Mortality and the business cycle: evidence from an estimated DSGE model for Germany

Shamsfakhr, Farzaneh Article — Published Version Mortality and the business cycle: evidence from an estimated DSGE model for Germany International Economics and Economic Policy Provided in Cooperation with: Springer Nature Suggested Citation: Shamsfakhr, Farzaneh (2024) : Mortality and the business cycle: evidence from an estimated DSGE model for Germany, International Economics and Economic Policy, ISSN 1612-4812, Springer, Berlin, Heidelberg, Vol. 22, Iss. 1, https://doi.org/10.1007/s10368-024-00633-9 This Version is available at: https://hdl.handle.net/10419/315216 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ International Economics and Economic Policy (2025) 22:10 https://doi.org/10.1007/s10368-024-00633-9 ORIGINAL PAPER Mortality and the business cycle: evidence from an estimated DSGE model for Germany Farzaneh Shamsfakhr1 Accepted: 8 August 2024 © The Author(s) 2024 Abstract This study addresses the relationship between transitory macroeconomic conditions and health by analyzing the dynamics of death over business cycle fluctuations in Germany during 1998:Q4–2014:Q4. A dynamic stochastic general equilibrium (DSGE) model with population growth is developed to incorporate demographic shocks including mortality. The estimation results indicate that mortality in Germany is counter-cyclical, suggesting that health in Germany deteriorates during recessions whereas it improves over economic expansions. Moreover, the structure of mortality is found to vary with respect to the business cycles. While for most of the sample period non-working population seems to be more exposed to death during recessionary times, there are evidences of higher fatality of working people in Germany during the recent financial and economic crisis. In the light of the demographic change that Germany is currently experiencing, findings of this study have important implications for health policies concerning aging as well as working-age population. 1 Introduction While there is not much doubt on the favorable health outcome of long-lasting economic growth, the consequences of short-term economic upturns on individuals’ well-being have become quite a controversy. The argument was primarily triggered by Ruhm (2000), who found a pro-cyclical pattern in mortality in the US during 1972– 1995. The counter-intuitive nature of Ruhm’s finding inspired further analysis on the relationship between mortality, as one of the main indicators of the overall health status, and transitory economic conditions. Similarly, using the same method as Ruhm, Gerdtham and Ruhm (2006) capture pro-cyclical variations in mortality for OECD countries during 1960–1997, which is found to hold for different sources of death in these countries. Besides, additional investigations have been through to unveil the BFarzaneh Shamsfakhr [email protected] 1Department of Economics, University of Duisburg-Essen, Universittsstrae 2, D-45117 Essen, Germany 0123456789().: V,-vol 123 10 Page 2 of 28 Int Econ Econ Policy (2025) 22:10 different aspects of this phenomenon and the mechanisms at work, which can also be specific to economic and social settings of a country (Lee 1997). Altogether, changes in lifestyle, quality of sleep, nutrition, and leisure time; an increase in work-related strain, working pace, and time; and work-related accidents following strengthening the economy and intense use of labor in response to high demand are identified as the main causes of pro-cyclicality of fatality observed in industrialized countries.1 Although based on existing literature one can hardly draw a clear conclusion on the channels through which temporary economic variations can lead to death, mortality is shown to be cyclical and time varying related to business cycles. The current paper aims to examine these features through a unique approach, which has been barely applied by previous studies. I develop and estimate a non-linear DSGE model to investigate the dynamics of mortality over business cycle fluctuations in Germany. This study makes a multi-fold contribution to the existing empirical studies. Firstly, the non-linear estimation allows to capture the possible time variability of mortality variations with respect to economic oscillations. Second, contrary to all the preceding works, no specific restrictive pre-assumption about links between mortality, or other measures of health, and economic variables is imposed in the model; instead, the data is let to talk. Furthermore, observing both variables of GDP and employment in the model allows to track the changes in death with respect to different measures of the business cycle, which in turn reconciles with the prior arguments. Also, the presence of population growth in the model makes it possible to infer the health outcome of both working people and those out of the labor market. In addition, including the components of demographic change in the model enables the study of the behavior of fertility and migration along with