MATH 4350/MSDS 5350/MBA 5393
Final Project
How risky is it to open a restaurant?
To answer this question, read the article “Nine out of 10 fail? Check, please” (posted on Blackboard). Ideally, we would be able to recreated what was done in the article but cannot do so due to the lack of access to data. Instead, we will use restaurant inspection data as proxy data for how long restaurants stay in business. This data is posted on Blackboard, and can also be found at the following website: https:
data.cityofchicago.org/Health-Human-Services/Food-Inspections/4ijn-s7e5
With this data you will need to create a time and censoring variable, and each restaurant should only be included once. For the time variable, the difference between when a license is issued and when it is out of business or date of its last inspection can serve as a time variable. You will need to decide how you want to count the time (months or years). For a censoring variable, you will need to look at the last inspection date (if it is not listed as out of business) and decide if that is an indication if the restaurant is still open or not (e.g., if an inspection has not been conducted in four years does that mean the restaurant is closed or hasn’t been inspected)
On Blackboard there is a script file to get you started with the data set. The script file gives an example of way to create a time variable, but you will need to create the censoring variable. Make sure to look at the facility type – we only want to use restaurants for this project.
Once you have the data set up, conduct a basic survival analysis for restaurant survival in Chicago.
The final project is due on Sunday, December 12. You will need to submit a write-up of your analysis and the code used.
Nine out of 10 restaurants fail? Check, please
Remember that fabulous restaurant you “discovered” when it opened three months ago? It’s dark now;
closed for ever. Another great new place is gone! Was
it bad luck – or was failure par for the course? It’s most
likely the latter, right? It happens all the time, or so
you’ve heard. Don’t 9 out of 10 restaurants fail in their
first year?
They do not. Entrepreneurs, lenders, and the
media consider restaurants to be particularly risky
start-ups. But there has been a steady 2% per year
growth in the number of restaurants in the US over the
past decade. On average, US households spend 5–6%
of their income eating out, which equates to over $50
per week. And a number of studies in the last 15 years
find restaurants to have far lower failure rates than
eceived wisdom would suggest.1
We are fortunate to have detailed data to measure
just how risky restaurants are: 20 years of microdata
from the US Bureau of Labor Statistics Quarterly
Census of Employment and Wages (QCEW) in the
western US. These longitudinal data are tantamount
to a census of businesses, allowing us to estimate
failure rates with low bias and no sampling e
or.
In contrast, typical studies of business survival are
sample-based and tend to be local or to have relatively
small sample sizes, making even regional extrapolation
uncertain. Longitudinal studies of business mortality
are typically cohort-based, which controls for some
sources of confounding, but limits sample sizes and
exace
ates other sources of confounding, including
macroeconomic events.
For this analysis, we compare single-
establishment independently owned full-service
estaurants to all other single-establishment service-
providing businesses in the western US. We exclude
multi-establishment and “chain” restaurants because
Figure 1. Quarterly birth and death rates of (a) service-providing businesses and (b) restaurants
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Quarterly Birth and Death Rates of All
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NBER Recession
All services: Birth rate
All services: Death Rate
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Quarterly Birth and Death Rates of
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Restaurants: Birth Rate
Restaurants: Death Rate
(a) (b)
Nine out of 10 restaurants
fail? Check, please
Tian Luo and Philip B. Stark use Bureau of Labor Statistics
data to put paid to a persistent myth about the riskiness of the
estaurant business
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25april2015
usiness
their operational structure, management and
capitalisation are so different. For details
of data and methodology, see the box on
page 29.
Let us start by looking at birth and death
ates over time for all service businesses, and
for restaurants specifically. Figure 1 (page
25) shows that but for seasonality, there is
no discernible pattern to either measure
etween 1992 and 2011, so the QCEW
Figure 2 shows that business failure
ates generally decrease as the number of
employees at birth increases. Compared
to businesses that started with 5 or fewer
employees (small), start-ups with 6–20
employees (medium) had an annual failure
ate 1.6% lower, while those with 21 or more
staff (large) had a failure rate 2.8% lower.
