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Economic Data and the Identification Problem
Economic Data and the Identification
Problem
In Chapter 3 we discuss the laws of demand and supply and illustrate how the demandand-supply apparatus can be used to help us understand movements in prices and quantities. Sometimes economists want to have quite precise information about demand or
supply curves so they can make quantitative predictions about how a specific tax or
change in preferences or technology is likely to affect the demand and supply curves.
In other words, economists often want to “identify” demand and supply curves using data
drawn from the real world. In this web-based section, we discuss the difficulties involved
in solving this “identification problem.”
Some Data on Prices and Quantities
Suppose you are interested in the Canadian market for newsprint and want to have reasonably precise estimates of the demand and supply curves for that product. Your
research into the Canadian newsprint industry results in some annual observations on
price and quantity over nine years. Price is measured as the price in dollars per tonne of
newsprint, and quantity is measured as thousands of tonnes per year. The annual price
and quantity data that you collect are shown in Figure 1. Although Figure 1 shows
hypothetical data, the cyclical movements shown over the nine-year period are quite
characteristic of the real-world newsprint industry.
Nine Years of Price and Quantity Data for Newsprint
FIGURE 1
Price
($/tonne)
Quantity
(000’s of
tonnes)
700
70
600
60
500
50
400
40
300
30
200
20
100
10
0
A
B
C
D
E
F
G
H
I
Time
0
A
B
C
D
E
F
G
H
I
Time
Price and quantity fluctuate considerably in most industries. These two figures showing the price and quantity exchanged
of newsprint over nine years are typical ways of displaying basic industry information. The data are hypothetical, but
are quite realistic in terms of the size of their cyclical fluctuations.
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Economic Data and the Identification Problem
For the purposes of this discussion we assume that newsprint is neither imported into
Canada nor exported from Canada. Both assumptions are incorrect (both imports to
Canada and exports from Canada occur) but it simplifies the analysis by allowing us to
focus on demand and supply within Canada, ignoring demand and supply conditions in
other countries.
Armed with the data in Figure 1, what can you conclude about the demand and
supply curves in the Canadian newsprint industry? Can we get precise estimates of these
curves? Since demand and supply curves show relationships between price and quantity
(demanded or supplied), you may find it useful to plot the data in price-quantity space,
as when drawing a demand curve or a supply curve. After plotting the data in this manner, you have a scatter-plot like the one shown in Figure 2.
How can we use the demand and supply apparatus that we learned in Chapter 3 to
explain these movements in price and quantity? For the first year in our sample, both price
and quantity fall. For the next two years, price falls while quantity rises. After that, the
price of newsprint begins a four-year rise while the quantity fluctuates. Finally, the price
is stable and then declines in the last year of the sample, while quantity continues to
fluctuate.
The data do not appear to trace out either a demand curve (negative relationship
between price and quantity) or a supply curve (positive relationship between price and
quantity). What’s wrong? Is there no demand curve or supply curve to identify?
Scatter-plot of Price and Quantity for the Newsprint
Industry
FIGURE 2
Price
A
700
600
Dollars per tonne
2
G
H
500
B
I
400
F
E
C
300
200
D
100
0
10
20
30
40
50
60
70
80
90
Quantity
Thousands of tonnes per year
A scatter-plot of price-quantity observations, by itself, cannot identify the underlying demand
and supply curves. The data shown here are drawn from Figure 1. It is unclear from the data
what the demand and supply curves in this market look like.
Copyright © 2005 Pearson Education Canada Inc.
Economic Data and the Identification Problem
The Identification Problem
There is nothing wrong. The only “problem” is that correctly identifying the demand and
supply curves from the available data is much more difficult than simply tracing out
the demand or supply curves by connecting the data points. We cannot simply connect
some of the data points into a downward-sloping line and label that line a demand
curve. Nor can we simply connect some of the data points into an upward-sloping line
and label that line a supply curve. Before we can identify either the demand curve or
the supply curve, we need to know much more about what is going on in the newsprint
market than just the price-quantity combinations at various points in time. In particular, we need to know why the price and quantity are changing at various times.
In our example, as in the real world, price and quantity data are generated by the continual interaction of demand and supply, including the adjustment in price that occurs
whenever demand or supply changes. Thus, we must view each price-quantity combination as the equilibrium point in the market—the intersection of the underlying demand
and supply curves. And as these demand and supply curves shift, a new equilibrium
point is generated, and a new price-quantity combination is observed. Figure 3 shows the
underlying demand and supply curves, and their shifts, which resulted in the data shown
in Figure 1.
Take a few moments to understand the story that is revealed in Figure 3. First, note
that the figure reveals three possible positions for the demand curve, each perhaps reflecting different average income levels in Canada (the greater is average income, the more
firms seek to advertise in newspapers, and thus the greater is the demand for newsprint).
Demand and Supply Shifts in the Newsprint Industry
FIGURE 3
Price
S0
Dollars per tonne
700
S1
A
600
S2
H
500
G
B
I
400
300
D1
D
100
0
D2
E
C
200
S3
F
10
20
30
40
50
D0
60
70
80
90
Quantity
Thousands of tonnes per year
Each price-quantity combination can be viewed as the intersection of the underlying demand
and supply curves. The demand and supply curves are not visible to the economist but are
shown here. With them, we can understand the sequence of events (demand and supply
shifts) that generated the data shown in Figures 1 and 2. Over specific intervals, when either
the demand curve or the supply curve is stable, the price-quantity observations can be used
to identify one of the curves.
