Relationship Between % GDP Growth and % Pasture Area Growth

Last time we talked we hypothesized that a country’s annual % change in GDP was correlated with the annual % change in pasture area. As the following two graphs show, this is not the case either across coutnries or for the narrow set of countries that account for the most global pasture area. There is a very small negative correlation between GDP and pasture area change for the high and low-middle income countries, but it is insubstantial and does not hold for upper-middle and low icnome countries.

Among the 9 countries with the largest pasture area, the hypothesis of pasture area growth going down with greater rates of GDP growth also does not hold. This relationship only appears for China, S. Africa, and the US (see 2nd graph below). FOr most other countries, pasture area growth increased with GDP growth or remained relatively constant.

Relationship Between Absolute GDP and % Pasture Area Growth

As we noted earlier in graphs showing pasture area change by income group, pasture area stalled for middle income countries and declined for high income countries over time (as their GDP has also increased).

However, there is little clear pattern of pasture area slowing or falling as GDP rises across all countries. The relationship maydoes look substantial. There is a slight negative correlation between higher GDP and pasture area change. However, it is a small correlation. On average (according to the linear model fit), observations at the highest end of the GDP range have an average pasture growth change of -1% compared to an average change of 0% for countries on the lowest end of the GDP. Additionally, many of the countries on the hgiher GDP per capita range have relatively small amounts of pasture area, such as France or Germany. This underscores the importance of looking at change in absolute pasture area or weighting correlations and regressions by countries’ pasture area.

This hypothesized relationship of pasture area falling with GDP increases holds more strongly for some countries with the most pasture area. Brazil, China and Russia had the lowest rates of pasture area growth when they had higher GDP and largest rates of expansion when they had lower GDP. However, this relationship doesnt hold for other countries and the opposite pattern is even seen in Argentina where pasture area expanded more quickly when the country had a higher GDP.

Regression analysis of area

The following regression (notably specification 2) indicates that pasture area generally increases with the numer of cattle, consumption and population, and decreases with yield and GDP per capita. The variables are logged since their distribution is not normal. The simplest specifications to understand here are 1 and 2. The 3rd specification includes year fixed effects and has qualitatively similar results as the 2nd specification.

Regression Results
Dependent variable:
log(area)
(1) (2) (3) (4)
log(m_head) 0.017*** 0.016***
(0.004) (0.004)
log(m_yld) -0.079*** -0.073***
(0.018) (0.018)
log(m_cons_total + 1) 0.077*** 0.074***
(0.008) (0.008)
log(gdp_pc) 0.006** -0.024*** -0.014*** -0.016**
(0.002) (0.003) (0.004) (0.007)
log(pop) 0.122*** 0.058*** 0.067***
(0.009) (0.012) (0.020)
Constant 17.186*** 15.314*** 16.339*** 16.155***
(0.035) (0.148) (0.223) (0.370)
Country Fixed effects? Yes Yes Yes Yes
Year Fixed effects No No No Yes
Observations 7,858 7,858 6,421 6,421
R2 0.996 0.996 0.996 0.996
Adjusted R2 0.996 0.996 0.996 0.996
Residual Std. Error 0.193 (df = 7683) 0.191 (df = 7682) 0.181 (df = 6269) 0.181 (df = 6217)
F Statistic 11,719.940*** (df = 174; 7683) 11,909.070*** (df = 175; 7682) 11,195.500*** (df = 151; 6269) 8,328.423*** (df = 203; 6217)
Note: p<0.1; p<0.05; p<0.01

These results indicate a statistically significant, but weak relationship between GDP per capita and pasture area The logged specifications indicates that for a 10% increase in GDP per capita, we’d expect a 0.14% to 0.24% drop in pasture area (calculated here as 1.1^beta coefficient). The range of results I report is from taking the range of beta coeffients across the 3 specifications.

Here I also regress % change in pasture area on log absolute GDP. You can see that GDP is positively associated with pasture area, but that its also positively associated with population, which is why the GDP coefficient in the second specification decreases.

Regression Results
Dependent variable:
pct_chg_area
(1) (2) (3) (4)
log(gdp) 0.042*** 0.021*** 0.049*** 0.046***
(0.002) (0.004) (0.005) (0.009)
log(pop) 0.091*** 0.088*** 0.079***
(0.015) (0.017) (0.020)
log(m_yld) -0.090*** -0.097***
(0.022) (0.023)
log(d_yld) -0.059*** -0.057***
(0.009) (0.009)
Constant 0.082 -0.970*** -0.370 -0.154
(0.066) (0.187) (0.256) (0.418)
Country Fixed effects? Yes Yes Yes Yes
Year Fixed effects No No No Yes
Observations 7,861 7,858 6,898 6,898
R2 0.781 0.782 0.778 0.780
Adjusted R2 0.776 0.777 0.773 0.772
Residual Std. Error 0.242 (df = 7686) 0.242 (df = 7682) 0.240 (df = 6734) 0.240 (df = 6682)
F Statistic 157.670*** (df = 174; 7686) 157.625*** (df = 175; 7682) 144.937*** (df = 163; 6734) 109.901*** (df = 215; 6682)
Note: p<0.1; p<0.05; p<0.01

