*1998; Last Modified 14 August 1998*

In this

chapter we examine two procedures for testing whether an observed difference

in averages (means) is statistically significant. The first case looks at the

difference between unemployment rates for blacks and whites. In this example,

we ask whether the observed differences are large enough and systematic enough

to give us a high degree of confidence that unemployment affects the black population

more severely than whites. This form of inquiry is an attempt to rule out the

possibility that the observed differences are solely a reflection of random

variation in unemployment rates for both groups.The second case

asks a general question about the US's experience with supply side economics

during the 1980s. Supply side policy makers and journalists made extravagant

claims about the positive effects of supply side economics. In particular,

they argued that deep tax cuts and extensive deregulation would improve incentives

for working, investing, and saving. It is well known and widely accepted that

higher savings and investment rates are associated with faster growth in real

GDP and productivity. In its most extreme form, supply siders argued that

the tax cuts would help to shrink the federal deficit. Their flawed reasoning

was based on a serious overestimate of the growth stimulus provided by tax

cuts and deregulation. In simple terms, they argued that when government revenue

becomes a smaller percentage of GDP, the economy grows so much that the dollar

size of revenue is actually more in dollar terms.In order to examine

these issues, we must conceptualize the economy as a process which generates

many different outcomes. The outcomes are the measured values of the variables

in the dataset. The measured values, however, are not entirely determined

by the systematic operation of our economic system. There are also random

factors that play a role, as well as a certain (unknown) amount of measurement

error. The value of every variable in the data set is a result of all three

of these factors: the systematic processes of the economy, random and uncontrollable

factors external to the economy, and measurement error.Recognition of

a randomness and measurement error complicates the simple act of comparing

variables. For example, we would like to compare black and white unemployment

rates in order to determine the average difference. We have already calculated

averages for both races, and black rates are higher. The problem, however,

is that we cannot say for certain if there is a systematic component to the

difference given that the higher unemployment rates for blacks could be due

to a couple of years of random events or a couple of years of measurement

errors. Hypothesis tests for a difference in means enables us to test this

possibility. As you might imagine, the procedure depends on both the average

unemployment rates, and the amount of variation they exhibit over time.We may also want

to compare the values of a single variable measured at different points in

time. For example, the 1980s look different from the 1970s. Deficits were

higher, inflation was lower, real rates of interest were higher, and so forth.

Once again, however, the differences may not be large enough to rule out the

possibility that they are due to measurement error or random, non-repeated

processes. What we really want to know is whether these differences are systematic

enough to give us a high degree of confidence that they cannot be fully explained

by the normal amount of variation which is always occurring.In the following,

we are trying to determine if the observed difference in black and white unemployment

rates is large enough and persistent enough so that we can rule out the possibility

that the "true" underlying difference is zero. Formally, let m_{B}represent

the true average rate of unemployment for blacks, and m_{W}the rate

for whites. Our hypothesis is m_{B}= m_{W}, or alternatively,

m_{B}- m_{W}= 0. If we rule this out, then it must be the

case that m_{B}¹m_{W}, which we will designate our alternative

hypothesis. Formally we call these the null and alternative hypotheses, where

the term "null" conveys the idea of no difference. Symbolically, they can be

written:H

_{0}:

m_{B}= m_{W},

H_{1}: m_{B}¹m_{W},where H

_{0}:

is the symbol for the null hypothesis.In fact, however,

we never observe the true averages. Instead, we have sample averages which

are based on the available data for a group of years. The sample averages

are subject to measurement error and random variation due to unique events

in particular years. In addition, they are due to the systematic and persistent

factors that determine unemployment rates for each group. The relationship

between the sample and average and the true average is:

Sample average

= x-bar =

m± (t statistic)(standard error of the sample average),where the standard

error of the sample average is the standard deviation of the unemployment

rate (s_{ur}) divided by the square root of the sample size (Ö

n). The t-statistic is the relevant value of a student's t distribution for

n-1 degrees of freedom, and (usually) .025 in each tail. (See a statistics

text for a complete treatment.)The procedure

for carrying out this test in SPSS is straightforward. We will test three

pairs of unemployment rates, those for black and white men, women, and teens.

