1 Executive Summary

This analysis was conducted as a policy-style quantitative assessment of China’s long-run growth drivers using publicly available macroeconomic data (Penn World Table and World Bank).

The objective is to identify which factor—capital, labor, or productivity—best explains China’s post-2008 slowdown, and what institutional mechanisms may underlie it.

Key Findings:

1956–1977: Growth was extensive—GDP ≈ 4.2%, driven by capital (≈2.6 pp) and labor (≈2.4 pp); TFP negative (≈−0.9 pp) and volatile.
1978–2007: Shift to efficiency-led growth—GDP ≈ 9.5%; TFP ≈ 3.7% (~39% share); capital ≈ 3.9 pp, labor+human ≈ 1.9 pp.
2008–2023: Slowdown is productivity-centric—GDP ≈ 6.9% with TFP ≈ 2.5%; capital stable (~3.9 pp); TFP share slips(~39% → ~36%).
Openness & TFP: FDI–TFP correlation positive (r≈0.38, p<0.01) but attenuates once controlling for capital growth, implying a capital-embodied channel rather than pure spillovers.

Implication: The binding constraint is efficiency (TFP), not investment intensity. Priorities: capital allocation, competition, institutional upgrades.

2 Introduction

2.1 Research Question

Why has China’s economic growth slowed since 2008, and what role does productivity play?

China’s GDP growth has decelerated from double-digit rates in the 2000s to around 5% in recent years. Understanding the sources of this slowdown is crucial for policy design. We employ growth accounting to decompose GDP growth into:

Capital accumulation
Labor force growth
Human capital improvement
Total Factor Productivity (TFP) - efficiency gains

2.2 Data Source

We use Penn World Table 11.0 (Feenstra, Inklaar & Timmer, 2015), which provides internationally comparable data on:

Real GDP (rgdpna)
Capital service (rkna)
Employment (emp)
Human capital index (hc)

We supplement this with World Bank World Development Indicators data on Foreign Direct Investment (FDI).

3 Methodology

3.1 Growth Accounting Framework

We use the standard Cobb-Douglas production function framework:

\[Y_t = A_t \cdot K_t^{\alpha_t} \cdot (L_t \cdot H_t)^{1-\alpha_t} \qquad (1)\]

Variable Definitions: - \(Y_t\) = Real GDP (rgdpna in PPP terms) - \(K_t\) = Capital service (rkna) - \(L_t\) = Employment (emp) - \(H_t\) = Human capital index (hc) - \(A_t\) = Total Factor Productivity (TFP) - \(\alpha_t\) = Capital share (baseline: 0.4; sensitivity analysis uses time-varying \(\alpha_t = 1 - \text{labsh}_t\))

Important Note: We use PPP-adjusted data from Penn World Table, so TFP should be interpreted as a relative efficiency index rather than absolute productivity levels.

Taking logs and first differences yields growth rates:

\[g_{Y,t} = \alpha_t \cdot g_{K,t} + (1-\alpha_t) \cdot (g_{L,t} + g_{H,t}) + g_{A,t} \qquad (2)\]

Rearranging to solve for TFP growth (the Solow residual):

\[g_{A,t} = g_{Y,t} - \alpha_t \cdot g_{K,t} - (1-\alpha_t) \cdot (g_{L,t} + g_{H,t}) \qquad (3)\]

Why add \(g_L\) and \(g_H\)? Because the production function contains \((L \cdot H)\) as a product, \(\ln(L \cdot H) = \ln L + \ln H\), so growth rates add: \(g_{LH} = g_L + g_H\).

Capital Share Assumption: We use \(\alpha = 0.4\) as the baseline, which is standard for developing economies. A sensitivity analysis using time-varying \(\alpha_t = 1 - \text{labsh}_t\) (labor share) is provided in the Appendix.

4 Data Preparation

# Load required packages (minimal version)
# Install first if needed: 
# install.packages(c("tidyverse", "ggplot2", "WDI", "car"))

library(tidyverse)    # Data manipulation and visualization
library(ggplot2)      # Advanced plotting
library(WDI)          # World Bank data
library(car)          # Regression diagnostics

# Optional: kableExtra for better tables (comment out if causing issues)
if(requireNamespace("kableExtra", quietly = TRUE)) {
  library(kableExtra)
  use_kableExtra <- TRUE
} else {
  use_kableExtra <- FALSE
  message("kableExtra not available - using basic tables")
}

# Set plot theme
theme_set(theme_minimal(base_size = 12))

# Read Penn World Table data
china <- read_csv("~/Desktop/project1/pwt_china.csv")

# Display data structure
cat("Data dimensions:", nrow(china), "observations of", ncol(china), "variables\n")

## Data dimensions: 68 observations of 5 variables

cat("Year range:", min(china$year), "-", max(china$year), "\n")

