Econ 190

ASSIGNMENT #2: EXPERIMENTAL DESIGN & HYPOTHESES SECTION

The first section of the paper that you will write is actually the second section of the pa- per. The first section is the introduction, but we will write the introduction at the very end. As I mentioned in class, you can think of the introduction as a version of an ‘execu- tive summary’ of the paper. It is difficult to write a good executive summary before you actually have the rest of the paper.

The Experimental Design & Hypotheses section consists of four parts, as we saw in class:

(1) Subsection 2.1 Basic Environment

(2) Subsection 2.2 Treatments

(3) Subsection 2.3 Hypotheses

(4) Subsection 2.4 Procedures

Let me go over each subsection, as I did in class. For the assignment you will work on the Sec2-Design.tex file of your overleaf folder.

Subsection 2.1 Basic Environment

Here you have to describe the problems at the heart of the study.  You can start by de- scribing what a lottery is. You can say, for example, that a lottery L(Y,Z) is an object that pays Y with 50% chance and Z with 50% chance.

You can then say that each problem involves a choice between two options:  a relatively safer (S) and a relatively riskier (R) lottery.  And you can also describe how each option can be generically described as: X + L(Y,Z).

Then you would describe the three frames. For example, in the ‘lottery frame’ you would have X=0.  In the ‘INS+ frame,’ you would have a positive X. But notice that you can- not just say that Y and Z in the INS+ frame are the same as in the lottery frame because then it would not just be a change of frame.  So, here is a suggestion on how to do it: use subscripts.  You would describe an option in the lottery frame as XLot + L(YLot,ZLot ) and say that XLot=0.  To do the INS+ frame you would say that an option is XIN S++ L(YIN S+,ZIN S+).   To make it clear that it is just a frame, you would say that XIN S++ YIN S+=Y Lot and X IN S++ ZIN S+=ZLot.

An Aside: You may be wondering: ‘How doI write a subscript. using latex?’  The easiest way to find out is: google it and there will be somebody describing the answer. But for this one, I’ll add something here. To write X IN S+, what I actually needed to type in latex is X$_{INS+}$. The $ tells latex that something ‘mathy’ is about to start. The _ is the way to indicate: ‘subscript’. If you wanted to indicate superscript, you would have to type ^ instead.  The { } indicates what you want latex to write as a subscript. Finally the $ tells latex that themathy part is over.

In the same manner, you can introduce the ‘Ins- frame’.

Then you can introduce the 10 problems using the Table there.  In the the code Sec2- Design.tex file, find the code for the table (starting approximately inline 6). In that piece of code you can see the following line: \label{tab:Values}. This line there creates a label. You will use this label to refer to this table. For instance, if you want to latex to write: “Ta- ble 1 presents all 10 problems” you would actually write: “Table \ref{tab:Values} presents all 10 problems”

You can describe how the problems differ, using the table. You can describe that the first four problems have expected payoffs for the safe option higher than for the risky option, that problems 6-9 have the opposite, and that problems 5 and 10 have dominated options.

Then explain that each problem can be organized depending on σ .  [The way you write σ in latex is by typing $\sigma$.] You don’t need to go into details on what a CRRA is. Maybe you just want to say something like this:

“According to the CRRA, a payoff of x generates utility given by:  u (x) = x(1−σ)/(1 − σ) if σ ≠ 1 and u (x) = ln(x) if σ = 1.  Negative coefficients indicate risk lovingness, σ = 0 captures risk neutrality, and positive coefficients indicate risk aversion.”

[You may wonder how to write the math in the previous paragraph using latex.  For latex to print u (x) = x(1−σ)/(1−σ) if σ ≠ 1, what you actually have to write is $u(x)=x^{(1-\sigma)/(1- \sigma)$ if $\sigma\neq1$]}. I assume that from this you can figure out how to write the case where σ = 1.]

You can simply explain that for each problem it is possible to solve for the value of the parameter σ in a CRRA utility function that would make a decision maker indifferent between the two options.  You can even use problem  1 as an example and describe in words what σ = −0.42 means there, as I did in class.  Then use that to explain what happens as you move to other problems.

This subsection can take a page or maybe a page and a half.  If you want to explain for longer, that is totally fine.

Subsection 2.2 Treatments

Here you have to describe the three treatments that we covered in class.

First, explain that it will be a between-subjects design. Recall that this means the follow- ing. Subjects will be assigned to participate in only one of the three treatments.

Describe the thing that treatments have in common:

• Participants face 40 choices.

• There are blocks of 10 choices, that correspond to the 10 problems described in the previous part.

• Each treatment has two parts. Each part involves 20 rounds (2 blocks of 10 prob- lems).

• All treatments have one part of 20 rounds in which subjects face the 10 problems the lottery frame. twice.

Describe then how treatments differ:

• In the Insurance+ treatment the other part with 20 rounds involves two blocks of 10 problems in the‘INS+ frame’.

• In the Insurance- treatment the other part with 20 rounds involves two blocks of 10 problems in the‘INS- frame’.

• In the Insurance treatment the other part with 20 rounds involves one block of 10 problems in the‘INS+ frame’and another block of 10 problems in the‘INS- frame’.

Recall to describe how things are randomized:

• Within each block of 10 problems the order in which participants face the prob- lems is random.

• Which of the two parts of 20 rounds participants see first and which one they see second is also random.

• In each problem, which of the two options is presented first and which is pre- sented second is randomized.

This subsection should not take more than a page.

Subsection 2.3 Hypotheses

Here you need to describe the two hypotheses that we covered in class.

For this, you need to describe how we will classify each participant in each block of 10 problems. Here it is useful to refer to each block of 10 problems as‘an elicitation.’Recall that for each block of 10 problems (each elicitation) a participant can be classified in one of seven‘bins’or‘intervals for where their σ would lie’. The seven intervals are described in detail in the slides Iused in class.  So, you will describe the seven bins. And you will explain that based on their answers to a block of 10 problems, a participant is classified in one of the 7 intervals.

It is useful to introduce notation here. For some elicitation A, you will say that IA  is the interval that the subject was assigned to. That is,IA ∈ 1, 2..., 7 so that if, for example,IA =3 it means that in elicitation A the participant’s choices placed her in the third interval.

Then you can state the hypotheses, which I will write in more words here than I did in the slide in class:

• Hypothesis 1 (within frame): For two elicitations A and B of the same frame, we say that a participant’s preferences are stable in that within-frames comparison if IA =IB.

• Hypothesis 2 (across frames): For two elicitations A and B of the different frame, we say that a participant’s preferences are stable in that across-frames comparison if IA =IB.

This subsection should take approximately a page, maybe a bit less, maybe a bit more.

Subsection 2.4 Procedures

For this subsection simply follow the procedures slides from class. You can say that par- ticipants are Amazon Turk workers and describe the final samples in each treatment.

You can then describe how there was an instruction period before participants faced the forty problems and how making mistakes in the instructions would disqualify them from the rest of the study.

Explain that no feedback was provided after each decision and how a participant was paid.

Let me remind you what the ‘bonus part’ in the slide refers to.  After participants com- pleted the 40 problems, they were presented with three simple adding/subtracting prob- lems.

Finally, describe the average earnings of a participant and the average duration of the study.

For further details, see the screenshots of the full study that I posted on canvas. This subsection should not take more than a page.