mortality. Lastly, since economic enhancement is usually anticipated to be a driver of both output and employment, by involving different shocks in the model, I am able to disentangle, at the same time, the possible effects of technological advances, from changes in hours worked concerning mortality, the task that could not be exercised by traditional empirical analysis. The rest of this paper is organized as follows: the next chapter has a brief but comprehensive review of the strands of arguments on the health outcome of business cycles. Section 3outlines the model used for the estimation. The elements incorporated in the model in order to analyze the dynamics of mortality are explained in this chapter. Section 3describes the data and the estimation strategy. Estimation results described in tables and figures are discussed in details in Section 4. Finally, Section 5summarizes the findings of the study and concludes. 1Some studies still do not support these notions. A microdata analysis in Finland by Böckerman et al. (2007) shows that obesity decreases during economic upturns measured by employment rate. However, they do not capture any significant effect of economic expansions on physical activity. Likewise, Colman and Dave (2014) find empirical evidence of a drop in fast food intake and expenditure on physical activity during recessions in the US, due to the following income effect on households’ resources. Nonetheless, the ultimate outcome on health is shown to be moderate and uncertain. Also, Johansson (2004)’s analysis of average hours worked per employee over economic successions and its transitory effect on health in 23 OECD countries during 1960–1997 indicates that, controlling for income, higher working hours during phases of economic upturns is associated with less mortality. 123 Int Econ Econ Policy (2025) 22:10 Page 3 of 28 10 2 Literature review Ruhm (2000) shows that in the US during 1972–1995 unemployment rate is negatively related to total mortality, as one percentage point increase in state’s joblessness declines the fatality rate by 0.5 to 0.6%. He also observes a reduction in physical activity and an increase in smoking, obesity, and unhealthy intake over temporary economic growth in the US. Through a closer examination of microdata, Ruhm (2003) finds that deterioration of physical health during economic upturns is more pronounced among employed Americans. Neumayer (2004) and Granados (2005) replicate (Ruhm 2000)’s analysis for German and Spanish data, respectively, and find a pro-cyclical pattern for aggregate mortality, and for the majority of death causes in these countries. Granados (2005) attributes the death pattern in Spain mainly to traffic-related injuries, which is amplified following economic recoveries. Similarly, Lin (2009) finds evidences of health improvement over economic downturns in Asia-Pacific countries over the period 1976 to 2003. On the contrary, some other research captures counter-cyclical patterns of mortality over economic fluctuations. This shape of variations is usually attributed to the pressures of job losses and economic distresses during recessions, which lead to higher stress, and unhealthy behaviors such as greater tendency to smoke and alcohol consumption that impair the health conditions and consequently increase mortality rates.2 In this regard, it is discussed that the presence of some sort of insurance schemes might alleviate the recessions’ hardships that consequently changes the magnitude or direction of effects. However, the cross-country analysis of Gerdtham and Ruhm (2006) suggests the stronger pro-cyclical effects in countries with relatively inferior social security system. Following these contradictory findings, some literature criticizes the use of unemployment rate as the measure of business cycle due to possible time lags between business cycles and employment variations.3Accordingly, based on Probit models, Gerdtham and Johannesson (2005) apply other business cycle indicators rather than unemployment rate including GDP variants and find a counter-cyclical mortality risk that is only significant for men and is more noticeable for working-age ones in Sweden during 1981–1996. Furthermore, some others have favored studying age-specific mortality instead of overall death fluctuations. Miller et al. (2009) closely searches the mechanisms behind pro-cyclical behavior of mortality in the US captured by Ruhm (2000), by repeating his analysis with lengthy data until 2004 and running the regression for a wider range 2Almost all the empirical literature are unanimous that the rate of suicides increases over economic recessions (Ruhm 2000; Granados 2005; Edwards 2008;Lin2009). The only exception, presumably, is Neumayer (2004) who shows that suicide is pro-cyclical in Germany. 3Clark and Summers (1982) also suggest that unemployment rate is a misleading measure of labor market condition since it does not reflect the variations in participation in response to changes in aggregate demand. Instead, employment rate is a better indicator of the labor market dynamics. 