2: Theories, data and beliefs

Data types

Data come in several forms. One form is time-series, which reflects a set of measurements made in sequence at different points in time. The first column in Table 2.1 reports the values for house prices in North Vancouver for the first quarter of each year, between 2001 and 2011. Evidently this is a time series. Annual data report one observation per year. We could, alternatively, have presented the data in monthly, weekly, or even daily form. The frequency we use depends on the purpose: If we are interested in the longer-term trend in house prices, then the annual form suffices. In contrast, financial economists, who study the behaviour of stock prices, might not be content with daily or even hourly prices; they may need prices minute-by-minute. Such data are called high-frequency data, whereas annual data are low-frequency data.

In contrast to time-series data, cross-section data record the values of different variables at a point in time. Table 2.2 contains a cross-section of unemployment rates for Canada and Canadian provinces economies. For January 2012 we have a snapshot of the provincial economies at that point in time, likewise for the months until June. This table therefore contains repeated cross-sections.

When the unit of observation is the same over time such repeated cross sections are called longitudinal data. For example, a health survey that followed and interviewed the same individuals over time would yield longitudinal data. If the individuals differ each time the survey is conducted, the data are repeated cross sections. Longitudinal data therefore follow the same units of observation through time.

Graphing the data

Data can be presented in graphical as well as tabular form. Figure 2.1 plots the house price data from the second column of Table 2.1. Each asterisk in the figure represents a price value and a corresponding time period. The horizontal axis reflects time, the vertical axis price in dollars. The graphical presentation of data simply provides a visual rather than numeric perspective. It is immediately evident that house prices increased consistently during this 11-year period, with a single downward 'correction' in 2009. We have plotted the data a second time in Figure 2.2 to illustrate the need to read graphs carefully. The greater apparent slope in Figure 2.1 might easily be interpreted to mean that prices increased more steeply than suggested in Figure 2.2. But a careful reading of the axes reveals that this is not so; using different scales when plotting data or constructing diagrams can mislead the unaware viewer.

Figure 2.1 House prices in dollars 1999-2012

Figure 2.2 House prices in dollars 1999-2012

Percentage changes

The use of percentages makes the analysis of data particularly simple. Suppose we wanted to compare the prices of New York luxury condominiums with the prices of homes in rural Mississippi. In the latter case, a change in average prices of $10,000 might be considered enormous, whereas a change of one million dollars in New York might be pretty normal – because the average price in New York is so much higher than in Mississippi. To make comparisons between the two markets, we can use the concept of a percentage change. This is defined as the change in the value of the variable, relative to its initial value, multiplied by 100.

The third column of Table 2.1 contains the values of the percentage change in house prices for two pairs of years. Between 2002 and 2003 the price change was $35,000. Relative to the price in the first of these two years this change was the fraction 35,000/395,000=0.097. If we multiply this fraction by 100 we obtain a percentage price change of 9.7%. Evidently we could calculate the percentage price changes for all pairs of years. A second price change is calculated for the 2008-2009 pair of years. Here price declined and the result is thus a negative percentage change.

Consumer prices

Most variables in economics are averages of the components that go into them. When variables are denominated in dollar terms it is important to be able to interpret them correctly. While the house price series above indicates a strong pattern of price increases, it is vital to know if the price of housing increased more or less rapidly that other prices in the economy. If all prices in the economy were increasing in line with house prices there would be no special information in the house price series. However, if house prices increased more rapidly than prices in general, then the data indicate that something special took place in the housing market during the decade in question. To determine an answer to this we need to know the degree to which the general price level changed each year.

Statistics Canada regularly surveys the price of virtually every product produced in the economy. One such survey records the prices of goods and services purchased by consumers. Statistics Canada then computes an average price level for all of these goods combined for each time period the survey is carried out (monthly). Once Statistics Canada has computed the average consumer price, it can compute the change in the price level from one period to the next. In Table 2.1 two such values are entered in the following data column: Consumer prices increased by 3% between 2002 and 2003, and by 1.6% between 2008 and 2009. These percentage changes in the general price level represent inflation if prices increase, and deflation if prices decline.

In this market it is clear that housing price changes were substantially larger than the changes in consumer prices for these two pairs of years. The next column provides information on the difference between the house price changes and changes in the general consumer price level, in percentage terms. This is (approximately) the change in the relative price of housing, or what economists call the real price of housing. It is obtained by subtracting the rate of change in the general price index from the rate of change in the variable of interest.

