17 Fixed Effects

Solutions

This file demonstrates three approaches to estimating “fixed effects” models (remember this is what economists call “fixed effects,” but other disciplines use “fixed effects” to refer to something different). We’re going to use the wbstats package to download country-level data from the World Bank for 2015 - 2018 (the most recently available for the variables I chose). We’ll then estimate models with country fixed effects, with year fixed effects, and with both country and year fixed effects. We’ll estimate each model three ways: using the within transformation, using dummy variables, and using the plm package to apply the within transformation for us. If you don’t know what these are, go through LN5 first.

Note that the model we’ll estimate isn’t a great model in terms of producing interesting, reliable result. This is by design. Part of this chapter is introducing you to another API you can use to get data. You’ve worked with the US Census Bureau’s API to get data on US counties. Now you have experience getting data on countries from the World Bank. You are free to use either source for data for your RP. If the model here was a great one, it might take away something you want to do for your RP. This way you get experience with fixed effects models and with getting data from the World Bank, but don’t waste any potential ideas you might have for your RP. So just don’t read too much into the results. They like suffer from reverse causation and omitted variable bias (both violations of ZCM). If you’re interested in cross-country variation in life expectancy you’ll need to dig much deeper than we’ll go in this chapter.

So what do you have to do? First, go through the details of the models with country fixed effects. I already did it for you, but you should go through it (together with going through LN5) to make sure you understand. After you feel you understand country fixed effects, try to estimate the models with Year Fixed Effects yourself. Once you’ve figured that out, try to estimate the models with both Country and Year Fixed Effects yourself. Just look for the code chunk comments that say “YOUR CODE GOES HERE” or “Un-comment this out after you estimate the models.”

Solutions are posted in Moodle. The bare minimum you need to do is copy what I have in the solutions and paste it into this file. Doing that will not be considered cheating (in some classes that would be considered cheating, so always make sure you know whether using posted solutions is ok or not). If all you do is copy the solutions, however, you clearly won’t come away with a better understanding of the material, so I strongly encourage you to try to work through the questions on your own before looking at the solutions. But when you’re stuck or just can’t figure out what I’m asking, use the solutions rather than wasting time.

library(wbstats) # To get data from the World Bank API
library(plm) # To estimate fixed effects models
library(formattable) # to make colorful tables similar to Excel's conditional formatting
library(stargazer)
library(tidyverse)

## Set how many decimals at which R starts to use scientific notation 
options(scipen=3)

# This shows you a lot of what's available from the World Bank API
## listWBinfo <- wb_cachelist

# List of countries in the World Bank data
countryList <- wb_countries()

# List of all available variables (what they call "indicators")
availableIndicators <- wb_cachelist$indicators

## Sometimes it's easier to look through the indicator list if you write it to CSV and open it in Excel (you can do the same thing with the US Census data). The following does that: 
# write.csv(select(availableIndicators,indicator_id, indicator, indicator_desc),"indicators.csv")

## NOTE: if you use any of these (the full list of variables, exporting it to CSV), make sure you do NOT leave that in your final code. It doesn't belong in your RMD file. I just put these thigns in here so you see how to get to this information. 

## We'll use the following variables: 
# SP.DYN.LE00.IN    Life expectancy at birth, total (years)
# NY.GDP.PCAP.KD    GDP per capita (constant 2016 US$)
# SP.POP.TOTL   Population, total
# SP.POP.TOTL.FE.ZS Population, female (% of total population)
# SP.RUR.TOTL.ZS    Rural population (% of total population)


## Create named vector of indicators to download
indicatorsToDownload <- c(
  lifeExp = "SP.DYN.LE00.IN", 
  gdpPerCapita ="NY.GDP.PCAP.KD", 
  pop = "SP.POP.TOTL",
  pctFemale = "SP.POP.TOTL.FE.ZS",
  pctRural = "SP.RUR.TOTL.ZS"
)

## Download descriptions of on World Bank indicators (i.e., variables)
indicatorInfo <- availableIndicators %>% 
                  filter(indicator_id %in% indicatorsToDownload)


## Build description of our variables that we'll output in the HTML body
sDesc <- ""
for(i in 1:nrow(indicatorInfo)){
  sDesc <- paste0(sDesc
                  ,"<b>",
                  indicatorInfo$indicator[i],
                  " (",indicatorInfo$indicator_id[i]
                  , ")</b>: "
                  ,indicatorInfo$indicator_desc[i]
                  ,"<br>")
}

## Download data
mydataOrig <- wb_data(indicatorsToDownload, 
                      start_date = 2015, 
                      end_date = 2018)

## get vector of TRUE and FALSE where FALSE indicates there's one or more NA
noNAs <- complete.cases(mydataOrig)

## When writing this code, I first checked how many rows do have NAs, and then out of how many rows 
# sum(noNAs)
## out of how many rows:
# nrow(noNAs)

## keep rows without any NA
mydata <- mydataOrig[noNAs,]

## get count of rows for each country
countOfYearsByCountry <-  mydata %>% count(country)

## merge the count variable with the data
mydata <- inner_join(mydata,countOfYearsByCountry, by="country")

## keep only countries that have all 4 years complete
mydata <- mydata %>% filter(n==4)

## drop count variable (since all are now 4)
mydata <- mydata %>% select(-n)


## For the purposes of this chapter, lets only examine one group of countries 
## so that we can output results without it taking up hundreds of lines
## If this weren't a BP chapter we wouldn't do this

## Merge in country info (e.g., region)
mydata <- inner_join(mydata,select(countryList,country,region),by="country")

## Keep only region "Latin America & Caribbean" (so we end up with only 31 countries)
mydata <- mydata %>% filter(region == "Latin America & Caribbean") %>% select(-region)

mydata <- mydata %>% rename(year=date)

## Change scale of variables. This re-scales regression coefficients (instead of getting 0.00000123)
####  Measure population in millions of people instead of people
####  Measure GDP per Capita in thousands of 2010 US $ (instead of 2010 US $)
mydata <- mydata %>% mutate(pop=pop/1000000, 
                            gdpPerCapita=gdpPerCapita/1000)

mydata %>% select(lifeExp, gdpPerCapita, pop, pctFemale, pctRural) %>% as.data.frame() %>%
  stargazer(., type = "html",summary.stat = c("n","mean","sd", "min", "p25", "median", "p75", "max"))

Statistic	N	Mean	St. Dev.	Min	Pctl(25)	Median	Pctl(75)	Max
lifeExp	124	74.780	3.419	62.485	73.206	74.799	76.821	80.095
gdpPerCapita	124	9.122	6.447	1.261	4.838	7.664	11.188	28.845
pop	124	19.394	41.699	0.094	0.575	6.315	15.632	209.469
pctFemale	124	50.600	0.892	49.071	49.962	50.566	51.090	53.114
pctRural	124	36.488	20.834	4.666	20.210	33.952	47.906	81.485

17.1 Variables

Variable descriptions from the World Bank API. These descriptions do not reflect two changes we made (that are reflected in the table of summary statistics above and in the regression results that follow): population is measured in millions of people and GDP per capita is measured in thousands of 2010 US dollars.

