Forecasting with estimated dynamic stochastic general equilibrium models: The role of nonlinearities

In this paper we study the e®ects of nonlinearities on the forecast- ing performance of a dynamic stochastic general equilibrium model. We compute ¯rst and second-order approximations to a New Keyne- sian monetary model, and use arti¯cial data to estimate the model's structural parameters based on its linear and quadratic solution. We and that, although our model in not far from being linear, the fore- casting performance improves by capturing the second-order terms in the solution. Our ¯ndings suggest that accounting for nonlinearities will improve the predictive abilities of DSGE models in many appli- cations.

Fiscal policy in a monetary economy with capital and finite lifetime

This paper develops a dynamic stochastic general equilibrium model with nominal rigidities, capital accumulation and finite lifetimes. The framework exhibits intergenerational wealth effects and is intended to investigate the macroeconomic implications of fiscal policy, which is specified by either a debt-based tax rule or a balanced-budget rule allowing for temporary deficits. When calibrated to euro area quarterly data, the model predicts that fiscal expansions generate a tradeoff in output dynamics between short-term gains and medium-term losses. It is also shown that the effects of fiscal shocks crucially depend upon the conduct of monetary policy. Simulation analysis suggests that balanced-budget requirements enhance the determinacy properties of feedback interest rate rules by guaranteeing inflation stabilization. JEL Classification: E52, E58, E63Capital Accumulation, Finite Lifetime, Fiscal Policy, monetary policy, nominal rigidities, Simulations

Developing dynamic machine learning surrogate models of physics-based industrial process simulation models

