As we discussed in Chapter 1, economists are not only concerned with devising models of how the economy works. They must also be concerned with establishing the validity of those models, usually by looking at data from the real world. The tools used for this purpose are studied in the field of econometrics (literally,
‘‘economic measuring’’). Because many of the applications that appear in this book are taken from econometric studies, and because econometrics has come to play an increasingly important role in all of economics, here we briefly discuss a few aspects of this subject. Any extended treatment is, of course, better handled in a full course on econometrics; but discussion of a few key issues may be helpful in understanding how economists draw conclusions about their models. Specifically, we look at two topics that are relevant to all of econometrics: (1) random influ- ences, and (2) imposing theceteris paribusassumption.
Random Influences
If real-world data fit economic models perfectly, econometrics would be a very simple subject. For example, suppose an economist hypothesizes that the demand for pizza (Q) is a linear function of the price of pizza (P) of the form
Q¼abP (1A:24)
where the values foraandbwere to be determined by the data. Because any straight line can be established by knowing only two points on it, all the researcher would have to do is (1) find two places or time periods where ‘‘everything else’’ was the same (a topic we take up next), (2) record the values ofQandPfor these observa- tions, and (3) calculate the line passing through the two points. Assuming that the
A P P L I C A T I O N 1 A . 3
Can Supply and Demand Explain Changing World Oil Prices?
Crude oil prices rose to more than $120 per barrel during the summer of 2008. This sharp run-up in price led to demands for all sorts of actions, including imposing punitive taxes on oil companies and sharply limiting ‘‘speculation’’ in the oil market. Before jumping on such a bandwagon, it is always prudent for an economist to ask whether such price move- ments might simply reflect the familiar forces of supply and demand in the oil market.
A Simple Model
To examine the question, let’s consider a simple supply- demand model for crude oil that was introduced in the previous edition of this book. This model seeks to explain two variables: The price of crude oil per barrel (P, measured in dollars) and the quantity of oil produced (Q, measured in millions of barrels per day) according to the equations:
Demand Q¼850:4P
Supply Q¼55þ0:6P ð1Þ Solving these equations simultaneously yields:
850:4P¼55þ0:6PorP¼30,Q¼73 ð2Þ This solution is approximately what was observed in crude oil markets during the period 2000–2002—price was about
$30 per barrel, and about 70–75 million barrels were pro- duced per day.1
Increasing Demand
Since 2000–2002, demand for crude oil has increased sub- stantially throughout the world. Probably the most important factor has been the rapid economic growth in the world’s
two most populous countries—India and China. Not surpris- ingly, it seems that citizens of these countries want to drive cars and enjoy modern appliances just as much as do citizens of Western countries. Overall, the influence of such growth may have been to increase the world demand for crude oil by as much as 3–4 percent each year. Taking the larger of these two numbers, the demand equation for crude oil might have shifted outward toQ¼112.4Pby 2008. If we re-solve the model in Equation 1A.1 using this new demand, we get P¼57,Q¼87. This new equilibrium is shown in Figure 1A. Although our model does indeed predict a large rise in price as a result of increased demand, the actual price in the summer of 2008 was much higher than this prediction.
Hence, we need to look further for a full explanation.
Measuring Price Correctly
In microeconomics, it is important to remember that the price shown in supply-demand graphs should be taken to be a relative price—that is, it should reflect the price of the item being studied relative to other prices. We must make two adjustments to the relative price predicted by our model to compare it to the actual 2008 price. First, we need to consider the increase in prices generally in the United States.
Overall, prices increased about 23 percent during this per- iod. Hence, in terms of 2008 prices, our prediction of $57 per barrel should be adjusted upward to about $70 per barrel.
Second, we need to consider the fact that oil is priced in U.S.
dollars, and the dollar suffered a significant decline in value relative to other currencies over the period. For example, the value of the euro relative to the dollar was 66 percent higher in 2008 than it was in 2001. Changes in the values of other major currencies were not so large, but still, we should pro- bably adjust the price of oil upward by about 35 percent to reflect the dollar’s decline. Hence, our predicted 2008 oil price now becomes about $94 per barrel.
1At this equilibrium, the price elasticity of demand for crude oil is .16, and the elasticity of supply is .25. Both figures approximate what can be found in the empirical literature.
Prices Fall Back
Overall, then, it appears that the increase in demand can explain a good portion of the price rise in the summer of 2008. The remaining rise in price may be attributable to short-run influences on the market (such as weather or other disruptions at some production locations) and possibly to some degree of ‘‘speculation’’. Ultimately, however, the
sharp run-up in prices proved rather short-lived because the world-wide recession that started in late 2007 sharply reduced oil demand. By March 2009 world oil prices had fallen below $50 per barrel in nominal terms. In real terms (as in Figure 1A) this decline took prices back toward their year 2000 levels.
Of course, nothing in world oil markets ever stays con- stant. By summer 2009 oil prices were again rising as econo- mies around the world began to recover from the recession.
