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, R, or Google Sheets 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 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

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

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

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

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

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

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

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

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

Solution figure 3.6 Change in the mean price per oz ounce 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 quite small, indicating that the data is not compatible with the hypothesis that there are no differences in the populations (before- and after-tax prices), as long as other assumptions about the data (e.g. stores were really sampled at random) were correct. Thus it is likely that the sugar tax had some effect on prices.

    On the other hand, the p-value for pharmacies is quite large, so we do not have strong evidence against our assumption that there are no differences in the populations.

Part 3.2 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

Solution figure 3.8 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.

  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.

    Based on the p-value, we can be reasonably confident in our assumption that the mean Berkeley and non-Berkeley prices of non-sugary beverages after the tax (in the population) are the same. In other words, there is reasonably strong evidence in favour of our assumption that there are no differences in the population means of these two groups.

    The p-value for sugary drinks, however, is small, implying that it is quite unlikely to see the sample differences we see (or more extreme ones) if in truth there were no differences.

    As we come to different conclusions about the after-tax price differences in drinks, this evidence is consistent with the hypothesis that the tax had an effect on sugary drinks prices.

  1. Except for caloric intake of non-taxed beverages, the p-values of the other entries are fairly large. This implies that the differences in consumption behaviour we observe are likely to have occurred even if, in truth, there was no difference (the null hypothesis being no difference).

    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. If possible, it is also important to prevent people from the taxed area from going to the neighbouring area to buy sugary drinks (which would be contrary to the purpose of the tax). 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.