ceteris paribus econometrics

1.4CAUSALITY AND THE NOTION OF CETERIS PARIBUS
IN ECONOMETRIC ANALYSIS
In most tests of economic theory, and certainly for evaluating public policy, the economist’s
goal is to infer that one variable has a causal effect on another variable (such
as crime rate or worker productivity). Simply finding an association between two or
more variables might be suggestive, but unless causality can be established, it is rarely
compelling.
The notion of ceteris paribus—which means “other (relevant) factors being
equal”—plays an important role in causal analysis. This idea has been implicit in some
of our earlier discussion, particularly Examples 1.1 and 1.2, but thus far we have not
explicitly mentioned it.
Chapter 1 The Nature of Econometrics and Economic Data
13
You probably remember from introductory economics that most economic questions
are ceteris paribus by nature. For example, in analyzing consumer demand, we
are interested in knowing the effect of changing the price of a good on its quantity demanded,
while holding all other factors—such as income, prices of other goods, and
individual tastes—fixed. If other factors are not held fixed, then we cannot know the
causal effect of a price change on quantity demanded.
Holding other factors fixed is critical for policy analysis as well. In the job training
example (Example 1.2), we might be interested in the effect of another week of job
training on wages, with all other components being equal (in particular, education and
experience). If we succeed in holding all other relevant factors fixed and then find a link
between job training and wages, we can conclude that job training has a causal effect
on worker productivity. While this may seem pretty simple, even at this early stage it
should be clear that, except in very special cases, it will not be possible to literally hold
all else equal. The key question in most empirical studies is: Have enough other factors
been held fixed to make a case for causality? Rarely is an econometric study evaluated
without raising this issue.
In most serious applications, the number of factors that can affect the variable of
interest—such as criminal activity or wages—is immense, and the isolation of any
particular variable may seem like a hopeless effort. However, we will eventually see
that, when carefully applied, econometric methods can simulate a ceteris paribus
experiment.
At this point, we cannot yet explain how econometric methods can be used to estimate
ceteris paribus effects, so we will consider some problems that can arise in trying
to infer causality in economics. We do not use any equations in this discussion. For each
example, the problem of inferring causality disappears if an appropriate experiment can
be carried out. Thus, it is useful to describe how such an experiment might be structured,
and to observe that, in most cases, obtaining experimental data is impractical. It
is also helpful to think about why the available data fails to have the important features
of an experimental data set.
We rely for now on your intuitive understanding of terms such as random, independence,
and correlation, all of which should be familiar from an introductory probability
and statistics course. (These concepts are reviewed in Appendix B.) We begin
with an example that illustrates some of these important issues.
E X A M P L E 1 . 3
( E f f e c t s o f F e r t i l i z e r o n C r o p Y i e l d )
Some early econometric studies [for example, Griliches (1957)] considered the effects of
new fertilizers on crop yields. Suppose the crop under consideration is soybeans. Since fertilizer
amount is only one factor affecting yields—some others include rainfall, quality of
land, and presence of parasites—this issue must be posed as a ceteris paribus question.
One way to determine the causal effect of fertilizer amount on soybean yield is to conduct
an experiment, which might include the following steps. Choose several one-acre plots of
land. Apply different amounts of fertilizer to each plot and subsequently measure the yields;
this gives us a cross-sectional data set. Then, use statistical methods (to be introduced in
Chapter 2) to measure the association between yields and fertilizer amounts.
Chapter 1 The Nature of Econometrics and Economic Data
14
As described earlier, this may not seem like a very good experiment, because we have
said nothing about choosing plots of land that are identical in all respects except for the
amount of fertilizer. In fact, choosing plots of land with this feature is not feasible: some of
the factors, such as land quality, cannot even be fully observed. How do we know the
results of this experiment can be used to measure the ceteris paribus effect of fertilizer? The
answer depends on the specifics of how fertilizer amounts are chosen. If the levels of fertilizer
are assigned to plots independently of other plot features that affect yield—that is,
other characteristics of plots are completely ignored when deciding on fertilizer amounts—
then we are in business. We will justify this statement in Chapter 2.
The next example is more representative of the difficulties that arise when inferring
causality in applied economics.
E X A M P L E 1 . 4
( M e a s u r i n g t h e R e t u r n t o E d u c a t i o n )
Labor economists and policy makers have long been interested in the “return to education.”
Somewhat informally, the question is posed as follows: If a person is chosen from the
population and given another year of education, by how much will his or her wage
increase? As with the previous examples, this is a ceteris paribus question, which implies
that all other factors are held fixed while another year of education is given to the person.
