Regression Analysis (Econ 0211), Lab7: Interactions
Noe Vyizigiro
April, 2024
Important packages (libraries) for this lab:
- tidyverse
- sandwich: Helpful in estimating robust regression models
- ggrepel
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.5.1 ✔ purrr 1.0.2
## ✔ tibble 3.2.1 ✔ dplyr 1.1.4
## ✔ tidyr 1.2.1 ✔ stringr 1.4.1
## ✔ readr 2.1.2 ✔ forcats 1.0.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()if(!require("sandwich")) install.packages("sandwich") # for robust regression## Loading required package: sandwichlibrary(sandwich)
if(!require("ggrepel")) install.packages("ggrepel") # for robust regression## Loading required package: ggrepellibrary(ggrepel)
rm(list = ls())#Read data
inflation<-read_csv("FRED_inflation.csv")## Rows: 66 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (2): year, inflation
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.unemployment<-read_csv("FRED_unemployment.csv")## Rows: 75 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (2): year, unemployment
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.3. Merge the data and keep the dataset from 1960
infl_unemp<-unemployment%>%
left_join(inflation, by="year")%>%
filter(year>=1960)4. Graphing
# line graph
ggplot(infl_unemp, aes( year))+
geom_line(aes(y=inflation, color ="inflation"))+
geom_line(aes(y = unemployment, color ="unemployment"))+
scale_linetype_manual(values = c("inflation"="dash", "unemployment"="solid"))+
scale_x_continuous(breaks = seq(1960, 2020, by =10))+
labs(
title = "Evidence for the Phillips Curve",
subtitle= "FRED: 1960-2022",
x = "Years", y="Rates",
color = "Legend"
)+
theme_minimal()## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's linetype values.
# scatter plot
ggplot(infl_unemp, aes(unemployment, inflation))+
geom_point()+
labs(
title = "Evidence for the Phillipss Curve",
subtitle= "FRED: 1960-2022",
x = "Unemployment", y="Inflation",
color =""
)
5. Estimating phillips curve by regressing inflation on unemployment
phillips<-lm(inflation~unemployment, data = infl_unemp)
p_se1<-sqrt(diag(vcovHC(phillips,"HC1"))) #robust se
summary(phillips)##
## Call:
## lm(formula = inflation ~ unemployment, data = infl_unemp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8466 -1.5626 -0.7031 0.9438 8.3032
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.8474 1.2006 1.539 0.129
## unemployment 0.3124 0.1946 1.605 0.114
##
## Residual standard error: 2.46 on 61 degrees of freedom
## Multiple R-squared: 0.04054, Adjusted R-squared: 0.02481
## F-statistic: 2.577 on 1 and 61 DF, p-value: 0.1136infl_unemp$yhat<-predict(phillips)
ggplot(infl_unemp, aes(unemployment, inflation))+
geom_point()+
geom_line(aes(y=yhat, color ="yhat"))+
labs(
title = "Evidence for the Phillips Curve",
subtitle= "FRED: 1960-2022",
x = "Unemployment", y="Inflation",
color ="Legend "
)
6. Regraph
ggplot(infl_unemp, aes(unemployment, inflation))+
geom_point()+
ggplot2::geom_text(aes(label = year), size = 3, vjust = -0.5, hjust = -0.5) +
scale_color_viridis_d() +
labs(
title = "Evidence for the Phillips curve",
subtitle= "FRED: 1960-2022",
x = "Unemployment", y="Inflation",
color ="Legend"
)
# to make results more clear
# Create a new variable to identify the subsets
infl_unemp$period <- with(infl_unemp,
ifelse(year >= 1974 & year <= 1983, "1974-1983",
ifelse(year >= 2020, "2020+",
"Others")))
# Create the plot
ggplot(infl_unemp, aes(x = unemployment, y = inflation, color = period, label = year)) +
geom_point() +
geom_text_repel(size = 3) +
scale_color_manual(values = c("1974-1983" = "red", "2020+" = "green", "Others" = "blue")) +
labs(
title = "Evidence for the Phillips Curve",
subtitle = "FRED data 1960-2021",
x = "Unemployment",
y = "Inflation",
color = "Legend"
) ## Warning: ggrepel: 2 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
7. Investigate non-linearity
#creating a dummy variable
infl_unemp<-infl_unemp%>%
mutate(oilyears =ifelse(year >= 1974 & year <= 1983, 1,0))
# run a regression
phillips2<-lm(inflation~unemployment+oilyears, data = infl_unemp)
p_se2<-sqrt(diag(vcovHC(phillips2,"HC1"))) #robust se
summary(phillips2)##
## Call:
## lm(formula = inflation ~ unemployment + oilyears, data = infl_unemp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7564 -1.1164 -0.4024 1.2132 4.1681
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.2295 0.7882 5.366 1.36e-06 ***
