Empirical Project 3 Solutions

These are not model answers. They are provided to help students, including those doing the project outside a formal class, to check their progress while working through the questions using the Excel or R walk-throughs. There are also brief notes for the more interpretive questions. Students taking courses using Doing Economics should follow the guidance of their instructors.

Part 3.1 The treatment group: before-and-after comparisons of retail prices

Store Type Dec 2014 Jun 2015 Total
1 177 209 386
2 407 391 798
3 87 102 189
4 73 96 169
Grand total 744 798 1,542

Frequency table: All stores in December 2014 and June 2015.

Solution figure 3.1 Frequency table: All stores in December 2014 and June 2015.

The number of observations for each store type is similar in each time period. Store type 4 is associated with the largest percentage change over time of about 32%.

Store Type No Tax Tax Total
1 92 85 177
2 196 211 407
3 44 43 87
4 34 39 73
Grand total 366 378 744

Numbers of taxed and untaxed beverages by store type, December 2014.

Solution figure 3.2 Numbers of taxed and untaxed beverages by store type, December 2014.

Store Type No Tax Tax Total
1 111 98 209
2 192 199 391
3 52 50 102
4 44 52 96
Grand total 399 399 798

Numbers of taxed and untaxed beverages by store type, June 2015.

Solution figure 3.3 Numbers of taxed and untaxed beverages by store type, June 2015.

In both periods, the number of taxed and non-taxed beverages is similar for each store type.

Row Labels Dec 2014 Jun 2015 Total
Energy 56 58 114
Energy-diet 49 54 103
Juice 70 64 134
Juice Drink 19 17 36
Milk 63 61 124
Soda 239 262 501
Soda-diet 128 174 302
Sport 11 16 27
Sport-diet 2 2 4
Tea 52 45 97
Tea-diet 6 6 12
Water 48 38 86
Water-sweet 1 1 2
Grand total 744 798 1,542

Products types available, December 2014 and June 2015.

Solution figure 3.4 Products types available, December 2014 and June 2015.

The SODA type has the highest number of observations. The SPORT-DIET type has the lowest number of observations.

Beverages belonging to more popular types are more likely to be in the panel of beverages. More popular types therefore tend to have more observations, since they are likely to be available in a greater number of stores.

Non-taxed Taxed
Store type Dec 2014 Jun 2015 Dec 2014 Jun 2015
1 11.19 11.48 15.62 16.93
3 15.20 16.08 18.18 19.08

Average price per ounce of taxed and non-taxed beverages, by time period and store type.

Solution figure 3.5 Average price per ounce of taxed and non-taxed beverages, by time period and store type.

  Non-taxed Taxed
Large supermarkets 0.29 1.31
Pharmacies 0.88 0.90

Change in the average price per oz ounce for taxed and non-taxed beverages, by store type.

Solution figure 3.6 Change in the average price per oz ounce for taxed and non-taxed beverages, by store type.

Mean change in price per oz for taxed and non-taxed beverages, by store type.

Solution figure 3.7 Mean change in price per oz for taxed and non-taxed beverages, by store type.

Note: When comparing these values to those in Silver et al. (2016), you will find that the data match for the ‘Large Supermarket’ and ‘Pharmacy store’ types, but not for the ‘Small Supermarket’ and ‘Gas Station store’ types. These discrepancies are due to the differences in categories used by Silver et al. (2016) - for example, Silver et al. use ‘Independent corner stores and independent gas stations’ and ‘Small chain supermarkets and chain gas stations’ instead of ‘Small supermarkets’ and ‘Gas stations’.

  1. The p-value for large supermarkets is less than the significance level of 0.05. The null hypothesis that the difference is 0 should therefore be rejected. This evidence is in support of the existence of some effects of the taxes on prices.

    The p-value for pharmacies is greater than 0.05. We therefore do not reject the null hypothesis that the difference is 0. This result is not in support of the existence of effects of taxes on prices.

Part 3.2 The control group: before-and-after comparisons with prices in other areas

  1. Ideally, we would like the characteristics of the non-Berkeley stores to be the same as those of the Berkeley stores, so that patterns observed for the non-Berkeley stores can inform us about the patterns of Berkeley stores, if there had not been tax changes. If the two regions are sufficiently similar, then the differences in changes in the mean prices can be attributed to the tax policy.

    The researchers chose suitable comparison stores, as the stores’ characteristics are very similar to those in Berkeley.