Our simple model suggests that a full recovery will return prices to a real value of about $60 per barrel in year 2000 prices – that is, to perhaps $95 in nominal terms. But all such projections should be greeted with a large degree of skepti- cism because no one knows what additional factors may arise to affect the market.
TOTHINKABOUT
1. Because crude oil that is not produced today can be sold tomorrow, firms (and countries) must take prospects for future sales into account in their current supply decisions.
How would the supply curve for oil be affected by wide- spread expectations that oil prices will increase dramati- cally in the future? Would the resulting change in price suggest to producers that their expectations might be correct? If so, would these effects create a speculative
‘‘bubble’’ in world oil prices? What factors might limit the extent of such a bubble?
2. The supply and demand curves shown in Figure 1A implicitly assume that the world oil market is reasonably competitive. This assumption may be dubious for the supply side of the market in which the OPEC cartel con- trols about 50 percent of world oil production. Does the existence of the OPEC cartel seriously undermine using supply and demand curves to explain trends in world oil markets? What added factors should be taken into account in modeling the world oil market to account for the influence of the cartel? How do you think govern- ments in the cartel actually model the world oil market for their own purposes?
FIGURE 1AWorld Oil Market
70
50 60
40
30
0 70 75 80 85
D (2008)
Quantity (Millions bbl/day) Price
($2000/barrel)
S
D (2000)
Model predicts that increasing demand between 2000 and 2008 raises relative price from $30 to $57.
demand Equation 1A.24 holds in other times or places, all other points on this curve could be determined with perfect accuracy.
In fact, however, no economic model exhibits such perfect accuracy. Instead, the actual data onQ and P will be scattered around the ‘‘true’’ demand curve because of the huge variety of random influences (such as whether people get a yearning for pizza on a given day) that affect demand. This situation is illustrated in Figure 1A.7. The true demand curve for pizza is shown by the blue line, D.
Researchers do not know this line. They can ‘‘see’’ only the actual points shown in color. The problem the researcher faces then is how to infer what the true demand curve is from these scattered points.
Technically, this is a problem in statistical inference. The researcher uses various statistical techniques in an attempt to see through all of the random things that affect the demand for pizza and toinferwhat the relationship betweenQandP actually is. A discussion of the techniques actually used for this purpose is beyond the scope of this book, but a glance at Figure 1A.7 makes clear that no technique will find a straight line that fits the points perfectly. Instead, some compromises will have to be made in order to find a demand curve that is ‘‘close’’ to most of the data points. Careful consideration of the kinds of random influences present in a problem can help in devising which technique to use.7A few of the applications in this text describe how researchers have adapted statistical techniques to their purposes.
F I G U R E 1 A . 7
Infe rring th e Dem and C urve fro m Real-W orld Data Price (P)
D
Quantity (Q)
Even when theceteris paribusassumption is in force, actual data (shown by the points) will not fit the demand curve (D) perfectly because of random influences. Statistical proce- dures must be used to infer the location ofD.
Statistical inference Use of actual data and statistical techniques to determine quantitative economic relationships.
7In many problems, the statistical technique of ‘‘ordinary least squares’’ is the best available. This technique proceeds by choosing the line for which the sum of the squared deviations from the line for all of the data points is as small as possible. For a discussion, see R. Ramanathan,Introductory Econometrics with Applications, 5th ed.
(Mason, OH: South-Westen College Publishing, 2001).
The Ceteris Paribus Assumption
All economic theories employ the assumption that ‘‘other things are held constant.’’
In the real world, of course, many things do change. If the data points in Figure 1A.7 come from different weeks, for example, it is unlikely that conditions such as the weather or the prices of pizza substitutes (hamburgers?) have remained unchanged over these periods. Similarly, if the data points in the figure come from, say, different towns, it is unlikely that all factors that may affect pizza demand are exactly the same in every town. Hence, a researcher might reasonably be concerned that the data in Figure 1A.7 do not reflect a single demand curve. Rather, the points may lie on several different demand curves, and attempting to force them into a single curve would be a mistake.
To address this problem, two things must be done: (1) Data should be collected on all of the other factors that affect demand, and (2) appropri- ate procedures must be used to control for these measurable factors in analysis. Although the con- ceptual framework for doing this is fairly straight- forward,8 many practical problems arise. Most important, it may not in fact be possible to measure all of the other factors that affect demand. Con- sider, for example, the problem of deciding how to measure the precise influence of a pizza advertising campaign on pizza demand. Would you measure the number of ads placed, the number of ad readers, or the ‘‘quality’’ of the ads? Ideally, one might like to measure people’s perceptions of the ads—but how would you do that without an elaborate and costly survey? Ultimately, then, the researcher will often have to make some compromises in the kinds of data that can be collected, and some uncertainty will remain about whether the ceteris paribus assumption has been imposed faithfully. Many con- troversies over testing the reliability of economic models arise for precisely this reason.
Exogenous and Endogenous Variables
In any economic model, it is important to differentiate between variables whose values are determined by the model and those that come from outside the model.
