1 Introduction

Hall and Jones hypothesized that greater social infrastructure improves a country’s productive capacity, measures in output per worker. In their 1999 paper, they were able to show evidence that supported their hypothesis that strong institutions and government policy explain output variation across countries.

The implication here for development economics is that stronger institutions are not only more conducive to growth, but are the determining factor when it comes to output in an economy.

2 Output and Capital per Worker

The following charts show Output per worker on the x axis and capital per worker on the y axis. The charts show a strong positive relationship between the two, meaning higher capital per worker corresponds with higher output per worker. This makes intuitive sense and confirms the economic theory which the intuition is based upon. Labor is more productive, in terms of output, when it has more capital to work with. Increasing labor when leaving capital unchanged will lead to diminishing marginal productivity of labor. However, when both labor and capital are increased, output is able to expand at higher rates without diminishing.

3 Regression: Output and Capital per Worker

When running a simple linear regression model explaining output per worker as a function of capital per worker, we find a similar relationship to that explained in the previous charts. Increased capital per worker increases output per worker, and the change in capital per worker is explained by changes in output per worker at an \(R^2\) of 0.896. The coefficient of 0.655 can be interpreted as the percentage change in the output per worker associated with a 1% increase in the capital per worker.

Specifically, for each 1% increase in the independent variable (log capital per worker), the dependent variable (log output per worker) is estimated to increase by approximately 0.655%.

## 
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                               hjlogyl          
## -----------------------------------------------
## hjlogkl                      0.655***          
##                               (0.020)          
##                                                
## Constant                     2.705***          
##                               (0.186)          
##                                                
## -----------------------------------------------
## Observations                    127            
## R2                             0.897           
## Adjusted R2                    0.896           
## Residual Std. Error      0.347 (df = 125)      
## F Statistic         1,091.269*** (df = 1; 125) 
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

4 Regression: Social Infrastructure

The measure of social infrastructure is shown to have a greater impact on output per worker than the capital per worker, by almost three times. and \(R^2\) of 0.578 means almost 60% of variation in output across countries is explained by the differences in social infrastructure measure. Specifically, for each 1% increase in the independent variable (social infrastructure index), the dependent variable (log output per worker) is estimated to increase by over 3%, a much higher value that capital per worker, which was examined in the previous regression.

This is the big takeaway from the Hall and Jones paper, and this shows in its incredible number of citations, well into the thousands. Institutions and social infrastructure are a critical component for growth, and this shows in the high social infrastructure and high TFP from developed nations.

## 
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                               hjlogyl          
## -----------------------------------------------
## hjsocinf                     3.289***          
##                               (0.250)          
##                                                
## Constant                     7.208***          
##                               (0.133)          
##                                                
## -----------------------------------------------
## Observations                    127            
## R2                             0.582           
## Adjusted R2                    0.578           
## Residual Std. Error      0.700 (df = 125)      
## F Statistic          173.760*** (df = 1; 125)  
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

5 Total Factor Productivity

Total Factor Productivity is shows the growth not attributed to increases in labor or capital factor inputs. In the form of a Cobb-Douglas production function, total output is represented by:

\[ Y = AK^\alpha L^\beta \]

TFP is represents by \(A\), while capital and labor inputs are \(K\) and \(L\), respectively. \(Y\) is the measure of total output in the economy (on a country level).

The equation I will use will be modified for capital and output measures on a per worker level. In addition, since the dataset contains variables in log scale, we can taken the log of the above equation to calculate TFP.

\[ logY = A * \alpha logK * \beta log L \]

Solving for \(A\) :

\[ A = \frac{logY}{\alpha logK * \beta logL} \]

Using this methodology, I come close to reproducing the Hall and Jones TFP calculation seen in the Productivity Calculations (Table 1). The TFP (A) is presented as a ratio to US values. In comparison to the USA, Kenya and India have very low TFP, while Italy has a higher TFP. My calculations are off in some sense as the USSR shows higher TFP despite being a much lower value in the Hall and Jones paper.

## # A tibble: 8 × 2
##   country  A_scaled
##   <chr>       <dbl>
## 1 KENYA       0.296
## 2 ZAIRE      -0.412
## 3 U.S.A.      1.00 
## 4 CHINA       0.499
## 5 INDIA       0.173
## 6 ITALY       1.23 
## 7 U.K.        0.783
## 8 U.S.S.R.    1.33