Abstract. Dynamic physics-based models of industrial processes can be computationally heavy which prevents using them in some applications, e.g. in process operator training. Suitability of machine learning in creating surrogate models of a physics-based unit operation models was studied in this research. The main motivation for this was to find out if machine learning model can be accurate enough to replace the corresponding physics-based components in dynamic modelling and simulation software Apros® which is developed by VTT Technical Research Centre of Finland Ltd and Fortum. This study is part of COCOP project, which receive funding from EU, and INTENS project that is Business Finland funded. The research work was divided into a literature study and an experimental part. In the literature study, the steps of modelling with data-driven methods were studied and artificial neural network architectures suitable for dynamic modelling were investigated. Based on that, four neural network architectures were chosen for the case studies. In the first case study, linear and nonlinear autoregressive models with exogenous inputs (ARX and NARX respectively) were used in modelling dynamic behaviour of a water tank process build in Apros®. In the second case study, also Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) were considered and compared with the previously mentioned ARX and NARX models. The workflow from selecting the input and output variables for the machine learning model and generating the datasets in Apros® to implement the machine learning models back to Apros® was defined. Keras is an open source neural network library running on Python that was utilised in the model generation framework which was developed as a part of this study. Keras library is a very popular library that allow fast experimenting. The framework make use of random hyperparameter search and each model is tested on a validation dataset in dynamic manner, i.e. in multi-step-ahead configuration, during the optimisation. The best models based in terms of average normalised root mean squared error (NRMSE) is selected for further testing. The results of the case studies show that accurate multi-step-ahead models can be built using recurrent artificial neural networks. In the first case study, the linear ARX model achieved slightly better NRMSE value than the nonlinear one, but the accuracy of both models was on a very good level with the average NRMSE being lower than 0.1 %. The generalisation ability of the models was tested using multiple datasets and the models proved to generalise well. In the second case study, there were more difference between the models’ accuracies. This was an expected result as the studied process contains nonlinearities and thus the linear ARX model performed worse in predicting some output variables than the nonlinear ones. On the other hand, ARX model performed better with some other output variables. However, also in the second case study the model NRMSE values were on good level, being 1.94–3.60 % on testing dataset. Although the workflow to implement machine learning models in Apros® using its Python binding was defined, the actual implementation need more work. Experimenting with Keras neural network models in Apros® was noticed to slow down the simulation even though the model was fast when testing it outside of Apros®. The Python binding in Apros® do not seem to cause overhead to the calculation process which is why further investigating is needed. It is obvious that the machine learning model must be very accurate if it is to be implemented in Apros® because it needs to be able interact with the physics-based model. The actual accuracy requirement that Apros® sets should be also studied to know if and in which direction the framework made for this study needs to be developed.Dynaamisten surrogaattimallien kehittäminen koneoppimismenetelmillä teollisuusprosessien fysiikkapohjaisista simulaatiomalleista. Tiivistelmä. Teollisuusprosessien toimintaa jäljittelevät dynaamiset fysiikkapohjaiset simulaatiomallit voivat laajuudesta tai yksityiskohtien määrästä johtuen olla laskennallisesti raskaita. Tämä voi rajoittaa simulaatiomallin käyttöä esimerkiksi prosessioperaattorien koulutuksessa ja hidastaa simulaattorin avulla tehtävää prosessien optimointia. Tässä tutkimuksessa selvitettiin koneoppimismenetelmillä luotujen mallien soveltuvuutta fysiikkapohjaisten yksikköoperaatiomallien surrogaattimallinnukseen. Fysiikkapohjaiset mallit on luotu teollisuusprosessien dynaamiseen mallinnukseen ja simulointiin kehitetyllä Apros®-ohjelmistolla, jota kehittää Teknologian tutkimuskeskus VTT Oy ja Fortum. Työ on osa COCOP-projektia, joka saa rahoitusta EU:lta, ja INTENS-projektia, jota rahoittaa Business Finland. Työ on jaettu kirjallisuusselvitykseen ja kahteen kokeelliseen case-tutkimukseen. Kirjallisuusosiossa selvitettiin datapohjaisen mallinnuksen eri vaiheet ja tutkittiin dynaamiseen mallinnukseen soveltuvia neuroverkkorakenteita. Tämän perusteella valittiin neljä neuroverkkoarkkitehtuuria case-tutkimuksiin. Ensimmäisessä case-tutkimuksessa selvitettiin lineaarisen ja epälineaarisen autoregressive model with exogenous inputs (ARX ja NARX) -mallin soveltuvuutta pinnankorkeuden säädöllä varustetun vesisäiliömallin dynaamisen käyttäytymisen mallintamiseen. Toisessa case-tutkimuksessa tarkasteltiin edellä mainittujen mallityyppien lisäksi Long Short-Term Memory (LSTM) ja Gated Recurrent Unit (GRU) -verkkojen soveltuvuutta power-to-gas prosessin metanointireaktorin dynaamiseen mallinnukseen. Työssä selvitettiin surrogaattimallinnuksen vaiheet korvattavien yksikköoperaatiomallien ja siihen liittyvien muuttujien valinnasta datan generointiin ja koneoppimismallien implementointiin Aprosiin. Koneoppimismallien rakentamiseen tehtiin osana työtä Python-sovellus, joka hyödyntää Keras Python-kirjastoa neuroverkkomallien rakennuksessa. Keras on suosittu kirjasto, joka mahdollistaa nopean neuroverkkomallien kehitysprosessin. Työssä tehty sovellus hyödyntää neuroverkkomallien hyperparametrien optimoinnissa satunnaista hakua. Jokaisen optimoinnin aikana luodun mallin tarkkuutta dynaamisessa simuloinnissa mitataan erillistä aineistoa käyttäen. Jokaisen mallityypin paras malli valitaan NRMSE-arvon perusteella seuraaviin testeihin. Case-tutkimuksen tuloksien perusteella neuroverkoilla voidaan saavuttaa korkea tarkkuus dynaamisessa simuloinnissa. Ensimmäisessä case-tutkimuksessa lineaarinen ARX-malli oli hieman epälineaarista tarkempi, mutta molempien mallityyppien tarkkuus oli hyvä (NRMSE alle 0.1 %). Mallien yleistyskykyä mitattiin simuloimalla usealla aineistolla, joiden perusteella yleistyskyky oli hyvällä tasolla. Toisessa case-tutkimuksessa vastemuuttujien tarkkuuden välillä oli eroja lineaarisen ja epälineaaristen mallityyppien välillä. Tämä oli odotettu tulos, sillä joidenkin mallinnettujen vastemuuttujien käyttäytyminen on epälineaarista ja näin ollen lineaarinen ARX-malli suoriutui niiden mallintamisesta epälineaarisia malleja huonommin. Toisaalta lineaarinen ARX-malli oli tarkempi joidenkin vastemuuttujien mallinnuksessa. Kaiken kaikkiaan mallinnus onnistui hyvin myös toisessa case-tutkimuksessa, koska käytetyillä mallityypeillä saavutettiin 1.94–3.60 % NRMSE-arvo testidatalla simuloitaessa. Koneoppimismallit saatiin sisällytettyä Apros-malliin käyttäen Python-ominaisuutta, mutta prosessi vaatii lisäselvitystä, jotta mallit saadaan toimimaan yhdessä. Testien perusteella Keras-neuroverkkojen käyttäminen näytti hidastavan simulaatiota, vaikka neuroverkkomalli oli nopea Aprosin ulkopuolella. Aprosin Python-ominaisuus ei myöskään näytä itsessään aiheuttavan hitautta, jonka takia asiaa tulisi selvittää mallien implementoinnin mahdollistamiseksi. Koneoppimismallin tulee olla hyvin tarkka toimiakseen vuorovaikutuksessa fysiikkapohjaisen mallin kanssa. Jatkotutkimuksen ja Python-sovelluksen kehittämisen kannalta on tärkeää selvittää mikä on Aprosin koneoppimismalleille asettama tarkkuusvaatimus

The representative household's demand for money in a cointegrated VAR model

A representative household model with liquidity services directly in the utility function is used to derive a stable, data congruent error correction model of broad money demand in Iceland. This model gives a linear, long-run relation between real money balances, output and the opportunity cost of holding money that is used to over-identify the cointegrating space. The over-identifying restrictions suggest that the representative household is equally averse to variations in consumption and real money holdings. Finally, a forward-looking interpretation of the short-run dynamics, assuming quadratic adjustment costs, cannot be rejected by the data.

