Assignment 05

Link to the assignment's solutions

knitr::opts_chunk$set(cache = TRUE, autodep = TRUE)

Instructions

1. Fork this repository to your GitHub account.
2. Write your solutions in R Markdown in a file named solutions.Rmd.
3. When you are ready to submit your assignment, initiate a pull request. Title your pull request "Submission".

To update your fork from the upstream repository:

1. On your fork, e.g. https://github.com/jrnold/Assignment_04 click on "New Pull reqest"
2. Set your fork jrnold/Assignment_04 as the base fork on the left, and UW-POLS503/Assignment_04 as the head fork on the right. In both cases the branch will be master. This means, compare any chanes in the head fork that are not in the base fork. You will see differences between the US-POLS503 repo and your fork. Click on "Create Pull Request", and if there are no issues, "Click Merge" A quick way is to use this link, but change the jrnold to your own username: https://github.com/jrnold/Assignment_04/compare/master...UW-POLS503:master.

Libraries used

library("pols503")
library("rio")
library("ggplot2")
library("dplyr")
library("broom")

If you do not have the pols503 package installed, you can install it with,

library("devtools")
install_github("UW-POLS503/r-pols503")

Interactions

In the social sciences the effect of a variable $x$ on another variable $y$ often varies depending on the context or, in other words, another variable $z$. For example, let's say we are interested in studying the effect that income inequality ($x$) has on political mobilization ($y$) at the country level. Our basic argument is that as income inequality increases, the number of protests in a country also increase. However, not all countries are created equal, and while some have democratic institutions, others are authoritarian regimes. Do we expect income inequality to have the same effect on political mobilization independently of the political institutions in place? Probably not. If we take a democracy scale (e.g. Polity IV), we can theorize that in highly authoritarian regimes the effect of income inequality on political mobilization is practically null because people is afraid of repression. As countries are less authoritarian, income inequality is likely to have a larger impact on political mobilization; and maybe, in countries with very strong and representative democratic institutions, income inequality has again a smaller effect on political mobilization because citizens have effective formal channels to address the issue.

Data

In this assignment we will use replication data for Kastner's (2007) "When Do Conflicting Political Relations Affect International Trade". The replication dataset is from Berry, Golder, and Smith's (2012) "Improving Tests of Theories Positing Interaction".

Use the import() function of the rio package to import the STATA file TradConflict.dta. The file contains 74,415 rows and 43 columns/variables. Each row contains information about a country pair or dyad. The authors built the dataset using information from 76 countries from 1960 to 1992.

db <- import("TradeConflict.dta")

Theory

Kastner (2007) argues that "conflicting political interests between countries can have a detrimental effect on their economic relations" but that the "effects of international political conflict on trade are less severe in cases where internationalist economic interests have relatively strong political clout domestically."

Dependent Variable:

• Trade (lnrtrade): The log of the bilateral trade between the two countries $i$ and $j$ in year $t$ (constant 1992 dollars).

Independent Variables of interest:

• Conflict (logUNsun): Whether two countries have similar voting patterns in the UN General Assembly. The log of a 1-3 scale, where 1 = most similar' and 3 = most dissimilar'.

• Trade Barriers (avpctBCFE): Trade Barriers as a proxy for the domestic political power of economic elites with internationalist economic interests. Logged form of the Hiscox and Kastner (2002) index that evaluates trade barriers. Higher numbers mean more closed trade policies, range: {1.61 , 60.53}.

Model

$Trade = \beta_{0} + \beta_{c}Conflict + \beta_{b} TradeBarriers + \beta_{cb}(Conflict \times TradeBarriers) + \beta Controls + \epsilon$

This model is similar to their Model 1 in Table 1 (p. 676):

mod1 <- lm(lnrtrade ~ lnrpciab + avremote + landlocked + island + 
              landratio + pciratio + jointdem + laglnrtrade +
              lnrgdpab + lndist + logUNsun * avpctBCFE, 
           data = db)

A: Create a new variable avpctBCFEcat3 by splitting the variable avpctBCFE into 3 categories.

B: Run a new version of mod1 (mod2) but in this case ignore the interaction effect between the variables logUNsun and avpctBCFE, and substitute the variable avpctBCFE for the new categorical you just created.

C: Plot the predicted values of the model mod2 against the covariate logUNsun. Draw a linear regression line on it.

D: If you used geom_point() in the previous plot, you probably saw that there are a lot of data points. Replicate the same plot using stat_binhex() instead of geom_point(). You can find the documentation here.