123 10 Page 4 of 28 Int Econ Econ Policy (2025) 22:10 of age groups. Their results demonstrate the most (pro-) cyclical mortality rates for those age groups with probably the lowest labor force participation, including the young adults between 18 and 24. However, the age group over 80 contributes the most (about 70%) to overall mortality fluctuations. Based on these findings, Miller et al. suggest that mechanisms behind pro-cyclical behavior of mortality should be sought out of labor market and beyond the individuals’ own health and work behavior, factors that Miller et al. attribute to business cycle externalities. They also go rather further by analyzing the age-specific pattern of different causes of death over business cycles, and they find no evidence of work-stress-related deaths among working population. There is more empirical evidence of pro-cyclical variations in the health status of the age groups with small labor market attachments in developed countries (Stevens et al. 2015; Rolden et al. 2013). These findings are suggestive of other contributing factors rather than job-related stress, such as air pollution, social support, or caregiving, in the mortality of elderly people during economic expansions. Comparatively, employing the same approach as Ruhm (2000) for Canadian data, Ariizumi and Schirle (2012) observe that the pro-cyclical pattern found for the US does not hold for aged population in Canada who rather enjoy specific elderly health care facilities provided by the Canadian government. Nevertheless, the working-age population in Canada still shows a pro-cyclical mortality over economic fluctuations. In addition, it is discussed that the relationship between macroeconomic conditions and mortality may alter over time. Consequently, some recent studies have examined this link with more recent data. Ruhm (2015) extends his analysis to 2009 for the US and concludes that over the last three decades, total mortality changed from being strongly pro-cyclical to being mostly unrelated to business cycles. Similarly, Tekin et al. (2013) do not capture any evidence of the effects of the recent financial crisis on health behavior in the US. Also, based on aggregate data for the US over 1961–2010 and using a time-varying parameter (TVP) model, Lam and Piérard (2017) conclude that in recent years, the destructive influence of increased working hours on individuals’ health status during upward economic fluctuations is dominated by the positive effect of medical developments for most of the age groups. Nevertheless, they still observe a pro-cyclical movement in mortality caused by motor vehicle accidents although this pattern has weakened over time. Finally, some prior research looks at mortality behavior among different socioeconomic groups. Edwards (2008) finds that the pro-cyclical mortality in the US is limited to working-age males with high school or higher educational attainment. In addition, Xu (2013) find evidence of worsening the mental health of educated employed individuals during the economic boost. These studies, although with opposing results, address different aspects of individuals’ health behavior over economic fluctuation. Accordingly, the possible dissimilarity in health outcome of working and non-working populations pointed out by the literature is worthy of attention. Nonetheless, as these studies mainly rely on regression analysis, they can be highly subject to omitted variables biases. The DSGE approach employed by this study resolves this quandary also and, at the same time, fulfills some other gaps in the literature. 123 Int Econ Econ Policy (2025) 22:10 Page 5 of 28 10 3Themodel The benchmark new Keynesian DSGE model with nominal price and wage rigidities and frictions in consumption and investment introduced by Fernández-Villaverde and Rubio-Ramírez (2006) is employed as the baseline model for this study. In a closed-economy framework, following Burriel et al. (2010), I adjust the model to be expressed in per-capita terms and extended along a balanced steady-state growth path determined by technology and population growth. As described later, the presence of population growth in the model allows to explore the behavior of mortality, as one of the component parts of population change, over business cycle fluctuations. A detailed description of the model is presented below. 