GDP per capita (constant 2010 US$) (NY.GDP.PCAP.KD): GDP per capita is gross domestic product divided by midyear population. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. Data are in constant 2010 U.S. dollars.
Life expectancy at birth, total (years) (SP.DYN.LE00.IN): Life expectancy at birth indicates the number of years a newborn infant would live if prevailing patterns of mortality at the time of its birth were to stay the same throughout its life.
Population, total (SP.POP.TOTL): Total population is based on the de facto definition of population, which counts all residents regardless of legal status or citizenship. The values shown are midyear estimates.
Population, female (% of total population) (SP.POP.TOTL.FE.ZS): Female population is the percentage of the population that is female. Population is based on the de facto definition of population, which counts all residents regardless of legal status or citizenship.
Rural population (% of total population) (SP.RUR.TOTL.ZS): Rural population refers to people living in rural areas as defined by national statistical offices. It is calculated as the difference between total population and urban population.

Source of data definitions: wbstats package

(Note that this is not how you would describe your variables in a paper, but for the purposes of this assignment, it’s an easy way to get an accurate description of each variable)

17.2 OLS

Our focus is fixed effects models, but often when estimating fixed effects models we also estimate regular OLS without fixed effects for comparison.

ols <- lm(data=mydata,lifeExp~gdpPerCapita+pop+pctFemale+pctRural)

17.3 Country Fixed Effects

Our basic OLS model is the following: \[ lifeExp_{it} = \beta_0+\beta_1 gdpPerCapita_{it} + \beta_2 pop_{it} + \beta_3 pctFemale_{it} + \beta_4 pctRural_{it} + v_{it} \] To save on notation, we’ll use generic variables (and I wrote out the “composite error term”), i.e.,

\[ y_{it} = \beta_0+\beta_1 x_{1it} + \beta_2 x_{2it} + \beta_3 x_{2it} + \beta_4 x_{4it} + (c_i + u_{it}) \]

Below there are 3 equations. The first is for country \(i\) in year \(t\) (the same as the one above). The second equation is the average over the four years for country \(i\), where \(\bar{y}_{i}=\sum_{t=2015}^{2018}y_{it}\) is the average value of \(y_{it}\) over the 4 years for country \(i\), \(\bar{x}_{ji}=\sum_{t=2015}^{2018}x_{jti}\) is the average value of \(x_{jti}\) over the 4 years for country \(i\) for the four explanatory variables \(j\in\{1,2,3,4\}\), \(\bar{c}_{i}=\sum_{t=2015}^{2018}c_{i}=c_i\) is the average value of \(c_{i}\) over the 4 years for country \(i\) (which just equals \(c_i\) because \(c_i\) is the same in all years for country \(i\)), and \(\bar{u}_{i}=\sum_{t=2015}^{2018}u_{it}\) is the average value of \(u_{it}\) over the 4 years for country \(i\). For the final equation, subtract country \(i\)’s average from the value in each year \(t\).

\[ \begin{align} y_{it} &= \beta_0+\beta_1 x_{1it} + \beta_2 x_{2it} + \beta_3 x_{2it} + \beta_4 x_{4it} + (c_i + u_{it}) \\ \bar{y}_{i} &= \beta_0+\beta_1 \bar{x}_{1i} + \beta_2 \bar{x}_{2i} + \beta_3 \bar{x}_{3i} + \beta_4 \bar{x}_{4i} + (\bar{c}_i + \bar{u}_{i}) \\ y_{it}-\bar{y}_{i} &= (\beta_0-\beta_0)+\beta_1 (x_{1it}-\bar{x}_{1i}) + \beta_2 (x_{2it}-\bar{x}_{2i}) + \beta_3 (x_{3it}-\bar{x}_{3i}) \\ &\hspace{6cm} + \beta_4 (x_{4it}-\bar{x}_{4i}) + (c_i-\bar{c}_i + u_{it}-\bar{u}_{i}) \end{align} \]

This final equation simplifies to the “within transformation” for country \(i\), \[ y_{it}-\bar{y}_{i} = \beta_1 (x_{1it}-\bar{x}_{1i}) + \beta_2 (x_{2it}-\bar{x}_{2i}) + \beta_3 (x_{3it}-\bar{x}_{3i}) + \beta_4 (x_{4it}-\bar{x}_{4i}) + (u_{it}-\bar{u}_{i}) \] because \(\beta_0-\beta_0=0\) and \(c_i-\bar{c}_i=0\), where \(\bar{c}_i=c_i\) because \(c_i\) is the same in all years for country \(i\). Mathematically, this is why the fixed effects model allows us to control for unobservable factors that do not change of time (or whatever is measured by \(t=1,,,,.T\)). If \(c_i\) is not constant for all time periods, then \(\bar{c}_i=c_i\) isn’t correct and it doesn’t drop out of the final equation. That means it remains in the equations we estimate, and our coefficients are biased.

At the end of this file there are tables that demonstrate the within transformation for our dataset. There is a table for each variable. Look at the table for Life expectancy. Find the row for Argentina (iso3c code ARG). It’s average value of life expectancy is 76.3. In 2015, their value was 76.07, which is 0.23 below Argentina’s four-year average value of 76.3. In 2016, Argentina’s life expectancy was 76.22, which is 0.08 above Argentina’s four-year average. Below this table for life expectancy is a similar table for each explanatory variable. When economists say a model has country “fixed effects,” they mean estimating an OLS regression using data transformed by this “within” transformation.

Alternatively, a model with country “fixed effects” can be estimated using the original OLS equation with the addition of a dummy variable for each country (omitting one).

\[ y_{it} = \beta_0+\beta_1 x_{1it} + \beta_2 x_{2it} + \beta_3 x_{2it} + \beta_4 x_{4it} + \sum_{i=2}^{50}\sigma_idC_i + (c_i + u_{it}) \]

where \(dC_i\) is a dummy variable with a value of 1 if that observation is country \(i\) and equals 0 otherwise (and \(\sigma_i\) is the coefficient on dummy variable \(dC_i\)).

These two models, the “within transformation” and the model with a dummy variable for each country, are mathematically and empirically equivalent. To see that they are empirically equivalent, we’ll estimate both models and compare the results. Note that the standard errors and \(R^2\) values are not equivalent, as discussed below.