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Economic Data and the Identification Problem
Second, there are four possible positions for the supply curve, perhaps reflecting different prices for pulp, a major input to the production of newsprint (as the price of pulp rises,
costs of producing newsprint increase, thus reducing the supply for newsprint).
We begin the story at point A. Demand for newsprint is D1 and supply is S0. The price
of newsprint is approximately $650 per tonne and the quantity exchanged (both
demanded and supplied) is roughly 23 000 tonnes per year. Then in the next year there
are two changes. First, demand for newsprint falls to D0; second, the supply of newsprint
increases to S1. The combined effect is to move to point B, where price has fallen to
about $400 per tonne and quantity has fallen to approximately 20 000 tonnes. Since both
the demand and the supply curves shifted, the movement from point A to point B cannot be used to help us identify either of the curves. This brings us to our first general rule:
If both the demand and supply curves are shifting, data on price and quantity are not sufficient to identify either the demand curve or the supply curve.
Now consider what happens as we move to points C and D. Over both years, the
demand curve is stable at D0 (because income and other factors that shift the demand
curve are not changing). But the supply curve in each year shifts to the right, first to S2
and then again to S3 (this may reflect a falling price of pulp over this period). Thus, the
movement from point B to point C and then to point D is a movement along a stable
demand curve. We can therefore use these specific price-quantity observations to “identify” the demand curve. For example, by examining the change in price and quantity
between points B and D, we can compute the slope of the demand curve D0. This brings
us to our second rule:
If the demand curve is stable while the supply curve is shifting, it is possible to identify
the demand curve from observations of price and quantity.
Now consider the movement from point D to point E. Over this period, demand
increases from D0 to D1 whereas the supply curve is stable at S3. As a result of the
increase in demand, both price and quantity increase in this industry. As is clear from the
figure, we can use these two price-quantity observations to identify the supply curve
(and compute its slope). This brings us to our third general rule:
If the supply curve is stable while the demand curve is shifting, it is possible to identify
the supply curve from observations of price and quantity.
We leave it to you to proceed yourself through the sequence of demand and supply
shifts that generate points F, G, H, and I (note that points F and I are the same). You
should conclude that it is possible to identify the demand curve D1 using the data at
points E and F and the supply curve S2 using data at points F and G. Between G and H,
both the demand curve and the supply curve are shifting, and thus the movement from
G to H cannot be used to identify either curve. Finally, between points H and I, the data
can be used to identify the demand curve D1.
Solving the Identification Problem
One crucial problem for economists interested in identifying demand and supply curves
in particular markets is that real-world data can never be presented in the form of Figure
3 for the simple reason that economists are unable to observe the underlying demand and
supply curves that generate the data. Data can easily be presented as shown in Figures
1 and 2, but this was our starting point above—and it is not clear how to use these data
to identify the demand and supply curves. How do we identify demand and supply
curves in the real world? There are two approaches.
Copyright © 2005 Pearson Education Canada Inc.
Economic Data and the Identification Problem
First, sometimes reasonably detailed knowledge of the market in question can help
the economist identify periods in which either the demand curve or the supply curve is
reasonably stable, with the consequence that the observed price-quantity points can
then be used to identify that curve. For example, suppose during the second, third, and
fourth periods in our sample of newsprint data the economist had good reason to believe
that the demand for newsprint was stable. This belief would not just be a wild guess—
instead, it would be an informed judgement based on the knowledge that average income
and other factors that shift the demand curve for newsprint were themselves relatively
constant. In this very special situation, the stability of the demand curve implies that
any price-quantity observations during this period must be due to shifts in the supply curve
and must also lie along a stable demand curve. Thus, the price-quantity observations
can be used to identify the demand curve.
Special circumstances sometimes provide economists with the knowledge that either the
demand curve or the supply curve is stable. In such situations, any fluctuations in price
and quantity can be used to identify that (stable) curve.
These situations are very special, however, and will occur infrequently. Thus, economists need more general methods to solve the identification problem.
The second general approach is to use advanced statistical analysis to identify
demand or supply curves. This approach requires the collection of a great deal of data,
not just on price and quantity, but also on the many variables that are expected to shift
both the demand and supply curves. For example, in our case of the newsprint industry,
in addition to price and quantity of newsprint, we would need to collect data on average household income (a factor that shifts the demand curve) and the price of pulp (a factor that shifts the supply curve). Preferably, we would collect data on all of the factors
that shift the two curves—the more and better data we collect, the better our final estimates of the demand and supply curves in that industry.
Once the data are collected (which is often much more difficult than it sounds!),
the economist can then use some advanced statistical techniques to estimate the demand
and supply curves, including one technique called multiple regression analysis. When
you go on to study advanced courses in economics and econometrics (literally, “the
measurement of economics”), you will learn how to use these techniques.
Summary
The estimation or identification of demand and supply curves is not simple. The approach
of producing a scatter-plot of the price-quantity observations and then “connecting the
dots” is definitely not the way to do it correctly. This is because, in general, demand
and supply curves are often shifting and thus “connecting the dots” will identify neither the demand curve nor the supply curve (though it may produce lovely pictures!).
The correct estimation of demand or supply curves requires more than just data on
prices and quantities. Either it requires knowledge of the various variables that shift
both the demand and supply curves so that advanced statistical estimation can be undertaken, or it requires special knowledge that either the demand curve or the supply curve
is stable during a specific period of time (which, in turn, requires knowledge regarding
the other variables). In either case, however, knowledge of price and quantity alone is not
sufficient to identify either the demand curve or the supply curve. Keep this important
lesson in mind next time you’re wondering about the underlying demand and supply
curves when viewing diagrams like Figures 1 or 2.
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