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Chapter 2, Microeconomic Tools for Health EconomicsFolland, S., Goodman, AC., Stano, M. The economics of health and health care. Third edition, 2001 This chapter is a review of microeconomic theory that is necessary to know in order to study health economy. Production Possibility FrontierThis is a curve that is drawn to illustrate the tradeoffs between two categories of goods. The curve shows that our choices are constrained by the fact that we cannot have everything. Which combination of goods we choose is determined by our preferences. Supply and DemandThe demand curve shows the demand for a good or a service at a specific time period for each possible price. The demand curve can shift outwards or inwards due to a number of reasons. Possible demand shifters include the following:
For instance, if we deal with normal goods, an increased income will shift the demand curve outwards. The supply curve shows the supply for a good or service at a specific time period for each possible price. Possible supply curve shifters are:
For instance, if the wages increases for a workforce producing a certain product, this would reduce the suppliers’ willingness to offer as much for sale at the original price. The supply curve shifts downwards. Equilibrium is reached where the demand and the supply curve intersect. Derived demand: The demand for one good can stipulate the demand for another good. The demand for a final good often stipulates a demand for input factors of production for this good. UtilityUtility is a measure of a person’s level of satisfaction with various combinations of consumer goods. Cardinal utility means a metric measure. The problem with this is that it is often difficult to quantify how much happier a person is of consuming one good instead of another. Therefore, ordinal utility is more common. This means that the consumer simply ranks his/her preferences instead of scaling them. Utility is often expressed as indifference curves where the consumer’s preferences are depicted over two or more goods. Budget ConstraintsThe budget constraint indicates the set of bundles the consumer can afford with a given income. To maximise satisfaction, the consumer chooses the highest attainable indifference curve that is still not outside the budget constraint. It is possible to derive the consumer’s demand curve from a set of indifference curves and budget constraints. For instance, if the price of chicken rises constantly, the consumer changes his consumption from ABCD in the picture below. This gives a derived demand curve for different prices of chicken. The market demand is derived simply by summarising horizontally the individuals demand in the market. ElasticityElasticity is the percentage change in the dependent variable resulting from a 1 percent change in the independent variable. For instance, price elasticity is the percentage change in quantity sold resulting from one percentage change in price: The Production FunctionThe production function shows the maximum output that can be obtained from all the various possible combinations of inputs. The law of diminishing returns represents the idea that the marginal product of an input will eventually fall as more is added. In practise, production usually involves several different inputs. Isoquant/Isocost CurvesAn isoquant curve shows combinations of inputs that produce equal output levels. An isocost curve shows the combination of two inputs that generate the maximum output given a fixed budget. Perfect CompetitionThe assumptions behind the idea of perfect competition are:
At equilibrium, the marginal revenue is equal to demand and to marginal cost. It is impossible to raise price since the consumer is perfectly informed and, hence, would buy from another producer. The firms maximises its output where marginal revenue equals marginal cost. Since the firm can sell all that it produces, it will continue to produce until revenue from selling one more unit is equal to the cost of producing one more unit. See diagram below. Firms in many other market structures have market power. This means that they can affect prices and, hence, also change the optimal price or quantity. When price is higher than marginal cost, the consumers incur a loss. This is referred to as the welfare loss. See diagram below. The EdgeWorth BoxThe EdgeWorth box is a good tool to illustrate interrelated markets. For instance, we have a two good market. Only two people exist in this market. Then it is possible to construct an EdgeWorth box that depicts the Pareto efficient distribution. The Pareto efficient (optimal) situation is where it is impossible to improve the lot of anyone without harming the lot of someone else. This is illustrated in the diagram below. For instance, point B is more efficient than point A. The tools developed in this chapter are basic microeconomic tools and the tools used later in the chapter will be direct applications of these tools. Chapter 3. Statistical Tools for Health Economics (Peter Olofsson) This chapter is pure statistics. If you already master this subject, I suggest that you jump to the next chapter. Economic theory predicts that demand curves will slope downward, but it does not predict the degree of responsiveness of demand to price and other variables; it is the task of statistical analysis to estimate this. Measurements of the economic behaviours may be crucial in analysing whether drug companies raise drug prices, whether income subsidies will cause people to buy more drugs, or whether mandated levels of health care are economically efficient. This chapter considers statistical methods that econometricians use to draw inferences from data that are collected. Hypothesis Testing When health care economists are confronted with statements like: “Twentyyearold men have different cholesterol levels than twentyyearold women”, they demand some validation. Statistical methods suggest formulating this statement as a hypothesis and collecting data to determine whether they are correct. The null hypothesis would then be: Men’s levels (c_{m}) equal women’s levels (c_{w}), or H_{0}: c_{m }=_{ }c_{w} against the alternative hypothesis that c_{m} does not equal c_{w} : H_{1}: c_{m }≠_{ }c_{w} Difference of Means Cholesterol levels depend on many factors and therefore we would want to avoid bias in our results. We should then make sure that our sample of women was not drawn primarily from one particular group with particular characteristics that may impact the cholesterol level, while the men where drawn from another (random picking is a good idea). To compare men’s and women’s cholesterol levels we need a test that can determine the differences between two distributions of continuous^{1} data. To get a reliable test it is logical to test several men and women and compute the mean for comparison. The Variance of a Distribution Suppose we get an average cholesterol level of 173,5 for women and 163,3 for men in a test. Although the mean levels differ, some men have higher levels than some women. The variance of a distribution is a useful way to summarize its dispersion: Variance = (110 – 173,5)^{2 }+ (125 –173,5)^{ 