## Dummy variable for each country (it automatically omits one)
countryDummies <- lm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural+factor(country),data=mydata)

## Within transformation (subtract country averages from each observation for each variable)

## Create Country Averages
mydata <- mydata %>%
  group_by(country) %>%
  mutate(cAvg_lifeExp=mean(lifeExp),
         cAvg_gdpPerCapita=mean(gdpPerCapita),
         cAvg_pop=mean(pop),
         cAvg_pctFemale=mean(pctFemale),
         cAvg_pctRural=mean(pctRural)
         ) %>%
  ungroup()

## Within transformation
mydataCountry <- mydata %>%
  mutate(lifeExp=lifeExp-cAvg_lifeExp,
         gdpPerCapita=gdpPerCapita-cAvg_gdpPerCapita,
         pop=pop-cAvg_pop,
         pctFemale=pctFemale-cAvg_pctFemale,
         pctRural=pctRural-cAvg_pctRural
         )  %>%
  ungroup()

## Estimate within transformation using the transformed data
countryWithin <- lm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural,data=mydataCountry)

## Using plm package
countryPlm <- plm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural,data=mydata, index=c("country"), model = "within", effect="individual")

stargazer(countryDummies,countryWithin,countryPlm, 
          type = "html", 
          report=('vcs*'),
          single.row = TRUE,
          digits = 4,
          keep.stat = c("n","rsq","adj.rsq"), 
          notes = "Standard Errors reported in parentheses, <em>&#42;p&lt;0.1;&#42;&#42;p&lt;0.05;&#42;&#42;&#42;p&lt;0.01</em>", 
          notes.append = FALSE)

	Dependent variable:
	lifeExp
	OLS		panel
			linear
	(1)	(2)	(3)
gdpPerCapita	0.0781 (0.0567)	0.0781 (0.0490)	0.0781 (0.0567)
pop	0.0757 (0.0290)**	0.0757 (0.0251)***	0.0757 (0.0290)**
pctFemale	-0.1519 (0.4495)	-0.1519 (0.3887)	-0.1519 (0.4495)
pctRural	-0.3383 (0.0388)***	-0.3383 (0.0335)***	-0.3383 (0.0388)***
factor(country)Argentina	-26.1200 (2.5877)***
factor(country)Bahamas, The	-24.0784 (2.1213)***
factor(country)Barbados	-0.0934 (0.2628)
factor(country)Belize	-8.9356 (1.6161)***
factor(country)Bolivia	-21.0753 (2.4996)***
factor(country)Brazil	-37.6904 (5.5544)***
factor(country)Chile	-19.6422 (2.4795)***
factor(country)Colombia	-21.9239 (2.3659)***
factor(country)Costa Rica	-15.1925 (2.5761)***
factor(country)Cuba	-16.1903 (2.4769)***
factor(country)Dominican Republic	-22.2571 (2.6692)***
factor(country)Ecuador	-14.1840 (2.1316)***
factor(country)El Salvador	-18.9725 (1.8990)***
factor(country)Grenada	-8.0250 (1.3951)***
factor(country)Guatemala	-12.2289 (1.5310)***
factor(country)Guyana	-7.4116 (1.1430)***
factor(country)Haiti	-23.4308 (1.7766)***
factor(country)Honduras	-12.5249 (1.9995)***
factor(country)Jamaica	-12.4726 (1.8348)***
factor(country)Mexico	-29.5143 (3.4670)***
factor(country)Nicaragua	-13.7110 (1.9065)***
factor(country)Panama	-13.3533 (2.1755)***
factor(country)Paraguay	-15.3045 (2.3842)***
factor(country)Peru	-20.3696 (2.4266)***
factor(country)Puerto Rico	-21.6200 (2.3663)***
factor(country)St. Lucia	1.4818 (0.5706)**
factor(country)St. Vincent and the Grenadines	-13.3274 (2.0799)***
factor(country)Suriname	-19.1217 (2.3163)***
factor(country)Trinidad and Tobago	-13.5569 (1.3738)***
factor(country)Uruguay	-23.2122 (2.7061)***
Constant	108.8921 (24.8138)***	0.0000 (0.0115)
Observations	124	124	124
R2	0.9986	0.6407	0.6407
Adjusted R2	0.9981	0.6286	0.5034
Note:	Standard Errors reported in parentheses, *p<0.1;**p<0.05;***p<0.01

We’ve changed a few of the stargazer options for this chapter. We’re displaying standard errors instead of p-values so that we can use only one row per variable (it lets us report coefficient and standard error on one line, but not if we use p-values instead). I modified the note to say that standard errors are reported in parentheses.

Now look at the coefficient estimates. The 3 models all have the same coefficients on gdpPerCapita, pop, pctFemale, and pctRurla. In LN5 we discuss how the within transformation is equivalent to including dummy variables for each group (in this case, countries). That’s exactly what see in the table. The PLM package estimates the within transformation for us.

You also may notice that the standard errors (and statistical significance stars) are different in the middle column. When we estimate the model with dummy variables (column 1), the regular OLS standard errors are correct. But when we apply the within transformation, we need to adjust the standard errors to account for the within transformation. This would be a bit difficult for us to do. Thankfully, the PLM package correctly adjusts the standard errors (and thus p-values) for us. Thus, in practice we won’t actually want to apply the within transformation ourselves. We’re doing it in this chapter so you can see exactly what it is in practice and see that the coefficient estimates for all 3 versions result in the same coefficients.

If you compare the \(R^2\) values across models, you’ll notice that the \(R^2\) for the model with dummy variables is much higher. Including all the dummy variables makes it artificially high. We want to use the \(R^2\) from the within transformation. The PLM model does this for us.

Another reason we want to use the PLM model when we estimate fixed effects models is that we often don’t want to see all of the coefficients on the dummy variables. For country fixed effects, the coefficient on each country dummy is estimated off of only 4 observations. Thus, it is not a reliable estimate of the effect of being Argentina (or Belize, etc). It still allows us to estimate the model with country fixed effects, even if we don’t care about the coefficient estimates themselves. However, if we had not dropped all countries except South America, we would have hundreds of dummy variables. If we were estimating a model using US county data, we would have over 3000. R probably wouldn’t even let us estimate a model with that many variables. This again makes the PLM package preferable.

17.4 Year Fixed Effects

Above you saw how to estimate models with country fixed effects in three different ways. Here, you should estimate models with year fixed effects in the same three ways. Hint: you just have to switch “country” with “year” and everythign else is the same.

## Dummy variable for each year (it automatically omits one)
yearDummies <- lm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural+factor(year),data=mydata)

## Within transformation (subtract year averages from each observation for each variable)

## Create Year Averages
mydata <- mydata %>%
  group_by(year) %>%
  mutate(yrAvg_lifeExp=mean(lifeExp),
         yrAvg_gdpPerCapita=mean(gdpPerCapita),
         yrAvg_pop=mean(pop),
         yrAvg_pctFemale=mean(pctFemale),
         yrAvg_pctRural=mean(pctRural)
         ) %>%
  ungroup()

## Within transformation
mydataYear <- mydata %>%
  mutate(lifeExp=lifeExp-yrAvg_lifeExp,
         gdpPerCapita=gdpPerCapita-yrAvg_gdpPerCapita,
         pop=pop-yrAvg_pop,
         pctFemale=pctFemale-yrAvg_pctFemale,
         pctRural=pctRural-yrAvg_pctRural
         )  %>%
  ungroup()



## Estimate within transformation using the transformed data
yearWithin <- lm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural,data=mydataYear)

