Models

LaTeX Equations

\[ \begin{aligned} \text{TradeUSD}_i =\ & \beta_0 + \beta_1 \cdot \text{Post2008}_i + \beta_2 \cdot \text{Year}_i \\ &+ \beta_3 \cdot (\text{Post2008}_i \times \text{Year}_i) + \varepsilon_i \end{aligned} \]

This model estimates the raw dollar value of trade (TradeUSD) for each observation i, and how it is influenced by time and the 2008 crisis.

β₀ — Intercept: baseline level of trade in the year 2000 (your centered year = 0)

Post2008ᵢ — Dummy variable (1 if year ≥ 2009, 0 otherwise)

Yearᵢ — The number of years since 2000 (e.g., 2002 = 2)

Post2008ᵢ × Yearᵢ — Interaction term, captures how the trend changes after the crisis

εᵢ — Error term (everything not captured by the model)

Purpose: Shows whether there was a shift in the level and trend of imports after 2008, even without controlling for different types of commodities.

\[ \begin{aligned} \log(\text{TradeUSD}_i) =\ & \beta_0 + \beta_1 \cdot \text{Post2008}_i + \beta_2 \cdot \text{Year}_i \\ &+ \beta_3 \cdot (\text{Post2008}_i \times \text{Year}_i) \\ &+ \sum_{c} \gamma_c \cdot \text{Commodity}_{ic} + \varepsilon_i \end{aligned} \]

This is a more refined model that applies a log transformation and controls for specific commodities.

log(TradeUSDᵢ) — Now modeling the percentage change in trade, not absolute dollars (helps with skewed data)

∑ γ_c · Commodity_ic — Adds dummy variables for each commodity type, like cattle, sheep, poultry, etc. This controls for differences in trade patterns by animal type

All other terms are the same as above.

Purpose: This version is more robust. It accounts for the fact that not all live animals are traded equally and helps identify true shifts in import behavior after 2008 across different commodities.

Tables

Top 10 U.S. Live Animal Imports Before 2008
Commodity	Years	Obs.	Mean Trade (USD)	SD
Bovine animals, live, except pure-bred breeding	2000–2008	9	1312397897	440900927
Swine, live except pure-bred breeding > 50 kg	2000–2008	9	292789824	69628690
Plants, live (including their roots),nes	2000–2008	9	275514146	19363040
Horses, live except pure-bred breeding	2000–2008	9	274154798	38638698
Swine, live except pure-bred breeding < 50 kg	2000–2008	9	178242196	72071116
Animals, live, except farm animals	2000–2008	9	112265093	37654624
Horses, live pure-bred breeding	2000–2008	9	37252082	37487032
Poultry, live except domestic fowls, < 185 grams	2000–2008	9	15843652	2390764
Bovine animals, live pure-bred breeding	2000–2008	8	7119180	8406064
Poultry, live except domestic fowls, > 185 grams	2000–2008	9	6943814	2176344

The Preceptor Table summarizes U.S. live animal import behavior before the 2008 global financial crisis. This pre-crisis snapshot identifies the most traded commodities by value and provides context for changes in volume and variability over time.

Summary of U.S. Live Animal Imports (2000–2016)
Period	Years	Obs.	Unique Commodities	Total Trade (USD)	Avg. Trade (USD)
Post-2008	2009–2016	122	16	24161178026	198042443
Pre-2008	2000–2008	134	16	22721519785	169563580

The Population Table offers a side-by-side summary of U.S. live animal imports before and after the 2008 crisis, capturing shifts in volume, commodity diversity, and economic scale. It’s designed to identify long-term trends possibly triggered by the financial shock.

Linear Regression Model


Call:
lm(formula = trade_usd ~ year + crisis, data = us_all_imports)

Residuals:
       Min         1Q     Median         3Q        Max 
-5.958e+09 -4.573e+09 -3.413e+09 -1.951e+09  2.405e+12 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.401e+11  3.041e+11  -1.447    0.148
year         2.215e+08  1.521e+08   1.456    0.145
crisis      -4.235e+08  2.501e+09  -0.169    0.866

Residual standard error: 7.504e+10 on 12064 degrees of freedom
Multiple R-squared:  0.0004088, Adjusted R-squared:  0.0002431 
F-statistic: 2.467 on 2 and 12064 DF,  p-value: 0.08487

Trade value (trade_usd) is regressed on year, controlling for country_or_area and commodity fixed effects. The year coefficient shows the average yearly change in trade value, holding country and commodity constant.