- Select

Statistics from the menu bar, choose Compare Means, and Paired Samples

t test;- Highlight

bm20u in the variable list box (this clicks it into the Current Selections

box);- Highlight

wm20u in the variable list box, and click the arrow to put them into the

Paired Variables list box;- Do the

same for bw20u and ww20u;- Do the

same for btu and wtu;- Click Okay.
The SPSS output

for black and white men is inTable 5. SPSS prints two tables for each

pair of variables. In the upper part of the table, it prints a set of descriptive

statistics, including means, standard deviations, and standard error of the

estimate of the mean (SE Mean). The latter is an estimate of the possible range

for the "true" population mean, given that this is a sample based on 25 observations.

Between the descriptive statistics for bm20u and wm20u, SPSS prints the number

of observations (25), the correlation coefficient (0.949--see Chapter 5), and

a test statistic to determine if bm20u and wm20u are significantly correlated.Table 5T-tests for Paired Samples

Variable Number

of pairsCorr 2-tail

SigMean SD SE of

MeanBM20U

11.3147

2.894

0.57925 0.949 0.000 WM20U

4.98401.263

0.253

Paired differences

Mean SD SE of

Meant-value df 2-tail

Sig

6.3307

1.742

0.348

18.17

24

0.000

In the second part

of the table, SPSS puts the results of the test H_{0}: m_{B}

= m_{W}. This is the most important information, and the point at which

interpretation of results becomes important. The average difference is 6.3307;

the t-statistic for the test is 18.17. The 2-tail Sig is the probability of

a t-statistic which is 18.17, or larger, in absolute value. To three decimal

places, it has a zero probability. Another way to look at the t-statistic is

as the value of the mean difference (6.3307) when it is transferred to a t-distribution

scale under the assumption that the null hypothesis is true (no difference in

the "true" population mean). Since the t has a zero probability, we can conclude

that there is also a zero probability of getting a sample difference of 6.3307

when the true difference is zero. Hence, we reject the null hypothesis.What about women?

Is the difference between black and white women significant (i.e. significantly

different from zero)? What about teens? In general, should we reject the idea

that the underlying "true" rates are the same? How confident can you be about

this?Proponents of supply

side economics appeared on the scene in the late 1970s, at a time when the traditional

Keynesian consensus was in disarray. Growth had fallen in the 1970s, inflation

had continued to creep up, unemployment rates were consistently higher than

they had been in the 1960s, and Keynesian policy prescriptions seemed to hold

little promise for improving the situation. Compounding these macroeconomic

problems were several microeconomic ones. The US automobile industry experienced

some of its worst years ever and the onslaught of more fuel efficient and reliable

Japanese imports began to swamp Detroit. The US steel industry, consumer electronics,

machine tools, and a number of other traditional manufacturing strengths also

experienced their first real challenge in domestic markets. Some of these industries

disappeared from the US altogether (consumer electronics) while others were

forced to make painful choices in order to restructure over a period of years

(steel).Given the turmoil

in domestic markets and the macroeconomy, it is not surprising that radical

alternatives to mainstream economic analysis suddenly began to appear. The

supply siders were the most successful of the radical views. They managed

to win the support of an extremely popular president and were blessed (or

cursed) with the opportunity to enact major parts of their program.During the 1970s,

mainstream conservative economists began to examine the macroeconomic effects

of taxes and regulations. They came up with a number of widely accepted and

credible empirical studies which showed that various taxes and business regulations

had become obstacles to economic growth. The conclusion of many of their studies

was that if these disincentives to work and invest were addressed, then there

would probably be modest improvements in the overall rate of economic growth.