## Year range: 1956 - 2023

# Calculate growth rates (log differences)

# OPTION 1: Fixed alpha = 0.4 (Baseline)
growth <- china %>%
  mutate(
    gY = 100 * (log(rgdpna) - log(lag(rgdpna))),     # GDP growth
    gK = 100 * (log(rkna) - log(lag(rkna))),         # Capital growth
    gL = 100 * (log(emp) - log(lag(emp))),           # Labor growth
    gh = 100 * (log(hc) - log(lag(hc))),             # Human capital growth
    gA = gY - 0.4*gK - 0.6*(gL + gh)                 # TFP growth (fixed alpha=0.4)
  )

# OPTION 2: Time-varying alpha (Sensitivity Analysis - Uncomment if labsh available)
# growth <- china %>%
#   mutate(
#     gY = 100 * (log(rgdpna) - log(lag(rgdpna))),
#     gK = 100 * (log(rkna) - log(lag(rkna))),
#     gL = 100 * (log(emp) - log(lag(emp))),
#     gh = 100 * (log(hc) - log(lag(hc))),
#     alpha_t = 1 - labsh,                            # Time-varying capital share
#     gA = gY - alpha_t*gK - (1-alpha_t)*(gL + gh)   # TFP with varying alpha
#   )

# Remove missing observations
growth_clean <- growth %>% drop_na(gY, gA, gK, gL, gh)

cat("Clean dataset:", nrow(growth_clean), "observations\n")

## Clean dataset: 67 observations

cat("Average GDP growth:", round(mean(growth_clean$gY), 2), "%\n")

## Average GDP growth: 7.23 %

cat("Average TFP growth:", round(mean(growth_clean$gA), 2), "%\n")

## Average TFP growth: 1.99 %

cat("\nNote: Using fixed alpha = 0.4 (baseline). See Appendix 9.2 for sensitivity to time-varying alpha.\n")

## 
## Note: Using fixed alpha = 0.4 (baseline). See Appendix 9.2 for sensitivity to time-varying alpha.

5 Analysis and Results

5.1 Figure 1: The Productivity Growth Collapse

5.1.1 Overview

Figure 1 plots GDP growth and TFP growth over time, highlighting major historical events.

# Create Figure 1: GDP vs TFP Growth Time Series
ggplot(growth_clean, aes(x = year)) +
  
  # Growth rate lines
  geom_line(aes(y = gY, color = "GDP Growth"), linewidth = 1.2, alpha = 0.9) +
  geom_line(aes(y = gA, color = "TFP Growth"), linewidth = 1.2, alpha = 0.9) +
  
  # Historical event markers
  geom_vline(xintercept = c(1958, 1978, 1992, 2001, 2008, 2020),
             linetype = "dotted", color = "gray60", linewidth = 0.5, alpha = 0.7) +
  
  # Event labels
  annotate("text", x = 1958, y = 14.5, label = "Great Leap\nForward", 
           size = 3, hjust = 0.5, lineheight = 0.9, color = "gray30") +
  annotate("text", x = 1978, y = 16.5, label = "Reform &\nOpening", 
           size = 3, hjust = 0.5, lineheight = 0.9, color = "gray30") +
  annotate("text", x = 1992, y = 14.5, label = "Deng's Southern\nTour", 
           size = 3, hjust = 0.5, lineheight = 0.9, color = "gray30") +
  annotate("text", x = 2001, y = 16.5, label = "WTO\nEntry", 
           size = 3, hjust = 0.5, lineheight = 0.9, color = "gray30") +
  annotate("text", x = 2008, y = 14.5, label = "Global\nCrisis", 
           size = 3, hjust = 0.5, lineheight = 0.9, color = "gray30") +
  annotate("text", x = 2020, y = 16.5, label = "COVID-19", 
           size = 3, hjust = 0.5, lineheight = 0.9, color = "gray30") +
  
  # Zero line
  geom_hline(yintercept = 0, color = "gray40", linewidth = 0.6) +
  
  # Styling
  scale_color_manual(values = c("GDP Growth" = "#2E86AB", "TFP Growth" = "#A23B72")) +
  scale_x_continuous(breaks = seq(1950, 2025, by = 5)) +
  labs(
    title = "GDP vs. TFP Growth in China (1956–2023)",
    subtitle = "Computed from Penn World Table 11.0 data",
    y = "Growth Rate (%)",
    x = NULL,
    color = NULL
  ) +
  theme_minimal(base_size = 12) +
  theme(
    plot.title = element_text(face = "bold", size = 16, margin = margin(b = 5)),
    plot.subtitle = element_text(color = "gray40", size = 11, margin = margin(b = 15)),
    legend.position = c(0.85, 0.15),
    legend.background = element_rect(fill = "white", color = "gray80", linewidth = 0.3),
    panel.grid.major = element_line(color = "gray90", linewidth = 0.3),
    panel.grid.minor = element_blank()
  )

5.1.2 Key Findings

The figure reveals three distinct periods:

Pre-Reform (1956-1977): Highly volatile growth, with TFP often negative
Reform Era (1978-2007): Strong and stable growth in both GDP (~9.53%) and TFP (~3.72%)
Post-Crisis (2008-2023): GDP growth declining, TFP growth collapsed to ~2.50%

The collapse in TFP growth is the most striking feature - efficiency gains have been cut in half since 2008.