Index numbers

Statistics Canada and other statistical agencies frequently present data in index number form. An index number provides an easy way to read the data. For example, suppose we wanted to compute the percentage change in the price of housing between 2001 and 2007. We could do this by entering the two data points in a spreadsheet or calculator and do the computation. But suppose the prices were entered in another form. In particular, by dividing each price value by the first year value and multiplying the result by 100 we obtain a series of prices that are all relative to the initial year – which we call the base year. The resulting series in column 6 of Table 2.1 is an index of house price values. Each entry is the corresponding value in column 2, divided by the first entry in column 2. For example, the value 124.0 in row 4 is obtained as . The key characteristics of indexes are that they are not dependent upon the units of measurement of the data in question, and they are interpretable easily with reference to a given base value. To illustrate, suppose we wish to know how prices behaved between 2001 and 2007. The index number column immediately tells us that prices increased by 80%, because relative to 2001, the 2007 value is 80% higher.

Furthermore, index numbers enable us to make comparisons with the price patterns for other goods much more easily. If we had constructed a price index for automobiles, which also had a base value of 100 in 2001, we could make immediate comparisons without having to compare one set of numbers defined in thousands of dollars with another defined in hundreds of thousands of dollars. In short, index numbers simplify the interpretation of data.

House prices – theory

Remember from Chapter 1 that a theory is a logical argument regarding economic relationships. A theory of house prices would propose that the price of housing depends upon a number of elements in the economy. In particular, if borrowing costs are low then buyers are able to afford the interest costs on larger borrowings. This in turn might mean they are willing to pay higher prices. Conversely, if borrowing rates are higher. Consequently, the borrowing rate, or mortgage rate, is a variable for an economic model of house prices. A second variable might be available space for development: If space in a given metropolitan area is tight then the land value will reflect this, and consequently the higher land price should be reflected in higher house prices. A third variable would be the business climate: If there is a high volume of high-value business transacted in a given area then buildings will be more in demand, and that in turn should be reflected in higher prices. For example, both business and residential properties are more highly priced in San Francisco and New York than in Moncton, New Brunswick. A fourth variable might be environmental attractiveness: Vancouver may be more enticing than other towns in Canada. A fifth variable might be the climate.

House prices – evidence

These and other variables could form the basis of a theory of house prices. A model of house prices, as explained in Chapter 1, focuses upon what we would consider to be the most important subset of these variables. In the limit, we could have an extremely simple model that specified a dependence between the price of housing and the mortgage rate alone. To test such a simple model we need data on house prices and mortgage rates. The final column of Table 2.1 contains data on the 5-year fixed-rate mortgage for the period in question. Since our simple model proposes that prices depend (primarily) upon mortgage rates, in Figure 2.3 we plot the house price series on the vertical axis, and the mortgage rate on the horizontal axis, for each year from 2001 to 2011. As before, each point (shown as a '+') represents a pair of price and mortgage rate values.

Figure 2.3 Price of housing

The resulting plot (called a scatter diagram) suggests that there is a negative relationship between these two variables. That is, higher prices are correlated with lower mortgage rates. Such a correlation is consistent with our theory of house prices, and so we might conclude that changes in mortgage rates cause changes in house prices. Or at least the data suggest that we should not reject the idea that such causation is in the data.

House prices – inference

To summarize the relationship between these variables, the pattern suggests that a straight line through the scatter plot would provide a reasonably good description of the relationship between these variables. Obviously it is important to define the most appropriate line – one that 'fits' the data well.1 The line we have drawn through the data points is informative, because it relates the two variables in a quantitative manner. It is called a regression line. It predicts that, on average, if the mortgage rate increases, the price of housing will respond in the downward direction. This particular line states that a one point change in the mortgage rate will move prices in the opposing direction by $105,000. This is easily verified by considering the dollar value corresponding to say a mortgage value of 6.5, and then the value corresponding to a mortgage value of 7.5. Projecting vertically to the regression line from each of these points on the horizontal axis, and from there across to the vertical axis will produce a change in price of $105,000.

Note that the line is not at all a 'perfect' fit. For example, the mortgage rate declined between 2008 and 2009, but the price declined also – contrary to our theory. The model is not a perfect predictor; it states that on average a change in the magnitude of the x-axis variable leads to a change of a specific amount in the magnitude of the y-axis variable.

In this instance the slope of the line is given by -105,000/1, which is the vertical distance divided by the corresponding horizontal distance. Since the line is straight, this slope is unchanging.

