# ------------------------------------------------------------------- # MPO1-A Advanced Quantitative Research Methods # Lec 6: SEM # Libraries: lmtest, sandwich, AER, systemfit source("http://klein.uk/R/myfunctions.R") ls() # ------------------------------------------------------------------- # --- Ex 10: ----------------------------- fish <- read.csv("http://klein.uk/R/Lent/fish.csv", header=T) str(fish) # --- Ex 10: c) --- fish$weekday <- ifelse(fish$mon==1,"Mon", ifelse(fish$tues==1,"Tue", ifelse(fish$wed==1,"Wed", ifelse(fish$thurs==1,"Thu","Fri")))) fish$weekday <- as.factor(fish$weekday) levels(fish$weekday) head(fish) # Assume that the demand equation can be written in equilibrium for each period as: # log(totqty_t) = const + alpha_1 log(avgprice) + week day dummy effects + error # Demand is allowed to differ across days of the week. # Price variable is endogenous. # Q: What additional information # do we need to consistently estimate the demand-equation parameters? # To estimate the demand equations, need at least one exogenous variable that # appears in the supply equation (equation for price = marginal cost). # If we are to estimate the equation for price, and the variables we have are # wave2t and wave3t - measures of ocean wave heights over past few days, # Q: what assumptions are needed to use wave2 and wave3 as IVs for price # in the demand equation? # Two assumptions: # That wave2t and wave3t can be properly excluded from the demand equation. # Arguable, as wave heights are determined partly by weather, # and demand at a local fish market could depend on weather. # Second assumption is that at least one of them appears in the supply equation. # Check are the two variables are jointly significant in the # reduced form for log(avgprc_t) lm10c <- lm(lavgprc ~ weekday + wave2 + wave3, data=fish) #summary(lm10c) coeftest(lm10c, vcov=hc0) linearHypothesis(lm10c, c("wave2=0","wave3=0"), vcov=hc0) # The variables wave2t and wave3t are jointly significant. # --- Ex 10: d) --- # Now, estimate the demand equation by 2SLS. What is the 95% confidence interval for the # price elasticity of demand? Is the estimated elasticity reasonable? library(systemfit) #?systemfit ## Specify the system eqDemand <- ltotqty ~ lavgprc + weekday eqSupply <- lavgprc ~ ltotqty + wave2 + wave3 system <- list( demand = eqDemand, supply = eqSupply ) inst <- ~ wave2 + wave3 + weekday ## 2SLS estimation lm10d.sem <- systemfit(system, "2SLS", inst=inst, data=fish) coeftest(lm10d.sem) linearHypothesis(lm10d.sem, c("demand_weekdayMon=0","demand_weekdayTue=0","demand_weekdayWed=0","demand_weekdayThu=0")) ## OLS estimation lm10d.ols <- systemfit(system, data=fish) coeftest(lm10d.ols) #The point estimate of demand elasticity -0.82: #a 10 percent increase in price reduces quantity demanded by about 8.2%. #Given the supply equation evidently depends on the wave variables, #what assumptions would we need to make in order to estimate #the price elasticity of supply? #have to assume that the day-of-the-week dummies do NOT appear in the supply equation, #AND they do appear in the demand equation. #saw earlier that there are day-of-the-week effects in the demand function. #So, in the reduced form equation for log(avgprc) #Q: are the day-of-the-week dummies jointly significant? # --- Ex 10: e) --- lm10e <- lm(lavgprc ~ weekday + wave2 + wave3, data=fish) coeftest(lm10e, vcov=hc0) linearHypothesis(lm10e, c("weekdayMon=0","weekdayTue=0","weekdayWed=0","weekdayThu=0"), vcov=hc1) #Conclusion about being able to estimate the supply elasticity? #In the estimation of the reduced form for log(avgprct) variables #mon, tues, wed, and thurs are jointly insignificant #Need to examine the demand function (do these variables appear?} lm10d.iv <- ivreg(ltotqty ~ lavgprc + weekday | wave2 + wave3 + weekday, data=fish) lm10d.iv coeftest(lm10d.iv, vcov=hc0) linearHypothesis(lm10d.iv, c("weekdayMon=0","weekdayTue=0","weekdayWed=0","weekdayThu=0"), vcov=hc1) #The joint test rejects the null that mon, tues, wed, and thurs are jointly insignificant in the demand function # so supply is identified # --- based on paper: --- # Testing for Imperfect Competition at the Fulton Fish Market # in Rand Journal of Economics, 1995, 26, 75-92.