Transcript Random-coefficient Models

Random-coefficient Models
1. Markov-switching model (MRS)
2. Threshold model
3. Quantile Regression model (QR)
Constant-coefficient regression
• Constant-coefficient regression models have
been applied extensively in statistics
• Various random-coefficient models have also
emerged as viable competitors in particular
fields of application
– Quantile regression
– Threshold model
– Markov switching model
• The conventional regression model
– Cross-sectional data
– Time-series data
Constant-coefficient regression
yi  x    ui
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i
yt  x    ut
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t
Constant-coefficient regression
• We assume the sensitivities (i.e. β) of y to
the x variables are identical for all
observations
• the beta is uniform from i=1…,N
• the beta is uniform from t=1…,T
• The beta= the first derivative of y with
respect to x
Threshold Models
• The state is observable
• The state is identified by if a threshold
variable exceed a critical value
• The keys
– how to define the threshold variable?
– how to estimate the threshold parameter?
• Applications
– cross-sectional data
– time-series data
Markov-switching Models
• The state is unobservable
• Estimate the probability of a specific state
at each time point
• Transition probability system
– How to decide the probability?
• Applications
– Time-series data
Quantile regression (QR) model
• The effect of x on y could change by the quantile
level of y
• What is the quantile?
– the quantile is a statistical term describing a division
of observations into certain defined intervals based
upon the values of the data
– The magnitude of the y variable in term of probability
• Applications
– Cross-sectional data
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