Non-taxed Taxed
Year/Month Berkeley Non-Berkeley Berkeley Non-Berkeley
2013
1 5.72 5.35 8.69 7.99
2 5.81 5.37 8.66 8.19
3 5.86 5.42 8.82 8.19
4 5.86 5.65 9.02 8.25
5 5.83 5.21 8.73 7.81
6 5.79 5.06 8.61 7.46
7 5.97 5.15 8.32 7.27
8 5.90 5.14 8.92 7.57
9 5.91 5.15 9.13 7.90
10 5.87 5.24 9.10 7.85
11 6.08 5.37 9.23 8.07
12 6.09 5.34 9.06 7.89
2014
1 6.12 5.37 8.98 8.00
2 6.20 5.53 9.20 7.95
3 6.47 5.84 9.53 8.17
4 6.38 5.80 9.64 8.35
5 6.52 5.73 9.66 8.50
6 6.56 5.80 9.19 8.11
7 6.48 5.59 9.29 8.24
8 6.37 5.66 9.34 8.10
9 6.65 5.84 9.32 8.60
10 6.38 5.60 9.48 8.58
11 5.85 5.65 8.03 8.47
12 6.19 5.52 9.67 8.53
2015
1 6.41 5.85 10.02 8.82
2 6.39 5.66 9.24 8.49
3 6.51 5.71 10.02 8.82
4 6.48 5.83 10.38 8.76
5 6.64 5.82 10.34 8.94
6 6.64 5.83 10.42 8.69
7 6.37 5.73 10.58 8.90
8 6.45 5.69 11.10 9.03
9 6.51 5.67 10.44 8.71
10 6.54 5.67 10.70 8.79
11 6.67 5.85 10.71 8.98
12 6.56 5.76 10.54 8.59
2016
1 6.58 5.87 10.57 8.96
2 6.55 5.76 10.81 8.73
Grand total 6.27 5.58 9.58 8.35

Average prices of taxed and non-taxed beverages in Berkeley vs non-Berkeley stores.

Solution figure 3.8 Average prices of taxed and non-taxed beverages in Berkeley vs non-Berkeley stores.

Average prices of taxed and non-taxed beverages in Berkeley vs non-Berkeley stores.

Solution figure 3.9 Average prices of taxed and non-taxed beverages in Berkeley vs non-Berkeley stores.

Non-taxed goods in Berkeley are more expensive than those outside Berkeley. The difference in prices before the tax indicates there are fundamental differences between the two regions irrespective of the tax policy. The difference stays roughly the same after the tax. This suggests that there were probably no other changes in the period that affected the difference in prices.

Taxed goods in Berkeley are more expensive than those outside Berkeley. The difference in prices increased after the tax was implemented (March 2015 onwards).

The prices of taxed goods and non-taxed goods in non-Berkeley regions have similar time trends. The time trends of goods in non-Berkeley regions are also similar to those in Berkeley. If we strip away the time trend, the prices of taxed and non-taxed goods in non-Berkeley regions remain roughly the same before and after the tax. This means that any events that took place during the period did not affect the level of prices in Berkeley and its neighbouring areas.

  1. The difference between the mean Berkeley and non-Berkeley price of non-sugary beverages after the tax reflects the effect of being in Berkeley as opposed to being in non-Berkeley regions. The difference between the mean Berkeley and non-Berkeley price of sugary beverages after the tax reflects not only the effect of being in Berkeley but also the effect of the tax. The difference in differences is the effect of the tax.

    We fail to reject the null hypothesis that the mean Berkeley and non-Berkeley prices of non-sugary beverages after the tax are the same. Other than the tax, there were no events that took place specifically in Berkeley that could have driven the results.

    Since the p-value is less than 0.01, we can reject the null hypothesis that the mean Berkeley and non-Berkeley prices of sugary beverages after the tax are the same. Since the difference between mean Berkeley and non-Berkeley price of non-sugary beverages after the tax is statistically indistinguishable from 0, the difference between the mean Berkeley and non-Berkeley price of sugary beverages after the tax is the effect of the tax. There is therefore evidence supporting the hypothesis that the tax had an effect.

  1. All p-values are well above the 5% significance level. We fail to reject the hypothesis that the difference before and after the tax is 0. In other words, there was not a statistically significant change in consumption behaviour in Berkeley after the tax.

    Beverages form a small proportion of the total budget of consumers. Consumers are unlikely to change their consumption by much given the tiny effect the price rise has on their budgets.

    The two major ingredients in sugary beverages, water and sugar, are craved by the human body due to their importance for survival. Beverage companies have devoted tremendous efforts to make their beverages attractive to consumers. Many beverages have become part of people’s daily routines and have also become viewed as necessities for certain occasions. These factors mean that the demand for sugary beverages is price inelastic (not responsive to price changes).

    People take time to change their consumption habits. Consumption patterns may change slowly over a long period of time. We need data for later periods to study the long-term effect of the tax.

  1. Some of the limitations listed in the paper are:

    • The study cannot fully distinguish the effect of the tax from the effect of other events, such as political campaigns related to the tax, which took place over the same period. The study cannot therefore establish the ceteris paribus causal effect of the tax. A more distant control (for example, another location that was not subject to these events) could be used to capture better the combined effects of the events and the tax.
    • The study cannot tell whether the changes in behaviours were due to anticipation of the tax or changes in prices and sales.
    • The sample of stores is too small and not representative. Consumption of SSB is small and the effect size is small relative to the high standard error. Future studies should use larger and more representative samples.
    • There are limitations in the data from independently-owned small corner stores. The possible effect of shifts in purchases to these stores cannot be studied using the data in the study.
  1. A tax change could be implemented unexpectedly to reduce the effects of events such as campaigns in the periods of observation and to prevent behaviours from adjusting even before the experiment begins. If possible, ensure that there are no other policy changes that could affect the outcomes in the observation period. Also ensure that the treatment and control groups stay the same over the period, for example, by preventing the relocation of stores in response to the tax change. Listing these factors helps to clarify the difficulties involved in establishing the conditions for a clean natural experiment in the real-world setting of policy implementation. In most countries, for example, it is not possible to prevent the relocation of stores and it would not be desirable to do so.