## Using plm package
yearPlm <- plm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural,data=mydata, index=c("year"), model = "within", effect="individual")

stargazer(yearDummies,yearWithin,yearPlm, 
          type = "html", 
          report=('vcs*'),
          single.row = TRUE,
          digits = 4,
          keep.stat = c("n","rsq","adj.rsq"), 
          notes = "Standard Errors reported in parentheses, <em>&#42;p&lt;0.1;&#42;&#42;p&lt;0.05;&#42;&#42;&#42;p&lt;0.01</em>", 
          notes.append = FALSE)

	Dependent variable:
	lifeExp
	OLS		panel
			linear
	(1)	(2)	(3)
gdpPerCapita	0.1938 (0.0498)***	0.1938 (0.0492)***	0.1938 (0.0498)***
pop	-0.0009 (0.0072)	-0.0009 (0.0071)	-0.0009 (0.0072)
pctFemale	0.2027 (0.3512)	0.2027 (0.3468)	0.2027 (0.3512)
pctRural	-0.0347 (0.0149)**	-0.0347 (0.0147)**	-0.0347 (0.0149)**
factor(year)2016	0.1555 (0.7745)
factor(year)2017	0.2926 (0.7746)
factor(year)2018	0.4222 (0.7747)
Constant	63.8247 (17.6194)***	-0.0000 (0.2704)
Observations	124	124	124
R2	0.2497	0.2474	0.2474
Adjusted R2	0.2045	0.2221	0.2020
Note:	Standard Errors reported in parentheses, *p<0.1;**p<0.05;***p<0.01

17.5 Country and Year Fixed Effects

Now that you’ve estimated the models with year fixed effects, estimate models with both country and year fixed effects. It works the same way as above, just doing it for both country and year.

## Dummy variable for each country and each year (it automatically omits one of each)
countryyearDummies <- lm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural+factor(year)+factor(country),data=mydata)

## Within transformation (subtract country AND year averages from each observation for each variable)
## We already created the country averages and year averages above so we don't need to create them again

## Within transformation
mydataCountryYear <- mydata %>%
  mutate(lifeExp=lifeExp-cAvg_lifeExp-yrAvg_lifeExp,
         gdpPerCapita=gdpPerCapita-cAvg_gdpPerCapita-yrAvg_gdpPerCapita,
         pop=pop-cAvg_pop-yrAvg_pop,
         pctFemale=pctFemale-cAvg_pctFemale-yrAvg_pctFemale,
         pctRural=pctRural-cAvg_pctRural-yrAvg_pctRural
         )  %>%
  ungroup()

##Estimate within transformation using the transformed data
countryYearWithin <- lm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural,data=mydataCountryYear)

##Using plm package
countryYearPlm <- plm(lifeExp~gdpPerCapita+pop+pctFemale+pctRural,data=mydata, index=c("country","year"), model = "within", effect="twoways")

stargazer(countryyearDummies,countryYearWithin, countryYearPlm, 
          type = "html", 
          report=('vcs*'),
          single.row = TRUE,
          digits = 4,
          keep.stat = c("n","rsq","adj.rsq"), 
          notes = "Standard Errors reported in parentheses, <em>&#42;p&lt;0.1;&#42;&#42;p&lt;0.05;&#42;&#42;&#42;p&lt;0.01</em>", 
          notes.append = FALSE)

	Dependent variable:
	lifeExp
	OLS		panel
			linear
	(1)	(2)	(3)
gdpPerCapita	-0.0727 (0.0365)**	-0.0727 (0.0310)**	-0.0727 (0.0365)**
pop	-0.0108 (0.0188)	-0.0108 (0.0160)	-0.0108 (0.0188)
pctFemale	-0.5372 (0.2734)*	-0.5372 (0.2324)**	-0.5372 (0.2734)*
pctRural	-0.1683 (0.0270)***	-0.1683 (0.0230)***	-0.1683 (0.0270)***
factor(year)2016	0.1390 (0.0239)***
factor(year)2017	0.2773 (0.0277)***
factor(year)2018	0.4118 (0.0335)***
factor(country)Argentina	-11.7615 (1.9356)***
factor(country)Bahamas, The	-12.2177 (1.5912)***
factor(country)Barbados	1.2681 (0.1922)***
factor(country)Belize	-7.5257 (0.9843)***
factor(country)Bolivia	-15.1800 (1.5823)***
factor(country)Brazil	-10.2146 (4.0039)**
factor(country)Chile	-7.7168 (1.7726)***
factor(country)Colombia	-9.6142 (1.7322)***
factor(country)Costa Rica	-7.0988 (1.6843)***
factor(country)Cuba	-8.0607 (1.6304)***
factor(country)Dominican Republic	-13.7683 (1.7485)***
factor(country)Ecuador	-8.2193 (1.3730)***
factor(country)El Salvador	-11.7421 (1.2833)***
factor(country)Grenada	-7.7944 (0.8441)***
factor(country)Guatemala	-8.5278 (0.9716)***
factor(country)Guyana	-9.1034 (0.7054)***
factor(country)Haiti	-19.9505 (1.1098)***
factor(country)Honduras	-8.8861 (1.2436)***
factor(country)Jamaica	-9.0430 (1.1426)***
factor(country)Mexico	-10.3310 (2.5908)***
factor(country)Nicaragua	-9.7683 (1.1949)***
factor(country)Panama	-6.9810 (1.4088)***
factor(country)Paraguay	-10.9304 (1.4829)***
factor(country)Peru	-10.4522 (1.6648)***
factor(country)Puerto Rico	-7.4365 (1.8210)***
factor(country)St. Lucia	-0.7730 (0.3896)*
factor(country)St. Vincent and the Grenadines	-10.9295 (1.2721)***
factor(country)Suriname	-13.7941 (1.4627)***
factor(country)Trinidad and Tobago	-8.8542 (0.9102)***
factor(country)Uruguay	-10.9637 (1.9026)***
Constant	118.0087 (15.0183)***	-108.9780 (12.1646)***
Observations	124	124	124
R2	0.9995	0.3170	0.3170
Adjusted R2	0.9993	0.2941	0.0232
Note:	Standard Errors reported in parentheses, *p<0.1;**p<0.05;***p<0.01

17.6 Comparison of all models

Below we have comparisons of the four models: ols, country fixed effects, year fixed effects, and country and year fixed effects. The comparisons are done three times, one for each method of estimating the models.

