EDUCATIONAL OUTCOMES IN OECD COUNTRIES
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5.1.4. Parameter values
Implementing the projection model requires a number of parameter assumptions.
Three parameter choices have already been indicated: the duration of the education
reform of 20 years, the length of a working life of 40 years, and the overall time horizon
of 80 years. In addition, the model requires assumptions about the growth coefficient,
the rate of potential growth without the education reform, and the discount rate. Here,
we outline the parameter choices for the baseline scenario. Below, we will also provide
robustness analyses of results to alternative parameter choices.
The simulation does not adopt any specific reform package but instead focuses just on
the ultimate change in achievement. For the purposes here, reforms are assumed to take
20 years to complete, and the path of increased achievement during the reform period is
taken as linear. For example, an average improvement of 25 points on PISA is assumed
to reflect a gain in the student population of 1.25 points per year. This might be realistic,
for example, when the reform relies upon a process of upgrading the skills of teachers -
either by training for existing teachers or by changing the workforce through
replacement of existing teachers. This linear path dictates the quality of new cohorts of
workers at each point in time.
The expected work life is assumed to be 40 years, which implies that each new cohort
of workers is 2.5 percent of the workforce. Thus, even after an educational reform is
fully implemented, it takes 40 years until the full labor force is at the new skill level. We
are not aware of direct estimates of this parameter in the literature. However, estimates
for Germany based on pension insurance data suggest values in the range of 35 to 40
years for the length of the average working life (see Woessmann and Piopiunik (2009)
for details).
The length of the time period over which gains are calculated is somewhat arbitrary
and depends in part on the use of the analysis for any policy decisions. The benchmark
here considers all economic returns that arise during the lifetime of a child that is born at
the beginning of the reform in 2010. According to the most recent data (that refer to
2006), a simple average of male and female life expectancy at birth over all OECD
countries is 79 years (Organisation for Economic Co-operation and Development
(2009c)).16 Therefore, the baseline calculations take a time horizon until 2090,
considering all future returns that accrue until then, but neglecting any returns that
accrue after 2090.
In order to consider the impacts of improvement on OECD countries, the simulations
rely on the estimates of growth relationships derived from the 24 OECD countries with
complete data. As indicated in column (2) of Table 2, the coefficient estimate is 1.864,
suggesting that, e.g., a 50 point higher average PISA score (i.e., one-half standard
deviation higher) would be associated with 0.93 percent higher annual growth in the long
run. This estimate clearly includes some uncertainty, a factor that is also included in the
robustness analyses below. (Below we also consider a neoclassical alternative where the
16 Note that these life expectancy numbers are based on age-specific mortality rates prevalent in 2006, and as such do not
include the effect of any future decline in age-specific mortality rates. Life expectancy at birth has increased by an average of
more than 10 years since 1960.