3.1 Households It is assumed that the economy is inhabited by a continuum of homogeneous households indexed by jwith the following lifetime utility function: E0 ∞  0 βtLtdt{log (cjt −hcjt−1)+υlog mjt pt −ϕtψ (ls jt)1+γ 1+γ}(1) where cjt is per-capita consumption, mjt/ptper-capita real money balances, and ls jt per-capita hours worked. Ltdenotes the size of infinity-lived households that changes by population growth. βindicates the discount factor, hthe habit persistence, and γthe inverse of Frisch labor supply elasticity. Variables dtand ϕtrepresent an intertemporal preference shock and a labor supply shock, respectively, and are formulated as a firstorder autoregressive process AR(1): dt=ρddt−1+σdεd,twhere εd,t∼N(0,1)(2) ϕt=ρϕϕt−1+σϕεϕ,twhere εϕ,t∼N(0,1)(3) 3.1.1 Population dynamics The size of the household Ltis supposed to follow a random walk with drift: Lt=Lt−1exp (L+zL,t)where zL,t=σLεL,tand εL,t∼N(0,1). (4) Accordingly, the population growth is defined as follows: γL t=Lt Lt−1 =exp(L+zL,t)(5) where Lcorresponds to steady-state growth of population. In demographic terms, the natural change in population is triggered by three components of death, birth, and migration. I use this notion and incorporate these three 123 10 Page 6 of 28 Int Econ Econ Policy (2025) 22:10 features in population growth. This adjustment simply allows the study of the dynamics of mortality within this set-up. By definition, I design the population growth as follows4: γL t=(γ B t)αB(γ D t)−αD(γ M t)αM(6) where γB t,γD t, and γM trespectively represent the growth of birth, death, and net migration. Parameters of αB,αD, and αMindicate the rate of corresponding events. The vital events of births and deaths, also net migration, are supposed to be exposed to three shocks that, in turn, stimulate the changes in population through changes in mortality, fertility, and migration. These processes are accordingly formulated as follows, with persistence around their corresponding mean: γB t=exp(B+zB,t)(7) γD t=exp(D+zD,t)(8) γM t=exp(M+zM,t)(9) Households can trade an amount of Arrow-Debreu securities ajt+1, that pay one unit of consumption in event ωj,t+1,tpurchased by household jat time tat real price qjt+1,t. Households also hold an amount bjt of government bonds that pay a nominal gross interest rate of Rt.Itisassumedthata[1]=0, aand a>0. In addition, households own the capital ktthat earns a market real rental rate rtand is formed based on following law of motion: γL t+1kjt =(1−δ)kjt−1+1−κ[γL t xjt xjt−1 ]xjt (10) where δis the depreciation rate of capital and κ[.]is an adjustment cost function such that κ[x]=0, κ[x]=0, and κ[x]>0. xspecifies the growth rate of investment. Given these assumptions, the household’s per-capita budget constraint reads as follows: cjt +xjt +mjt pt +bjt+1 pt +qjt+1,tajt+1dωjt+1,t =wjtls jt +(rtujt −[ujt])kjt−1+1 γL t mjt−1 pt +Rt−1 1 γL t bjt pt +1 γL t ajt +Tt+Ft(11) where wjt indicates the real wage, and ujt >0 shows the intensity of capital utilization. Moreover, [ujt]is the physical cost of use of capital in resource terms. It is assumed that [1]=0, and  >0. Also, Ttis the lump-sum transfer, and Ftis the profit of the firm. 4Population aged 15 years and over are considered in this study; thus, the birth variable is entered into the model with a lag of 56 periods, since liveborns normally take 14 years to join the sample population. 123 Int Econ Econ Policy (2025) 22:10 Page 7 of 28 10 Therefore, the first-order conditions for the representative household with respect to cjt,bjt,ujt,kjt, and xjt take the following forms: dt(cjt −hcjt−1)−1−hEtβγ L t+1dt+1(cjt+1−hcjt)−1=λjt (12) λjt =Etβλjt+1 Rt t+1(13) rt=[ujt](14) qjt EtγL t+1=βEtγL t+1λjt+1 λjt (1−δ)qjt+1+rt+1ujt+1−a[ujt+1] (15) 1=qjt1−κγL t xjt xjt−1−κγL t xjt xjt−1γL t xjt xjt−1 +Etβγ L t+1qjt+1 λjt+1 λjt κγL t+1 xjt+1 xjt γL t+1xjt+1 xjt 2 (16) with (marginal) Tobin’s qt, defined as Qt λtthe ratio of two Lagrangian multipliers in the Lagrangian function related to household’s maximization problem. The differentiated labor supplied by each household in each period ls jt is accumulated by intermediate good producers through the following production function: Ld t=Lt1 0 (ls jt) η−1 ηdjη η−1=Ltld t(17) where 0 ≤η≤is the elasticity of substitution among different types of labor, and ld t and Ld trepresent per-capita and aggregate labor demand, respectively. Subject to this production function, intermediate good producers maximize their profit: maxljt wtLtld t−1 0 wjtLtls jtdj (18) with wjt showing the differentiated labor wages and wtthe aggregate wage. This delivers the per-capita labor demand function and aggregate wage as follows: ls jt =wjt wt−η ld t(19) wt=1 0 w1−η jt dj1 1−η(20) Households follow Calvo price setting to set their wages. In this sense, it is assumed that in each period, only a fraction of households (1−θw)update their wage wand 123 10 Page 8 of 28 Int Econ Econ Policy (2025) 22:10 the rest θwindex their wage to inflation in the previous period. Indexation is adjusted by χw∈[0,1]parameter. This yields the real wage as follows: w1−η t=θwχw t−1 t1−η w1−η t−1+(1−θw)w∗1−η t 3.2 Final good producer Perfectly competitive final good producer aggregates intermediate goods yit using the following design: yt=1 0 (yit)−1 di −1(21) where is the substitution elasticity among intermediate goods. Maximizing its profit subject to the production function, the final good producer arrives at the following input demand function: yit =pit pt− yd t(22) pt=1 0 p1− it di1 1−(23) with yd tindicating final good producer’s aggregate per-capita demand and ptindicating aggregate price. 