E: Take a look at the plot and at the coefficient for logUNsun in mod2. What can you say about the relationship betweeh this covariate and the outcome variable lnrtrade?

F: Replicate the same plot (logUNsun v. fitted values of mod2) but in this case use again geom_point() and color the dots differently depending on their values for avpctBCFEcat3. Make sure you also plot 3 different lines describing the relationship between logUNsun and the predicted values of lnrtrade for each group of avpctBCFEcat3. What do you see? How would you interpret this new plot?

G: Run a new model (mod3) similar to mod2 but in this case interact the variables logUNsun and avpctBCFEcat3.

H: Keeping all the control variables at their means, calculate the predicted values for the following scenarios:

#	logUNsun	avpctBCFEcat3
1	0	low
2	1	low
3	0	medium
4	1	medium
5	0	high
6	1	high

I: Calculate the following:

- `dif1`: Difference between the predicted values of scenarios 2 and 1: (`logUNsun` == 1 & `avpctBCFEcat3` == low) - (`logUNsun` == 0 & `avpctBCFEcat3` == low).
- `dif2`: Difference between the predicted values of scenarios 4 and 3: (`logUNsun` == 1 & `avpctBCFEcat3` == medium) - (`logUNsun` == 0 & `avpctBCFEcat3` == medium).
- `dif3`: Difference between the predicted values of scenarios 6 and 5: (`logUNsun` == 1 & `avpctBCFEcat3` == high) - (`logUNsun` == 0 & `avpctBCFEcat3` == high).
- `dif4`: Difference between the predicted values of scenarios 3 and 1: (`logUNsun` == 0 & `avpctBCFEcat3` == medium) - (`logUNsun` == 0 & `avpctBCFEcat3` == low).
- `dif5`: Difference between the predicted values of scenarios 5 and 1: (`logUNsun` == 0 & `avpctBCFEcat3` == high) - (`logUNsun` == 0 & `avpctBCFEcat3` == low).
- `dif6`: Difference between `dif2` and `dif1`.
- `dif7`: Difference between `dif3` and `dif1`.

J: Explain in your own words what do all these differences represent.

K: Create a dataset with all these differences

L: Create and print a table showing the mod1 coefficients, standard errors, t-statistic and p.value for only the Intercept and the covariates: logUnsun, avpctBCFEcat3, and their interactions.

M: Compare the coefficients to the differences you previously calculated. Can you now interpret the coefficients?

N: Keeping all the other covariates at their mean, use mod3 to predict (+ 95% confidence interval) the following 300 scenarios. Hint: create a new dataset (scenarios2) containing the information of all these scenarios and use it for the newdata argument in the predict() function.

#	logUNsun	avpctBCFEcat3
1	min(logUNsun)	low
...	...	low
100	max(logUNsun)	low
101	min(logUNsun)	medium
...	...	medium
200	max(logUNsun)	medium
201	min(logUNsun)	high
...	...	high
300	max(logUNsun)	high

O: Plot the predicted values against the logUNsun values. You should plot 3 lines, one for each group of avpctBCFEcat3 (low, medium, high). You should also include a 95% confidence interval around each line. Hint: You need to merge first the dataset scenarios2 with the resulting dataset from the predictions.

P: Explain in your own words what the plot is showing.

Q: Keeping all the other covariates at their mean, use now mod1 (where avpctBCFE is contious and not categorical) to predict (+ 95% confidence interval) the following 110 scenarios. Hint: create a new dataset (scenarios3) containing the information of all these scenarios and use it for the newdata argument in the predict() function.

#	logUNsun	avpctBCFE
1	min(logUNsun)	quantile(avpctBCFE, 0.0)
...	...	quantile(avpctBCFE, 0.0)
10	max(logUNsun)	quantile(avpctBCFE, 0.0)
11	min(logUNsun)	quantile(avpctBCFE, 0.05)
...	...	quantile(avpctBCFE, 0.05)
20	max(logUNsun)	quantile(avpctBCFE, 0.05)
201	min(logUNsun)	quantile(avpctBCFE, 1)
...	...	quantile(avpctBCFE, 1)
210	max(logUNsun)	quantile(avpctBCFE, 1)

R: Plot the predicted values against the logUNsun values. You should plot a different line for each different value of avpctBCFE. You don't need to include a 95% confidence interval around these lines. Hint: Although now we are using the continuous instead of the categorical representation of the variable avpctBCFE, to plot different lines according to different values of avpctBCFE, you will need to define the variable as a factor() in the ggplot's aesthetics.