As mentioned earlier, short-term increases in yield should appear directly in the GDP accounts if land under cultivation is relatively fixed in the short term, and agricultural output constitutes a sizable share of GDP. Table 5 presents fixed effects OLS estimators for equation , covering five-year growth periods from 1965 to 2000. Consistent with the growth literature , the coefficient on lagged GDP per capita is close to 0.7, suggesting a convergence coefficient of approximately -0.06 per annum. Barro and Sala-i-Martin summarize the debate on the true underlying meaning of this coefficient, which is not our main variable of interest and therefore not discussed in detail here. Our main variable of interest is a lagged value of cereal yield, which has a very large and significant coefficient of 0.08 in the first column of Table 5. The within-country standard deviation of yields is 0.5 tons, so we proceed to interpret the instrumented yield coefficient in terms of a marginal increase of 0.5 tons. The coefficient implies that a half ton per hectare increase in yields is linked to a 4 percent increase in GDP per capita. The implied long-run coefficient on yields is 0.29.7.Investment over the previous five years is positively correlated with growth, while inflation, government consumption as a percentage of GDP, u planting gutter and total fertility rates are all negatively correlated with growth. Note that Column I does not limit the sample, while Column II limits the sample to the 58 countries that have data on non-agricultural value added per worker. For consistency we retain the 58-country sample moving forward. Note that keeping this consistent sample throughout the analysis implies limiting the time period to starting in 1970, since the NAVA estimations involve longer lags in the independent variables.

In unreported results, allowing a larger sample in Table 5 leads to consistent coefficients on the yield variable, however these are not always significant at 5 percent levels. We employ the instrumental variables framework to look at how shocks to yield through the fertilizer channel might show up in GDP, both contemporaneously and with a lag. Column III instruments for yields using the same instrument described above, and then GDP per capita is regressed on the fitted value for yields in Column IV. The first stage indicates a good instrument, with a strongly significant coefficient of -31.84 and an F-statistic of 8.76. In the second stage the coefficient on yield is significant at the 5 percent level and equal to 0.35, four times larger than the OLS regression of Column I. The magnitude implies that a 0.5 ton increase in yield leads to 19 percent higher GDP per capita.8 This increase in the coefficient from fixed effects to the 2SLS specification might be due to attenuation bias due to measurement error in the reduced form, or else to omitted variables that are correlated to high yields and low GDP per capita growth. For example, overly pro-rural government policy could boost yields but hurt the economy as a whole. In Columns V-VI of Table 5, we control for the other elements of standard growth regressions . The first stage coefficient on the instrument continues to be very significant and has an F-statistic of 12.34, while the second-stage coefficient on yield is now 0.25. This implies that a half ton increase in cereal yields leads to a 13 percent higher GDP per capita, even when controlling for five-year lag of GDP. While this may seem like a surprisingly large result, one should keep in mind that in the 1960s agriculture constituted over 30 percent of GDP in many countries. In fact, in an unreported result, when we limit the sample in Regressions V-VI to the 30 countries above the median in terms of percentage of GDP in agriculture in 1960 , the coefficient on yield in the second stage is 0.41. This is consistent with the theory that yields increases should boost GDP more in agriculture-dependent countries. Note that Table 5 uses a one-year lagged value of yield, keeping in mind that both the GDP and yield variables are both three-year moving averages. We tested from zero- to five-year lags in the specification of Columns III-IV in order to explore the lag structure of this causally identified effect of yield shocks on GDP, and found an effect in the contemporaneous year as well as one and two years later. The lagged coefficients with 95 percent confidence intervals are graphed in Figure 11, and suggest a statistical relationship between a three-year moving average of GDP per capita centered at time t with a yields t, t-1 and t-2. We opt to present our estimates using yield centered at t-1. Another trenchant way to explore the broader economic growth effects of yield increases in developing countries is to test the links to economic activity entirely outside of agriculture.

Table 7 does this by replicating the same basic growth specification as the GDP and labor share tables but instead tests non-agricultural value added per non-agricultural worker as the dependent variable. Given that we expect a delay between having a boost in yields and spillovers to the non-agriculture sector, and that there is no theoretical prior on what the lag structure is, we first plot out the lag structure of cereal yields on non-agricultural value added per worker. Figure 13 shows the results of regressions of non-agricultural value added per worker tested against 15 respective lags of instrumented cereal yields. Two things are evident when comparing this graph to the one relating cereal yields and GDP per capita. First, the statistical signal is weaker . Second, the statistically significant impact of yields on the non-agricultural sector productivity occurs with a longer lag . This longer delay might indicate that the relationship between yields and non-agricultural value added per worker might occur through slower-moving channels such as movement of labor from agriculture to non-agriculture as opposed to faster channels, such as relative price changes or increases in food immediately generating disposable income for investment in other sectors. Given the lag structure evidence, Table 7 shows results for non-agricultural value added regressions using a nine-year lag on cereal yield . Column 1 presents the fixed-effects regression with no controls. The nine-year lagged value on cereal yields is positively associated with increases in non-agricultural worker productivity, with a coefficient of 0.05, although only significant at the 10 percent level. This implies 0.5 ton per hectare yield increases are associated with a 2.5 percent higher non-agriculture productivity level around nine years later. Column II adds investment and inflation; the lag NAVA coefficient drops from 0.88 to 0.73, similar to the coefficient in the GDP regression, while the yield coefficient is 0.06 and falls just short of the 5 percent significance level. Investment rates are positively correlated with non-agricultural productivity growth, while inflation is negatively correlated. Column III adds government consumption and the total fertility rate. The coefficient on yield remains consistent at 0.03, although it is not significant in this specification. Government consumption is negatively correlated to non-agricultural productivity growth, while the total fertility rate is insignificant. The rest of Table 7 employs the same identification strategy as in the GDP per capita regressions.

