The California
county data set and the MSA data set are both derived from the REIS and contain
the same variables. The same exercises that are appropriate for the MSA data
set are also appropriate here, and vice versa. A number of exercises are repeated,
including the more difficult set of problems, exercises 6-8. These exercises
concentrate on a question that has occupied economists for some time: are income
levels in different regions (or countries) converging or diverging?
1. Correlation
It is often argued
that increased manufacturing employment is the path to higher incomes. Cities
compete to attract manufacturing, local economic development groups try to
develop strategies for raising the manufacturing share of their regional economies,
and politicians and others talk about the harm done to our standard of living
when manufacturing jobs disappear. Do cities with higher levels of manufacturing
employment have higher incomes?
(a) Compute per
capita personal income: tpi90pc = tpi90/pop90.
(b) Compute
manufacturing employment share of total employment: mane90s = mane90/e90.
(c) Correlate
tpi90pc and mane90s.
2. Calculating
confidence intervals for means
In the average
city, how much of total employment is engaged in manufacturing? In services?
(a) Compute manufacturing
and services shares of total employment:
mane90s = mane90/e90
(as before)
se90s = se90/e90
(b) Run Statistics,
Compare Means, One Sample t test.
3. Comparing
means, paired samples.
Did federal employment
grow faster, on average, than state and local government employment? On average,
state and local employment in MSAs grew, 1970 to 1990, over 100%. During the
same period, federal employment grew over 107%. Can we conclude that the average
growth of federal civilian employment was greater than the average for state
and local?
4. Simple Regression
The primary determinant
of the total income of an MSA is population. More people means more people
working and more income. Simple regressions lets us see the power of population
as an explanatory variable for the amount of income created in a MSA.
(a) Run Statistics,
Regression. Use TPI90 as the dependent variable, POP90 as the dependent.
5. Multiple Regression
Exercise 5 is
neither difficult nor surprising. A more interesting question concerns the
determinants of per capita income. Lets return to the topic in exercise 1:
Does manufacturing or services contribute more to per capita income? Many
people fear that we are becoming a nation of hamburger flippers, and that
the growth of services is intimately tied to a stagnation in income growth.
(a) Run Statistics,
Regression. Use the per capita income variable (tpi90pc) from exercise 1 as
the dependent variable, and manufacturing and services share of total employment
(mane90s, se90s, from exercise 2) as the dependent variables.
6. through
8.: Economic convergence
The idea of convergence
is supported if incomes are approaching the same level, and divergence is
supported if this is not happening. In order for convergence to occur, counties
with lower incomes at the start of the period must grow faster in percentage
terms than counties with higher incomes. We will look at this issue.
6. Calculating
the average annual growth rate of per capita income.
First, we need
to put everything on a per capita basis in order to eliminate the effects
of size.
(a) Compute tpi90pc
= tpi90/pop90, and tpi70pc = tpi70/pop70.
Next, we need a
good estimate of the mean rate of growth of per capita incomes. We could compute
the simple percentage change:
[(tpi90pc-tpi70pc)/tpi70pc]*100.
Unfortunately, this
give the percentage change over the whole period, 1970 to 1990. Strictly speaking,
we cannot divide this by 20 to get the annual average because economic growth,
like money in the bank, has a compounding component. Growth today gets added
to the base on which growth tomorrow takes place, just like interest today is
added to your principal on which interest will be paid in future periods.
Since economic
growth is mathematically similar to compound interest, we can borrow the formula
for compounding interest and use it to calculate the growth rate. In 20 years,
a deposit today of $100 which compounds at the rate "g" will be worth:
Future value =
$100(1+g)20.
In our analogy,
the future value is tpi90pc, and we don’t know the rate of growth, g:
Solving this for
"g" the growth rate, gives
g = [exp((ln(tpi90pc)-ln(tpi70pc))/20]
- 1,
which looks much
worse than it really is. In SPSS, the Compute command can handle this easily.
(b) Compute GROW
= [exp((ln(tpi90pc)-ln(tpi70pc))/20] - 1,
7. Descriptive
Statistics
It is useful
to look at the new variable GROW in order to get a sense of its magnitude
and distribution.
(a) Run Statistics,
Summarize, Frequencies. Turn off the frequency table, but under Charts, turn
on Histogram and Normal Curve. Hit Continue. Click the Statistics button in
the Frequencies window, and check all the Measures of Dispersion, as well
as Mean and Median.
8. Simple Regression
Now we are ready
to check for convergence. To reiterate, if convergence occurred between 1970
and 1990, then the counties with lower levels of per capita income in 1970
(tpi70pc) should have higher growth rates in their per capita incomes. This
is a testable hypothesis with the variables we now have.
(a) Run Statistics,
Regression. Use GROW as the dependent variable, tpi70pc as the independent.
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