Figure 2

The column magnola_region is the treatment condition. We created a new column called magnola_region_cat, a categorical variable, that takes the value High Exposure if magnola_region == 1, otherwise Low Exposure. Then we use converted the variable magnola_region_cat into a factor variable. Factors are how categorical variables are represented in R.

We then assign such variables into ‘levels’.

For example, High Exposure is now the first level. That means it will be drawn first when we re-create Figure 2. If we want to perfectly re-create Figure 2, we need High Exposure to be drawn second. So, we have to re-order the levels in the column.

We then plot the categories with the error bar.

Figure 2b

Figure 2b shows the fraction of subjects that traded by camp and distance to the village Magnola. The scatter plot is distance on the x-axis and the mean of trade in the y-axis, and total trade as the magnitude shown by the size of the circle.

Figure 3

We now combine both charts to see them side by side

Table 1

The main finding is that the High Exposure subjects are less likely to trade and thus exhibit endowment effects. This finding is seen in Table 1.

Table 1

## 
## Call:
## lm(formula = trade ~ mangola_region_cat + distance_to_mangola + 
##     lighter + (lighter * distance_to_mangola), data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.6140 -0.2847 -0.2157  0.4732  0.7847 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)                      0.496565   0.153222   3.241  0.00142 **
## mangola_region_catHigh Exposure -0.285900   0.145628  -1.963  0.05119 . 
## distance_to_mangola              0.001437   0.002627   0.547  0.58508   
## lighter                          0.079017   0.098073   0.806  0.42150   
## distance_to_mangola:lighter     -0.002969   0.002272  -1.307  0.19293   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.471 on 177 degrees of freedom
## Multiple R-squared:  0.09322,    Adjusted R-squared:  0.07273 
## F-statistic: 4.549 on 4 and 177 DF,  p-value: 0.001603

Notice how the coefficients above are the same as Table 1 Specification 5 but the standard errors are different. This is because the authors cluster the standard errors at the village level. Before we dive into clustering, we need to appreciate why we care about the standard errors.

The standard error is the estimate of the variance of a regression coefficient, and it plays a huge role in hypothesis testing. Recall that the null hypothesis test on any coefficient is that its expected value is zero (i.e., no or “null” effect of the variable on the outcome). The test statistic of the hypothesis test is thus distributed around zero, and the probability that we should observe our regression coefficient assuming the null hypothesis is true is the area underneath the curve above and below the test statistic. This probability is the p-value, and the p-value determines whether we reject or fail-to-reject the null hypothesis. So, if we have the wrong estimate of the standard error, we will make the wrong inference about our regression coefficient.

The t-stat is:

The P-Value is:

Individuals from the same tribe could show high degrees of correlation because behaviors among the group are very similar. To remove this potential bias—say, subjects make individual decisions based on what they think ‘the group’ would make—the leaders of this experiment clustered the standard errors by tribe.

The results are:

Now we cluster the errors.

The standard errors changed, and thus the p-values. Coefficients remained the same.