3.3 Intermediate good producers The technology used by intermediate good producer iis Cobb-Douglas and expressed (in per-capita terms) as follows: yit =Atkα it−1ld it1−α−φ(24) where φis the fixed cost of production and Atis the level of technology with the following low of motion: At=At−1exp (A+zA,t)where zA,t=σAεA,tand εA,t∼N(0,1). (25) μz tdetermines the long-run growth of output and is given as: μz t=exp (A+zA,t)(26) In a perfectly competitive factor market, intermediate good producers rent inputs so as to: kit−1 ld it =α 1−α wt rt (27) 123 Int Econ Econ Policy (2025) 22:10 Page 15 of 28 10 prior assumption for labor supply elasticity as well as death and birth rate parameters is shown to perfectly mirror the information in the data. In general, the parameters are found to be strongly identified, and the data seems to be quite informative. In addition, the stability of the estimation is evaluated with Brooks and Gelman (1998) diagnostic tool of MCMC Convergence. Qualitatively speaking, through this method, one can infer if the sample delivered by the MCMC simulation makes a good representation of the posterior distribution. The corresponding results for individual parameters (univariate) and the whole set of parameters simultaneously (multivariate) in the form of graphs are presented in Appendix (Figs. 11,12,13 and 14). 4.4 Effect of shocks The importance of the shocks in explaining macroeconomic fluctuations can be assessed through analyzing the Bayesian variance decomposition, impulse-response functions (IRFs), and historical decomposition obtained from the estimation. These properties are discussed in this section, mainly with the focus on the effect of mortality shock. 4.4.1 Variance decomposition The result of unconditional variance decomposition is summarized in Table 3.The figures demonstrate the percentage share of the variations in the key observed variables that are explained by three shocks describing the population dynamics over an infinite horizon. As expected, the major part of the fluctuations in the German economy is determined by other shocks in the model including labor supply, technology, and preference shocks, altogether measure up to more than 98%. The rest is explained by the components of population growth contributing the most to the changes in consumption. Among these three demographic shocks, migration has the most and fertility has the least impact on the German economy. As visible, 0.002 and 0.001% of volatility in respectively GDP and employment growth in Germany is driven by mortality shock. 4.4.2 Impulse-response functions The reaction of the key variables of the model to stochastic shocks can be identified through IRFs. Figures1,2,3,4,5, and 6depict the trajectory of response of the model to one standard deviation shock over 40 periods (10 years) horizon, drawn as Table 3 Variance decomposition Variable Shocks Growth rate Mortality Fertility Migration GDP 0.002 0.001 0.13 Hours 0.001 0.00 0.04 Consumption 0.02 0.006 1.20 123 10 Page 16 of 28 Int Econ Econ Policy (2025) 22:10 010203040 -5 0 5 rel. dev. f. steady-state 10-4 Production (growth) 0 10203040 -2 0 2 rel. dev. f. steady-state 10-4 Employment (growth) 010203040 -5 0 5 rel. dev. f. steady-state 10-4 Consumption (growth) 0 10203040 0 0.05 rel. dev. f. steady-state Death (growth) Fig. 1 Mortality shock solid black lines surrounded by 90% confidence intervals. Accordingly, the narrow confidence interval seen around the estimated paths indicates a high certainty over the obtained estimates. As it is seen, the stochastic mortality shock of a size of one percent directly increases the number of deaths by about 0.4%. This leads to a decline in total output growth by about 0.002% and consumption growth by about 0.004%. Following an increase in mortality, the growth of hours worked per head goes up by roughly 0.001% as the first reaction to a fall in the size of the labor force. Nevertheless, within one period, when the impact of the shock seems to disappear, we observe a decline in the supplied labor following the mortality shock. Although the size of the effect on employment is small, it takes about 10 periods to rebound. Comparatively, the migration shock has a larger impact on the German economy, as 1 standard deviation shock expands the net migration growth by about 3%. This, in turn, adds about 0.01% and 0.02% to GDP and consumption growth, respectively. The effect of the shock on employment is rather small, limiting the growth of hours worked by about 0.007% in the first quarter. Nevertheless, after the first period, there seems to be some small movement in employment stimulated by probably added migrant workers to the market (Fig.2). 