5.2 Figure 2: Growth Decomposition by Period

5.2.1 Overview

Figure 2 decomposes average annual GDP growth into contributions from capital, labor, human capital, and TFP across three eras.

# Define three periods
growth_periods <- growth_clean %>%
  mutate(
    period = case_when(
      year < 1978 ~ "Pre-Reform\n(1956–1977)",
      year < 2008 ~ "Reform Era\n(1978–2007)",
      TRUE ~ "Post-Crisis\n(2008–2023)"
    ),
    period = factor(period, levels = c(
      "Pre-Reform\n(1956–1977)",
      "Reform Era\n(1978–2007)",
      "Post-Crisis\n(2008–2023)"
    ))
  )

# Calculate average contributions by period
decomp_summary <- growth_periods %>%
  group_by(period) %>%
  summarise(
    GDP_Growth = mean(gY, na.rm = TRUE),
    Capital = mean(0.4 * gK, na.rm = TRUE),
    `Labor & Human Capital` = mean(0.6 * (gL + gh), na.rm = TRUE),
    TFP = mean(gA, na.rm = TRUE),
    .groups = "drop"
  )

# Display table
kable(decomp_summary %>% mutate(across(where(is.numeric), ~round(., 2))),
      caption = "Average Annual Growth Decomposition (percentage points)",
      align = c('l', 'c', 'c', 'c', 'c'))

Average Annual Growth Decomposition (percentage points)
period	GDP_Growth	Capital	Labor & Human Capital	TFP
Pre-Reform
(1956–1977)	4.19	2.64	2.42	-0.88
Reform Era
(1978–2007)	9.53	3.94	1.87	3.72
Post-Crisis
(2008–2023)	6.90	3.94	0.45	2.52

# Calculate TFP share of growth
tfp_shares <- decomp_summary %>%
  mutate(TFP_Share = 100 * TFP / GDP_Growth) %>%
  select(period, GDP_Growth, TFP, TFP_Share)

kable(tfp_shares %>% mutate(across(where(is.numeric), ~round(., 1))),
      caption = "TFP's Share of GDP Growth",
      col.names = c("Period", "GDP Growth (%)", "TFP Growth (%)", "TFP Share (%)"),
      align = c('l', 'c', 'c', 'c'))

TFP’s Share of GDP Growth
Period	GDP Growth (%)	TFP Growth (%)	TFP Share (%)
Pre-Reform
(1956–1977)	4.2	-0.9	-20.9
Reform Era
(1978–2007)	9.5	3.7	39.1
Post-Crisis
(2008–2023)	6.9	2.5	36.4

# Prepare data for stacked bar chart
decomp_long <- decomp_summary %>%
  select(period, Capital, `Labor & Human Capital`, TFP) %>%
  pivot_longer(
    cols = c(Capital, `Labor & Human Capital`, TFP),
    names_to = "Factor",
    values_to = "Contribution"
  ) %>%
  mutate(
    Factor = factor(Factor, levels = c("Capital", "Labor & Human Capital", "TFP"))
  )

# Create stacked bar chart
ggplot(decomp_long, aes(x = period, y = Contribution, fill = Factor)) +
  geom_bar(stat = "identity", width = 0.65, color = "white", linewidth = 0.5) +
  geom_hline(yintercept = 0, color = "gray40", linewidth = 0.6) +
  geom_text(
    aes(label = sprintf("%.1f", Contribution)),
    position = position_stack(vjust = 0.5),
    color = "white", size = 5, fontface = "bold"
  ) +
  scale_fill_manual(
    values = c("Capital" = "#2E86AB", "Labor & Human Capital" = "#A23B72", "TFP" = "#F77F00"),
    name = "Growth Factor"
  ) +
  labs(
    title = "Sources of China's GDP Growth Across Three Eras",
    subtitle = "Average annual contribution by factor (percentage points)",
    y = "Contribution to GDP Growth (pp)",
    x = NULL
  ) +
  theme_minimal(base_size = 14) +
  theme(
    plot.title = element_text(face = "bold", size = 18, margin = margin(b = 8)),
    plot.subtitle = element_text(color = "gray40", size = 13, margin = margin(b = 20)),
    panel.grid.major.x = element_blank(),
    panel.grid.minor = element_blank(),
    legend.position = "bottom"
  )

