Chapter 4.
Measurement of Unemployment in States and Local Areas
Estimation Methodology
Estimates for States
Monthly labor force data for all States, the District of Columbia, the Los Angeles-Long
Beach metropolitan area, New York City, and the balances of California and New York are
based on the time series approach to sample survey data (Scott and Smith, 1974; Bell and
Hillmer, 1990). The purpose of this approach is to reduce the high variability in monthly
CPS estimates for these geographic areas due to small sample sizes. The actual monthly CPS
sample estimates are represented in signal plus noise form as the sum of a stochastic true
labor force series (signal) and error (noise) generated by sampling only a portion of the
total population.
where:
= CPS estimate
= true labor force value
= sampling error
The signal is represented by a time series model that incorporates historical
relationships in the monthly CPS estimates along with auxiliary data from the Unemployment
Insurance and Current Employment Statistics (CES) programs. This time series model is
combined with a noise model that reflects key characteristics of the sampling error (SE)
to produce estimates of the true labor force values. This estimator is optimal under the
model assumptions and has been shown to be design-consistent under general conditions by
Bell and Hillmer (1990).
Two modelsone for the employment-to-population ratio and one for the unemployment
rateare developed for each State using over 15 years of data. The signals for both
models are based on a core model of the following form:
where Xt is a single
explanatory variable with coefficient and Tt, St, and It are the trend, seasonal and irregular components. The
variable used in the employment model is the statewide monthly estimate of workers on
payrolls in non-farm industries from the CES program divided by the intercensal estimate
of the State's population of working age. The unemployment model uses the ratio of the
number of State workers claiming unemployment insurance benefits to the payroll employment
estimate. The regression coefficient is allowed to change over time to adapt to changing
relationships between the CPS and the explanatory variable. The trend and seasonal
components change smoothly over time to control for systematic variation in the CPS not
accounted for by the explanatory variable. The irregular component accounts for transitory
residual variation not captured by other components of the model.
The degree to which the regression coefficient and the time series components vary over
time is determined empirically for each State. Occasionally, the trend is a constant,
acting as a fixed intercept. In some cases, the seasonal component is estimated to have a
fixed pattern from year-to-year. For most models, the irregular component is zero.
Occasionally, there are sudden changes, either temporary or permanent, in the CPS that
are not predictable from past history. These effects, manifested as aberrant observations
or outliers, are handled by intervention analysis techniques which introduce dummy
variables into the model components. Shifts in level are incorporated into the trend
component and transitory changes into the irregular component.
The second major component of the signal plus noise model deals with CPS standard
errors. Because of this survey's complex design, the behavior of the observed sample
estimates differ in important ways from the true values. Sampled households are rotated in
and out of the CPS over a period of 16 months, such that 75 percent of the sample from
month-to-month consists of the same households and 50 percent from year-to-year. (See chapter 1.) Also, redesigns and major fluctuations in the size of
the labor force cause major changes in the variance of the standard errors. These two
features of the CPS, an overlapping sample design and changes in reliability, induce
strong positive autocorrelation and heteroscedasticity in the standard error. These
characteristics can seriously contaminate estimates of the true labor force if the
standard error is ignored in the estimation process. For this reason, it is important to
specify a model of the standard error process and combine it with the model of the signal
to estimate the unobserved components of the CPS. The standard error model is specified as
follows:
with
reflecting the autocovariance structure, assumed to follow an ARMA process and representing a changing variance
over time. The parameters of the ARMA model are derived from standard error
autocorrelations developed independently of the time series model from design based
information. The standard error variances (equivalent to the square of the standard error
described in chapter 1) are estimated using the method of
generalized variance functions (Zimmerman and Robison, 1996).
The unknown hyperparameters of the signal are estimated by maximum likelihood using the
Kalman filter algorithm. Given these estimated hyperparameters, the Kalman filter is used
to decompose the observed CPS into its signal and noise components. This algorithm
efficiently updates the model estimates as new data become available each month. For the
latest month, the Kalman filter calculates estimates based on all available data, but does
not revise estimates for the previous months with the latest data. Previous estimates are
updated by a Kalman filter "smoother" which revises an estimate at time t using
all available data before and following time t. Smoothing is performed at the end of each
year.
Benchmarking. This process is a general statistical procedure used to adjust
estimates to a control total. Each year, historical model estimates are benchmarked to the
annual average CPS State estimates of employment and unemployment. The goal of
benchmarking is twofold: (1) To insure that the annual average of the final benchmarked
series equals the CPS annual average, and (2) to preserve the pattern of the model series
as much as possible. In practice, these two goals are conflicting, and some changes to the
pattern of the time series are made to meet the first goal. The Denton benchmarking method
has been used since the introduction of model-based estimates in 1989. It avoids
discontinuities between December and January estimates and, through a constrained
quadratic minimization approach, minimizes the distortion to the original time-series
estimates. The benchmarked series are seasonally adjusted with X-11 ARIMA.
Next: Estimates for
Sub-State AreasThe Handbook Method
|