Antti Tanskanen

Antti Tanskanen

PhD, Actuary

Publications

A rich life cycle model of labor supply in Finland

Published in https://arxiv.org/abs/2511.00660, 2025

A life cycle model of consumption and labor supply describes employment decisions of a collection of individuals during their lifetime. We develop a life cycle model describing a heterogeneous population operating in Finland under a wide variety of employment states and life situations. A rich life cycle model requires a large state space representing the possible states of simulated agents. The results demonstrate that the model reproduces a number of statistics of the Finnish employment market such as the age structures of employment rate and unemployment rate, distributions of observed effective marginal tax rates and participating tax rates, and proportion of part time work. As an application of analysis of a reform, we analyze how the program of Orpo government influences employment and public finances in Finland.

Recommended citation: Tanskanen, A.J. 2025. “A rich life cycle model of labor supply in Finland” arXiv:2511.00660 https://doi.org/10.48550/arXiv.2511.00660 https://arxiv.org/abs/2511.00660

Can total fertility rate be predicted?

Published in SocArXiv. March 25. osf.io/preprints/socarxiv/v78f4, 2023

The Finnish birth rate has fallen dramatically since 2010: the number of children born in Finland has fallen from 61,000 in 2010 to 44,900 in 2022. According to the preliminary data for 2022, the total fertility rate is at 1.31, which is the lowest ever. The downward trend has continued for almost the entire period 2010-2022, so there is no question of whether this is a result of random variation. In this study, I review how well the fertility forecast made in 2018 has performed. It turns out that the forecast is quite good. The forecast manages to predict the total fertility number in Finland almost exactly in 2022, and the trend from 2018-2022 quite well. As a further development, I refit the factor model to a more recent data and present a new forecast for years 2023-2030. The main factors driving fertility in the factor model are urbanization, the rate of marriages and the ratio of daily users in social media platforms. Changes in these factors can largely explain the reduction in the total fertility number in Finland. According to the revised fertility forecast, the future looks bleak, but love may surprise.

Recommended citation: Tanskanen, A.J. 2023. “Can Total Fertility Rate Be Predicted?.” SocArXiv. March 25. osf.io/preprints/socarxiv/v78f4 https://osf.io/preprints/socarxiv/v78f4/

Deep reinforced learning enables solving rich discrete-choice life cycle models to analyze social security reforms

Published in Social Sciences & Humanities Open 5 (1), 100263, 2022

Discrete-choice life cycle models of labor supply can be used to estimate how social security reforms influence employment rate. In a life cycle model, optimal employment choices during the life course of an individual must be solved. Mostly, life cycle models have been solved with dynamic programming, which is not feasible when the state space is large, as often is the case in a realistic life cycle model. Solving a complex life cycle model requires the use of approximate methods, such as reinforced learning algorithms. We compare how well a deep reinforced learning algorithm ACKTR and dynamic programming solve a relatively simple life cycle model. To analyze results, we use a selection of statistics and also compare the resulting optimal employment choices at various states. The statistics demonstrate that ACKTR yields almost as good results as dynamic programming. Qualitatively, dynamic programming yields more spiked aggregate employment profiles than ACKTR. The results obtained with ACKTR provide a good, yet not perfect, approximation to the results of dynamic programming. In addition to the baseline case, we analyze two social security reforms: (1) an increase of retirement age, and (2) universal basic income. Our results suggest that reinforced learning algorithms can be of significant value in developing social security reforms.

Recommended citation: Tanskanen, A.J. (2022). "Deep reinforced learning enables solving rich discrete-choice life cycle models to analyze social security reforms" Social Sciences & Humanities Open 5 (1), 100263 https://www.sciencedirect.com/science/article/pii/S2590291122000171

Lafferin käyrä heterogeenisessa populaatiossa – ja miksi verolajilla on väliä

Published in Kansantaloudellinen aikakauskirja, 2021

Taxation influences incentives to work. This article considers the so called Laffer curve connecting tax rate to sum of taxes collected. In Finnish.

Recommended citation: Tanskanen, A.J., Kotamäki, M. (2021). "Lafferin käyrä heterogeenisessa populaatiossa – ja miksi verolajilla on väliä" Kansantaloudellinen aikakauskirja. 117 (3), 383-406. https://www.taloustieteellinenyhdistys.fi/wp-content/uploads/2021/10/KAK_3_2021_WEB-53-76.pdf

Työllisyysvaikutuksien arviointia tekoälyllä: Unelmoivatko robotit ansiosidonnaisesta sosiaaliturvasta?

Published in Kansantaloudellinen aikakauskirja, 2020

Generous social security displaces work. If the incentives for employment are too weak, a high level of social security leads not only to a low employment rate, but also to an erosion of the financial base of the welfare state. When reforming social security, it is important to assess the effects of possible reforms on employment, which is best achieved with a calculation model that takes behavioral effects into account. In this research, a stochastic life cycle model describing the incentives of social security, taxation and work is developed, in which individuals make the best choices from their point of view by optimizing their own benefit over the life cycle. Traditionally, such models have been solved with dynamic programming, but with the development of algorithms, artificial intelligence solutions using artificial neural networks have become possible. The life cycle model reproduces the observed age-specific employment and unemployment rates well, and can be used to evaluate the effects of policy reforms on employment and unemployment rates. The study presents estimates of the employment effects of two policy reforms. The entire source code of the calculation model is freely available.

