Decomposing wheat yield volatility

To answer the question of how volatility differs across regions and over time, as well as to disentan-gle its drivers, we decompose the standard deviation of the wheat growth rates (see Fig. 3). We illus-trate these measures in Fig. 4 (based on Tab. S11, SA). Actual, weather- and input-induced volatili-ties are plotted for two sub- periods: 1996–2002 and 2003–2009 (grey-solid and grey-dashed circles).

Averaging over regions and time, inputs explain ca. 49% of the total actual wheat yield volatility,

Results and discussion

32

while weather explains 43% (evaluated at the sample means, based on values in Tab. S11, SA).

Comparing actual volatilities for the sub-periods over time, wheat yield volatility increases except for one state (North Rhine-Westphalia, Fig. 4-a). Riskier areas regarding weather and inputs are found in the eastern part of Germany.

We use regional aggregated yield data at the federal state level. Spatially uncorrelated risks, that is, idiosyncratic shocks, “self-diversify” at this higher aggregation level compared to firm-level data, while more systemic variation remains (Woodard and Garcia, 2008, p. 37; Marra and Schurle, 1994).¹⁰ Hence, weather- induced volatility at the state level can be interpreted as a measure of systemic weath-er risk in agricultural production (cf. Xu et al., 2010, p. 267–268). As illustrated in Fig. 4-b, weathweath-er- weather-caused volatility differs slightly by region with higher volatilities in the eastern part. Comparing these volatilities with those caused by input adjustments (Fig. 4-c), we find for the entire eastern region, as well as some western regions, higher input-induced volatilities compared to the volatilities traced back to weather changes (e.g., Bavaria). Over time, we observe increases in actual volatility, on average.

However, this can only be traced back to joint increases in weather and inputs in some regions (e.g., Saxony), while in other regions weather- and input-induced volatility changes reveal opposite signs.

For instance in Brandenburg, weather-induced yield volatility considerably increases but input-induced volatility decreases. Still, the overall increase of actual volatility cannot be fully traced back to weather and input adjustments.

Fig. 4. Actual, weather- and input-induced wheat yield volatility for two sub-periods. Note: Bubbles indicate volatilities of different magnitudes. B: Berlin, BB: Brandenburg, BR: Bremen, BV: Bavaria, BW: Baden-Wuerttemberg, HE: Hesse, HH: Hamburg, LS: Lower Saxony, MWP: Mecklenburg-West Pomerania, NRW: North Rhine-Westphalia, RP: Rhineland-Palatinate, SA: Saxony-Anhalt, SH: Schleswig–Holstein, SL: Saarland, SY: Saxo-ny, TH: Thuringia.

10 Note that the illustration of the aggregation argument by Woodard and Garcia (2008, p. 37–38) does not acknowledge that a part of the weather risk might be included among the idiosyncratic risks that self-diversify. Precipitation and relat-ed variables that are functions of the latter are expectrelat-ed to vary more across space than temperature.

We find a higher share of explained actual volatility, for the first compared to the second period. To illustrate an extreme, in Hesse from 1996–2002, about 93% of the actual volatility are explained (6.11 volatility inputs and weather; 6.55 actual volatility, values according to Tab. S11, SA); from 2003–

2009 this amounts to 35%, however. Averaging over all regions, we find 83% of the actual volatility explained by inputs and weather from 1996–2002, while 44% in the period 2003–2009. These findings can be explained in part by the use of time dummy variables in the regression model, which are isolat-ed in the volatility measures for inputs and weather but are particularly important in the second period.

Hence, we likely underestimate the weather effect because common weather shocks are captured by time dummy variables. As a robustness check, we investigated whether the different geographical siz-es of the statsiz-es affect our rsiz-esults (aggregation bias); this is not the case (see SA for details).

Weather-driven volatility at the state level seems to be rather low given that we would expect higher changes caused by varying weather conditions. In other words, we conjecture that systemic risk can-not only be traced back to weather as measured in our model (regional temperature, solar radiation, precipitation and evapotranspiration). Common shocks at the macro (i.e. national) level are relevant.

The latter include weather extremes but also policy and price changes affecting many farms as well as consequential input-adjustments. The significant year dummy variables from 2000 onwards cap-ture exactly such macroeconomic and policy changes (Tab. 3). In this period several reforms of the CAP affected farms production (intensity) decisions, for instance, the de-coupling of direct payments from the crop being planted starting in Germany in 2000, which was discussed in 2003, reinforced in 2005 and verified in 2008. The price boom for agricultural commodities in 2007/08 also occurred during this period. The national level volatility based on year dummy variables reflects the increasing importance of common shocks: 5% in 1996–2002, 11.2% in 2003–2009 (see Fig. 3 and Tab. S11, SA).

How would the results, particularly the weather-induced volatility, look like if input adjustments were neglected? Similar to the full model 1, the estimates for the reduced form model 2 reveal in-creases in weather-induced volatility for some regions, while for others decreasing measures for the second period prevail (Tab. S11, SA). The unexplained share of volatility and the national level vola-tility are also higher in the second period. Averaging over regions and time, weather explains practi-cally the same fraction of the total actual volatility in model 2 (both models: 43.5%). Comparing the regional volatility estimates within period 1996–2002, some are overestimated in model 2 (e.g., Sax-ony-Anhalt and Brandenburg) while some are underestimated (e.g., Hesse). In period 2003–2009, the majority of the measures of the reduced form model overestimate the weather component, though in some regions only by a minor rate. For only one state (Hesse) the two models differ qualitatively:

while the full model detects decreases in weather-induced volatility in period 2003–2009, model 2 finds small increases. Thus, one could draw misleading conclusions regarding the weather- induced

Concluding remarks

34 volatility in both sign and size while neglecting inputs.

However, and most importantly, the unexplained part is higher compared to the full model. As a con-sequence, too much emphasis would be placed on the interpretation of the common shocks (significant for all years in model 2, considerably higher estimates; this results in higher national level volatility).

As such, the systemic macro risk would be overestimated. At the same time, input- adjustments as possible consequences of price and policy shocks, which are simply rational adaptation by farmers, would not be discussed at all.