Assignment 4

Widgets are a heavily regulated product in each of the ten provinces, and the federal government restricts the movement of widgets between provinces. Recently, in response to public outcry about the unaffordability of widgets, the Canadian Regulatory Economic Analysis group proposed that the federal government allow inter-provincial trade of widgets to improve market access and reduce prices. Before considering designing a new policy, however, the federal government would like to evaluate how prices for widgets have increased in recent years. The federal government is also considering an intermediate policy to allow intra-regional trade of widgets (e.g., within Atlantic Canada), while prohibiting trade between regions (e.g., between Atlantic Canada and the Prairies). In order to assess the necessity of policy action, a price index is needed for the provincial widget markets, each region, and the country as a whole.

Widgets come in a variety of types, and a survey was used to collect monthly price quotes for a selection of representative widgets of types “A” to “J” from January 2018 to December 2019. These data are stored in the Globular Prices System. These survey data are supplemented with publicly available data for type “K” widget transactions which could not be sampled over this period, as well as the value of widgets transacted in each province in 2018 and 2019. Note that type “I” widgets were a new product in 2019, and these type of widgets replaced type “J” widgets in the sample in 2019. Due to provincial regulations, only two brands of type “B” widgets are sold in British Columbia.

All of these data are summarized as follows.

File name Data
gps_prices Monthly price quotes for widget types “A” to “J” from January 2018 to December 2019 from the Globular Prices System.
micro_prices Publicly available microdata for daily transactions of type “K” widgets from January 2018 to December 2019.
weights Value of widget transaction (in thousands of dollars) in each province for 2018 and 2019.

Your goal is to build a fixed-base monthly price index for widgets, from January 2018 to December 2019, with base period January 2018, for each of the ten provinces, each of the five regions, and the country as a whole. You will use this index to answer the following questions.

  1. Consult your monthly, fixed-based indices. Which province saw the largest increase in prices since the beginning of 2018? By how much did prices change? Which province saw the smallest increase in prices since the beginning of 2018? By how much did prices change?

  2. Convert your fixed-based index into a month-over-month index. What was the single largest month-over-month movement in prices at the provincial level? In which province and month did this occur? (Hint: You can use piar’s unchain() function to convert a fixed-base index into a month-over-month one.)

  3. Convert your monthly fixed-base index into a quarterly index, and rebase it to Q1 2019. Which region had the highest prices in Q4 2019 as compared to Q1 2019? What was the value of the quarterly index there in that quarter? Which region had the the lowest prices in Q1 2018 as compared to Q1 2019? What was the value of the quarterly index there in that quarter? (Hint: you can use piar’s mean() method to convert a monthly index to a quarterly one.)

  4. For each Atlantic (10-13) and Prairie (46-48) province, calculate the variance of the month-over-month index. According to your results, which regional index indicates greater price volatility? Would you reach the same conclusion looking at the individual provincial indices? Explain the apparent discrepancy. (Hint: It may help to look at covariances, not just variances.)