0 5 10 15 20 25 30 35 40 -2 0 2 rel. dev. f. steady-state 10-3 Production 0 5 10 15 20 25 30 35 40 -2 0 2 rel. dev. f. steady-state 10-3 Employment 0 5 10 15 20 25 30 35 40 -5 0 5 rel. dev. f. steady-state 10-3 Consumption 0 5 10 15 20 25 30 35 40 0 2 4 rel. dev. f. steady-state Migration Fig. 2 Migration shock 123 Int Econ Econ Policy (2025) 22:10 Page 17 of 28 10 0 10203040 -0.01 0 0.01 rel. dev. f. steady-state Production (growth) 010203040 -0.02 0 0.02 rel. dev. f. steady-state Employment (growth) 0 10203040 -0.01 0 0.01 rel. dev. f. steady-state Consumption (growth) Fig. 3 Productivity shock Clearly, a positive shock to technology increases the output and consumption growth in the first period. In response to a 1% shock, output growth goes up by 0.02% and growth rate of consumption by 0.04%. However, in line with Gali (1999), we observe that hours worked respond negatively to the positive technology shock in the first quarter by dropping by about 0.1%. This can be attributed to the price and wage rigidities in the market that lead to a lagged reaction of firms in upgrading the demanded labor services. As can be seen, the growth of hours worked recovers and picks up in the second period that, in turn, reinforces the growth of output. The impact of technology shock to the model fades after almost 20 periods (Fig.3). A positive shock to household time preferences encourages their current consumption and increases its growth by 0.1% in the first quarter that consequently boosts the output growth. The following higher demand and production require higher hours of work. As a result, in response to the shock, the growth rate of hours develops by 0.07%. The enhanced growth gradually slows down after the first period, but it takes about 15 periods to rebound (Fig. 4). In response to a 1% negative labor supply shock, the growth rate of hours worked per unit shortly drops by 0.2%. This translates to a cutback in consumption growth by about 0.08% and a decrease of roughly 0.2% in GDP growth in the first period. 0 10203040 -0.01 0 0.01 rel. dev. f. steady-state Production (growth) 010203040 -0.01 0 0.01 rel. dev. f. steady-state Employment (growth) 0 10203040 -0.02 0 0.02 rel. dev. f. steady-state Consumption (growth) Fig. 4 Preference shock 123 10 Page 18 of 28 Int Econ Econ Policy (2025) 22:10 0 10203040 -0.05 0 0.05 rel. dev. f. steady-state Production (growth) 010203040 -0.05 0 0.05 rel. dev. f. steady-state Employment (growth) 0 10203040 -0.01 0 0.01 rel. dev. f. steady-state Consumption (growth) Fig. 5 Labor supply shock Following the decrease in employment, the real wages are expected to rise that, in turn, encourage work and subsequently consumption. As a result, as it is evident, in line with employment and consumption, the output growth turns around in the 10th quarter and moves upwards. The volatility caused by the labor supply shock needs about 30 quarters to fade out (Fig.5). Finally, a 1% shock to fertility raises the number of live births by roughly 0.2%; however, as expected, this does not have any visible impact on the economy over the first 40 periods after the shock onset (Fig.6). 4.4.3 Historical decomposition The contribution of shocks to the historical path of the growth variables can be investigated through historical decomposition figures. As expected, the productivity shock, the preference shock, and the labor supply shock are the main determinants of the change in GDP growth, growth rates of consumption, and hours worked in Germany over the sample time horizon. Accordingly, as the dynamics of mortality is of the main interest in this paper, I focus here only on elements of population change and 010203040 -1 0 1 rel. dev. f. steady-state 10-4 Production (growth) 0 10203040 -1 0 1 rel. dev. f. steady-state 10-4 Employment (growth) 010203040 -2 0 2 rel. dev. f. steady-state 10-5 Consumption (growth) 0 10203040 0 0.02 0.04 rel. dev. f. steady-state Birth (growth) Fig. 6 Fertility shock 123 Int Econ Econ Policy (2025) 22:10 Page 19 of 28 10 analyze the capacity of a mortality shock, as well as fertility and migration shocks to influence the movement of target variables. Figures7,8, and 9display the historical decomposition of respectively GDP growth rate, consumption growth rate, and growth rate of employment in terms of hours worked. The deviation of the growth variables from their corresponding steady states is plotted in dappled bars. The parts related to the cumulative contribution of shocks to the deviations are filled in solid colors with red, green, and blue representing mortality shock, migration shock, and fertility shock, respectively. The overall impact of population underlying forces, however small, is obvious, with net migration having relatively the largest and birth event having the least contribution to growth. EU enlargements of 2004 and 2007 and the following labor mobility are clearly captured by the migration shock, indicating a positive contribution of subsequent migration flows to the German production and consumption growth. The positive effect of migration on the German labor market appears to lag. In general, as Fig.7suggests, the phases of downward output growth in Germany are correlated with a descending migration growth and contrariwise, displaying a pro-cyclical design of migration in Germany. Mortality in Germany however shows a different pattern. As Fig.7shows, during the sample period, the sequences of upward economic growth are associated with declining death growth while during the episodes of depressed economic growth fatality is seen to