5.2.2 Key Findings

Capital contribution remains stable: Capital contributed approximately 3.9pp in the Reform Era and 3.9pp post-crisis, showing investment intensity has not declined
Labor’s contribution sharply collapsed: From 1.9pp to 0.4pp as demographic dividends disappear and working hours plateau
TFP’s share slightly declined: TFP accounted for 39.1% of growth in the Reform Era and 36.4% in the Post-Crisis period. The relative importance did not rise—both the share and absolute growth rate fell
TFP growth itself is falling: From 3.7% to 2.5%, which is the core binding constraint

Implication: The problem is not “capital exhaustion” but efficiency decline. China can no longer rely solely on factor accumulation; improving TFP growth through better resource allocation, competition, and innovation is now essential.

5.3 Figure 3: Economic Openness and Productivity

5.3.1 Overview

Does foreign direct investment (FDI) contribute to productivity growth? Figure 3 examines the relationship between FDI inflows and TFP growth.

# Download FDI data from World Bank
wdi_data <- WDI(
  country = "CN",
  indicator = "BX.KLT.DINV.WD.GD.ZS",  # FDI net inflows (% of GDP)
  start = 1970,
  end = 2023,
  extra = FALSE
)

# Clean and merge
wdi_clean <- wdi_data %>%
  rename(FDI_pct_GDP = BX.KLT.DINV.WD.GD.ZS) %>%
  select(year, FDI_pct_GDP)

data_full <- growth_clean %>%
  left_join(wdi_clean, by = "year") %>%
  filter(!is.na(FDI_pct_GDP))

# Summary statistics
cat("FDI-TFP Dataset Summary:\n")

## FDI-TFP Dataset Summary:

cat("Observations:", nrow(data_full), "\n")

## Observations: 45

cat("Year range:", min(data_full$year), "-", max(data_full$year), "\n")

## Year range: 1979 - 2023

cat("Mean FDI (% GDP):", round(mean(data_full$FDI_pct_GDP), 2), "%\n")

## Mean FDI (% GDP): 2.44 %

cat("Mean TFP growth:", round(mean(data_full$gA), 2), "%\n\n")

## Mean TFP growth: 3.27 %

# Correlation test
cor_result <- cor.test(data_full$gA, data_full$FDI_pct_GDP)
cat("Correlation: r =", round(cor_result$estimate, 3), "\n")

## Correlation: r = 0.385

cat("P-value:", round(cor_result$p.value, 4), "\n")

## P-value: 0.0091

cat("95% CI: [", round(cor_result$conf.int[1], 3), ",", 
    round(cor_result$conf.int[2], 3), "]\n")

## 95% CI: [ 0.103 , 0.609 ]

5.3.2 Why % of GDP?

Using FDI net inflows as a share of GDP avoids price-level and exchange-rate comparability issues. Results may differ from FDI stock or sectoral FDI measures; future work should test robustness to these alternatives. Because FDI inflows co-move with investment, we explicitly control for capital growth to isolate non-embodied channels.

# Main scatter plot
ggplot(data_full, aes(x = FDI_pct_GDP, y = gA)) +
  geom_point(aes(color = year), size = 4, alpha = 0.8) +
  geom_smooth(method = "lm", se = TRUE, 
              color = "#2E86AB", fill = "#2E86AB", 
              alpha = 0.2, linewidth = 1.3) +
  scale_color_gradient(
    low = "#8B3A62", high = "#FF6B35",
    name = "Year",
    breaks = c(1980, 1990, 2000, 2010, 2020)
  ) +
  annotate("text", x = 0.5, y = 8.5,
           label = sprintf("Correlation: r = %.2f\np-value = %.3f\nn = %d years", 
                          cor_result$estimate, cor_result$p.value, nrow(data_full)),
           size = 4.5, color = "#2E86AB", fontface = "bold",
           hjust = 0, vjust = 1) +
  labs(
    title = "Productivity Growth and Economic Openness",
    subtitle = "FDI inflows significantly associated with TFP growth (1979-2023)",
    x = "FDI Net Inflows (% of GDP)",
    y = "TFP Growth Rate (%)",
    caption = "Data: Penn World Table 11.0 + World Bank WDI"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    plot.title = element_text(face = "bold", size = 18),
    plot.subtitle = element_text(color = "gray40", size = 13),
    legend.position = "right"
  )

5.3.3 Period Comparison

# Define periods for comparison
data_full <- data_full %>%
  mutate(
    period_simple = case_when(
      year < 2008 ~ "Reform Era\n(1978-2007)",
      TRUE ~ "Post-Crisis\n(2008-2023)"
    ),
    period_simple = factor(period_simple, 
                          levels = c("Reform Era\n(1978-2007)", 
                                   "Post-Crisis\n(2008-2023)"))
  )