Recommended citation: Tanskanen, A.J., (2020). "Työllisyysvaikutuksien arviointia tekoälyllä: Unelmoivatko robotit ansiosidonnaisesta sosiaaliturvasta?" Kansantaloudellinen aikakauskirja. 117 (3), 383-406 https://www.taloustieteellinenyhdistys.fi/wp-content/uploads/2020/06/KAK_2_2020_WEB-94-123.pdf

Random selection of factors preserves the correlation structure in a linear factor model to a high degree

Published in PloS one 13 (12), 2018

In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen stochastically based on the random projection method. Randomness of factors has the consequence that correlation and covariance matrices are well preserved in a linear factor representation. It also enables derivation of probabilistic bounds for the accuracy of the random factor representation of time-series, their cross-correlations and covariances. As an application, we analyze reproduction of time-series and their cross-correlation coefficients in the well-diversified Russell 3,000 equity index.

Recommended citation: Tanskanen, A.J., Lukkarinen, J., Vatanen, K. (2007). "Random selection of factors preserves the correlation structure in a linear factor model to a high degree" PloS one 13 (12) https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0206551

Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

Published in University of Helsinki, 2008

In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models.

Recommended citation: Tanskanen, Antti J. (2008). "Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte." PhD thesis. University of Helsinki. https://helda.helsinki.fi/bitstream/handle/10138/21279/mathemat.pdf?sequence=2

Voltage noise influences action potential duration in cardiac myocytes

Published in Mathematical biosciences 208 (1), 125-146, 2007

Stochastic gating of ion channels introduces noise to membrane currents in cardiac muscle cells (myocytes). Since membrane currents drive membrane potential, noise thereby influences action potential duration (APD) in myocytes. To assess the influence of noise on APD, membrane potential is in this study formulated as a stochastic process known as a diffusion process, which describes both the current–voltage relationship and voltage noise. In this framework, the response of APD voltage noise and the dependence of response on the shape of the current–voltage relationship can be characterized analytically. We find that in response to an increase in noise level, action potential in a canine ventricular myocytes is typically prolonged and that distribution of APDs becomes more skewed towards long APDs, which may lead to an increased frequency of early after-depolarization formation. This is a novel mechanism by which voltage noise may influence APD. The results are in good agreement with those obtained from more biophysically-detailed mathematical models, and they suggest that increased voltage noise (due to gating noise) may partially underlie an increased incidence of early after-depolarizations in heart failure.

Recommended citation: Tanskanen, A.J., Alvarez, L.H.R (2007). "Voltage noise influences action potential duration in cardiac myocytes" Mathematical biosciencesn 5 (1), 125-146 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2568901/

The role of stochastic and modal gating of cardiac L-type Ca 2+ channels on early after-depolarizations

Published in Biophysical journal 87 (6), 3723-3736, 2004

Approximate reinforced learning methods enable the analysis of consequences of social security reforms.

Recommended citation: Antti J. Tanskanen, Joseph L. Greenstein, Brian O’Rourke, Raimond L. Winslow, (2005) The Role of Stochastic and Modal Gating of Cardiac L-Type Ca2+ Channels on Early After-Depolarizations, https://www.sciencedirect.com/science/article/pii/S0006349505730897

A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes

Published in Biophysical journal 87 (6), 3723-3736, 2004

Calcium (Ca2+)-induced Ca2+ release (CICR) in cardiac myocytes exhibits high gain and is graded. These properties result from local control of Ca2+ release. Existing local control models of Ca2+ release in which interactions between L-Type Ca2+ channels (LCCs) and ryanodine-sensitive Ca2+ release channels (RyRs) are simulated stochastically are able to reconstruct these properties, but only at high computational cost. Here we present a general analytical approach for deriving simplified models of local control of CICR, consisting of low-dimensional systems of coupled ordinary differential equations, from these more complex local control models in which LCC-RyR interactions are simulated stochastically. The resulting model, referred to as the coupled LCC-RyR gating model, successfully reproduces a range of experimental data, including L-Type Ca2+ current in response to voltage-clamp stimuli, inactivation of LCC current with and without Ca2+ release from the sarcoplasmic reticulum, voltage-dependence of excitation-contraction coupling gain, graded release, and the force-frequency relationship. The model does so with low computational cost.

Recommended citation: R. Hinch, J.L. Greenstein, A.J. Tanskanen, L. Xu, R.L. Winslow (2004) A Simplified Local Control Model of Calcium-Induced Calcium Release in Cardiac Ventricular Myocytes, https://www.sciencedirect.com/science/article/pii/S2590291122000171s

Fair valuation of path-dependent participating life insurance contracts

Published in Insurance: Mathematics and Economics 33 (3), 595-609, 2003

Fair valuation of insurance contracts, and of options embedded in them, is an important, incompletely understood issue. With the coming IAS insurance contract standard, the valuation of liabilities in life insurance is due to a drastic change. We present a computationally tractable model for fair valuation of participating life insurance contracts with given, almost arbitrary bonus policies. Unlike traditional valuation methods, our model captures several essential features of participating life insurance contracts, such as fair values of interest rate guarantees and of various bonus policies. In the model, fair value of life insurance contracts is understood as the arbitrage free price in the presence of liquid markets for liabilities. In addition to numerical results, the model gives solutions in closed form.

Recommended citation: Tanskanen, A.J., Lukkarinen, J. (2003). "Fair valuation of path-dependent participating life insurance contracts" Insurance: Mathematics and Economics 33 (3), 595-609 https://www.sciencedirect.com/science/article/abs/pii/S016766870300177X