA process with an AR coefficient ρ w , an MA coefficient θ w , and an i.i.d. error term w,t with variance σ w :

. Domestic good producers
The domestic consumption goods come in many varieties. Each domestic firm h specializes in one variety of goods, producing according to a Cobb-Douglas production function: where K t (h) denotes the physical capital stock used by firm h for production, L t (h) is an index of different types of labor services, A t denotes total factor productivity, Z t is a long-run labor-augmenting productivity factor that grows with the exogenous rate (γ), and Φ is a constant parameter indicating fixed costs of production in relation to the exogenous productivity factor. Each firm behaves as a monopolistic competitor, setting prices p t (h) and p * t (h) in the local and foreign market to maximize profits, taking as given the households' and government's demand for that good, . The firm's problem can be decomposed into a cost minimization problem and a profit maximization problem, as set out in the following.

Appendix F.4.2. Producer as a cost minimizer
Cost minimization by the firm provides information on the optimal capital-labor ratio. The minimization problem of an individual firm h is given by which yields first order conditions for firm h described in the following.
Labor demand L t (h): or rewriting it as the labor demand function: or rewriting it as the capital demand function: If the labor demand function, equation (F.39), is joined with the capital demand function, equation (F.40), the optimal capital-labor ratio is obtained. This optimal ratio will be the same for all domestic intermediate goods producers, and thus concurs with the economy-wide capital-labor ratio: By inserting the labor and capital demand functions into the production function, equation (F.38), one can derive the following expression for nominal marginal costs, which is the same for all firms, i.e., MC nom t (h) = MC nom t , as it only depends on aggregate prices: (F.42) Appendix F.4.3. Producer as a profit maximizer According to the Calvo price setting mechanism, firms may not be allowed to change their price every period. Rather, it is assumed that they cannot change their price unless they receive a price-change signal. The probability that a given price can be re-optimized at period t is assumed to be constant and equal to ξ P . Furthermore, it is assumed that each firm h has market power in the market for the good it produces, and maximizes expected profit according to a discount rate (from period t to period t + k). Define by Ω t,t+k = β Λ t,t+k Λ t P t P t+k the households' stochastic discount factor from period t to period t + k. Under sticky prices according to the Calvo mechanism, with partial indexation to producer prices (Ind p t,k ), and assuming producer currency price setting, the firm maximization problem is given by: where the producer price indexation rule Ind p t,k , similarly to the case for wages above, is given by (F.44) The parameter ι p indicates the degree of price indexation. Solving this maximization problem with respect to the price charged by firm h, p t (h), yields the following optimal price for firm h, p o t (h): Under the assumption of producer currency price setting, the law of one price holds at the level of individual goods, and the price level of firm h in the foreign economy, p * t (h), is given by: From these equilibrium price indices and the optimal price setting relation, one can derive how prices evolve over time (with indexation): 49 Note that when prices are not sticky, equation (F.45)) reduces to the standard expression: where π H,t = P H,t P H,t−1 .
Appendix F.4.4. Good Market Clearing According to the optimality conditions described above, the goods market clearing condition is then given as follows: The role of fiscal policy in the model is highly simplified. Government spending is assumed to be financed by lump-sum taxes (T t below denotes net transfers, that is, total government transfers minus taxes). The government is not allowed to run budget deficits, and its budget constraint therefore is: The monetary authority is assumed to apply a standard interest-feedback rule. The interest rate targets inflation as well as the output gap, and is set according to a Taylor rule: where R t is the short term money market interest rate (policy rate) set exogenously by the central bank (and thus also the interest rate on bond holdings by households as in the household budget constraint, see equation (F.2)), R is the policy rate in the steady state, π t is inflation at time t, π is the inflation target set by the central bank, y t is output at time t, y is the output target by the central bank, ρ R is the degree of interest rate smoothing by the central bank, ρ π denotes the weight the central bank places on inflation targeting, ρ Y is the weight the central bank places on the output gap, and ε R t is an exogenous shock to monetary policy.