Regression analysis of meat yields

I hypothesize that there is more of a relationships between GDP and yields than between GDP and pasture area. I regress beef yields on GDP per capita, with several specifications below including other controlling variables, country and year fixed effects.
Beef Yield ~ GDP Regression Results
Dependent variable:
log(m_yld)
(1) (2) (3) (4)
log(gdp_pc) 0.121*** 0.087*** 0.084*** 0.037***
(0.002) (0.002) (0.003) (0.005)
log(m_head) -0.029*** -0.029***
(0.003) (0.003)
log(m_cons_total + 1) 0.100*** 0.107***
(0.005) (0.005)
log(pop) -0.034*** -0.191***
(0.009) (0.015)
log(stocks) -0.053*** -0.035***
(0.008) (0.008)
Constant 6.496*** 6.750*** 8.077*** 10.468***
(0.015) (0.025) (0.135) (0.226)
Country Fixed effects? No Yes Yes Yes
Year Fixed effects No No No Yes
Observations 7,080 7,080 6,421 6,421
R2 0.361 0.852 0.859 0.864
Adjusted R2 0.361 0.848 0.855 0.860
Residual Std. Error 0.270 (df = 7078) 0.132 (df = 6914) 0.130 (df = 6269) 0.128 (df = 6217)
F Statistic 3,997.896*** (df = 1; 7078) 240.589*** (df = 165; 6914) 252.237*** (df = 151; 6269) 195.107*** (df = 203; 6217)
Note: p<0.1; p<0.05; p<0.01

These results indicate a statistically significant, but weak relationship between GDP per capita and yields. The specifications including country fixed effects indicates that for a 10% increase in GDP per capita, we’d expect a 0.04% to 0.8% increase in beef yields (calculated here as 1.1^beta coefficient). Overall, the relationship between GDP per capita and yields is either stronger or weaker than the relationship with pasture area shown above depending on your preferred specification.

Regression analysis of dairy yields

I conduct a similar relationship here for milk yields, first just regression yields on GDP, then additing country fixed effects, controlling variables, and year fixed effects. The results are similar.
Milk Yield ~ GDP Regression Results
Dependent variable:
log(d_yld)
(1) (2) (3) (4)
log(gdp_pc) 0.449*** 0.213*** 0.095*** 0.046***
(0.005) (0.004) (0.007) (0.013)
log(pop) 0.391*** 0.149***
(0.023) (0.036)
log(stocks) 0.065*** 0.106***
(0.018) (0.018)
log(d_head) -0.152*** -0.137***
(0.013) (0.013)
log(d_cons_total + 1) 0.151*** 0.144***
(0.017) (0.017)
Constant 6.019*** 7.326*** 1.646*** 5.036***
(0.040) (0.060) (0.328) (0.551)
Country Fixed effects? No Yes Yes Yes
Year Fixed effects No No No Yes
Observations 7,444 7,444 6,354 6,354
R2 0.504 0.908 0.918 0.922
Adjusted R2 0.504 0.906 0.916 0.920
Residual Std. Error 0.760 (df = 7442) 0.331 (df = 7282) 0.311 (df = 6204) 0.304 (df = 6152)
F Statistic 7,570.984*** (df = 1; 7442) 446.942*** (df = 161; 7282) 468.908*** (df = 149; 6204) 364.066*** (df = 201; 6152)
Note: p<0.1; p<0.05; p<0.01

These results indicate a statistically significant and substantial relationship between GDP per capita and milk yields. The specifications that include country fixed effects indicate that for a 10% increase in GDP per capita, we’d expect a 0.04% to 0.9% increase in yields (calculated here as 1.1^beta coefficient).

Percent Change in Yield vs. Consumption vs. Pasture

Last time we talked, we decided to plot yield, consumption and pasture. We wanted to do this since pasture area should start declining when productivity growth (including yield and other factors) outpaces consumption growth. However, the following graphs illustrate that the relationship is more complicated. Although the first regression above indicates that a 10% increase in yields would balance out the effect on pasture area of a 10% increase in consumption (yields and consumption have similar coefficients, but opposite signs). However, other factors such as population and non-yield productivity measures make it such that no clear relationship appears in graphs of beef consumption, beef yields, and pasture area growth.

## $y
## [1] "% Change since 1961"
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## $title
## [1] "Percent Change Area, Yield, Stocking, Consumption since 1961"
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## attr(,"class")
## [1] "labels"

Instead of a clear pattern of growth in yields and stocks per pasture area surpassing consumption, we instead see consumption far outpacing the other variables. This is not surprising given the large growth in population and the fact that pasture area has primarily been growing since 1961.

This mixed relationship between yields, stocking, consumption and area is visible at the country and regional level as well (minor regions in appendix)

However, when we look at trends since 1990, an interesting pattern emerges. It appears that recently, increases in non-yield productivity (here just captured by stocks per pasture area) have increased faster than yields. I have yet to look into this further.

Appendix 1: Relationship between Percent Change in GDP PER CAPITA and Pasture Area Growth

The trends for % GDP growth and pasture area hold for % GDP per capita growth as well. There doesn’t appear anything interesting here to note except that trends in pasturea area are generally disconnected from GDP growth.

Appendix 2: Relationship Between Absolute GDP Per capita and Percent Pasture Area Growth

The relationship between GDP per capita and pasturea area growth looks substantial, just as the pattern for GDP did. As the following grpah shows, there is a negative correlation between higher GDP per capita and pasture area change. However, it is a small correlation. On average (according to the linear model fit), observations at the hgihest end of teh GDP per capita range have n average pasture growth change of -1% compared to an average change of 0% for countries on the lowest end of the GDP per capita range. Additionally, many of the countries on the hgiher GDP per capita range have negligible amounts of pasture area — Luxembourg, Isle of Man, Liechtenstein all have particularly high GDP per capita values for instance. This underscores the importance of looking at change in absolute pasture area or weighting correlations and regressions by countries’ pasture area.

Appendix 3: Alternate Measures of Productivity vs. Consumption

## $y
## [1] "% Change since 1961"
## 
## $title
## [1] "Percent Change Area, Production/Area and Consumption since 1961"
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## [1] "labels"

Appendix 4: Productivity, Consumption and Area by Minor Region