We can imagine a social planner designing an experiment to get at this issue, much as
the agricultural researcher can design an experiment to estimate fertilizer effects. One
approach is to emulate the fertilizer experiment in Example 1.3: Choose a group of people,
randomly give each person an amount of education (some people have an eighth grade
education, some are given a high school education, etc.), and then measure their wages
(assuming that each then works in a job). The people here are like the plots in the fertilizer
example, where education plays the role of fertilizer and wage rate plays the role of
soybean yield. As with Example 1.3, if levels of education are assigned independently of
other characteristics that affect productivity (such as experience and innate ability), then an
analysis that ignores these other factors will yield useful results. Again, it will take some
effort in Chapter 2 to justify this claim; for now we state it without support.
Unlike the fertilizer-yield example, the experiment described in Example 1.4 is
infeasible. The moral issues, not to mention the economic costs, associated with randomly
determining education levels for a group of individuals are obvious. As a logistical
matter, we could not give someone only an eighth grade education if he or she
already has a college degree.
Even though experimental data cannot be obtained for measuring the return to education,
we can certainly collect nonexperimental data on education levels and wages for
a large group by sampling randomly from the population of working people. Such data
are available from a variety of surveys used in labor economics, but these data sets have
a feature that makes it difficult to estimate the ceteris paribus return to education.
Chapter 1 The Nature of Econometrics and Economic Data
15
People choose their own levels of education, and therefore education levels are probably
not determined independently of all other factors affecting wage. This problem is a
feature shared by most nonexperimental data sets.
One factor that affects wage is experience in the work force. Since pursuing more
education generally requires postponing entering the work force, those with more education
usually have less experience. Thus, in a nonexperimental data set on wages and
education, education is likely to be negatively associated with a key variable that also
affects wage. It is also believed that people with more innate ability often choose
higher levels of education. Since higher ability leads to higher wages, we again have a
correlation between education and a critical factor that affects wage.
The omitted factors of experience and ability in the wage example have analogs in
the the fertilizer example. Experience is generally easy to measure and therefore is similar
to a variable such as rainfall. Ability, on the other hand, is nebulous and difficult to
quantify; it is similar to land quality in the fertilizer example. As we will see throughout
this text, accounting for other observed factors, such as experience, when estimating
the ceteris paribus effect of another variable, such as education, is relatively
straightforward. We will also find that accounting for inherently unobservable factors,
such as ability, is much more problematical. It is fair to say that many of the advances
in econometric methods have tried to deal with unobserved factors in econometric
models.
One final parallel can be drawn between Examples 1.3 and 1.4. Suppose that in the
fertilizer example, the fertilizer amounts were not entirely determined at random.
Instead, the assistant who chose the fertilizer levels thought it would be better to put
more fertilizer on the higher quality plots of land. (Agricultural researchers should have
a rough idea about which plots of land are better quality, even though they may not be
able to fully quantify the differences.) This situation is completely analogous to the
level of schooling being related to unobserved ability in Example 1.4. Because better
land leads to higher yields, and more fertilizer was used on the better plots, any
observed relationship between yield and fertilizer might be spurious.
E X A M P L E 1 . 5
( T h e E f f e c t o f L a w E n f o r c e m e n t o n C i t y C r i m e L e v e l s )
The issue of how best to prevent crime has, and will probably continue to be, with us for
some time. One especially important question in this regard is: Does the presence of more
police officers on the street deter crime?
The ceteris paribus question is easy to state: If a city is randomly chosen and given 10
additional police officers, by how much would its crime rates fall? Another way to state the
question is: If two cities are the same in all respects, except that city A has 10 more police
officers than city B, by how much would the two cities’ crime rates differ?
It would be virtually impossible to find pairs of communities identical in all respects
except for the size of their police force. Fortunately, econometric analysis does not require
this. What we do need to know is whether the data we can collect on community crime
levels and the size of the police force can be viewed as experimental. We can certainly
imagine a true experiment involving a large collection of cities where we dictate how many
police officers each city will use for the upcoming year.
Chapter 1 The Nature of Econometrics and Economic Data
16
While policies can be used to affect the size of police forces, we clearly cannot tell each
city how many police officers it can hire. If, as is likely, a city’s decision on how many police
officers to hire is correlated with other city factors that affect crime, then the data must be
viewed as nonexperimental. In fact, one way to view this problem is to see that a city’s
choice of police force size and the amount of crime are simultaneously determined. We will
explicitly address such problems in Chapter 16.
The first three examples we have discussed have dealt with cross-sectional data at
various levels of aggregation (for example, at the individual or city levels). The same
hurdles arise when inferring causality in time series problems.