Variables whose values are determined by a model are calledendogenous variables (‘‘inside variables’’), and those whose values come from outside the model are called M i c r o Q u i z 1 A . 6
An economic consulting firm is hired to estimate the demand for broccoli in several cities. Explain using a graph why each of the following
‘‘solutions’’ to theceteris paribusproblem is incorrect—why would the demand curves developed by applying each approach probably be wrong?
Approach 1:Collect data over several years for the price and quantity of broccoli in each city.
Then graph the data separately for each city and estimate a separate ‘‘demand curve’’ for each city.
Approach 2:Collect data over several years for the price and quantity of broccoli in each city and average each city’s data over the years available.
Now graph the resulting averages and draw a
‘‘demand curve’’ through these points.
8To control for the other measurable factors (X) that affect demand, the demand curve given in Equation 1A.22 must be modified to include these other factors asQ¼abPþcX. Once the values fora, b, andchave been determined, this allows the researcher to holdXconstant (as is required by theceteris paribusassumption) while looking at the relationship betweenQandP. Changes inXshift the entireQ-Prelationship (that is, changes inXshift the demand curve).
exogenous variables(‘‘outside’’ variables). In many microeconomic models, price and quantity are the endogenous variables, whereas the exogenous variables are factors from outside the particular market being considered, often variables that reflect macroeconomic conditions. To illustrate this distinction, we return to the simultaneous model specified in Equation 1A.22 but change the notation so thatP andQ represent the price and quantity of some good. The values of these two variables are determined simultaneously by the operations of supply and demand.
The market equilibrium is also affected by two exogenous variables,WandZ.W reflects factors that positively affect demand (such as consumer income), whereas Z reflects factors that shift the supply curve upward (such as workers’ wages). Our economic model of this market can be written as:
Q¼ PþW
P¼QþZ (1A:25)
After we specify values forWandZ, this becomes a model with two equations and two unknowns and can be solved for (equilibrium) values ofPandQ. For example, ifW¼3,Z¼ 1, this is identical to the model in Equation 1A.22, and the solution isP¼1,Q¼2. Similarly, ifW¼5,Z¼ 1, the solution to this model isP¼2, Q¼3. Notice the solution strategy here. First, we must know the values for the exogenous variables in the model. We then plug these into the model and proceed to solve for the values of the endogenous variables. This is how practically all eco- nomic models work.
The Reduced Form
There is a shortcut to solving these models if you need to do so many times that involves solving for the endogenous variables in terms of the exogenous variables.
By plugging the second equation in 1A.25 into the first, we get 2Q¼WZ orQ¼ ðWZÞ=2
P¼QþZ orP¼ ðWþZÞ=2 (1A:26)
You should check that inserting the values for W and Z used previously into Equation 1A.26 will yield precisely the same values forPandQthat we found in the previous paragraph.
The equations in 1A.26 are called thereduced formof the ‘‘structural’’ model in Equations 1A.25. Not only is expressing all the endogenous variables in a model in terms of the exogenous variables a useful procedure for making predictions, but also there may be econometric advantages of estimating reduced forms rather than structural equations. We will not pursue such issues in this book, however.
SUMMARY
This chapter reviews material that should be familiar to you from prior math and economics classes. The fol- lowing results will be used throughout the rest of this book:
• Linear equations have graphs that are straight lines. These lines are described by their slopes and by their intercepts with theY-axis.
• Changes in the slope cause the graph of a linear equation to rotate about itsY-intercept. Changes in theX- orY-intercept cause the graph to shift in a parallel way.
• Nonlinear equations have graphs that have curved shapes. Their slopes change asXchanges.
• Economists often use functions of two or more variables because economic outcomes have many causes. These functions can sometimes be graphed
in two dimensions by using contour lines. These lines show trade-offs that can be made while hold- ing the value of the dependent variable constant.
This is especially difficult in the case of simulta- neous equations that determine the values of endo- genous variables.
• Simultaneous equations determine solutions for two (or more) variables that satisfy all of the equa- tions. An important use of such equations is to show how supply and demand determine equili- brium prices.
• Testing economic models usually requires the use of real-world data together with appropriate econometric techniques. An important problem in all such applications is to ensure that theceteris paribusassumption has been imposed correctly.
KEEPinMIND
How to Know When a Problem Is Solved
A frustration experienced by many students who are beginning their study of microeconomics is that they cannot tell when they have arrived at a suitable solution to a problem. Making the distinction between endogenous and exogenous variables can help you in this process. After you identify which variables are being specified from outside a model and which are being determined within a model, your goal is usually to solve for the endogenous variables (i.e., price and quantity). If you are given explicit values for the exogenous variables in the model (i.e., prices for firms’ input costs), a solution will consist of explicit numerical values for all of the endogenous variables in the model. On the other hand, if you are just given symbols for the exogenous variables, a solution will consist of a reduced form in which each endogenous variable is a function only of these exogenous variables. Any purported
‘‘solution’’ that fails to solve for each of the endogenous variables in a model is not complete.
Throughout this book, we will point out situations where students sometimes make this sort of mistake.