Empirical Project 2 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 2.1 Collecting data by playing a public goods game


Unless otherwise specified, numerical values are shown to two decimal places.

  1. The example data used in Questions 1 and 2 is from Excel walk-through 2.1.

Solution figure 2.1 Average contribution over time.

As shown in Solution figure 2.1, the average contributions over the course of the game fluctuate around a mean value of about 11.

  1. For period 1, the contribution in the example game (9) is lower than the average contribution in Hermann et al. (2008). Results in Hermann et al. (2008) display a downward pattern over time, unlike those in the example game, which fluctuate without a clear trend.
  1. There are many possible reasons why results may be similar or different, including:

    • social norms about how much people should contribute
    • groups are not anonymous in your experiment (you know who your group members are even though the contribution of each member is anonymous); if you are friends with your group members, you may be able to sustain higher contributions.

Part 2.2 Describing the data

Without punishment With punishment
10.58 10.64
10.63 11.95
10.41 12.66
9.81 12.97
9.31 13.33
8.45 13.50
7.84 13.57
7.38 13.64
6.39 13.57
4.38 12.87

Solution figure 2.2 Mean contributions by period, with and without punishment.

Solution figure 2.3 Comparison of mean contributions over time.

  1. Solution figure 2.4 shows the mean contribution in the first and last period for both experiments.

Solution figure 2.4 Average contributions in Periods 1 and 10, with and without punishment.

Period Without punishment With punishment
1 2.02 3.21
10 2.19 3.90

Solution figure 2.5 Standard deviations in both experiments.

  1. The maximum and minimum for Periods 1 and 10 for both experiments are given in Solution figure 2.6.
Without punishment With punishment
Period Minimum Maximum Minimum Maximum
1 7.96 14.10 5.82 16.02
10 1.30 8.68 6.20 17.51

Solution figure 2.6 Minimum and maximum values for both experiments.

  Mean Standard deviation Minimum Maximum
Contribution (Period 1, without punishment) 10.58 2.02 7.96 14.10
Contribution (Period 10, without punishment) 4.38 2.19 1.30 8.68
Contribution (Period 1, with punishment) 10.64 3.21 5.82 16.02
Contribution (Period 10, with punishment) 12.87 3.90 6.20 17.51

Solution figure 2.7 Summary tables for contributions in both experiments.

Part 2.3 Did changing the rules of the game affect behaviour?

Outcome sequence 1 Outcome sequence 2
Tails Heads
Heads Heads
Heads Tails
Heads Tails
Tails Tails
Tails Tails

Solution figure 2.8 Example data from two coin-toss experiments.

  1. There can be systematic differences between the lab and the outside world that influence human behaviour. The environment of the lab experiment has unique features that are not present in the real world. The experience of being a subject, the subjects’ awareness that they are being monitored, the power of the experimenter, and the significance of the situation can all cause subjects’ behaviour to be different from behaviour in the real world. As a result, we need to be cautious when extrapolating lab findings to the outside world.

    There are many limitations to discuss, including the following examples.

    • An individual’s behaviour in a situation can be affected by the degree of anonymity. Differing degrees of anonymity between an experiment scenario and its real-world counterpart reduce the generalizability of lab findings. For example, subjects in the experiment may be unrelated to each other and forbidden from communicating with each other. In the real world, however, people can be related through family, work, and friendship, and are usually able to communicate with each other. For the experimental situation to be representative of its real-world counterpart, it is therefore important to ensure that the degree of anonymity is similar to that of the real world.
    • Lab experiments aim to isolate the effects of changes in one variable by controlling all other variables. Human behaviour is dependent on a large number of variables, many of which are not even measurable. Examples of such variables include past experiences, social norms, and ability. It is difficult, if not impossible, for social scientists to completely control for all these variables. Because of this, social scientists may fail to obtain the ceteris paribus effects of interest. Social scientists should explore new ways to measure these variables and control for them, especially if they affect the relationships being studied.
    • Behaviour can be dependent on the size of the stake involved. Stakes in the real world are typically higher than in experiments. The lab findings may therefore reveal little about real-world behaviour.
    • Individuals with certain characteristics tend to select themselves into experiments, resulting in samples that are not representative of the population. For example, college students interested in the research and seeking additional income are more likely to become experimental subjects. If these characteristics affect the relationships of interest, then the results are biased. The sample selection problem means lab findings cannot be generalized to the outside world. Researchers should try random sampling of the population rather than relying on volunteers. Econometric methodologies that mitigate the effects of sample selection should be adopted.
    • Subjects in the typical experiment face limited and well-specified instructions and choices. In the real world, the choice set can be infinitely large and vaguely defined. Individuals may even be able to influence rules in the real world. Lab experiments usually last no longer than a few hours, whereas in the real world, many decisions are made over long periods of time. Individuals may behave differently as the time horizon expands.

    In general, in experimental social science studies involving human subjects, it is difficult to ensure perfectly that the sample is representative of the population of interest and that the situation in the experiment is representative of its real-world counterpart. These difficulties limit the generalizability of lab findings to the real world. To alleviate these problems, researchers can use random sampling and design the experiment to be as realistic as possible. Models of laboratory behaviour can be used to anticipate issues, inspiring adjustments to be made to the study. Designs that recognize the weaknesses of the lab can be adopted. Researchers can also use econometric methodologies that mitigate the problems and extract valuable information from imperfect data.