Impact of Budget Deficits on Treasury Yields with XGBoost

Charles Schwab analysts said that historically, budget deficits have had minimal impact on Treasury yields, primarily due to the United States’ economic dominance and its status as the issuer of the world’s reserve currency.

The variable importance analysis with the XGBoost machine learning model confirms the aforementioned statement.

Source code:

library(tidyverse)
library(tidymodels)
library(tidyquant)

#30-year Treasury yield (^TYX) 
df_yield_30 <- 
  tq_get("^TYX") %>% 
  tq_transmute(select = close,
               mutate_fun = to.monthly,
               col_rename = "yield_30") %>% 
  mutate(date = as.Date(date))

#Federal Surplus or Deficit [-] (MTSDS133FMS)
df_deficit <- 
  tq_get("MTSDS133FMS", get = "economic.data") %>% 
  select(date, deficit = price)

#Merging the datasets
df_merged <- 
  df_yield_30 %>% 
  left_join(df_deficit) %>% 
  drop_na()

#Data split
splits <- initial_time_split(df_merged, prop = 0.8)
df_train <- training(splits)
df_test <- testing(splits)

#Bootstrapping for tuning
set.seed(12345)
df_folds <- bootstraps(df_train,
                       times = 100)
#Model
model_spec <- 
  boost_tree(trees = tune(),
             learn_rate = tune()) %>%
  set_engine("xgboost") %>% 
  set_mode("regression")

#Preprocessing
recipe_spec <- 
  recipe(yield_30 ~ ., data = df_train) %>%
  step_date(date, features = "month", ordinal = FALSE) %>%
  step_dummy(all_nominal_predictors(), one_hot = TRUE) %>% 
  step_mutate(date_num = as.numeric(date)) %>%
  step_normalize(all_numeric_predictors()) %>%
  step_rm(date)


#Workflow sets
wflow_xgboost <- 
  workflow_set(
    preproc = list(recipe = recipe_spec),
    models = list(model = model_spec)
  ) 


#Tuning and evaluating all the models
grid_ctrl <-
  control_grid(
    save_pred = TRUE,
    parallel_over = "everything",
    save_workflow = TRUE
  )

grid_results <-
  wflow_xgboost %>%
  workflow_map(
    seed = 98765,
    resamples = df_folds,
    grid = 10,
    control = grid_ctrl
  )

#Accuracy of the grid results
grid_results %>% 
  rank_results(select_best = TRUE, 
               rank_metric = "rsq") %>%
  select(Models = wflow_id, .metric, mean)


#Finalizing the model with the best parameters
best_param <- 
  grid_results %>%
  extract_workflow_set_result("recipe_model") %>% 
  select_best(metric = "rsq")


wflw_fit <- 
  grid_results %>% 
  extract_workflow("recipe_model") %>% 
  finalize_workflow(best_param) %>% 
  fit(df_train)


#Variable importance
library(DALEXtra)

#Fitted workflow for KNN
set.seed(98765)

knn_wflow_fitted <- 
  workflow() %>% 
  add_recipe(rec_features) %>% 
  add_model(spec_knn) %>% 
  fit(df_train)

#Processed data frame for variable importance calculation
imp_data <- 
  recipe_spec %>% 
  prep() %>% 
  bake(new_data = NULL) 

#Explainer object
explainer_xgboost <- 
  explain_tidymodels(
    wflw_fit %>% extract_fit_parsnip(), 
    data = imp_data %>% select(-yield_30), 
    y = imp_data$yield_30,
    label = "",
    verbose = FALSE
  )


#Calculating permutation-based variable importance 
set.seed(1983)
vip_xgboost <- model_parts(explainer_xgboost, 
                           loss_function = loss_root_mean_square,
                           type = "difference",
                           B = 100,#the number of permutations
                           label = "")

#Plot VIP
vip_xgboost %>% 
  plot() +
  labs(color = "",
       x = "",
       y = "",
       subtitle = "Higher indicates more important",
       title = "Factors Affecting 30-year Treasury Yield") +
  theme_minimal(base_family = "Roboto Slab",
                base_size = 16) +
  theme(legend.position = "none",
        plot.title = element_text(hjust = 0.5, 
                                  size = 14,
                                  face = "bold"),
        plot.subtitle = element_text(hjust = 0.5, size = 12),
        panel.grid.minor.x = element_blank(),
        panel.grid.major.y = element_blank(),
        plot.background = element_rect(fill = "azure"))

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