develop. Likewise, the negative contribution of the mortality shock to GDP growth during the early 2000s recession as well as the recent financial crisis is worth noting. The negative impact of mortality on GDP growth is especially prominent in the second quarter of 2002 and also in the first quarter of 2009. These evidences demonstrate that mortality in Germany is anti-cyclical. This is in contrast with Neumayer (2004)who finds a negative relationship between the state unemployment rate and aggregate mortality rate for Germany during the years 1980–2000 based on a fixed-effect estimation. Fig. 7 Historical decomposition of GDP growth 123 10 Page 20 of 28 Int Econ Econ Policy (2025) 22:10 Fig. 8 Historical decomposition of employment growth However, he does not capture a pro-cyclical behavior of mortality for males and for age group 45–65 within a dynamic model. Tracking the movement of employment over the sample period provides further details on the behavior also structure of mortality in Germany. As an interesting fact, it is seen that except for the periods involved with the recent economic and financial crisis, mortality moves pro-cyclically with respect to employment as the lower growth rate of deaths is shown to proportionately shrink the growth of hours worked (per person) and vice versa (Fig.8). Since mortality data also includes the population who is out of labor force, this trend, as one could infer, implicitly shows that fatality in Germany mostly involves the non-working population specifically the elderly. However, remarkably, a Fig. 9 Historical decomposition of consumption growth 123 Int Econ Econ Policy (2025) 22:10 Page 21 of 28 10 reverse pattern is observed during the Great Recession of 2008. It is seen that in this interval, higher growth of mortality is associated with lower hours worked per person starting in 2008:Q3 when mortality shock is shown to reduce the growth of hours worked. Similarly, following the steep fall in GDP specifically in the first quarter of 2009, we see that developing mortality among people at work mitigates the downward push to employment by a positive contribution to growth of hours worked. In the second quarter of 2009, when the German economy experiences a substantial recovery, the labor market is still slow-moving. At this time, the effect of the death shock on the labor force is relatively strong. It visibly narrows the unemployment and, in turn, absorbs part of the depreciatory impact of sluggish employment growth on GDP. It is plain to see that the mortality shock positively contributes to GDP growth in 2009:Q2. Lastly, the effect of the fertility shock is observed only at the end of the sample period. It is seen that this shock accommodates a minor part of GDP growth variations from the last quarter of 2014. Likewise, at the same time, this shock marginally contributes to the change in consumption growth. The fertility effect observed here can be mainly attributed to a relatively significant swing in the pattern of pregnancy behavior in Germany during 2002, which, in turn, has delivered a delayed impact on the economy. As the data suggests, there was a relatively strong fall in the number of live births in Germany in the first quarter of 2002 probably resulting from the economic recession involving Germany in the early 2000s. Nevertheless, succeeding the end of recession the country witnessed a large increase in the number of live births in the last quarter of 2002. 4.5 Model evaluation As the standard practice in the DSGE literature, to assess the fit of the estimated model to the actual data, I compute and compare some statistics generated by the model based on the estimated posterior mean with those of the sample. Motivated by the question of interest, the standard deviation of the growth variable of mortality, in addition to birth and migration growth, and their cross-correlations with contemporaneous output and hours growth are provided and displayed in Table 4. As is evident, the estimated model is quite effective in replicating the second moments of the actual demographic data in Germany. The volatility inferred by the estimation is almost identical to that of the data. Nevertheless, the model delivers smaller correlations, although with equal signs, with GDP and employment growth compared to what is observed in the data. Table 4 Second moments Variable stdev. corr. GDP growth corr. HOURS growth Data Model Data Model Data Model Death 0.037 0.037 −0.227 −0.072 −0.303 −0.067 Birth 0.015 0.018 0.008 0.005 0.086 0.007 Net migration 3.370 3.326 −0.412 −0.036 −0.060 −0.030 123 10 Page 22 of 28 Int Econ Econ Policy (2025) 22:10 5 Conclusion The impact of transitory macroeconomic shocks on individuals’ health status has been questioned by several research. This paper has addressed this issue by analyzing the dynamics of death over business cycle fluctuations in Germany through developing and estimating a non-linear DSGE model that counts for time asymmetries in the data. The results provide evidence of the anti-cyclicality of mortality