Appendix F.7. Additional Equilibrium Conditions Arrow-Debreu securities are in zero net supply (the only security traded internationally is the F-bond; the Hsecurity is traded only domestically): Equilibrium in the factor markets requires: Appendix F.10.4. Calibrated parameters Unless explicitly mentioned otherwise, the parameters described below are set equally for the home and foreign economy. Some parameters are not estimated but calibrated for this model, closely adhering to standard values that have been well-tested by a large body of DSGE literature. The discount factor β is set to 0.9983, which would approximately imply a real interest rate of 0.7 percent in the steady state, reflecting the low-interest environment in Europe since the financial crisis of 2007-2008. The depreciation rate δ is set to 2.5 percent to correspond to the sample mean of the labour-output and investment-output ratios. The capital share in production, the Cobb-Douglas production function parameter α, is set to about 19 percent. The weight of domestic and foreign consumption goods in their respective overall aggregate net consumption index are reflected in the parameters γ C and γ * C , which are calibrated by using the measures of imports in private consumption from the GTAP database along the lines of Breuss and Rabitsch (2009). This implies a weight of γ C = 0.8964 on domestically produced consumption goods in Austria. For the EA this translates into a weight of goods produced in the EA without Austria of (1 − γ * C ) = 0.9974, where for simplicity's sake it is assumed that the weights in the respective CES indices do not differ from each other. The country share n of Austria in the total model economy in comparison to EA is set to 0.031, which approximately corresponds to the share of Austrian GDP in the EA within the calibration periods (2010:Q1-2013:Q4). This implies a size of the EA economy (1-n) of 0.969.
Appendix F.10.5. Prior and posterior distributions for estimated parameters Tables F.11 and F.13 show information about the prior and posterior distributions of the Bayesian estimation after the MCMC sampling procedure. For all parameter estimates used for simulations, part of which is shown below, the number of Metropolis-Hastings draws has been set to 250,000.

Appendix F.11. Variance Decomposition
A forecast error variance decomposition reveals which shocks drive different macro variables in the model economy by determining the extent to which the forecast error variance of each of these variables can be explained by the different exogenous shocks. For exposition, the unconditional variance decompositions (i.e., at horizon infinity) and the conditional variance decompositions (i.e., at the forecast horizon of 12 quarters) are shown for the first year to which the model is estimated (2010:Q1), as well as for the last year of model estimation (2013:Q4).
Appendix F.11.1. 2010:Q1 At first glance, the unconditional variance decomposition depicted in Table F.15 reveals some noteworthy results and valuable insights for the conditional forecast conducted in Section 3.3 above. This is especially so for the growth rates of consumption and investment, which are the variables that have to be partly controlled exogenously for the conditional forecast, as further laid out in Appendix F.12 below. 51 Consumption growth in Austria (dCC), as to be expected, is mostly determined by the risk shock to household bond holdings (η b t , which in essence corresponds to a "consumption shock"), all other influences seem to be relatively minor. This picture is somewhat different for the EA, even though the consumption shock (η b * t ) there also plays the most important role in determining changes in EA consumption (dCC * ). However, the importance of technology shocks, for consumption seems especially, to be higher in the EA. Investment growth both in Austria (dXX) and the EA (dXX * ), as would be expected according to economic intuition, are primarily determined by the shock to investment demand.
The conditional variance decomposition shown in Table F.16 below demonstrates that for the forecast horizon of 12 quarters (q), the decisive features of the unconditional variance decomposition remain unchanged. However, the importance of some shocks diminishes, while the influence of other shocks rises. Especially, in the short term, the degree of influence of the technology shock in the EA on employment and inflation is more than halved as compared to the long run variance decomposition. Compared to these noteworthy changes in the variance decompositions for the EA, it seems that for the Austrian economy the influences of shocks remain much more stable from the short to the long term, potentially related to the fact that economic developments in Austria are more subject to other exogenous influences such as exports or imports. The unconditional and conditional variance decompositions for the model estimated for 2013:Q4 qualitatively show a very similar picture as for 2010:Q1, with only minor differences in the quantitative degree of the various shocks determining the development of macro aggregates in the model. This shows that, over the forecast horizon, the model behavior is not expected to change qualitatively to a high degree. To replicate a setup of times series models with contemporaneous exogenous predictors for exports and imports 52,53 (as in the ARMAX and VARX models above) within a DSGE model, we run so called conditional forecasts 52 Since government consumption in the DSGE model is represented by a stochastic exogenous shock, we do not consider government consumption as an exogenous predictor for the DSGE mode. 53 For all analyses below and according to the logic of the DSGE model, exports from Austria to the EA (imports of EA from Austria) are represented by consumption (C * H ) and investment (X * H ) of Austrian goods in the EA, while imports of Austria from the EA (exports of EA to Austria) are represented by the domestic (Austrian) use of goods produces in the EA for consumption (C F ) and investment (X F ), respectively. in the DSGE model. For this purpose, we have to compute forecasts for a given constrained path of an endogenous variable. 