Spatial Externalities and Growth in a Mankiw-Romer-Weil World: Theory and Evidence

This paper presents a theoretical growth model that accounts for technological interdependence among regions in a Mankiw-Romer-Weil world. The reasoning behind the theoretical work is that technological ideas cannot be fully appropriated by investors and these ideas may diffuse and increase the productivity of other firms. We link the diffusion of ideas to spatial proximity and allow for ideas to flow to nearby regional economies. Through the magic of solving for the reduced form of the theoretical model and the magic of spatial autoregressive processes, the simple dependence on a small number of neighbouring regions leads to a reduced form theoretical model and an associated empirical model where changes in a single region can potentially impact all other regions. This implies that conventional regression interpretations of the parameter estimates would be wrong. The proper way to interpret the model has to rely on matrices of partial derivatives of the dependent variable with respect to changes in the Mankiw-Romer-Weil variables, using scalar summary measures for reporting the estimates of the marginal impacts from the model. The summary impact measure estimates indicate that technological interdependence among European regions works through physical rather than human capital externalities

Spatial Externalities and Growth in a Mankiw-Romer-Weil World: Theory and Evidence

This paper presents a theoretical growth model that accounts for technological interdependence among regions in a Mankiw-Romer-Weil world. The reasoning behind the theoretical work is that technological ideas cannot be fully appropriated by investors and these ideas may diffuse and increase the productivity of other firms. We link the diffusion of ideas to spatial proximity and allow for ideas to flow to nearby regional economies. Through the magic of solving for the reduced form of the theoretical model and the magic of spatial autoregressive processes, the simple dependence on a small number of neighbouring regions leads to a reduced form theoretical model and an associated empirical model where changes in a single region can potentially impact all other regions. This implies that conventional regression interpretations of the parameter estimates would be wrong. The proper way to interpret the model has to rely on matrices of partial derivatives of the dependent variable with respect to changes in the Mankiw-Romer-Weil variables, using scalar summary measures for reporting the estimates of the marginal impacts from the model. The summary impact measure estimates indicate that technological interdependence among European regions works through physical rather than human capital externalities.Series: Working Papers in Regional Scienc

Spatial Externalities and Growth in a Mankiw-Romer-Weil World: Theory and Evidence

This paper presents a theoretical growth model that accounts for technological interdependence among regions in a Mankiw-Romer-Weil world. The reasoning behind the theoretical work is that technological ideas cannot be fully appropriated by investors and these ideas may diffuse and increase the productivity of other firms. We link the diffusion of ideas to spatial proximity and allow for ideas to flow to nearby regional economies. Through the magic of solving for the reduced form of the theoretical model and the magic of spatial autoregressive processes, the simple dependence on a small number of neighbouring regions leads to a reduced form theoretical model and an associated empirical model where changes in a single region can potentially impact all other regions. This implies that conventional regression interpretations of the parameter estimates would be wrong. The proper way to interpret the model has to rely on matrices of partial derivatives of the dependent variable with respect to changes in the Mankiw-Romer-Weil variables, using scalar summary measures for reporting the estimates of the marginal impacts from the model. The summary impact measure estimates indicate that technological interdependence among European regions works through physical rather than human capital externalities. (author's abstract)Series: Working Papers in Regional Scienc

Asset Prices in Monetary Policy Rules: Should they stay or should they go?

The nature of the relationship between asset price movements and monetary policy is a currently hotly debated topic in macroeconomics. We analyse that relationship using a standard dynamic stochastic general equilibrium model, augmented by an equation featuring the asset prices deviations from a trend value. The calibration and subsequent simulation of that model allows us to conclude that it wouldn’t be desirable to include asset prices in the monetary policy rule, because of the higher interest rate and inflation volatility. The inclusion of a reaction to asset prices deviations in the monetary policy rule would only be justifiable in the context of a strong output gap sensibility to them and, even in that case, the gains of welfare would be so small that shouldn’t offset the costs attached to an explicit tracking of asset prices behaviour by the monetary authority. In conclusion, our results are consistent with a benign neglect view by the monetary authority towards asset prices. This attitude, where the ECB clearly fits in, implies that central banks could act in response to asset prices movements when there’s the need to avoid a sharp correction in the markets, which could have destabilising effects over the economy.Monetary policy Rules; Asset prices; DSGE models; European Central Bank

A Dynamic Macroeconometric Model of Pakistan’s Economy

In this study, an attempt has been made of develop a dynamic macroeconometric model of Pakistan’s economy to examine the behaviour of major macroeconomic variables such as output, consumption, investment, government expenditure, money, interest rates, prices, exports, and imports. The model consists of 21 equations, of which 13 are behavioural and the rest are identities. The Engle-Granger two-step cointegration procedure is used to derive the long-run and short -run elasticities for the period 1972-2009. The test of significance of each estimated equation seems to validate the model. The estimated long-run parameters are used to perform simulation experiments to determine the model’s ability to track historical data and to assess the behaviour of the key macroeconomic variables in response to the changes in selected exogenous variables. The results indicate that the majority of macroeconomic variables follow an increasing trend over the period of simulation, 2009-2013.Macroeconometric Model; Pakistan Economy, Cointegration, Forecasting