Page 55 - IJPS-11-1

International Journal of
Population Studies Macroeconomic factors and housing dynamics

fertility choice and the social security scheme and found stage life: the working stage and retirement stage. During
that the social security tax imposes a negative effect on the the retirement stage, retirees receive periodic pension
fertility rate and intensifies population aging. payments, which are equally distributed by the government.
This paper contributes to the existing literature in two We denote π as the probability of surviving onto age
j
aspects: first, our paper mainly focuses on the responses of j+1 conditional on any age j where j ∈ [0, J] and π ∈ (0, 1)
j
housing price and social security to the macroeconomic and π = 1 and π = 0 We denote cohort born at time t with
J
.
0
1
variables through incorporating an endogenous frictional age 1 as P and among these newborns, the number of
t
housing market into a two-sector lifecycle general = is π P + . The total population
1
+ s
equilibrium model. This model allows us to analyze the survivals through age s is∏ i = 1 i ts
fluctuations of the housing market and social security at any time t is denoted as N, and it can be calculated as the
t
benefits in a unified framework. Second, unlike previous sum of jJ all ij living individuals of all ages,
t

P ) . Since the survival possibilities are
(
j
studies (e.g., Floetotto et al., 2016), which mainly focus N j i1 i t
1
on macroeconomic factors such as credit constraint, fixed over time and the population grows at n, we can get
2
1
government intervention, and capital flow, our study delves the newborns at time t, which is P 1 n P t 2 , where P
t
t
into the fluctuations in housing prices under demographic is the cohort of age 2 at time t who were born at t−1. Now
changes, technology growth, and retirement policy let us denote µ as the fraction of individuals of age j in the
j
t
reforms. In line with the work of Kaplan et al. (2020), this whole population. Then, the fraction of newborns at time t
study investigates the fluctuations in equilibrium housing P 1 P 1
1
1
prices across various economic stages. is N t 1 jJ t ij j Due to P 1 n P t 2
t
t
t

it
The rest of this paper is organized as follows. In t P j 2 ( i 1 P )

section 2, we build up our benchmark model and the proportion of the age 2 group is 1 n 1 ,
1
2
t
1
t
calibrate the model. Section 3 presents our findings and and the fraction of individuals for age j = 2, 3,…, J can be
simulation results. Section 4 is the discussion and section computed recursively by j1 1 n 1 .
j
5 is the conclusion. The Appendix contains the details of t j t
equilibrium equations and the algorithm of our numerical 2.2. Household’s preference
solution methods.
Households enter into the economy with no financial assets
2. Life-cycle model and no real estate assets. Each household is endowed with
one unit of time in each period. Since leisure is not valued,
We constructed a life-cycle model to study the effects of the labor supply is inelastic. Households have no bequests
demographic changes and technology growth on house in our model and thus have no incentives to leave any
prices and social security. In this discrete-time general assets. Both financial and real estate assets of accidentally
equilibrium model, households enter and leave the dead individuals are collected by the government and
economy with zero net financial and housing assets. Each equally distributed to all living individuals in the next
period, households are endowed with 1 unit of labor time period in the form of government transfers.
and employed in non-durable or durable goods sectors.
Following the assumption of Favilukis et al. (2017), Households allocate their income between both non-
households can move freely between two sectors, and this durable goods and housing service flows to maximize their
lifetime utility:
free labor flow makes the equilibrium wage paid equally
across two sectors. Households allocate their financial and J j j )
β
( ,h
labor income among consumption and housing services ∑∏ π i uc j j (I)
to maximize their lifetime value function. Households j= 1 i= 1
can use their houses as collateral to borrow against when where β is the utility discount factor. Non-durable and
purchasing new houses. The frictional housing market housing consumption are denoted by c and h, respectively.
creates extra costs when a household sells its old house and The utility function is assumed to be a monotonic increase
moves to a new one. in both variables and concave. In particular, the period
utility function follows Favilukis et al. (2017) and can be
2.1. Demographics expressed as:
The demographic structure is assumed to be stationary
(Chen, 2010), and the population grows at a constant rate ch 1 χ − ) 1 σ− − 1
χ
n. Each individual has a maximum lifespan of J periods uc t t ) ( t t (II)
( ,h =
and retires at age Jr. Therefore, the household lives a two- 1 σ−
Volume 11 Issue 1 (2025) 49 https://doi.org/10.36922/ijps.3645