ECON0019: QUANTITATIVE ECONOMICS AND ECONOMETRICS EMPIRICAL PROJECT 2020
The mark for this essay is worth 5% of your total mark for the module.
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A cartel known as the Joint Executive Committee (JEC) controlled the rail transport of grain from the Midwest to Eastern cities in the United States during the 1880s. The cartel preceded the Sherman Antitrust Act of 1890, and it legally operated to increase the price of grain above what would have been the competitive price. From time to time, cheating by members of the cartel brought about a temporary collapse of the collusive price setting agreement. In this exercise, you will use variations in supply associated with the cartels collapses to estimate the elasticity of demand for rail transport of grain. The Stata data file ECON00192020.dta contains weekly observations on the rail shipping price and other factors from 1880 to 1886.
The main variables in the dataset are:
week – the week of observation. week = 1 if 1/1/1880-1/7/1880, week = 2 if 1/8/1880-1/14/1880, , week = 328 for final week
price – weekly index of price of shipping a ton of grain by rail.
cartel – dummy variable, = 1 railroad cartel is operative, = 0 otherwise.
quantity – total tonnage of grain shipped in the week
seas1,….,seas12 – twelve month dummy variables. To match the weekly data, the calendar has been divided into 13 periods, each approximately 4 weeks long. Thus: seas1 = 1 if date is January 1 through January 28, =0 otherwise; seas2 = 1 if date is January 29 through February 25, =0 other- wise; seas13 = 1 if date is December 4 through December 31, =0 otherwise. Since it is redundant, the last dummy variable, seas13, has been left out from the data set.
To manage the data in Stata you will need to declare that we are working with a time series ob- served at a weekly frequency starting in the first week of 1880. The following lines will achieve that:
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generate time=tw(1880w1)+ n-1 format time %tw
Answer the following questions:
1. Plot the two time series of log(price) and log(quantity). Do you see any seasonal patterns?
2. De-seasonalise log(price) and log(quantity). That is, regress log-prices and log-quantities on the month dummy variables and save the resulting residuals in logp and logq, respectively. Do the original log-price and log-quantity time series have significant seasonal effects?
3. Plot the de-seasonalised price and quantity time series and compare each of them with the time series plot of the corresponding raw time series.
4. Estimate an AR(1) model for logp and an AR model for logq. In other words, estimate logpt = γ0 + γ1logpt−1 + εt
and similarly for logq. Report the first 10 sample autocorrelations for logp and logq, respectively. In other words, report the sample correlations between logp in week t and logp in week t − k for k = 1,…,10 (and analogously for logq). Comment on how the first autocorrelation compare with the slope coefficient in the regression above. Are the autocorrelations consistent with an AR(1) model for these variables? (Hint: The lag of variable logp is obtained as L.logp in Stata and analogously for logq. Use the command corrgram for the correlogram.)
5. Let Yt be 1 if quantityt is above 23,000 in week t and zero otherwise. Estimate the following model:
Yt =1[α0 +α1logpt +vt ≥0]
where vt follows a standard normal distribution. Compute the Average Partial Effect and Partial
Effect at the Average and discuss their interpretation. Hint: This is a Probit model.
6. Suppose that the demand curve for rail transport of grain is specified as
logqt = β0 + β1logpt + ut Estimate the coefficients above via OLS.
7. The interaction between supply and demand may bias the OLS estimator. Consider using the variable cartel as an instrumental variable for logpt. Provide first-stage estimates for this regression. Is cartel a weak instrument? What are the TSLS estimates for the coefficients above?
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