--- title: "Models" format: html: theme: cosmo css: styles.css jupyter: false execute: echo: false warning: false message: false --- ```{r} #| cache: true ``` ```{r} library(tidyverse) library(tidymodels) library(primer.data) library(knitr) library(kableExtra) library(broom) library(gt) library(stringr) library(fixest) gct <- read_csv("commodity_trade_statistics_data.csv") ``` ### LaTeX Equations $$ \begin{aligned} \text{TradeUSD}_i =\ & \beta_0 + \beta_1 \cdot \text{Post2008}_i + \beta_2 \cdot \text{Year}_i \\ &+ \beta_3 \cdot (\text{Post2008}_i \times \text{Year}_i) + \varepsilon_i \end{aligned} $$ This model estimates the raw dollar value of trade (TradeUSD) for each observation i, and how it is influenced by time and the 2008 crisis. β₀ — Intercept: baseline level of trade in the year 2000 (your centered year = 0) Post2008ᵢ — Dummy variable (1 if year ≥ 2009, 0 otherwise) Yearᵢ — The number of years since 2000 (e.g., 2002 = 2) Post2008ᵢ × Yearᵢ — Interaction term, captures how the trend changes after the crisis εᵢ — Error term (everything not captured by the model) Purpose: Shows whether there was a shift in the level and trend of imports after 2008, even without controlling for different types of commodities. # $$ \begin{aligned} \log(\text{TradeUSD}_i) =\ & \beta_0 + \beta_1 \cdot \text{Post2008}_i + \beta_2 \cdot \text{Year}_i \\ &+ \beta_3 \cdot (\text{Post2008}_i \times \text{Year}_i) \\ &+ \sum_{c} \gamma_c \cdot \text{Commodity}_{ic} + \varepsilon_i \end{aligned} $$ This is a more refined model that applies a log transformation and controls for specific commodities. log(TradeUSDᵢ) — Now modeling the percentage change in trade, not absolute dollars (helps with skewed data) ∑ γ_c · Commodity_ic — Adds dummy variables for each commodity type, like cattle, sheep, poultry, etc. This controls for differences in trade patterns by animal type All other terms are the same as above. Purpose: This version is more robust. It accounts for the fact that not all live animals are traded equally and helps identify true shifts in import behavior after 2008 across different commodities. ### ```{r} live_animals <- gct %>% filter( country_or_area == "USA", flow == "Import", str_detect(tolower(commodity), "live"), year >= 2000, year <= 2016 ) %>% drop_na(trade_usd) %>% mutate( post_2008 = year >= 2009, year_group = case_when( year < 2009 ~ "Pre-2008", TRUE ~ "Post-2008" ) ) ``` ### Tables ```{r} preceptor_table <- live_animals %>% filter(year < 2009) %>% group_by(commodity) %>% summarise( Years = paste0(min(year), "–", max(year)), Observations = n(), Mean_Trade_USD = round(mean(trade_usd, na.rm = TRUE), 0), SD_Trade_USD = round(sd(trade_usd, na.rm = TRUE), 0) ) %>% arrange(desc(Mean_Trade_USD)) %>% head(10) kable(preceptor_table, caption = "Top 10 U.S. Live Animal Imports Before 2008", col.names = c("Commodity", "Years", "Obs.", "Mean Trade (USD)", "SD")) %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE, position = "center") ``` The Preceptor Table summarizes U.S. live animal import behavior before the 2008 global financial crisis. This pre-crisis snapshot identifies the most traded commodities by value and provides context for changes in volume and variability over time. # ```{r} population_table <- live_animals %>% group_by(year_group) %>% summarise( Years = paste0(min(year), "–", max(year)), Observations = n(), Unique_Commodities = n_distinct(commodity), Total_Trade_USD = round(sum(trade_usd, na.rm = TRUE), 0), Mean_Trade_USD = round(mean(trade_usd, na.rm = TRUE), 0) ) kable(population_table, caption = "Summary of U.S. Live Animal Imports (2000–2016)", col.names = c("Period", "Years", "Obs.", "Unique Commodities", "Total Trade (USD)", "Avg. Trade (USD)")) %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE, position = "center") ``` The Population Table offers a side-by-side summary of U.S. live animal imports before and after the 2008 crisis, capturing shifts in volume, commodity diversity, and economic scale. It’s designed to identify long-term trends possibly triggered by the financial shock. ### ### Linear Regression Model ```{r} library(tidyverse) us_all_imports <- gct %>% filter( country_or_area == "USA", flow == "Import" ) %>% mutate( crisis = if_else(year > 2008, 1, 0) ) %>% drop_na(trade_usd, year, crisis) model <- lm(trade_usd ~ year + crisis, data = us_all_imports) summary(model) ``` ```{r} ggplot(us_all_imports, aes(x = year, y = trade_usd)) + geom_point(alpha = 0.3, color = "sienna4") + geom_smooth(method = "lm", formula = y ~ x, color = "saddlebrown", se = TRUE) + scale_y_continuous(labels = scales::dollar_format(scale = 1e-9, suffix = "B")) + labs( title = "U.S. Import Trade Value Over Time", subtitle = "Linear trend over years", x = "Year", y = "Trade Value (Billions USD)", caption = "Data: Global Commodity Trade Statistics" ) + theme_minimal(base_family = "Segoe UI") ``` Trade value (trade_usd) is regressed on year, controlling for country_or_area and commodity fixed effects. The year coefficient shows the average yearly change in trade value, holding country and commodity constant. ###