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FISK NK Model

Abstract

This medium-sized New Keynesian Model (NK) is built to assess the macroeconomic consequences of fiscal policy in a small open economy within a monetary union. The model is characterized by a large fiscal block, multiple industries, Calvo pricing, habit persistence and variable capacity utilization.

Working paper

Technical model description

FISK OLG Model

Abstract and links

This paper presents an update of the technical description of the FISK OLG Model, a numerical overlapping generations (OLG) model of the Auerbach-Kotlikoff type, specifically developed for Austria. The FISK OLG model is designed to quantify the medium- and long-term effects of demographic changes and structural reforms. Household and firm decisions are microfounded, and the model operates dynamically in general equilibrium. Particular attention is given to a detailed representation of government revenues and expenditures. An extension of the model incorporates endogenous energy consumption and greenhouse gas emissions.

Model description (version 2.3): Working paper

FISK Fiscal Sustainability Report 2025: Full report

Codes for solving this class of models (toy versions of the large model): solveCGE

Model summary

The aim of the dynamic model of Auerbach-Kotlikoff-type is to address fiscal policy questions that are particularly relevant in the medium and long run. The model is designed and calibrated such that it captures the economic environment and institutional features specific to Austria. As demographic change is an important determinant of future fiscal developments, we put particular emphasis on a detailed representation of the population structure. Persons differ in the following dimensions: age (recorded in single years in the tradition of Auerbach and Kotlikoff, 1987), birth year, highest attained education (primary, secondary, or tertiary), and savings type (Ricardian “consumption smoother” or non-savers following Campbell and Mankiw, 1989). We refer to a particular combination of characteristics as a cell. Over time, persons move between cells, although the transition is subject to some rather intuitive restrictions. Obviously, persons cannot change their birth year, and age increases by exactly one year each year. Further, we assume that persons cannot change their savings type or highest attained education. The demographic module differentiates persons by sex and provides information on the number of persons and the vital rates (fertility, mortality, and net migration) per cell. In the economic part of the model, the household sector is populated by a representative unisex household per cell. Persons under the age of 15 do not make economic decisions and are allocated to the adult population by adjusting household weights accordingly. The representative households make decisions along the following margins: consumption, labor market participation, retirement, and hours supply. Therefore, age- and education-specific participation, income, consumption, etc., profiles by cohort are model outcomes. Aggregating these model outcomes across cells results in the macro aggregates of the household sector. The only source of uncertainty for an individual agent is the time of death, which follows a stochastic process. Besides that, agents are gifted with perfect foresight, i.e., future events are expected by agents with certainty. However, the model allows for unanticipated shocks.

The model is dynamic and solved in general equilibrium, i.e., prices are the result of interaction between households, firms, the government, and the rest of the world in product, factor, and asset markets. Representative firms make forward-looking decisions concerning investment, labor demand, and price setting. Firms take production factors labor, capital, and public capital as inputs and turn them into outputs. The labor-augmenting technological process that determines firm productivity is assumed to be exogenous. The government affects the economy by influencing agents’ resource constraints (via taxes and transfers) and by participating in product markets (via public consumption and public investment). Further, the government issues debt, which is an imperfect substitute for other asset types (domestic and foreign firm assets, and foreign public debt). Therefore, there is no arbitrage, and assets can earn different returns. Demand for different asset types is based on a portfolio optimization problem of households. Demand for goods is allocated between domestic and imported goods following the Armington (1969) assumption.

Particular emphasis was placed on capturing government revenues and expenditures. Most of the taxes are proportional, with the exception of a progressive income tax, which is based on non-linear tax functions. Demography-related expenditure is mostly modeled using age-skill-specific unit cost profiles. Special attention was given to the pension system. Pensions are based on persons’ income histories and are subject to different pension system regimes (the old systems differentiating between private sector employees and civil servants, and the new harmonized pension account system). In contrast to many comparable models, we do not treat a (current) base year or base period as a steady state. The model is fit to the historical time series with an initial steady state dating many generations in the past. This allows us to capture important non-stationarities as observed in the data. Examples of such dynamic developments are the non-stationary relationships between the current population structure and current vital rates, or between the current primary balance and the current level of debt. Furthermore, this approach ensures that future trends, such as aging, are already included in agents’ expectations. In addition, this approach allows us to incorporate historical reforms, such as pension reforms, with gradual, yet long-lasting consequences.

Selected results

Rmod

An R package to generically solve dynamic models.

Description

The typical use case is to solve (economic) dynamic models given by a simple input text file (*.Rmod) containing the model primitives (i.e., first-order conditions, resource constraints, etc.). From the given Rmod-file Rmod generates efficient code (R and/or C++ using RcppEigen) to solve dynamic transition paths for that model. Optionally, Rmod can generate R-packages for repeated use.

under construction