**Sample Exercises for Data Set **msassp.por

James Gerber, San Diego State University

*© The Author, 1998; Last Modified 16 August 1998*

The MSA (Metropolitain Statistical Area) data set (msassp.por) and the California county data set (cntysp.por) are both derived from the REIS and contain the same variables. The same exercises that are appropriate for the California county data set are also appropriate here, and vice versa. A number of exercises are repeated, including the more difficult set of problems, exercises 7-9. These exercises concentrate on a question that has occupied economists for some time: are income levels in different regions 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?

**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?

- (a) Compute the percentage change in federal civilian and state and local government employment:
- fceg = (fce90-fce70)/fce70

saleg = (sale90-sale70)/sale70.

(b) Run Statistics, Compare Means, Paired Samples.

**4. Comparing means, independent samples**
Some MSAs lost population between 1970 and 1990, while others gained population. Was there a significant difference in the structure of the economies of these two types of MSAs?

- (a) Compute the growth rate of population. Mathematically, this can be done several ways, from a simple percentage change to a compound rate of average annual growth. Call the variable "popg."
(b) Use Compute to create a grouping variable based on the growth rate of population. Call the new grouping variable "popup. " Have it equal 1 if population growth is greater than or equal to 0, and equal 0 if population growth is less than 0.

(c) Calculate the percentage change in the employment variable(s) of interest.

(b) Run Statistics, Compare Means, Independent Samples, for each of the employment growth variables created in step (c). Use "popup" as the grouping variable.

**5. 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.

**6. 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.

**7. through 9.: 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.

**7. 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 gives 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:
- tpi90pc = tpi70pc(1+g)
^{20}

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,

**8. 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.

**9. 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.