In no way did this body of work support the idea that the much higher rates

of growth of the 1950s and 1960s would return; rather it showed a potential

for relatively modest increases in economic growth.In the hands

of the supply siders, conservative ideas about taxes and regulation were turned

into a panacea for every economic problem, including inflation, budget deficits,

trade deficits, productivity growth, GDP growth, loss of manufacturing, low

savings and investment, and so on. The key promise they made, however, was

that with a cut in taxes, saving and investment rates would rise. They argued

that when people were allowed to keep a larger piece of future income, they

would work, save, and invest more. The rise in work effort, savings and investment

would raise the rate of growth of GDP and productivity (output per hour worked).In 1981, President

Reagan took office on the promise that he would enact many of the supply side

proposals. The cornerstone of his policy was an across the board income tax

cut. Legislation was quickly passed cutting everyone's income taxes by 10%

in 1981, 10% in 1982, and 5% in 1983. In addition, he continued the trend

that was begun under his predecessor, President Carter, of deregulating various

sectors of the economy.We will examine

a number of variables to see if their is any evidence to support the supply

siders' claims. In Chapter 3 we created the variable "is," the share of investment

in GDP. According to the proponents of supply side economics, this variable

should have increased in the 1980s. Similarly, the variable psp, personal

savings as a share of disposable personal income should have risen. The growth

rates of productivity (prod1 and/or prod2) and GDP should have risen and the

size of the average deficit should have shrunk.In each case,

we can test for the predicted effects by testing the hypothesis that the mean

value (is, psp, GDP growth, productivity growth, deficit as a share of GDP)

for 1970 is different from the 1980 mean. The steps to do this first require

the computation of the variables not already in the data set:

- Select

Transform from the menu bar, then choose Compute . . .;- If you

have not already done so, create new variables:- growth

rate of GDP;- deficits/GDP;
- growth

rate of productivity;- investment/GDP;
Use the recode function

to create a marker for the 1970s and 1980s (if you did not do this in the last

chapter).

- Select

Transform from the menu bar, then Recode, and Into Different Variable;- Highlight

year in the variable list and use the arrow to move it into the Numeric

Variable -> Output box;- Type sside

in the Output Variable box and click Change;- Click Old

and New Values;- In the

Old Value box, click the Range button and put 1971 and 1980 in the two

boxes;- In the

New Value box type 1 and click Add;- Go back

to the Range boxes and type 1981 and 1990;- In the

New Value box type 2 and click Add;- Click Continue

and then click OK.Test the hypothesis

for each variable,

H_{0}:

m_{70s}= m_{80s},H

_{1}: m_{70s}¹m_{80s},using the Independent

Samples t test:

- Select

Statistics from the menu bar, choose Compare Means, then Independent Samples

T-Test;- Highlight

psp and click the arrow to put it into the Test Variable(s) box;- Do the

same for the other variables (investment share, rate of growth of GDP

and productivity, deficits as a share of GDP);- Highlight

sside and click the arrow to put it into the Grouping Variable box, then

click Define Groups . . .;- In Group

1, type 1 and in Group 2, type 2;- Click Continue,

then OK;SPSS will perform

t-tests on each variable, comparing the mean value for the 1970s to the mean

for the 1980s. For each variable, there are two tables, one with the means and

standard deviations, and the second with the t value for the tests. Note that

SPSS also automatically performs a test to see if the variances are the same

during the two periods (Levene's test) and calculates separate t values for

each case (equal variances, unequal variances). If the variances are the same,

then the procedure pools all the data from both periods to calculate a pooled

variance. This makes the t-test slightly more powerful if it is valid to pool

the data.What can you

conclude? Did the growth rate of real GDP increase? Did any of the variables

perform as predicted by supply side politicians? Why do you suppose supply

side theory is ignored by mainstream economists?Krugman, Paul.

Peddling Prosperity: Economic Sense and Nonsense in the Age of DiminishedNew York: WW Norton. 1994.

Expectations.Krugman is

a leading American economist who has written an in-depth critique of supply

side economics that is accessible to non-economists.