17.6.1 Within Transformation

stargazer(ols,countryWithin,yearWithin,countryYearWithin, 
          type = "html", 
          report=('vcs*'),
          single.row = TRUE,
          digits = 3,
          keep.stat = c("n","rsq","adj.rsq"), 
          notes = "Standard Errors reported in parentheses, <em>&#42;p&lt;0.1;&#42;&#42;p&lt;0.05;&#42;&#42;&#42;p&lt;0.01</em>", 
          notes.append = FALSE)

	Dependent variable:
	lifeExp
	(1)	(2)	(3)	(4)
gdpPerCapita	0.194 (0.049)***	0.078 (0.049)	0.194 (0.049)***	-0.073 (0.031)**
pop	-0.001 (0.007)	0.076 (0.025)***	-0.001 (0.007)	-0.011 (0.016)
pctFemale	0.202 (0.347)	-0.152 (0.389)	0.203 (0.347)	-0.537 (0.232)**
pctRural	-0.035 (0.015)**	-0.338 (0.034)***	-0.035 (0.015)**	-0.168 (0.023)***
Constant	64.066 (17.414)***	0.000 (0.011)	-0.000 (0.270)	-108.978 (12.165)***
Observations	124	124	124	124
R2	0.248	0.641	0.247	0.317
Adjusted R2	0.222	0.629	0.222	0.294
Note:	Standard Errors reported in parentheses, *p<0.1;**p<0.05;***p<0.01

17.6.2 PLM Package

stargazer(ols,countryPlm,yearPlm,countryYearPlm, 
          type = "html", 
          report=('vcs*'),
          single.row = TRUE,
          digits = 3,
          keep.stat = c("n","rsq","adj.rsq"), 
          notes = "Standard Errors reported in parentheses, <em>&#42;p&lt;0.1;&#42;&#42;p&lt;0.05;&#42;&#42;&#42;p&lt;0.01</em>", 
          notes.append = FALSE)

	Dependent variable:
	lifeExp
	OLS	panel
		linear
	(1)	(2)	(3)	(4)
gdpPerCapita	0.194 (0.049)***	0.078 (0.057)	0.194 (0.050)***	-0.073 (0.036)**
pop	-0.001 (0.007)	0.076 (0.029)**	-0.001 (0.007)	-0.011 (0.019)
pctFemale	0.202 (0.347)	-0.152 (0.449)	0.203 (0.351)	-0.537 (0.273)*
pctRural	-0.035 (0.015)**	-0.338 (0.039)***	-0.035 (0.015)**	-0.168 (0.027)***
Constant	64.066 (17.414)***
Observations	124	124	124	124
R2	0.248	0.641	0.247	0.317
Adjusted R2	0.222	0.503	0.202	0.023
Note:	Standard Errors reported in parentheses, *p<0.1;**p<0.05;***p<0.01

17.6.3 Dummy Variables

stargazer(ols,countryDummies,yearDummies,countryyearDummies, 
          type = "html", 
          report=('vcs*'),
          single.row = TRUE,
          digits = 3,
          keep.stat = c("n","rsq","adj.rsq"), 
          notes = "Standard Errors reported in parentheses, <em>&#42;p&lt;0.1;&#42;&#42;p&lt;0.05;&#42;&#42;&#42;p&lt;0.01</em>", 
          notes.append = FALSE)

	Dependent variable:
	lifeExp
	(1)	(2)	(3)	(4)
gdpPerCapita	0.194 (0.049)***	0.078 (0.057)	0.194 (0.050)***	-0.073 (0.036)**
pop	-0.001 (0.007)	0.076 (0.029)**	-0.001 (0.007)	-0.011 (0.019)
pctFemale	0.202 (0.347)	-0.152 (0.449)	0.203 (0.351)	-0.537 (0.273)*
pctRural	-0.035 (0.015)**	-0.338 (0.039)***	-0.035 (0.015)**	-0.168 (0.027)***
factor(country)Argentina		-26.120 (2.588)***		-11.762 (1.936)***
factor(country)Bahamas, The		-24.078 (2.121)***		-12.218 (1.591)***
factor(country)Barbados		-0.093 (0.263)		1.268 (0.192)***
factor(country)Belize		-8.936 (1.616)***		-7.526 (0.984)***
factor(country)Bolivia		-21.075 (2.500)***		-15.180 (1.582)***
factor(country)Brazil		-37.690 (5.554)***		-10.215 (4.004)**
factor(country)Chile		-19.642 (2.480)***		-7.717 (1.773)***
factor(country)Colombia		-21.924 (2.366)***		-9.614 (1.732)***
factor(country)Costa Rica		-15.193 (2.576)***		-7.099 (1.684)***
factor(country)Cuba		-16.190 (2.477)***		-8.061 (1.630)***
factor(country)Dominican Republic		-22.257 (2.669)***		-13.768 (1.749)***
factor(country)Ecuador		-14.184 (2.132)***		-8.219 (1.373)***
factor(country)El Salvador		-18.972 (1.899)***		-11.742 (1.283)***
factor(country)Grenada		-8.025 (1.395)***		-7.794 (0.844)***
factor(country)Guatemala		-12.229 (1.531)***		-8.528 (0.972)***
factor(country)Guyana		-7.412 (1.143)***		-9.103 (0.705)***
factor(country)Haiti		-23.431 (1.777)***		-19.951 (1.110)***
factor(country)Honduras		-12.525 (2.000)***		-8.886 (1.244)***
factor(country)Jamaica		-12.473 (1.835)***		-9.043 (1.143)***
factor(country)Mexico		-29.514 (3.467)***		-10.331 (2.591)***
factor(country)Nicaragua		-13.711 (1.906)***		-9.768 (1.195)***
factor(country)Panama		-13.353 (2.176)***		-6.981 (1.409)***
factor(country)Paraguay		-15.304 (2.384)***		-10.930 (1.483)***
factor(country)Peru		-20.370 (2.427)***		-10.452 (1.665)***
factor(country)Puerto Rico		-21.620 (2.366)***		-7.436 (1.821)***
factor(country)St. Lucia		1.482 (0.571)**		-0.773 (0.390)*
factor(country)St. Vincent and the Grenadines		-13.327 (2.080)***		-10.930 (1.272)***
factor(country)Suriname		-19.122 (2.316)***		-13.794 (1.463)***
factor(country)Trinidad and Tobago		-13.557 (1.374)***		-8.854 (0.910)***
factor(country)Uruguay		-23.212 (2.706)***		-10.964 (1.903)***
factor(year)2016			0.156 (0.775)	0.139 (0.024)***
factor(year)2017			0.293 (0.775)	0.277 (0.028)***
factor(year)2018			0.422 (0.775)	0.412 (0.034)***
Constant	64.066 (17.414)***	108.892 (24.814)***	63.825 (17.619)***	118.009 (15.018)***
Observations	124	124	124	124
R2	0.248	0.999	0.250	1.000
Adjusted R2	0.222	0.998	0.204	0.999
Note:	Standard Errors reported in parentheses, *p<0.1;**p<0.05;***p<0.01

17.7 Data Summary by Country

stargazer(as.data.frame(mydata) , type = "html",digits = 2 ,summary.stat = c("n","mean","sd", "min", "median", "max"))