Seventy-nine per cent of small start-ups
failed by age 15, compared to 73% of medium
data include roughly equal numbers of
usinesses born in each year. (The spikes in
irth rates in 1997 and 1998 are apparently
caused by administrative changes that
affected unemployment insurance reporting
equirements.) However, it is important to note
that different birth cohorts affect different parts
of the cumulative failure function: businesses
orn late in the window do not contribute to
the estimate of the failure function in old age.
Figure 2. Failure rates of service-providing businesses born after the first quarter 1992, grouped by number of employees at birth: (a) cumulative failure rate; (b)
conditional annual failure rate, which is the rate of failure in a given year, given that the establishment was alive at the beginning of that yea
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Age (years)
Conditional annual failure rate, by startup
size
5 or fewe
6 to 20
21 or more
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Age (years)
Cumulative failure rate, by startup size
5 or fewe
6 to 20
21 or more
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26 april2015
start-ups and 67% of large start-ups. Larger
start-ups may need more initial capital, but
tend to survive longer.
One may view the failure curves
in Figure 2 as simply a summary of the
observations, or as an estimate of an
underlying theoretical population failure
curve from which the businesses in the
census are assumed to be a sample. We
prefer the former view since the data are
in fact a census. In the latter view, one
assumes that the survival times of different
establishments (of the same type) are
andom, independent and identically
distributed. This implies, in particular, that
the survival time of an establishment cannot
depend on when the establishment was
orn. To check whether this assumption
is consistent with the data, we examine
whether date of birth is related to longevity.
Figure 3 shows only negligible differences
among failure rates of establishments born
in different phases of economic cycles.
Figure 3. Cumulative failure rates of service-providing businesses by birth yea
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80%
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Age (years)
Cumulative Failure Rate
1992 Q2 to 2000 Q4 Expansion (871,423 establishments)
2001 Q1 to 2001 Q4 Recession (108,159 establishments)
2002 Q1 to 2007 Q3 Expansion (635,578 establishments)
2007 Q4 to 2009 Q2: Recession (158,688 establishments)
All years 1992 Q1 to 2011 Q4 (1,928,333 establishments)
Entrepreneurs, lenders, and the
media consider restaurants to
e risky start-ups. But there
has been a steady growth in
the number of restaurants in
the US over the past decade
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27april2015
How do restaurants fare?
From the QCEW data, we can see that about
17% of restaurants in the western US failed
in the first year – lower than the average first-
year failure rate of 19% for all other service-
providing businesses. Not only is the first-year
failure rate far lower than the commonly cited
90% figure, the 15-year cumulative failure rate
is less than 80%. Restaurants have median
lifetimes of roughly 4.5 years, compared
to 4.25 years for other service-providing
usinesses. Figure 4 shows the failure rate and
conditional quarterly failure rate of restaurants
and service-providing businesses. Restaurants
have slightly lower failure rates than other
service start-ups, but that difference is highly
statistically significant.
The quarterly conditional failure rates
(rate of failure in a given quarter, given that
the establishment was alive at the beginning
of that quarter) are fairly low but rising
in the first year. They peak at the start of
the second year, but decrease in a convex
fashion thereafter. Previous studies have also
found that conditional failure rates generally
decrease with age. The ‘liability of adolescence’
suggests that the first-year failure rate for a
firm is lower because businesses generally can
survive for a year on initial resources.4
Table 1 compares failure rates of
estaurants and other businesses for various
start-up sizes and birth epochs. In each size
group, the difference in failure rates between
estaurants and other service establishments
is about the same. In every birth period,
estaurants as a group have slightly longer
median lifetimes than other service
usinesses, but risk does depend on size at
irth. The median lifespan of restaurants that
started with 20 or fewer employees is about 3
months shorter than other businesses of the
same start-up size, but restaurants with 21 or
more employees had median lifespan about 9
months longer than other businesses with the
same start-up size.
Of over 500 different types of single-
establishment service start-ups (by 6-digit
Figure 5. (a)