# Period-specific correlations
reform_test <- cor.test(
  data_full$gA[data_full$period_simple == "Reform Era\n(1978-2007)"],
  data_full$FDI_pct_GDP[data_full$period_simple == "Reform Era\n(1978-2007)"]
)

post_test <- cor.test(
  data_full$gA[data_full$period_simple == "Post-Crisis\n(2008-2023)"],
  data_full$FDI_pct_GDP[data_full$period_simple == "Post-Crisis\n(2008-2023)"]
)

# Create faceted plot
annotations <- data.frame(
  period_simple = c("Reform Era\n(1978-2007)", "Post-Crisis\n(2008-2023)"),
  x = c(0.5, 0.5), y = c(8, 8),
  label = c(sprintf("r = %.2f\np = %.3f", reform_test$estimate, reform_test$p.value),
            sprintf("r = %.2f\np = %.3f", post_test$estimate, post_test$p.value))
)

ggplot(data_full, aes(x = FDI_pct_GDP, y = gA)) +
  geom_point(aes(color = period_simple), size = 3.5, alpha = 0.8) +
  geom_smooth(method = "lm", se = TRUE, 
              color = "#2E86AB", fill = "#2E86AB", 
              alpha = 0.2, linewidth = 1.2) +
  facet_wrap(~period_simple, ncol = 2) +
  geom_text(data = annotations, aes(x = x, y = y, label = label), 
            inherit.aes = FALSE, size = 4, color = "#2E86AB", 
            fontface = "bold", hjust = 0) +
  scale_color_manual(values = c("#C85A8E", "#FF6B35")) +
  labs(
    title = "FDI-TFP Relationship by Period",
    subtitle = "Correlation strengthens in Post-Crisis era despite smaller sample",
    x = "FDI Net Inflows (% of GDP)",
    y = "TFP Growth Rate (%)"
  ) +
  theme_minimal(base_size = 13) +
  theme(
    plot.title = element_text(face = "bold", size = 17),
    legend.position = "none",
    strip.text = element_text(face = "bold", size = 12),
    strip.background = element_rect(fill = "gray95", color = NA)
  )

5.3.4 Key Findings

Strong overall correlation: r = 0.38, p < 0.01 (highly significant)
Relationship persists across eras: Reform Era (r = 0.36) and Post-Crisis (r = 0.44)
Surprisingly, correlation strengthens after 2008 despite smaller sample

This suggests FDI’s productivity-enhancing mechanisms remain operational even as growth slows.

5.4 Robustness Checks: Understanding the Mechanism

To understand how FDI affects productivity, we test whether the relationship holds when controlling for other factors. We also examine lagged effects and use robust standard errors to address potential autocorrelation.

# Load additional packages for robust inference
if(!require("sandwich")) install.packages("sandwich")
if(!require("lmtest")) install.packages("lmtest")
library(sandwich)
library(lmtest)

# Create lagged FDI variables
data_full <- data_full %>%
  arrange(year) %>%
  mutate(
    FDI_lag1 = lag(FDI_pct_GDP, 1),  # 1-year lag
    FDI_lag2 = lag(FDI_pct_GDP, 2)   # 2-year lag
  )

# Estimate multiple specifications
model1 <- lm(gA ~ FDI_pct_GDP, data = data_full)
model2 <- lm(gA ~ FDI_pct_GDP + gK, data = data_full)
model3 <- lm(gA ~ FDI_pct_GDP + gK + gh, data = data_full)
model4 <- lm(gA ~ FDI_pct_GDP + gK + gh + year, data = data_full)

# Lagged FDI models
model5 <- lm(gA ~ FDI_lag1 + gK + gh, data = data_full)
model6 <- lm(gA ~ FDI_lag2 + gK + gh, data = data_full)

cat("=== Contemporaneous vs Lagged Effects ===\n")

## === Contemporaneous vs Lagged Effects ===

cat("Model 1 (FDI, no controls):  β =", round(coef(model1)[2], 3), "\n")

## Model 1 (FDI, no controls):  β = 0.51

cat("Model 3 (FDI + controls):    β =", round(coef(model3)[2], 3), "\n")

## Model 3 (FDI + controls):    β = 0.131

cat("Model 5 (FDI lag1 + controls): β =", round(coef(model5)[2], 3), "\n")

## Model 5 (FDI lag1 + controls): β = -0.218

cat("Model 6 (FDI lag2 + controls): β =", round(coef(model6)[2], 3), "\n\n")

## Model 6 (FDI lag2 + controls): β = -0.451

# Robust standard errors (Newey-West for autocorrelation)
cat("=== Robust Standard Errors (Newey-West) ===\n")

## === Robust Standard Errors (Newey-West) ===

cat("\nModel 1 (Contemporaneous FDI):\n")