Statistic	N	Mean	St. Dev.	Min	Median	Max
year	124	2,016.50	1.12	2,015	2,016.5	2,018
gdpPerCapita	124	9.12	6.45	1.26	7.66	28.85
lifeExp	124	74.78	3.42	62.48	74.80	80.10
pop	124	19.39	41.70	0.09	6.31	209.47
pctFemale	124	50.60	0.89	49.07	50.57	53.11
pctRural	124	36.49	20.83	4.67	33.95	81.48
cAvg_lifeExp	124	74.78	3.41	63.08	74.80	79.84
cAvg_gdpPerCapita	124	9.12	6.44	1.27	7.63	28.10
cAvg_pop	124	19.39	41.70	0.09	6.34	206.98
cAvg_pctFemale	124	50.60	0.89	49.13	50.57	53.05
cAvg_pctRural	124	36.49	20.83	4.81	33.95	81.41
yrAvg_lifeExp	124	74.78	0.19	74.52	74.78	75.03
yrAvg_gdpPerCapita	124	9.12	0.11	9.00	9.10	9.28
yrAvg_pop	124	19.39	0.23	19.08	19.39	19.71
yrAvg_pctFemale	124	50.60	0.01	50.59	50.60	50.61
yrAvg_pctRural	124	36.49	0.29	36.10	36.49	36.87

17.7.1 Average Values for Each Country

country	Avg lifeExp	Avg gdpPerCapita	Avg pop	Avg pctFemale	Avg pctRural
Antigua and Barbuda	76.68	14.15	0.09	51.83	75.21
Argentina	76.30	10.32	43.82	51.26	8.31
Bahamas, The	73.43	28.10	0.38	51.45	17.12
Barbados	78.94	16.11	0.29	51.73	68.81
Belize	74.28	4.24	0.37	50.14	54.44
Bolivia	70.77	2.46	11.11	49.76	31.09
Brazil	75.34	11.12	206.98	50.80	13.83
Chile	79.84	14.84	18.34	50.75	12.54
Colombia	76.82	7.63	48.57	50.96	19.73
Costa Rica	79.83	9.61	4.92	49.99	21.88
Cuba	78.64	6.64	11.33	50.32	23.04
Dominican Republic	73.57	7.16	10.45	49.97	20.16
Ecuador	76.47	5.22	16.64	49.96	36.39
El Salvador	72.76	3.41	6.37	53.05	29.13
Grenada	72.41	8.63	0.11	49.58	63.87
Guatemala	73.67	3.27	15.96	50.78	49.49
Guyana	69.53	5.53	0.77	49.90	73.48
Haiti	63.08	1.27	10.91	50.64	46.14
Honduras	74.80	2.14	9.35	50.06	43.87
Jamaica	74.23	4.78	2.91	50.32	44.75
Mexico	74.94	10.22	124.04	51.09	20.28
Nicaragua	73.96	1.89	6.34	50.71	41.80
Panama	78.05	11.29	4.07	49.88	32.80
Paraguay	73.91	5.17	6.82	49.13	38.83
Peru	76.16	6.29	31.21	50.34	22.37
Puerto Rico	79.57	27.54	3.35	52.30	6.40
St. Lucia	75.83	8.89	0.18	50.75	81.41
St. Vincent and the Grenadines	72.25	6.71	0.11	49.14	48.42
Suriname	71.41	8.11	0.57	49.70	33.95
Trinidad and Tobago	73.17	15.74	1.38	50.57	46.76
Uruguay	77.57	14.28	3.43	51.75	4.81

17.7.2 Variable-Specific Values and Within Transformation for Each Country

For each variable, display each country’s values in 2015, 2016, 2017, and 2018, followed by the country’s average. These 5 columns are shaded from red (lowest) to green (highest) for each country. Then, in the final 4 columns display the within transformation (i.e., subtract the country’s average from each year’s value). These last 4 columns are also shaded for each country.

17.7.3 Life expectancy

iso3c	2015 Life Exp	2016 Life Exp	2017 Life Exp	2018 Life Exp	Avg Life Exp		2015 Within	2016 Within	2017 Within	2018 Within
ARG	76.07	76.22	76.37	76.52	76.30		-0.23	-0.07	0.08	0.22
ATG	76.48	76.62	76.75	76.89	76.68		-0.20	-0.07	0.07	0.20
BHS	73.09	73.33	73.55	73.75	73.43		-0.34	-0.10	0.12	0.32
BLZ	74.03	74.22	74.36	74.50	74.28		-0.24	-0.06	0.09	0.22
BOL	70.28	70.63	70.94	71.24	70.77		-0.49	-0.15	0.17	0.47
BRA	74.99	75.23	75.46	75.67	75.34		-0.34	-0.11	0.12	0.33
BRB	78.80	78.89	78.98	79.08	78.94		-0.14	-0.05	0.04	0.14
CHL	79.65	79.78	79.91	80.04	79.84		-0.20	-0.06	0.07	0.20
COL	76.53	76.73	76.92	77.11	76.82		-0.29	-0.09	0.10	0.28
CRI	79.56	79.74	79.91	80.10	79.83		-0.26	-0.09	0.09	0.27
CUB	78.56	78.61	78.66	78.73	78.64		-0.08	-0.03	0.02	0.09
DOM	73.24	73.47	73.69	73.89	73.57		-0.33	-0.10	0.12	0.32
ECU	76.14	76.36	76.58	76.80	76.47		-0.33	-0.11	0.11	0.33
GRD	72.44	72.41	72.39	72.38	72.41		0.04	0.00	-0.02	-0.02
GTM	73.25	73.54	73.81	74.06	73.67		-0.42	-0.12	0.14	0.40
GUY	69.26	69.45	69.62	69.77	69.53		-0.27	-0.07	0.10	0.25
HND	74.50	74.70	74.90	75.09	74.80		-0.30	-0.09	0.10	0.29
HTI	62.48	62.90	63.29	63.66	63.08		-0.60	-0.19	0.21	0.58
JAM	74.10	74.17	74.27	74.37	74.23		-0.13	-0.05	0.04	0.14
LCA	75.60	75.75	75.91	76.06	75.83		-0.23	-0.08	0.08	0.23
MEX	74.90	74.92	74.95	74.99	74.94		-0.04	-0.02	0.01	0.05
NIC	73.65	73.86	74.07	74.28	73.96		-0.31	-0.10	0.11	0.31
PAN	77.78	77.96	78.15	78.33	78.05		-0.28	-0.09	0.09	0.27
PER	75.79	76.04	76.29	76.52	76.16		-0.37	-0.12	0.13	0.36
PRI	79.35	79.49	79.63	79.78	79.57		-0.21	-0.07	0.07	0.21
PRY	73.66	73.84	73.99	74.13	73.91		-0.24	-0.07	0.09	0.23
SLV	72.41	72.64	72.87	73.10	72.76		-0.34	-0.11	0.12	0.34
SUR	71.25	71.36	71.46	71.57	71.41		-0.16	-0.05	0.05	0.16
TTO	72.94	73.10	73.25	73.38	73.17		-0.23	-0.07	0.08	0.21
URY	77.37	77.50	77.63	77.77	77.57		-0.20	-0.07	0.06	0.20
VCT	72.10	72.19	72.30	72.42	72.25		-0.16	-0.06	0.05	0.16

