The simplest economic models use economic theory to explain how changes in one variable are affected by changes in others. The variable whose changes are explained is called an endogenous variable, while the one whose changes cause the other to change is exogenous. To borrow an oft-used example, we might model households' expenditures on food as depending on their incomes. In this case, we would be asking how changes in income affect food expenditures, so income would be the exogenous variable and food expenditures would be the endogenous variable. (The question of endogeneity vs. exogeneity can be quite complicated. To examine some of the more subtle issues, visit Special Topic: Endogenous and Exogenous Variables).
Once theory has suggested that there might be a causal relationship between the two variables, the next step in building a model is to specify that relationship as a simple mathematical function. There are many different functional forms that are used in economics, but theory rarely tells us very much about which one might be the best. The simplest (and one of the most commonly used) functional form is the linear function, which assumes that the graphical relationship between the variables can be represented as a straight line. In equation form, a linear function for our food-expenditure model can be written as E = B0 + B1 Y, where E measures food expenditures of household in a particular month, Y is the household's monthly income, and B0 and B1 are fixed constants that are generally unknown to the economist. The constants B0 and B1 are called coefficients or parameters of the model. They measure the position and slope of the line representing the expenditure function.
The linear functional form has the property that a change in Y of a given amount always causes the same change in E. A dollar of additional income causes food expenditures to increase by B1 dollars, regardless of the levels of the income and expenditures before the change occurs. If we graph the function with E measured on the vertical axis and Y on the horizontal axis, then B1 is the slope of the function. Economists often use linear functions for economic models, but sometimes other functional forms turn out to represent the model better. Some of these alternatives are examined in Special Topic: Alternative Function Forms.
While the level of a household's food expenditures is undoubtedly influenced by its income, there are surely other variables that also affect food spending. Food prices, the number of people in the household, the household's wealth, and the household's general preferences for food vs. other commodities all play a prominent role in decisions about food expenditures. In fact, there are probably thousands of factors that affect household decisions including such subtle factors as weather and mood. If we can measure some of these variables, when we can add them to the expenditure function. For example, we might include the price of food (P) and write the expenditure function as E = B0 + B1 Y + B2 P, where B2 is a constant parameter that measures the effect of a one-unit increase in food prices on food expenditures.
Many of the factors that influence food expenditures cannot be measured by the economist. Sometimes this is due to the inadequacy of his or her data set. For example, the number of people in the household is, in principle, measurable, but may not have been recorded in the survey that the economist is using. In other cases, the factor itself is innately immeasurable. There is no way of quantifying a household's general preferences for food consumption or its mood during a particular month. In empirical analysis, unmeasured variables cannot be included in the expenditure function. Instead, we add a general disturbance term or error term to the function to represent the effect of factors other than those included as exogenous variables. If we go back to our simplest expenditure model and add a disturbance term U, we get E = B0 + B1 Y + U.
Since we cannot measure the disturbance term directly, we usually assume that it behaves like a random variable. The value of the disturbance term for any given household is determined randomly; the economist is assumed to know nothing about what causes one household's value to be larger or smaller than another's. However, we usually assume that we know the shape of the probability distribution from which the random variable is drawn. In simple terms, the probability distribution answers questions like "Are positive and negative values equally likely to occur?" and "Are values near zero more likely than values considerably above or below zero?" The theory of probability distributions is well beyond the scope of this tutorial. For a brief introduction and some examples, look at Special Topics: Random Variables and Probability Distributions.
The presence of the disturbance term means that two households with the same level of income will not necessarily have the same level of food expenditures. For example, the Jones household might have a positive value for its disturbance term so that its expenditures are higher than would be typical for households with its income. This could happen if Mr. or Mrs. Jones had a particularly large appetite or a special fondness for expensive goods. If the Lopez family consists of only two people, then it might have a negative disturbance term; their food spending would be lower than the level that is normal for households with their income.
This means that the linear relationship between income and food expenditures is only approximate. Individual households may lie above or below the line representing the "typical" relationship. If we were to plot the values of income and food expenditure for many households on a graph, they would not all line up exactly on a single, straight line. Some households, such as the Joneses, would seem to be too high relative to most of the other points; those like the Lopezes would look too low. The technique of linear regression is a statistical method of finding the line that provides the "best fit" to a set of such data. If you understand this topic, you are ready to move on to the Next Topic: Linear Regression.
To explore a special topic related to Economic Models, click below:
Special Topic: Endogenous and Exogenous Variables
Special Topic: Alternative Function Forms
Special Topics: Random Variables and Probability Distributions
To continue to the next topic: Next Topic: Linear Regression
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