Page 58 - IJPS-11-1

International Journal of
Population Studies Macroeconomic factors and housing dynamics

• Wage equivalence and NIPA data between 1968 and 2018. The parameters
 K  c α νφ φ φν − − 1 are summarized in Table 1. One period in our model
−
1 φ
L
N
K
h
Z t c (1 α − )  t c  Z φ= h t (1 ν − )( ) ( ) ( ) p t h corresponds to 1 year of calendar time. The maximum age
h
t
t
t
 N t  an agent can live is 85 and the agent enters the economy
(XX) when he is 21, which implies the J = 65. The normal
retirement age for recent retirees is around 65 and thus, we
• Interest rate equivalence set Jr = 45. The survival probability π is calibrated to the
j
K 1 1 2021 Actuarial Life Table, and represents the average death
c

1

c
K
h
h
h
N
Z t c ZL p h t (XXI) probability for both males and females.
t
t
t
t
t
N t
The discount factor β is set to 0.97, which implies the
• Labor market clearance conditions long-term interest rate equal to 2.89%. The relative risk
l
c
N = N + N t h (XXII) aversion parameter σ is set to be 2, which is standard in the
macroeconomics literature. The weight of non-durable good
t
t
l
where N stands for the total labor force. In our model, consumption χ is calibrated by the steady-state equation:
t
l
the labor supply is inelastic, suggesting that N is the total c 1 r
t
number of the working-age population and can be ’ . The annual data we use is
r
jJr ij 1 h p h 1 p ( 1 )
h
h

t
l
P ) .
expressed as N ( it j from the BEA table between 1968 and 2018. The long-run
j1 i1 relative price is close to 1.2, implying that the x = 0.85.
• Housing market clearance conditions The housing market transaction cost τ is only paid
h
H t 1 H 1 h Y t h (XXIII) by the house seller, which commonly includes the agent

t
jJ ij commission, transfer taxes, and property taxes. The

t
where the aggregate housing stock H ( it j t j commission fee is around 6% paid to both the seller’s
P h ) .
j1 i1 and buyer’s agent. The taxes including transfers, property
taxes, attorney fees, and real estate fees are around 2–4%.
• Good market clearance conditions In total, the transaction cost falls between 8% and 10% in
c
Y C G I t (XXIV) the U.S. Since the government does not collect property
t
t
t
jJ ij tax which implies the transaction cost τ = 6%, the typical

h
t
where the aggregate consumption, C ( it j j t commission fee charged by the agency. The down payment
P c ) ,
j1 i1 ratio λ equals to 20%, implying the loan-to-value ratio
l
government spending, G = p L , and aggregate investment to be 80%. If a household’s down payment is lower than
t
t
h
I I I . 20%, the mortgage interest rate will be higher, and private
c
t
t
t
• Capital evolutional path mortgage insurance is required.
The depreciation rate of capital is calibrated to match
K = I +(1-δ) K (XXV)
t+1 t t the depreciation-capital ratio. The fixed assets data and
where K is the sum of two types of capital and is depreciation can be found on the BEA Real Depreciation
t
c
h
calculated as K K K . table. Private non-residential fixed assets contain two
t
t
t
• Savings types of capital: equipment and structures. They depreciate
at two different rates; the average depreciation rate of
K = S (XXVI) equipment and structures is 0.13 and 0.03, respectively.
t+1 t+1
The aggregate net savings equals the aggregate capital This paper takes the average and sets δ to 0.081. The house
stock. depreciation rate is calibrated through the depreciation-
residential investment ratio. The δ is set equal to 0.023,
h
A numerical method is applied to solve the stationary which is the average annual rate between 1999 and 2018.
equilibrium. In our model, we have three state variables,
and household problems can be solved by a specific The current payroll tax rate in the U.S. is set to 15.3%
dimension matrix. The detailed solution procedure is based on the Internal Revenue Service, which includes
presented in the Appendix. 6.2% from the employer, 6.2% from the employee, and
2.9% from Medicare. We mainly focus on social security
2.7. Model calibration which is τ= 12.4%.
In this section, we present our calibration procedure. The The paper calibrates the capital share α in the non-
model is calibrated based on the U.S. BEA, BLS, FHFA, durable goods production function, which takes the form
Volume 11 Issue 1 (2025) 52 https://doi.org/10.36922/ijps.3645