17.7.4 GDP per capita

iso3c	2015 GDP per Capita	2016 GDP per Capita	2017 GDP per Capita	2018 GDP per Capita	Avg GDP per Capita		2015 Within	2016 Within	2017 Within	2018 Within
ARG	10568.16	10239.48	10419.46	10049.56	10319.16		0.25	-0.08	0.10	-0.27
ATG	13328.15	13917.95	14220.50	15134.88	14150.37		-0.82	-0.23	0.07	0.98
BHS	27583.41	27705.93	28282.52	28845.26	28104.28		-0.52	-0.40	0.18	0.74
BLZ	4300.56	4216.98	4211.60	4217.21	4236.59		0.06	-0.02	-0.02	-0.02
BOL	2361.06	2425.56	2490.96	2559.51	2459.27		-0.10	-0.03	0.03	0.10
BRA	11431.15	10965.97	11021.72	11079.71	11124.64		0.31	-0.16	-0.10	-0.04
BRB	15836.38	16202.12	16254.24	16136.91	16107.41		-0.27	0.09	0.15	0.03
CHL	14722.37	14777.15	14741.19	15111.70	14838.10		-0.12	-0.06	-0.10	0.27
COL	7580.28	7633.39	7620.92	7694.43	7632.25		-0.05	0.00	-0.01	0.06
CRI	9219.39	9509.74	9775.85	9936.58	9610.39		-0.39	-0.10	0.17	0.33
CUB	6522.74	6550.27	6666.33	6816.90	6639.06		-0.12	-0.09	0.03	0.18
DOM	6661.87	7026.18	7273.35	7697.72	7164.78		-0.50	-0.14	0.11	0.53
ECU	5330.54	5176.06	5205.76	5180.60	5223.24		0.11	-0.05	-0.02	-0.04
GRD	8194.24	8449.31	8775.90	9091.76	8627.80		-0.43	-0.18	0.15	0.46
GTM	3210.87	3242.64	3286.74	3338.55	3269.70		-0.06	-0.03	0.02	0.07
GUY	5257.46	5429.80	5604.56	5825.04	5529.21		-0.27	-0.10	0.08	0.30
HND	2067.29	2111.19	2176.30	2219.44	2143.55		-0.08	-0.03	0.03	0.08
HTI	1260.60	1265.23	1277.37	1282.24	1271.36		-0.01	-0.01	0.01	0.01
JAM	4722.05	4761.94	4785.65	4855.26	4781.23		-0.06	-0.02	0.00	0.07
LCA	8491.99	8786.51	9046.27	9237.37	8890.54		-0.40	-0.10	0.16	0.35
MEX	10042.14	10183.03	10277.88	10385.83	10222.22		-0.18	-0.04	0.06	0.16
NIC	1836.01	1895.20	1957.84	1857.05	1886.53		-0.05	0.01	0.07	-0.03
PAN	10765.91	11107.22	11530.07	11755.11	11289.58		-0.52	-0.18	0.24	0.47
PER	6114.23	6262.37	6314.29	6453.56	6286.11		-0.17	-0.02	0.03	0.17
PRI	27518.77	27702.08	27561.05	27362.43	27536.09		-0.02	0.17	0.02	-0.17
PRY	4944.19	5089.61	5272.36	5379.58	5171.44		-0.23	-0.08	0.10	0.21
SLV	3314.70	3382.52	3441.31	3507.06	3411.40		-0.10	-0.03	0.03	0.10
SUR	8464.76	7912.69	7972.84	8100.37	8112.66		0.35	-0.20	-0.14	-0.01
TTO	16840.12	15696.90	15261.87	15161.07	15739.99		1.10	-0.04	-0.48	-0.58
URY	13938.79	14124.14	14437.38	14617.46	14279.45		-0.34	-0.16	0.16	0.34
VCT	6580.82	6686.64	6730.90	6852.60	6712.74		-0.13	-0.03	0.02	0.14

17.7.5 Population

iso3c	2015 Population	2016 Population	2017 Population	2018 Population	Avg Population		2015 Within	2016 Within	2017 Within	2018 Within
ARG	43131966	43590368	44044811	44494502	43815411.75		-0.68	-0.23	0.23	0.68
ATG	93566	94527	95426	96286	94951.25		0.00	0.00	0.00	0.00
BHS	374206	377931	381761	385640	379884.50		-0.01	0.00	0.00	0.01
BLZ	360933	368400	375769	383071	372043.25		-0.01	0.00	0.00	0.01
BOL	10869730	11031813	11192854	11353142	11111884.75		-0.24	-0.08	0.08	0.24
BRA	204471769	206163058	207833831	209469333	206984497.75		-2.51	-0.82	0.85	2.48
BRB	285324	285796	286233	286641	285998.50		0.00	0.00	0.00	0.00
CHL	17969353	18209068	18470439	18729160	18344505.00		-0.38	-0.14	0.13	0.38
COL	47520667	48175048	48909844	49661056	48566653.75		-1.05	-0.39	0.34	1.09
CRI	4847804	4899345	4949954	4999441	4924136.00		-0.08	-0.02	0.03	0.08
CUB	11324781	11335109	11339259	11338138	11334321.75		-0.01	0.00	0.00	0.00
DOM	10281680	10397743	10513131	10627165	10454929.75		-0.17	-0.06	0.06	0.17
ECU	16212020	16491115	16785361	17084357	16643213.25		-0.43	-0.15	0.14	0.44
GRD	109599	110261	110874	111454	110547.00		0.00	0.00	0.00	0.00
GTM	15567419	15827690	16087418	16346950	15957369.25		-0.39	-0.13	0.13	0.39
GUY	767432	771366	775221	779004	773255.75		-0.01	0.00	0.00	0.01
HND	9112916	9270795	9429013	9587522	9350061.50		-0.24	-0.08	0.08	0.24
HTI	10695542	10839970	10982366	11123176	10910263.50		-0.21	-0.07	0.07	0.21
JAM	2891021	2906238	2920853	2934855	2913241.75		-0.02	-0.01	0.01	0.02
LCA	179126	180024	180955	181889	180498.50		0.00	0.00	0.00	0.00
MEX	121858258	123333376	124777324	126190788	124039936.50		-2.18	-0.71	0.74	2.15
NIC	6223240	6303974	6384855	6465513	6344395.50		-0.12	-0.04	0.04	0.12
PAN	3968487	4037078	4106771	4176873	4072302.25		-0.10	-0.04	0.03	0.10
PER	30470734	30926032	31444297	31989256	31207579.75		-0.74	-0.28	0.24	0.78
PRI	3473232	3406672	3325286	3193354	3349636.00		0.12	0.06	-0.02	-0.16
PRY	6688746	6777872	6867062	6956071	6822437.75		-0.13	-0.04	0.04	0.13
SLV	6325124	6356143	6388122	6420744	6372533.25		-0.05	-0.02	0.02	0.05
SUR	559136	564883	570501	575987	567626.75		-0.01	0.00	0.00	0.01
TTO	1370328	1377564	1384072	1389858	1380455.50		-0.01	0.00	0.00	0.01
URY	3412009	3424132	3436646	3449299	3430521.50		-0.02	-0.01	0.01	0.02
VCT	109148	109459	109827	110210	109661.00		0.00	0.00	0.00	0.00