Road fatalities – theory, evidence and inference

Table 2.3 contains data on annual road fatalities per 100,000 drivers for various age groups. In the background, we have a theory, proposing that driver fatalities depend upon the age of the driver, the quality of roads and signage, speed limits, the age of the automobile stock and perhaps some other variables. Our model focuses upon a subset of these variables, and in order to present the example in graphical terms we specify fatalities as being dependent upon a single variable – age of driver.

The scatter diagram is presented in Figure 2.4. Two aspects of this plot stand out. First, there is an exceedingly steep decline in the fatality rate when we go from the youngest age group to the next two age groups. The decline in fatalities between the youngest and second youngest groups is 5.4 points, and between the second and third age groups is 1.7 points. The decline between the third and fourth groups is minimal - just 0.3 points. Hence, behaviour is not the same throughout the age distribution. Second, we notice that fatalities increase for the oldest age group, perhaps indicating that the oldest drivers are not as good as middle-aged drivers.

These two features suggest that the relationship between fatalities and age differs across the age spectrum. Accordingly, a straight line would not be an accurate way of representing the behaviours in these data. A straight line through the plot implies that a given change in age should have a similar impact on fatalities, no matter the age group. Accordingly we have an example of a non-linear relationship. Such a non-linear relationship might be represented by the curve going through the plot. Clearly the slope of this line varies as we move from one age category to another.

Figure 2.4 Non-linearity: Driver fatality rates Canada, 2009

Fatality rates vary non-linearly with age: At first they decline, then increase again, relative to the youngest age group.

Revisiting the definition of economics – core beliefs

This is an appropriate point at which to return to the definition of economics in Chapter 1 that we borrowed from Nobel Laureate Christopher Sims: Economics is a set of ideas and methods for the betterment of society.

If economics is concerned about the betterment of society, clearly there are ethical as well as efficiency considerations at play. And given the philosophical differences among scientists (including economists), can we define an approach to economics that is shared by the economics profession at large? Most economists would answer that the profession shares a set of beliefs, and that differences refer to the extent to which one consideration may collide with another.

• First of all we believe that markets are critical because they facilitate exchange and therefore encourage efficiency. Specialization and trade creates benefits for the trading parties. For example, Canada has not the appropriate climate for growing coffee beans, and Colombia has not the terrain for wheat. If Canada had to be self-sufficient, we might have to grow coffee beans in green-houses—a costly proposition. But with trade we can specialize, and then exchange some of our wheat for Colombian coffee. Similar benefits arise for the Colombians.

  
  A frequent complaint against trade is that its modern-day form (globalization) does not benefit the poor. For example, workers in the Philippines may earn only a few dollars per day manufacturing clothing for Western markets. From this perspective, most of the gains from trade go to the Western consumers and capitalists, come at the expense of jobs to western workers, and provide Asian workers with meagre rewards.

• A corollary of the centrality of markets is that incentives matter. If the price of business class seats on your favourite airline is reduced, you may consider upgrading. Economists believe that the price mechanism influences behaviour, and therefore favour the use of price incentives in the marketplace and public policy more generally. Environmental economists, for example, advocate the use of pollution permits that can be traded at a price between users, or carbon taxes on the emission of greenhouse gases. We will develop such ideas in Principles of Microeconomics Chapter 5 more fully.

• In saying that economists believe in incentives, we are not proposing that human beings are purely mercenary. People have many motivations: Self-interest, a sense of public duty, kindness, etc. Acting out of a sense of self-interest does not imply that people are morally empty or have no altruistic sense.

• Economists believe universally in the importance of the rule of law, no matter where they sit on the political spectrum. Legal institutions that govern contracts are critical to the functioning of an economy. If goods and services are to be supplied in a market economy, the suppliers must be guaranteed that they will be remunerated. And this requires a developed legal structure with penalties imposed on individuals or groups who violate contracts. Markets alone will not function efficiently.

  
  Modern development economics sees the implementation of the rule of law as perhaps the central challenge facing poorer economies. There is a strong correlation between economic growth and national wealth on the one hand, and an effective judicial and policing system on the other. The consequence on the world stage is that numerous 'economic' development projects now focus upon training jurists, police officers and bureaucrats in the rule of law!

• Finally, economists believe in the centrality of government. Governments can solve a number of problems that arise in market economies that cannot be addressed by the private market place. For example, governments can best address the potential abuses of monopoly power. Monopoly power, as we shall see in Microeconomics Chapter 10, not only has equity impacts it may also reduce economic efficiency. Governments are also best positioned to deal with environmental or other types of externalities – the impact of economic activity on sectors of the economy that are not directly involved in the activity under consideration.

In summary, governments have a variety of roles to play in the economy. These roles involve making the economy more equitable and more efficient by using their many powers.