2}+…+(215 –173,5)^{ 2} 30 Each observation (110 etc) is subtracted from the mean (173,5), the term is squared and then the sum is divided by the total number of observations (30). If the variance is large, then the dispersion around the mean is wide meaning that another woman tested might be far from our mean. 3.2.2 Standard Error of the Mean The variance is often deflated by taking the square root to get the standard deviation. We can use the square root in combination with the Central Limit Theorem, which states that no matter what the underlying distribution, the means of that distribution are distributed like a normal curve, to plot the normal distribution of means of women’s levels with a mean of 173,5 and a standard error of 4,4 (the square root of the variance divided by the square root of the number of observations). Statisticians then know that 68 percent of the area under the curve would be within one standard error i.e, (173,54,4) s = (4,4^{2} + 4,1^{2})^{0,5 }= 6,02 Figure 3.2 illustrates the difference of means and the confidence level. To sum up, this test would find good, although not absolutely conclusive, evidence that 20yearold women have higher cholesterol levels than 20yearold men. Hypotheses and Inferences This process illustrates the steps that are necessary to test hypotheses appropriately. The econometrician must do the following:
Problems with extreme values may be solved by using the median instead of the mean. Regression Analysis Regression analysis allows the econometrician to fit a straight line through a set of data points. For example, one might seek to estimate consumer demand for aspirin. It is then likely that the amount of aspirin purchased is related to prices of substitutes, incomes of consumers, side effects and other factors. The economist can then collect information about various determinants of demand to derive a demand function (for example how price affects quantity). He can plot the quantity purchased against the price and then draw a straight line to summarize the relationship (figure 3.3). 3.3.1 Ordinary Least Squares (OLS) Regressions Two rules are used to determine the line; (1) deviations from the line must sum to 0 and; (2) one should minimize the sum of the squared deviations of the actual data points from the line that is fitted. Even though the sum of the deviations is zero, the sum of the squared deviations must be positive and one can then choose the line with the least sum of the squared deviations, this is the OLS analysis. A Demand Regression Example: Q=20 – 6,1P, R^{2}=0,10, s=2,5. This equation indicates that a onedollar increase in the price of aspirin leads to the purchase of 6,1 bottles less with a standard error of 2,5. The expression R^{2} is used to measure the fraction of the variation of the quantity that is explained by the price alone. An R^{2} of 0,10 implies that 10 percent of the variation was explained. This in turn means that 90 percent of the variation was not explained by price. This is due to the regression not including some variables that are likely to be important e.g. prices of substitutes, income etc. The example is crosssectional since we do not follow the sample over time. Therefore these samples often explain less of the variance than panel data. 3.3.3 Estimating Elasticities Regressions are also used to estimate elasticities. The price elasticity of demand is the percentage change in quantity demanded, elicited by a one percent change in price. Multiple Regression Analysis The omission of important variables in a regression may lead to a particular behaviour in the error term (the variance that cannot be explained by the explaining variable in the regression). Due to this one might want to do a multiple regression to accommodate more than two dimensions. Example of a multiple regression: Q = a + bP + cP_{0} + dY + eG + ε (error term). With the simple regression, relating Q only to P, the econometrician would not know whether income, Y, or the price of alternative medications, P_{0}, was varying. Including them in this regression allows the econometrician to hold constant these other variables and thereby reduce the error. R^{2 }will always rise with more variables. 3.4.1 Dummy Variables In health care research, econometricians are often interested in whether particular groups of patients or subjects differ from others. These groups can be indicated by using dummy variables in the regression. For example, an econometrician may wish to indicate whether a household is headed by a woman ( FEMALE = 1 ) or not ( FEMALE = 0 ). The Identification Problem Suppose now that the econometrician wishes to measure the demand for aspirin from data that represents market outcomes. The market outcome will depend on the interaction of both supply and demand. Suppose the econometrician gets data on prices and quantities from 50 different markets and the sets up the following demand regression: Q = BP + ε. In a market setting, the quantity consumed in equilibrium represents simultaneously both the quantity supplied and the quantity demanded. The graph of the data will then reflect the intersection of 50 pairs of demand and supply curves (figure 3.6). The problem is known as the identification problem, because the data at hand are not sufficient to identify whether the price and quantity data indicate a demand function, a supply function, or some combination of the two. The econometrician’s task is to identify the true equations. If the econometrician can find a variable that affects only the supply curve, then he will trace the equilibria on a demand curve. The importance is however, to take particular care when dealing with crosssectional economic aggregates. 3.6 Discrete Choice Analysis We now move away from the continuous variables and look at discrete choice analyses, meaning that there are a small number of possibilities, discrete choices, rather than a continuous set of possibilities. For example, you may want to predict the factors that make people chose Dr. A instead of Dr. B so that variable Y is zero if the patient choose Dr. A and one if the patient chooses Dr. B. This relationship is understood as probabilistic. Although you see only values of 0 and 1 for Y, it is convenient to assume that there is an underlying response variable Y*: Y* = bX + ε. Each person may have some threshold value of Y*, related to common parameters b, and to the person’s error term. If Y* is greater than that threshold, than he chooses to go to Dr. B. Some of the variables that might push the individual over the threshold between Dr. A and Dr. B would be the price charged by each doctor, the distance to the doctor’s office etc. The interpretation of the coefficients in the resulting estimated equation and the testing of hypotheses are similar to that under OLS regression. Conclusions Because many policies, such as the provision of public health services, depend on accurate measurement of economic phenomena, it is essential that the measurements be accomplished carefully and scientifically. Statistics applied to health economics may provide important information even though individual statistical analyses may be flawed by the use of improper techniques. 