17.7.6 Percent female

iso3c	2015 %Female	2016 %Female	2017 %Female	2018 %Female	Avg %Female		2015 Within	2016 Within	2017 Within	2018 Within
ARG	51.27	51.26	51.25	51.24	51.26		0.02	0.01	-0.01	-0.02
ATG	51.88	51.84	51.81	51.79	51.83		0.05	0.01	-0.02	-0.04
BHS	51.47	51.45	51.44	51.43	51.45		0.02	0.01	-0.01	-0.02
BLZ	50.09	50.12	50.16	50.19	50.14		-0.05	-0.02	0.02	0.05
BOL	49.74	49.75	49.77	49.78	49.76		-0.02	-0.01	0.01	0.02
BRA	50.77	50.79	50.81	50.83	50.80		-0.03	-0.01	0.01	0.03
BRB	51.79	51.75	51.71	51.67	51.73		0.06	0.02	-0.02	-0.06
CHL	50.78	50.76	50.75	50.73	50.75		0.02	0.01	-0.01	-0.03
COL	50.99	50.97	50.95	50.93	50.96		0.03	0.01	-0.01	-0.03
CRI	49.97	49.98	49.99	50.01	49.99		-0.02	-0.01	0.01	0.02
CUB	50.31	50.31	50.32	50.33	50.32		-0.01	0.00	0.00	0.01
DOM	49.94	49.96	49.98	50.01	49.97		-0.04	-0.01	0.01	0.04
ECU	49.94	49.95	49.96	49.97	49.96		-0.01	0.00	0.00	0.01
GRD	49.56	49.58	49.59	49.61	49.58		-0.03	-0.01	0.01	0.02
GTM	50.81	50.79	50.78	50.76	50.78		0.02	0.01	-0.01	-0.02
GUY	50.00	49.92	49.86	49.81	49.90		0.10	0.03	-0.04	-0.09
HND	50.07	50.07	50.06	50.05	50.06		0.01	0.00	0.00	-0.01
HTI	50.64	50.64	50.65	50.65	50.64		-0.01	0.00	0.00	0.01
JAM	50.30	50.32	50.33	50.34	50.32		-0.02	-0.01	0.01	0.02
LCA	50.76	50.75	50.75	50.75	50.75		0.00	0.00	0.00	0.00
MEX	51.10	51.10	51.09	51.09	51.09		0.00	0.00	0.00	0.00
NIC	50.71	50.71	50.71	50.71	50.71		0.00	0.00	0.00	0.00
PAN	49.85	49.87	49.89	49.91	49.88		-0.03	-0.01	0.01	0.03
PER	50.33	50.35	50.35	50.34	50.34		-0.01	0.01	0.00	0.00
PRI	52.16	52.24	52.34	52.45	52.30		-0.14	-0.06	0.04	0.15
PRY	49.11	49.12	49.14	49.15	49.13		-0.02	-0.01	0.00	0.02
SLV	52.98	53.03	53.07	53.11	53.05		-0.07	-0.02	0.02	0.07
SUR	49.69	49.70	49.71	49.72	49.70		-0.01	0.00	0.01	0.01
TTO	50.54	50.56	50.57	50.59	50.57		-0.02	-0.01	0.01	0.02
URY	51.77	51.75	51.74	51.72	51.75		0.02	0.01	-0.01	-0.02
VCT	49.07	49.11	49.16	49.21	49.14		-0.06	-0.03	0.02	0.07

17.7.7 Percent rural

iso3c	2015 %Rural	2016 %Rural	2017 %Rural	2018 %Rural	Avg %Rural		2015 Within	2016 Within	2017 Within	2018 Within
ARG	8.50	8.37	8.25	8.13	8.31		0.18	0.06	-0.06	-0.18
ATG	75.00	75.15	75.29	75.40	75.21		-0.21	-0.06	0.08	0.19
BHS	17.25	17.17	17.08	16.98	17.12		0.14	0.05	-0.04	-0.14
BLZ	54.59	54.51	54.40	54.28	54.44		0.15	0.06	-0.04	-0.17
BOL	31.61	31.26	30.92	30.58	31.09		0.52	0.17	-0.17	-0.52
BRA	14.23	13.96	13.69	13.43	13.83		0.40	0.13	-0.14	-0.40
BRB	68.75	68.81	68.84	68.85	68.81		-0.06	-0.01	0.03	0.04
CHL	12.64	12.58	12.51	12.44	12.54		0.10	0.04	-0.03	-0.11
COL	20.24	19.89	19.55	19.22	19.73		0.51	0.17	-0.17	-0.50
CRI	23.14	22.26	21.44	20.66	21.88		1.26	0.39	-0.44	-1.22
CUB	23.10	23.07	23.02	22.96	23.04		0.06	0.03	-0.02	-0.08
DOM	21.43	20.56	19.72	18.93	20.16		1.27	0.40	-0.44	-1.24
ECU	36.60	36.47	36.33	36.18	36.39		0.21	0.07	-0.06	-0.22
GRD	64.00	63.93	63.84	63.73	63.87		0.13	0.05	-0.04	-0.15
GTM	50.03	49.68	49.32	48.95	49.49		0.54	0.19	-0.17	-0.55
GUY	73.56	73.52	73.46	73.39	73.48		0.08	0.03	-0.02	-0.09
HND	44.84	44.19	43.54	42.90	43.87		0.97	0.32	-0.32	-0.96
HTI	47.57	46.60	45.65	44.72	46.14		1.43	0.47	-0.48	-1.42
JAM	45.17	44.90	44.62	44.33	44.75		0.41	0.15	-0.13	-0.43
LCA	81.48	81.44	81.39	81.32	81.41		0.08	0.03	-0.02	-0.09
MEX	20.72	20.42	20.13	19.84	20.28		0.44	0.14	-0.15	-0.43
NIC	42.10	41.91	41.70	41.48	41.80		0.31	0.11	-0.10	-0.32
PAN	33.30	32.97	32.63	32.29	32.80		0.50	0.17	-0.17	-0.51
PER	22.64	22.46	22.28	22.09	22.37		0.27	0.09	-0.09	-0.28
PRI	6.38	6.40	6.41	6.42	6.40		-0.03	0.00	0.01	0.02
PRY	39.25	38.97	38.70	38.42	38.83		0.42	0.14	-0.13	-0.42
SLV	30.30	29.50	28.73	27.98	29.13		1.17	0.37	-0.40	-1.15
SUR	33.94	33.96	33.96	33.94	33.95		-0.01	0.01	0.01	-0.01
TTO	46.68	46.75	46.80	46.82	46.76		-0.08	-0.01	0.03	0.06
URY	4.96	4.86	4.76	4.67	4.81		0.15	0.05	-0.05	-0.14
VCT	49.04	48.63	48.22	47.80	48.42		0.62	0.21	-0.20	-0.62

17.8 Bookdown Style Note

To get the above tables to display in bookdown I added HTML code to allow the maximum width to be larger than the default setting. If you find this messes with the rest of your book, you can remove from here to the bottom of this file instide the HTML “style” tag.