54 While for the time series models these exogenous data directly enter the parameter estimation procedure, in the DSGE model-following Leeper and Zha (2003) or Smets and Wouters (2004) (where this conditional forecasting procedure is applied to interest rate paths)-it is necessary to control certain exogenous shocks. These exogenous shocks are unanticipated by the optimizing agent in the DSGE model, and are chosen so as to match the corresponding values of the exogenous predictors, which are the conditioning information, that is, in our case Austria's exports to and imports from the EA. In particular, the reduced-form, first-order, state-space representation is used to find the structural shocks that are needed to match the restricted, exogenous paths. When these controlled shocks are used, the state-space representation can be applied to forecasting. According to the variance decomposition conducted in Appendix F.11 above, we use the consumption shocks at home and abroad as the controlled exogenous shocks, which account for the large bulk of Austria's exports-namely, foreign consumption of goods produced at home-and imports, namely, consumption in Austria of goods produced abroad. Intensive testing of the DSGE model revealed that including additional controlled shocks for the conditional forecasts worsened the forecast performance. This also pertains to shocks to investment, which account for a minority of trade between Austria and the EA. For these reasons, and in line with the results from the variance decomposition, we restricted the amount of controlled shocks to consumption shocks.
The unconditional forecasting results for Austria shown in Table F.19 clearly indicate that the DSGE model outperforms the VAR(1) model especially for medium to long term horizons. DSGE forecasts for GDP improve on VAR(1) predictions by a considerable margin for a horizon up to 12q, while the VAR model has some advantages for shorter horizons of 1q and 2q. Moreover, the additional economic structure embedded in the theory-driven DSGE model seems to increase its forecasting performance over the VAR model for all other variables, and also for shorter horizons. Accordingly, the DSGE model outperforms the VAR(1) for almost all horizons-sometimes by a margin over 50 percent for longer horizons-for inflation, hours worked, wages, consumption and investment. The unconditional forecasting results for the EA depicted in Table F.20, show a similar picture to the results for Austria, but with slight variations. Interestingly, the DSGE model outperforms the VAR(1) model for all horizons in GDP forecasts, even in the short term of 1q and 2q, but has a smaller margin over the VAR(1) model in the longer run than for the Austrian case. This difference also relates to the forecast performance of the VAR model estimated to EA data, which is slightly worse than that of the VAR model for Austria especially for longer horizons. DSGE model forecasts of consumption in the EA are worse in relation to the VAR model compared with Austria. However, this deterioration in the forecast performance of the DSGE model for the EA in comparison with Austria is due to the performance of the VAR model, as the VAR model estimated to EA data seems to forecast consumption particularly well in comparison with other variables. What could also be noteworthy is that the Taylor rule embedded in the DSGE model tends to capture interest rates better at shorter than at longer horizons in comparison with the VAR model.  Table F.21 shows the forecast performance of the DSGE model in a conditional forecasting setup for Austria according to the methodology briefly described in Appendix F.12 above. As noted there, for this procedure consumption shocks are controlled to match the exogenously given paths of exports and imports in the DSGE model. The DSGE model delivers a fairly reasonable forecast performance in comparison to the VARX(1) model, which includes the same exogenous predictors. However, the DSGE model forecast performance deteriorates with respect to the unconditional case. This becomes most cleary visible when the DSGE forecast performance is looked at for consumption, which obviously decreases due to the controlling of consumption shocks to match the exogenous predictors. With this method, even though the overall forecast performance of the DSGE model increases with respect to the unconditional case, a price has to be paid with the distortion of the general equilibrium framework underlying the DSGE model that decreases its forecast performance. This is less so for Austria than for the Euroa Area, as the additional information of exogenously given exports and imports seems to largely outweigh the distortion of the endogenous variables in the model in the small open economy setting. Accordingly, except for consumption, DSGE model forecasts do not deteriorate to a large degree with respect to the unconditional case, sometimes even improving slightly, such as in the short horizon (1q, 2q) for GDP forecasts, and for almost all horizons for investment forecasts. Here, the additional information of exogenous exports and imports between Austria and the EA, which only accounts for a very small amount of economic activity in the EA, does not suffice to counter-balance the distortion introduced by the controlled shocks within the DSGE model.