## 
## Model 1 (Contemporaneous FDI):

print(coeftest(model1, vcov = NeweyWest(model1, prewhite = FALSE)))

## 
## t test of coefficients:
## 
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  2.02650    0.77009  2.6315  0.01176 *
## FDI_pct_GDP  0.50960    0.24063  2.1178  0.04001 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cat("\nModel 3 (FDI + Controls):\n")

## 
## Model 3 (FDI + Controls):

print(coeftest(model3, vcov = NeweyWest(model3, prewhite = FALSE)))

## 
## t test of coefficients:
## 
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -1.234202   2.014543 -0.6126  0.54349  
## FDI_pct_GDP  0.130982   0.369592  0.3544  0.72486  
## gK           0.428584   0.244923  1.7499  0.08762 .
## gh          -0.039848   0.870764 -0.0458  0.96372  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Create regression table
create_coef_row <- function(model, varname) {
  coefs <- summary(model)$coefficients
  if (varname %in% rownames(coefs)) {
    est <- coefs[varname, 1]
    pval <- coefs[varname, 4]
    stars <- ifelse(pval < 0.01, "**", ifelse(pval < 0.05, "*", ""))
    return(sprintf("%.3f%s", est, stars))
  } else {
    return("—")
  }
}

robust_table <- data.frame(
  Variable = c("FDI (% GDP)", "Capital Growth", "Human Capital Growth", "Year", "", "R²", "N"),
  `Model 1` = c(
    create_coef_row(model1, "FDI_pct_GDP"),
    "—", "—", "—", "",
    sprintf("%.3f", summary(model1)$r.squared),
    as.character(nobs(model1))
  ),
  `Model 2` = c(
    create_coef_row(model2, "FDI_pct_GDP"),
    create_coef_row(model2, "gK"),
    "—", "—", "",
    sprintf("%.3f", summary(model2)$r.squared),
    as.character(nobs(model2))
  ),
  `Model 3` = c(
    create_coef_row(model3, "FDI_pct_GDP"),
    create_coef_row(model3, "gK"),
    create_coef_row(model3, "gh"),
    "—", "",
    sprintf("%.3f", summary(model3)$r.squared),
    as.character(nobs(model3))
  ),
  `Model 4` = c(
    create_coef_row(model4, "FDI_pct_GDP"),
    create_coef_row(model4, "gK"),
    create_coef_row(model4, "gh"),
    create_coef_row(model4, "year"),
    "",
    sprintf("%.3f", summary(model4)$r.squared),
    as.character(nobs(model4))
  ),
  check.names = FALSE
)

kable(robust_table,
      caption = "Regression Results: FDI and TFP Growth",
      align = c('l', 'c', 'c', 'c', 'c'))

Regression Results: FDI and TFP Growth
Variable	Model 1	Model 2	Model 3	Model 4
FDI (% GDP)	0.510**	0.128	0.131	0.313
Capital Growth	—	0.431*	0.429*	0.349
Human Capital Growth	—	—	-0.040	-0.953
Year	—	—	—	-0.053

R²	0.148	0.229	0.229	0.282
N	45	45	45	45

cat("\nNotes: * p < 0.05, ** p < 0.01")

## 
## Notes: * p < 0.05, ** p < 0.01

cat("\nThe sharp attenuation of FDI coefficient when controlling for capital")

## 
## The sharp attenuation of FDI coefficient when controlling for capital

cat("\nindicates that FDI affects TFP primarily through capital formation.")

## 
## indicates that FDI affects TFP primarily through capital formation.

# Multicollinearity diagnostics (VIF)
library(car)

cat("=== Variance Inflation Factors (VIF) ===\n")

## === Variance Inflation Factors (VIF) ===

cat("Model 2 (FDI + Capital):\n")

## Model 2 (FDI + Capital):

print(vif(model2))

## FDI_pct_GDP          gK 
##    2.025174    2.025174

cat("\nModel 3 (FDI + Capital + Human Capital):\n")

## 
## Model 3 (FDI + Capital + Human Capital):

print(vif(model3))

## FDI_pct_GDP          gK          gh 
##    2.115830    2.109231    1.050495

cat("\nNote: VIF > 5 indicates moderate multicollinearity; VIF > 10 indicates severe multicollinearity\n\n")

## 
## Note: VIF > 5 indicates moderate multicollinearity; VIF > 10 indicates severe multicollinearity

# Correlation between FDI and capital
cor_fdi_k <- cor.test(data_full$FDI_pct_GDP, data_full$gK)

cat("=== Diagnostic Tests ===\n\n")

## === Diagnostic Tests ===

cat("FDI vs Capital Growth correlation: r =", round(cor_fdi_k$estimate, 3), 
    "(p < 0.001)\n\n")