We instrument for yields using the global price of fertilizer interacted with the inverse distance from agriculturally weighted centroid to nearest nitrogen production facility. The two-staged least squares results in Columns IV-V employ no macroeconomic controls; the instrument is highly significant in the first stage, and the F-statistic of 10.89 indicates that the instrument is strong. In the second stage, the coefficient on the instrumented lagged cereal yield is significant and rises in magnitude to 0.37. This suggests that an exogenous half ton increase in cereal yields leads to a 20 percent higher non-agricultural productivity nine years later, which translates to a 2 percent higher growth rate of annual productivity per worker. Regressions VI and VII add investment and inflation over the previous five years as controls. The results are consistent: the instrument is significant and has an F-statistic of 11.32; and in the second stage the coefficient on the instrumented cereal yields is significant at 5 percent levels. Its magnitude of 0.35 suggests that a 0.5 ton increase in yields increases non-agricultural productivity by 19 percent in around nine years. Investment and inflation are significant and have the expected signs. Finally, Regressions VIII and IX complete the set of standard macroeconomic growth variables by adding government consumption and the lagged total fertility rate. The first stage results are largely unchanged, with the instrument still highly significant and with an F-statistic of 7.01. The second stage coefficient on cereal yields drops slightly to 0.26, suggesting that 0.5 ton boost in cereal yields leads to a 1.4 percent higher annual growth rate in non-agricultural productivity. Column IX does not quite achieve statistical significance on yields. In Columns X-XI we drop the government consumption variable and find that the second stage yield coefficient returns to 0.36 and achieves 10 percent significance. Overall, Table 7 provides cautious but consistent results suggesting that exogenous half ton increases in yields lead to approximately 20 percent higher non-agricultural value added per worker a decade later. This lends empirical support for the potential role of agriculture in promoting structural change. In order to test the robustness of results,planting gutter particularly those linking yield increases to non-agricultural labor productivity, we conduct the following tests and report them here: adding region- or country-specific linear trends to the regressions; testing 10-year lags on yield instead of nine-year lags; and running the regressions using GMM instrumentation. Table 8 adds region-specific linear trends to the IV regressions of Table 7 using World Bank defined regions of East Asia and the Pacific, Latin America and the Caribbean, Middle East and North Africa, South Asia, and sub-Saharan Africa.

Column I shows that the instrument is still strongly correlated to yields after controlling for country and year fixed effects and now regional linear trends. The F-statistic, however, drops to 4.56, suggesting that the instrument is less strong after partialing out regional linear trends. Indeed, the second stage shows that the instrumented lagged value for cereal yields is no longer significant, although it maintains a similar magnitude , which suggests consistency given that the regional linear trends are reducing the variation available for regression. Regressions II and III add investment and inflation, and then IV and V add government consumption and the total fertility rate. The results are qualitatively similar: The instrument is still highly correlated to cereal yields, though the F-statistics on the instrument are hovering at only around 4.5. Second-stage estimates of the coefficient on cereal yields exhibit consistency in sign and magnitude with the results on Table 7; The coefficient is now 0.40 and consistent with the 0.36 in Table 7 Column XI, though with less precision here. We interpret these results as supporting our overall findings, even if the variation absorbed by the regional trends leads to imprecise estimates. For completeness, we tested country-specific linear trends, but doing so absorbs too much variation and neither first nor second stage regressions are able to identify relationships between the key variables. We further test robustness by changing the specifications in Table 7 from nine-year lags on yield to 10-year lags. As explained above, we chose nine-year lags because the statistical signal was strongest at that lag; nevertheless, we employ 10-year lags to assuage concerns of a spurious nine-year correlation. Columns I-III in Table 9 replicate the fixed effects OLS regressions in I-III in Table 7; the results are essentially unchanged, and the 10-year lag on cereal yield displays even stronger significance than the nine-year lag in Table 7. Columns IV-V introduce the instrumented version of yield with a 10-year lag; the first stage continues to show a strong correlation between the instrument and yield . The second stage coefficient on yields is 0.33, which is consistent with the coefficients in Table 7, however with a 10-year lag the coefficient in Column V is not significant. Columns VI-VII introduce investment and inflation; the coefficients are essentially the same as in Table 7 and the instrumented yield now achieves 10 percent significance.