## unemployment -0.2398 0.1339 -1.791 0.0784 .
## oilyears 5.7291 0.5836 9.817 4.29e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.536 on 60 degrees of freedom
## Multiple R-squared: 0.6318, Adjusted R-squared: 0.6196
## F-statistic: 51.49 on 2 and 60 DF, p-value: 9.569e-14infl_unemp$yhat2<-predict(phillips2)
# Create separate variables for oil and non-oil years
infl_unemp <- infl_unemp %>%
mutate(
p_oil = ifelse(oilyears == 1, yhat2, 0),
p_non_oil = ifelse(oilyears == 0, yhat2, 0)
)
# Create the plot
ggplot(infl_unemp) +
geom_point(aes(x = unemployment, y = inflation), color = "black") +
geom_point(aes(x = unemployment, y = p_oil, color = "Oil Years"), linetype = "solid", group =1) +
geom_point(aes(x = unemployment, y = p_non_oil, color = "Non-Oil Years"), linetype = "dashed", group =1) +
scale_color_manual(values = c("Oil Years" = "red", "Non-Oil Years" = "blue")) +
labs(
title = "Scatter Plot with Predicted Lines for Oil and Non-Oil Years",
x = "Unemployment",
y = "Inflation",
color = "Legend"
) ## Warning in geom_point(aes(x = unemployment, y = p_oil, color = "Oil Years"), :
## Ignoring unknown parameters: `linetype`## Warning in geom_point(aes(x = unemployment, y = p_non_oil, color = "Non-Oil
## Years"), : Ignoring unknown parameters: `linetype`
#theme_minimal()# plotting with conditions
ggplot(infl_unemp, aes(x = unemployment, y = inflation, color = period, label = year))+
geom_point()+
geom_line(data = subset(infl_unemp, year >= 1974 & year <= 1983), aes(x=unemployment,y=p_oil, colour = period))+
geom_line(data= subset(infl_unemp, year<1974 | year>1983), aes(x=unemployment,y=p_non_oil, colour = period))+
geom_text_repel(size = 3) +
scale_color_manual(values = c("1974-1983" = "red", "2020+" = "blue", "Others" = "blue")) +
labs(
title = "Evidence for the Phillips curve",
subtitle = "FRED data: 1960=2021"
)## Warning: ggrepel: 2 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
8)Introduce an Interaction Term
## generate the interaction variable on your own
infl_unemp<-infl_unemp%>%
mutate(oilyearsXunemployment =oilyears*unemployment)
# run a regression
phillips3<-lm(inflation~unemployment+oilyears+oilyearsXunemployment, data = infl_unemp)
p_se3<-sqrt(diag(vcovHC(phillips3,"HC1"))) #robust se
summary(phillips3)##
## Call:
## lm(formula = inflation ~ unemployment + oilyears + oilyearsXunemployment,
## data = infl_unemp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9436 -1.0660 -0.5469 1.1376 4.0519
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.8663 0.8438 4.582 2.44e-05 ***
## unemployment -0.1758 0.1441 -1.220 0.22751
## oilyears 8.9952 2.8296 3.179 0.00235 **
## oilyearsXunemployment -0.4511 0.3825 -1.179 0.24294
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.531 on 59 degrees of freedom
## Multiple R-squared: 0.6403, Adjusted R-squared: 0.622
## F-statistic: 35.01 on 3 and 59 DF, p-value: 3.974e-13infl_unemp$yhat3 =predict(phillips3) # predict yhat3
infl_unemp<-infl_unemp%>%
mutate(
p2_oil =ifelse(oilyears==1,yhat3,0),
p2_non_oil =ifelse(oilyears==0,yhat3,0)
)
# create a graph
interactions<-ggplot(infl_unemp) +
geom_point(aes(x = unemployment, y = inflation), color = "black") +
geom_point(aes(x = unemployment, y = p2_oil, color = "Oil Years")) +
geom_point(aes(x = unemployment, y = p2_non_oil, color = "Non-Oil Years")) +
scale_color_manual(values = c("Oil Years" = "red", "Non-Oil Years" = "blue")) +
labs(
title = "Scatter Plot with Predicted Lines for Oil and Non-Oil Years",
x = "Unemployment",
y = "Inflation",
color = "Legend"
)
#theme_minimal()
print(interactions)
9) Let’s see what the graph looks like now!
fancy_scatter<-ggplot(infl_unemp, aes(x = unemployment, y = inflation, color = period, label = year))+
geom_point()+
geom_line(data = subset(infl_unemp, year >= 1974 & year <= 1983), aes(x=unemployment,y=p2_oil, colour = period))+
geom_line(data= subset(infl_unemp, year<1974 | year>1983), aes(x=unemployment,y=p2_non_oil, colour = period))+
geom_text_repel(size = 3) +
scale_color_manual(values = c("1974-1983" = "red", "2020+" = "blue", "Others" = "blue")) +
labs(
title = "Evidence for the Phillips Curve?",
subtitle = "FRED data: 1960=2021"
)
print(fancy_scatter)## Warning: ggrepel: 2 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
ggsave(filename = "fancy_scatter.png", plot = fancy_scatter)## Saving 7 x 5 in image## Warning: ggrepel: 2 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps