Description
Price Elasticity of Fish Demand (55 points)
Use the data set in FISHEXAM.DTA, which comes from Graddy (1995). The data contains 97 daily price and quantity observations on sh prices at the Fulton Fish Market in New York City. Please check the de nitions of the variables carefully and also use the “browse” command to see how they are recorded in the data. You are going to use this data to analyze the determinants of sh prices and to estimate a demand function for sh. In some of the questions, you need to generate new variables.
Part 1: Determinants of Fish Prices
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(10 points) Estimate an empirical model to analyze the determinants of sh price. The model needs to answer how price varies (in percentage terms) by di erent days of the week and over time (use quadratic time trend). Interpret and discuss your ndings (coe cients, their signi cance and explanatory power of the model). Is there an evidence for a systematic variation in price within a week? What do the coe cients for quadratic time trend tell us?
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(5 points) Now, add the variables “wave2” and “wave3” (to the above model), which are measures of wave heights over the past several days. Interpret the coe cients of these new variables. Are these variables individually signi cant? Explain why stormy seas would increase the price of sh. Explain why these variables can be assumed to be exogenous (not correlated with error term).
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(5 points) Now, re-estimate the model in question (2) by using the daily growth rate in sh price
as the dependent variable. Interpret the size of coe cients that are signi cant at 0.10 signi cance level. Is there a signi cant time trend? How can we explain the di erent results that we obtained for time trend in questions (2) and (3)?
Part 2: Demand Fuction for Fish
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(10 points) Now, you are expected to estimate the price elasticity of sh demand. Again, you need to control for daily seasonality and the quadratic time trend in your demand function. Discuss your ndings. Interpret the size of the coe cients that are signi cant at 0.10 signi cance level. Discuss how your results might be a ected when there is a random measurement error in “demand” variable? Discuss how your results might be a ected when there is a random measurement error in “price” variable?
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(10 points) The variables “wave2” and “wave3” are measures of ocean wave heights over the past several days. What assumptions do we need to make in order to use “wave2” and “wave3” as instrumental variables for sh price in estimating the demand equation? Discus whether these assumptions are valid. Explain what
your results in question (2) indicate about validity of one of these assumptions.
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(10 points) Now, estimate the model in (4) by 2SLS approach using “wave2” and “wave3” as instruments (here, you are expected to implement the two stage procedure in STATA). Next, estimate this 2SLS model with correct standard errors (using “ivreg” command). What is your conclusion about the price elasticity of sh demand? Based on this result, is the demand for sh price elastic or inelastic (check the de nition of “elastic demand”)? How can you explain the di erence between elasticity estimates that are obtained in questions (4) and (6). What is the main methodological problem about the model estimated in (4) (Discuss the potential reason for a bias)? .
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(5 points) Now, re-estimate the demand equation in question (6), this time by eliminating the outlier observations for “wave2” and “wave3” variables (do not include the days when the “wave2” or “wave3” are larger than 10). How did your price elasticity estimate change as compared to question (6)? What might be the other approach to eliminate the impact of these outliers on your result? (Hint: You can check the scatterplot showing the relationship between wave height and prices.)
Determinants of Crime Rate (35 points)
Cornwell and Trumbull (1994) used data on 90 counties in North Carolina, for the years 1981 through 1987, to analyze crime rates. The data are contained in CRIMEEXAM.DTA. The crime rate is number of crimes per person, “prbarr” is the estimated probability of arrest, “prbconv” is the estimated probability of conviction (given an arrest), “prbpris” is the probability of serving time in prison (given a conviction), “avgsen” is the average sentence length served, and “polpc” is the number of police o cers per capita.
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(10 points) Discuss the summary statistics for the variables in the data. (For instance: What is the average crime rate in the counties etc.? Do this for all variables that you use in your model (in the next question))
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(10 points) Estimate a model analyzing the determinants of crime rate in the counties. Include both crime related variables ( “prbarr”, “prbconv”, “prbpris”, “avgsen” “polpc”, “avgsen” ). and the control variables in your model. Here you are expected to build the best model, which will reduce the risk of bias for crime related variables. Interpret the coe cients that are signi cant at 0.10 signi cance level. Are the signs of these signi cant coe cients (especially crime related variables) in line with your expectations? If not, what might be the reason for surprising ndings (explain clearly and provide an example reason for potential bias)?
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