Some Basic Stuff on Empirical Work Master en Economa Industrial - PDF document

21/11/2011 Some Basic Stuff on Empirical Work Master en Economía Industrial Matilde P. Machado Matilde Machado 1 Some Basic Stuff on Empirical Work • We usually talk about supply and demand as known continuous functions e.g. P S D Q Matilde Machado 2 1

21/11/2011 Some Basic Stuff on Empirical Work • However, researchers do not know these relationships. They must be estimated using data. • If data on price and quantity are available we may have a picture like: P Matilde Machado 3 Q Some Basic Stuff on Empirical Work • These dots are equilibrium prices and quantities and therefore represent the crossing of (different) aggregate demand and supply functions. • For example in the next figure we have three points corresponding to three different equilibria resulting from three different demand and supply functions (D 1 ,S 1 ), (D 2 ,S 2 ), and (D 3 ,S 3 ). Matilde Machado 4 2

21/11/2011 Some Basic Stuff on Empirical Work S 3 Price S 2 � S 1 D 3 � D 2 � D 1 Matilde Machado 5 Some Basic Stuff on Empirical Work • if we mistakenly take the three points as realizations of a single demand function instead of realizations of three different demand and supply functions, for example by running an OLS regression of quantity against price, we estimate the demand with a bias ˆ D Matilde Machado 6 3

21/11/2011 Some Basic Stuff on Empirical Work S 3 Price S 2 � S 1 D 3 � D 2 � D 1 D ˆ Matilde Machado 7 Some Basic Stuff on Empirical Work • Clearly we need to account for demand shifters i.e. other variables that may shift the demand function. For example, population (N), prices of related goods (Pr) and income (M) may explain the shifts in demand in different points in time (D 1 , D 2 , and D 3 ). • So suppose we estimate an equation as the following, would we obtain unbiased demand estimates? • = + + + + + Pr Q b b P b M b b N e d 0 1 2 3 4 d Matilde Machado 8 4

21/11/2011 Some Basic Stuff on Empirical Work • The answer is NO! Because of what is called the simultaneity problem. • Equilibrium prices and quantities are simultaneously determined by supply and demand. But what does that mean? and what does that imply? • It means that e d (which is correlated with Q d ) is also correlated with P = + + + + + Q b b P b M b Pr b N e d 0 1 2 3 4 d Matilde Machado 9 Some Basic Stuff on Empirical Work • Any shock to the demand or unobservable variable shifting the demand (e d ) will cause a change in price. For example, an increase in e d leads to a price increase for a given supply function: P’ P D Q Q’ Matilde Machado 10 5

21/11/2011 Some Basic Stuff on Empirical Work • Therefore, OLS estimates of the demand function are biased because the assumption of independence between the error term e d and the explanatory variables is violated. • Alternatives: – 1) estimate the demand function using Instrumental variables for the variable P. – 2) estimate a reduced form equation Matilde Machado 11 Some Basic Stuff on Empirical Work Alternative 1), Instrumental Variables • Instruments for price must be: – (strongly) Correlated with price (P) – Uncorrelated with the demand shock e d • Candidates for instruments are supply shifters that do not enter the demand functions such as cost determinants (e.g. W in the supply equation). = + + + Q c c P c W e s 0 1 2 s Matilde Machado 12 6

21/11/2011 Some Basic Stuff on Empirical Work Alternative 2) Reduced form equation: Putting the demand and supply equations together, we obtain the system:  = + + + Q c c P c W e s 0 1 2 s  = + + + + + ⇔ = + + + + +  Pr Pr Q b b P b M b b N e Q d d M d d N d W e d 0 1 2 3 4 d 0 1 2 3 4  = =  Q Q Q equilibriu m quantity d s Q only depends on exogenous variables, therefore no simultaneity problem, no bias. However, not possible to estimate demand- price elasticities. Matilde Machado 13 Some Basic Stuff on Empirical Work Cases where there is no simultaneity problem are cases where price may be considered exogenous. 1. Individual demand functions – individuals take prices as given 2. Price-taking firms’ demand functions Matilde Machado 14 7

21/11/2011 Some Basic Stuff on Empirical Work Example: Suppose we want to estimate the demand for doctors visits and we have prices and number of visits per person during a year. Suppose the demand for visits depends on price but also on the individuals’ level of exercise, for which there is no data and therefore is unobservable to the researcher. = ( , ) where P is the price of a visit and E is the average level of exercise Q f P � � E − − Matilde Machado 15 Some Basic Stuff on Empirical Work For the estimation take: = α + β = α + Q P E P u where u is an error term If u and P are not correlated then α is estimated without bias. However, since the level of exercise is in the error term it is likely that corr(E,P)=corr(u,P)<0 higher level of exercise, less demand of visits, lower price. This leads to a downward bias on the estimated α. Matilde Machado 16 8

21/11/2011 Some Basic Stuff on Empirical Work A simple example: α = -1; β = 15 Getafe Leganés P = 40 P = 30 E = 3.5 E = 4 Q =-1(40)+15(3)= 5 Q =-1(30)+15(4)=30 − 30 5 25 The estimated α is downward bias because it α = = − = − < − ˆ 2 . 5 1 − incorporates part of the effect of the physical 30 40 10 exercise. Matilde Machado 17 Some Basic Stuff on Empirical Work Graphically: α = -1; β = 15 P Q=-P+15*3.5 Q=-P+15*4=-P+60 G 40 L 30 Q=-2.5P+105 5 30 Q Matilde Machado 18 9