in Germany, suggesting that health in Germany deteriorates during recessions whereas it improves over economic expansions. Moreover, it is found that the structure of mortality can vary with respect to economic cycles. While for most of the sample period non-working population seems to be more exposed to death, there appears to be a higher fatality of working people during the recent financial and economic crisis. In Germany, working population enjoys favorable insurance schemes and job security provisions that can mitigate the adverse effects of economic hardships; however, this might not be efficient enough under a severe economic downturn. Besides, some other factors outside the labor market can play a determinant role. Perhaps by a deep recession, the opportunity costs of developing unhealthy habits such as alcohol use and smoking among employed people decrease, that consequently impairs their health. In addition, the counter-cyclical death observed for non-working individuals who are supposedly mostly the elderly10 shows the vulnerability of older population to economic fluctuation in Germany, although this group has the least attachment to the labor market. Despite the health care insurance coverage for elderly population in Germany, the access of this group to some medical care services might be changing over business cycles. Overall, the findings of this study highlight the adverse health outcomes of severe economic downturns, underscoring the need for policies that safeguard the health and well-being of the population during economic crises. The recent COVID-19 pandemic was a severe combined health and economic crisis, where government policies could alleviate a part of the economic burden. Notably, during the pandemic, unemployment in Germany increased only moderately, thanks to support measures such as short-time work schemes. These measures likely mitigated the detrimental economic impact of the crisis and their associated effects on public health. However, by forcing an emergency public health response, the pandemic inevitably affected the distribution of public health services. In particular, the public health response prioritized short-term emergency treatment over potential longer-term physical and mental health impairments. Recent studies have highlighted some of the longer-term negative effects of the COVID-19 pandemic on mental health among the adult population (Patzina et al. 2024). Similarly, long COVID, defined as a post-COVID syndrome (Kozłowski et al. 2024), is shown to have had a negative impact on labor supply and labor productivity in the EU (Ramos et al. 2024). This evidence brings to light the need for more targeted interventions that address the longer-term health implications of a crisis and support the most vulnerable groups to these effects. 10 According to official German statistics, in average, more than 80% of yearly deaths in Germany is related to people aged over 65 (Statistisches Bundesamt (Destatis), 2017). 123 Int Econ Econ Policy (2025) 22:10 Page 23 of 28 10 Appendix 0.1 0.2 0.3 0.4 0.5 0 100 200 300 Stdev. Technology shock 0.1 0.2 0.3 0.4 0.5 0 10 20 30 Stdev. Preference shock 00.511.522.5 0 5 10 Stdev. Labor supply shock 0.1 0.2 0.3 0.4 0.5 0 50 100 Stdev. Mortality shock 0.1 0.2 0.3 0.4 0.5 0 100 200 Stdev. Fertility shock 12345 0 2 4 6 8Stdev. Migration shock 0.66 0.68 0.7 0.72 0.74 0.76 0 10 20 30 40 Habit persistence 0510 0 0.1 0.2 0.3 0.4 Labor disutility 1.4 1.6 1.8 2 2.2 2.4 0 1 2 3 4 Inv. Frisch elasticity 0.4 0.6 0.8 1 0 10 20 30 Coeff. Preference shock 0.4 0.6 0.8 1 0 5 10 15 Coeff. Labor supply shock -202468 10-3 0 200 400 Technology growth -0.02 0 0.02 0 50 100 Death growth -0.02 0 0.02 0 100 200 Birth growth -5 0 5 0 0.5 1 Migration growth 8.5 9 9.5 10-3 0 2000 4000 Birth rate 9.5 10 10.5 10-3 0 2000 4000 Death rate 012 10-3 0 1000 2000 Migration rate Fig. 10 Prior and posterior distributions 123 10 Page 24 of 28 Int Econ Econ Policy (2025) 22:10 246810 104 1 2 3 410-3 Stdev. Technology shock (Interval) 246810 104 0.5 1 1.5 210-6 Stdev. Technology shock (m2) 24681 0 104 0 2 410-9 Stdev. Technology shock (m3) 246810 104 0.03 0.04 0.05 0.06 Stdev. Preference shock (Interval) 246810 104 1 2 3 410-4 Stdev. Preference shock (m2) 24681 0 104 0 0.5 1 1.5 10-5 Stdev. Preference shock (m3) 246810 104 0.3 0.4 0.5 0.6 Stdev. Labor supply shock (Interval) 246810 104 0.02 0.03 0.04 0.05Stdev. Labor supply shock (m2) 24681 0 104 0.005 0.01 0.015 0.02Stdev. Labor supply shock (m3) 246810 104 7 8 9 10 10-3 Stdev. Mortality shock (Interval) 246810 104 0.8 1 1.2 1.4 10-5 Stdev. Mortality shock (m2) 24681 0 104 2 4 6 810-8 Stdev. Mortality shock (m3) 246810 104 3 3.5 4 4.5 10-3 Stdev. Fertility shock (Interval) 246810 104 1.5 2 2.5 310-6 Stdev. Fertility shock (m2) 24681 0 104 4 6 810-9 Stdev. Fertility shock (m3) 246810 104 0.5 0.6 0.7 0.8Stdev. Migration shock (Interval) 246810 104 0.04 0.06 0.08 0.1 Stdev. Migration shock (m2) 24681 0 104 0.02 0.04 0.06 Stdev. Migration shock (m3) Fig. 11 Markov chain Monte Carlo univariate convergence diagnostics 123