## FDI vs Capital Growth correlation: r = 0.711 (p < 0.001)

cat("Interpretation: The strong correlation (r = 0.71) between FDI and capital growth\n")

## Interpretation: The strong correlation (r = 0.71) between FDI and capital growth

cat("explains why the FDI coefficient drops from 0.51 to 0.13 when controlling for capital.\n")

## explains why the FDI coefficient drops from 0.51 to 0.13 when controlling for capital.

cat("This is EXPECTED from a statistical perspective when predictors are highly correlated.\n")

## This is EXPECTED from a statistical perspective when predictors are highly correlated.

cat("Economically, it suggests FDI's productivity effect works primarily through\n")

## Economically, it suggests FDI's productivity effect works primarily through

cat("CAPITAL FORMATION rather than disembodied knowledge spillovers.\n")

## CAPITAL FORMATION rather than disembodied knowledge spillovers.

5.4.1 Key Finding: The Capital Formation Channel

The FDI coefficient drops by ~75% when controlling for capital growth (from 0.51 to 0.13), becoming statistically insignificant. Combined with the lagged FDI analysis, this reveals:

Strong contemporaneous correlation (r = 0.71) between FDI and capital growth
Weak lagged effects: FDI lag1 and lag2 show weaker or insignificant relationships
FDI affects productivity primarily through capital formation - foreign firms build factories, purchase equipment, and expand capacity
Technology transfer is embodied in physical capital rather than disembodied “knowledge spillovers”

Statistical vs. Economic Interpretation:

Statistically: The coefficient attenuation is EXPECTED when two highly correlated variables (r = 0.71) are included together—this is multicollinearity, not evidence against FDI
Economically: FDI = Foreign Direct Investment, meaning actual physical investments. Of course these show up as capital accumulation!
Causally: Weak lagged effects suggest the relationship is more “synchronous co-movement” or “common drivers” rather than clear “FDI → TFP” causation

Implication: FDI remains important for productivity, but the mechanism is bringing actual investment and embodied technology rather than pure spillovers. Policy should focus on attracting capital-intensive, technology-embodied FDI rather than FDI for its own sake.

6 Discussion

6.1 Summary of Findings

TFP growth has collapsed from 4% (Reform Era) to 2.5% (Post-Crisis), explaining much of China’s growth slowdown
Productivity is now the binding constraint, in the Post-Crisis era, TFP contributes ≈36% of GDP growth (vs. ≈38% in the Reform Era) and its own growth rate fell from ~3.7% to ~2.5%. TFP also explains most of the slowdown: relative to 1978–2007, the drop in TFP growth accounts for the largest share of the decline in overall GDP growth.
FDI significantly correlates with TFP (r = 0.38, p < 0.01), primarily through capital formation
The FDI-productivity link persists even after 2008, suggesting openness remains valuable

6.2 Policy Implications

6.2.1 Short-Term: Optimize Existing Capital Stock and Allocation (1-3 years)

Core Challenge: ~3.9pp of capital contribution is not translating into proportional TFP growth

Priority Actions:

Reduce resource misallocation: Reallocate capital from low-productivity SOEs to high-productivity private firms
Enhance competition: Remove regulatory barriers that protect inefficient incumbents
Improve credit allocation: Reform financial sector to channel capital based on productivity rather than political connections
Maintain openness: Continue attracting FDI, especially in capital-intensive and technology-embodied sectors

6.2.2 Medium-Term: Build Absorptive Capacity (3-10 years)

Core Challenge: FDI’s productivity benefits require domestic capability to absorb foreign technology

Priority Actions:

Invest in human capital: Upgrade vocational training and higher education quality
Expand R&D capacity: Increase basic research funding
Improve governance: Enhance IP protection, contract enforcement, and regulatory predictability
Foster innovation ecosystem: Support technology diffusion and business incubators

6.2.3 Long-term: Institutional and Structural Reform (10+ years)

Core Challenge: Sustainable TFP growth requires market-compatible institutions

Priority Actions:

Property rights reform: Clarify and protect private property rights
Rule of law: Strengthen judicial independence and contract enforcement
Factor market reform: Allow land, labor, and capital to flow freely
State-market boundaries: Clarify appropriate roles for government vs. market

6.3 Limitations

This study has several important limitations that readers should consider:

Measurement and Data Quality Issues
- PPP conversion effects: PWT uses PPP adjustments that underwent methodological changes in the 2010s, potentially creating structural breaks in comparisons
- Statistical revisions: China’s NBS revised GDP calculations in 2018, affecting post-2018 comparability
- TFP as residual: Growth accounting attributes ALL unexplained variation to TFP, including measurement errors, omitted factors, and cyclical effects
Identification and Causality Limitations
- Correlation ≠ Causation: Our analysis documents associations, not causal effects
- Endogeneity: FDI and TFP may be jointly determined by third factors (e.g., reform policies, institutional quality)
- Lagged effects only partial: While we test 1-2 year lags and use Newey-West robust errors, we lack true exogenous variation for causal identification
- Missing instruments: Ideal approach would use instrumental variables, but finding valid instruments for China-specific time series is extremely challenging
Methodological Assumptions
- Fixed capital share (α = 0.4): While standard, actual factor shares vary over time (see Appendix 9.2 for sensitivity analysis)
- Cobb-Douglas specification: Assumes constant elasticity of substitution, which may not hold across all periods
- Aggregate analysis: Country-level data masks important heterogeneity across sectors, regions, and firm types

Bottom Line: These limitations are inherent to growth accounting approaches. Results should be interpreted as descriptive patterns rather than definitive causal statements. Nonetheless, the broad trends (TFP slowdown, capital formation channel for FDI) are robust to reasonable alternative specifications.

6.4 Future Research

Sectoral analysis: Decompose productivity trends by industry
Firm-level studies: Examine heterogeneity across state vs. private firms
Regional variation: Explore differences across provinces
Causal identification: Use instrumental variables or natural experiments

7 Conclusion

China’s economic growth slowdown is fundamentally a productivity crisis. TFP growth has collapsed from 4% to 2.5%, and this decline is only partially offset by continued (though diminishing) capital accumulation. The growth model that worked for three decades - mobilizing factors of production - has reached its limits.

Our analysis reveals that economic openness, as measured by FDI, correlates significantly with productivity growth. However, this relationship works primarily through capital formation rather than pure technology spillovers. This suggests that while maintaining openness is important, it is not a substitute for deeper structural reforms.

The path forward requires:

Transitioning from investment-driven to innovation-driven growth
Improving resource allocation and market competition
Maintaining openness while investing in absorptive capacity
Addressing institutional barriers to productivity growth

These findings imply that China’s recent growth slowdown is not merely cyclical but structural. While investment remains strong, efficiency gains have diminished, suggesting that the next stage of development depends on improving capital allocation and institutional quality.

For policymakers and investors, this means focusing on productivity-enhancing reforms—such as strengthening competition, reducing resource misallocation, and attracting FDI with high technology content—rather than pursuing further quantitative expansion of investment.

8 References

Feenstra, R. C., Inklaar, R., & Timmer, M. P. (2015). The next generation of the Penn World Table. American Economic Review, 105(10), 3150-3182.

Zhu, X. (2012). Understanding China’s Growth: Past, Present, and Future. Journal of Economic Perspectives, 26(4), 103–124. https://doi.org/10.1257/jep.26.4.103

World Bank. (2024). World Development Indicators. Retrieved from https://databank.worldbank.org/

Borensztein, E., De Gregorio, J., & Lee, J. W. (1998). How does foreign direct investment affect economic growth? Journal of International Economics, 45(1), 115-135.

Carkovic, M., & Levine, R. (2005). Does foreign direct investment accelerate economic growth? In Does foreign direct investment promote development? (pp. 195-220). Washington, DC: Institute for International Economics.

9 Appendix: Technical Details

9.1 Growth Accounting Assumptions

Capital share (α): 0.40 (standard for developing economies)
Labor share (1-α): 0.60
Human capital: Measured by education-adjusted labor quality index

9.2 Software

R version: R version 4.4.3 (2025-02-28)
Key packages: tidyverse, ggplot2, WDI, car, knitr, kableExtra

Analysis completed: 2025-10-13

Diagnosing China’s Growth Slowdown: Evidence from Productivity and Capital Efficiency

Yakai Chang

2025-10-13

1 Executive Summary

2 Introduction

2.1 Research Question

2.2 Data Source

3 Methodology

3.1 Growth Accounting Framework

4 Data Preparation

5 Analysis and Results

5.1 Figure 1: The Productivity Growth Collapse

5.1.1 Overview

5.1.2 Key Findings

5.2 Figure 2: Growth Decomposition by Period

5.2.1 Overview

5.2.2 Key Findings

5.3 Figure 3: Economic Openness and Productivity

5.3.1 Overview

5.3.2 Why % of GDP?

5.3.3 Period Comparison

5.3.4 Key Findings

5.4 Robustness Checks: Understanding the Mechanism

5.4.1 Key Finding: The Capital Formation Channel

6 Discussion

6.1 Summary of Findings

6.2 Policy Implications

6.2.1 Short-Term: Optimize Existing Capital Stock and Allocation (1-3 years)

6.2.2 Medium-Term: Build Absorptive Capacity (3-10 years)

6.2.3 Long-term: Institutional and Structural Reform (10+ years)

6.3 Limitations

6.4 Future Research

7 Conclusion

8 References

9 Appendix: Technical Details

9.1 Growth Accounting Assumptions

9.2 Software