Economic consequences of changing fertility. Insights from an OLG model

1. OLG analysis of fertility shocks Economic consequences of changing fertility. Insights from an OLG model Magdalena Malec 1 2 Krzysztof Makarski 123 Pawel Strzelecki 123 with help from Oliwia Komada 1 Warsaw School of Economics 2 GRAPE 3 Economic Institute, National Bank of Poland EPC 2016. Presentation: 02.09.2016 1 / 19

2. OLG analysis of fertility shocks Motivation Economic response to succesfull family policy Projections beyond accounting - economic reactions of agents How to measure changes in fertility: Number of children and labour force participation Contributions: 1 scal and welfare analyses of pension systems using Overlapping Generations Model (OLG) under dierent fertility scenarios 2 the nal version of the model will also include changes in parity progression rates Today: the use of OLG model to asess the economic gains from higher fertility with example 2 / 19

7. OLG analysis of fertility shocks Motivation Questions How does demographics aect macroeconomic and scal stability? with lower fertility ⇒ less labor supply ⇒ worse economic dependency ratio but expecting lower fertility rational agents make provisions what if demography surprises and what if not? 3 / 19

11. OLG analysis of fertility shocks Motivation What do we do? We develop an OLG model and use it to measure the eects of fertility on the economy Things we really care for: private and public savings (inter-temporal choice) labor supply decision (intra-temporal choice) pension system is scally neutral (dened contribution) calibrating the model closely to the data exogenous but varying economic growth (technological progress) exogenous but varying fertility Things we simplify: production sector (competitive producers with C-D production function and depreciation) labor market (elastic labor) no heterogeneity within cohorts stable mortality (focus on fertility, isolate) 4 / 19

24. OLG analysis of fertility shocks Model Roadmap 1 Motivation 2 Model 3 Calibration 4 Results 5 Summary 5 / 19

25. OLG analysis of fertility shocks Model What we expect before modeling? with fertility below replacement population shrinks but per capita economy is constant (driven by deep parameters) shocks in fertility will necessitate adjustment ↑ savings (to match the same K/L) ↑ output (as a consequence of ↑ K) ↓ taxes ceteris paribus HENCE transitory lasting eects (↑ population, ↑ capital, ↑ output) transitory welfare eects a tool to test can we aord a given fertility policy a way to show, who pays and who gains 6 / 19

31. OLG analysis of fertility shocks Model Consumers are paid a market clearing wage for labor supplied receive market clearing interest on private savings are free to choose how much to work, retire at ¯J die with certitude at J, but have a non-zero probability of dying before Optimize lifetime utility derived from leisure and consumption Uj(cj,t, lj,t) = uj(cj,t, lj,t) + J−j s=1 δs πj+s,t+s πj,t u (cj+s,t+s, lj+s,t+s) (1) subject to (1 + τc,t)cj,t + sj,t + τj + υt = (1 − τι j,t − τl,t)wj,tlj,t ← labor income + (1 + rt(1 − τk,t))sj,t−1 ← capital income + (1 − τl,t)pι,j,t + bj,t ← pensions + bequests where u(c, l) = φ log(c) + (1 − φ) log(1 − l) 7 / 19

32. OLG analysis of fertility shocks Model Producers maximize Yt − wtLt − (rk t + d)Kt subject to Yt = Kα t (ztLt)1−α where the path of {z}∞ t=0 is exogenous (calibrated to AWG, by EC) Interest rate interest rate on capital rk t = MPK − d, endogenous 8 / 19

33. OLG analysis of fertility shocks Model Producers maximize Yt − wtLt − (rk t + d)Kt subject to Yt = Kα t (ztLt)1−α where the path of {z}∞ t=0 is exogenous (calibrated to AWG, by EC) Interest rate interest rate on capital rk t = MPK − d, endogenous 8 / 19

34. OLG analysis of fertility shocks Model Public nances Social Security Institution (ZUS) collects social security contributions and pays out pensions by construction of NDC, system scally balanced (full actuary fairness) Government collects taxes on earnings, interest and consumption + υ spends xed amount of GDP on consumption + services debt long run debt/GDP ratio xed Role of + υ if fertility did not change, υ would measure per capita tax/subsidy once fertility changes, we may measure deviations from υ express as % of initial GDP = gains from higher fertility 9 / 19

37. OLG analysis of fertility shocks Model What are the fertility shocks? 1 We start from decreasing population (fertility below replacement) ⇐ matched to data 2 For some xed period of time, we allow fertility change sudden, unexpected increase in the entry size by 10% for 10 years sudden, unexpected increase in the entry cohort size by 20% for 10 years additionally: sudden, unexpected decrease in entry cohort size by 10% for 10 years 3 Compute ˜υ relative to before change υ (expressed as % of GDP or in raw terms) What is baseline? Constant mortality Gradually decaying technological progress (fully expected) 10 / 19

41. OLG analysis of fertility shocks Calibration Roadmap 1 Motivation 2 Model 3 Calibration 4 Results 5 Summary 11 / 19

42. OLG analysis of fertility shocks Calibration Calibration to replicate 2010 economy Preference for leisure (φ) matches participation rate of 56.8% Contribution rate (ρ) matches benets/GDP ratio of 6% Labor income tax (τl) set to 11% to match PIT/GDP ratio Consumption tax (τc) set to match VAT/GDP ratio Capital tax (τk) de iure = de facto 12 / 19

43. OLG analysis of fertility shocks Calibration Labor augmenting technological progress Historical data, projection from AWG, new steady state at 1.7% 13 / 19

44. OLG analysis of fertility shocks Calibration Baseline fertility and other scenarios 14 / 19

45. OLG analysis of fertility shocks Results Roadmap 1 Motivation 2 Model 3 Calibration 4 Results 5 Summary 15 / 19

46. OLG analysis of fertility shocks Results What are the gains from higher fertility? Due to decreasing population, per capita taxes in general grow (= how much consumption people have to give up) (relative to initial steady state of app. 4.6% of GDP) 16 / 19

47. OLG analysis of fertility shocks Results What are the gains from higher fertility? If population is shrinking less, taxes grow by less 17 / 19

48. OLG analysis of fertility shocks Summary Roadmap 1 Motivation 2 Model 3 Calibration 4 Results 5 Summary 18 / 19

49. OLG analysis of fertility shocks Summary A proof of concept? We want to use macro models to evaluate eects of dierenet demographic scenarios Demographics drives majority of the macroeconomic changes in the foreseeable future Fiscal eects will be large and unavoidable but larger TFR can mitigate them Strong (political) discussions about ways to prevent demographic catastrophe... ...but what is the adequate cost of family policy - even if successful? Figures we obtain go beyond the simple calculations in Excel (forward looking agents) To do Full model with fertility choice Analyze alternative paths of fertility changes (more multiple vs less childless families) Provide welfare measures (caveat: welfare of the otherwise born and otherwise not-born) 19 / 19

Economic consequences of changing fertility. Insights from an OLG model

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Economic consequences of changing fertility. Insights from an OLG model