E X A M P L E 1 . 6
( T h e E f f e c t o f t h e M i n i m u m Wa g e o n U n e m p l o y m e n t )
An important, and perhaps contentious, policy issue concerns the effect of the minimum
wage on unemployment rates for various groups of workers. While this problem can be
studied in a variety of data settings (cross-sectional, time series, or panel data), time series
data are often used to look at aggregate effects. An example of a time series data set on
unemployment rates and minimum wages was given in Table 1.3.
Standard supply and demand analysis implies that, as the minimum wage is increased
above the market clearing wage, we slide up the demand curve for labor and total employment
decreases. (Labor supply exceeds labor demand.) To quantify this effect, we can study
the relationship between employment and the minimum wage over time. In addition to
some special difficulties that can arise in dealing with time series data, there are possible
problems with inferring causality. The minimum wage in the United States is not determined
in a vacuum. Various economic and political forces impinge on the final minimum
wage for any given year. (The minimum wage, once determined, is usually in place for several
years, unless it is indexed for inflation.) Thus, it is probable that the amount of the minimum
wage is related to other factors that have an effect on employment levels.
We can imagine the U.S. government conducting an experiment to determine the
employment effects of the minimum wage (as opposed to worrying about the welfare of
low wage workers). The minimum wage could be randomly set by the government each
year, and then the employment outcomes could be tabulated. The resulting experimental
time series data could then be analyzed using fairly simple econometric methods. But this
scenario hardly describes how minimum wages are set.
If we can control enough other factors relating to employment, then we can still hope
to estimate the ceteris paribus effect of the minimum wage on employment. In this sense,
the problem is very similar to the previous cross-sectional examples.
Even when economic theories are not most naturally described in terms of causality,
they often have predictions that can be tested using econometric methods. The following
is an example of this approach.
Chapter 1 The Nature of Econometrics and Economic Data
17
E X A M P L E 1 . 7
( T h e E x p e c t a t i o n s H y p o t h e s i s )
The expectations hypothesis from financial economics states that, given all information
available to investors at the time of investing, the expected return on any two investments
is the same. For example, consider two possible investments with a three-month investment
horizon, purchased at the same time: (1) Buy a three-month T-bill with a face value of
$10,000, for a price below $10,000; in three months, you receive $10,000. (2) Buy a sixmonth
T-bill (at a price below $10,000) and, in three months, sell it as a three-month T-bill.
Each investment requires roughly the same amount of initial capital, but there is an important
difference. For the first investment, you know exactly what the return is at the time of
purchase because you know the initial price of the three-month T-bill, along with its face
value. This is not true for the second investment: while you know the price of a six-month
T-bill when you purchase it, you do not know the price you can sell it for in three months.
Therefore, there is uncertainty in this investment for someone who has a three-month
investment horizon.
The actual returns on these two investments will usually be different. According to the
expectations hypothesis, the expected return from the second investment, given all information
at the time of investment, should equal the return from purchasing a three-month
T-bill. This theory turns out to be fairly easy to test, as we will see in Chapter 11.
SUMMARY
In this introductory chapter, we have discussed the purpose and scope of econometric
analysis. Econometrics is used in all applied economic fields to test economic theories,
inform government and private policy makers, and to predict economic time
series. Sometimes an econometric model is derived from a formal economic model,
but in other cases econometric models are based on informal economic reasoning and
intuition. The goal of any econometric analysis is to estimate the parameters in the
model and to test hypotheses about these parameters; the values and signs of the
parameters determine the validity of an economic theory and the effects of certain
policies.
Cross-sectional, time series, pooled cross-sectional, and panel data are the most
common types of data structures that are used in applied econometrics. Data sets
involving a time dimension, such as time series and panel data, require special treatment
because of the correlation across time of most economic time series. Other issues,
such as trends and seasonality, arise in the analysis of time series data but not crosssectional
data.
In Section 1.4, we discussed the notions of ceteris paribus and causal inference. In
most cases, hypotheses in the social sciences are ceteris paribus in nature: all other relevant
factors must be fixed when studying the relationship between two variables.
Because of the nonexperimental nature of most data collected in the social sciences,
uncovering causal relationships is very challenging.
Chapter 1 The Nature of Econometrics and Economic Data
18
KEY TERMS
Causal Effect Experimental Data
Ceteris Paribus Nonexperimental Data
Cross-Sectional Data Set Observational Data
Data Frequency Panel Data
Econometric Model Pooled Cross Section
Economic Model Random Sampling
Empirical Analysis Time Series Data

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