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We use equation (1) to jointly estimate both the long-run effect of different climates and the short-run effect of annual deviations from this climate⁶. The economic model and relevant assumptions are described in the Supplementary Information. Equation (1) is used for each of six dependent variables: farm profits and the yields of five major crops. The farm profits/yields (V) for subnational region i, in country j in year t are estimated in the preferred model as:

where is a vector that includes growing season temperature and precipitation and is the 30-year climatological average for the years preceding year t. Bold denotes vectors of coefficients. We control for unobserved, possibly nonlinear time trends at the country level using a country-by-year linear and quadratic time trend, unobserved time-constant variation between countries using a country fixed effect, and other observed within-country variation using a suite of controls. These controls include a vector of soil-quality variables (organic carbon content, water-holding capacity, erodibility, and soil type), altitude and altitude squared, subsidies received per hectare, irrigated area per hectare and a crop-price index.

Our source of economic and yield data is the EU Farm Accountancy Data Network (FADN) survey between 1989 and 2009 (ref. 26). The data we use are aggregated from the farm to the regional (subnational) level using weights based on the three-way stratified sampling methodology used by FADN. Therefore, the representativeness of these aggregated values depends on the soundness of the sampling and weighting schemes used by the EU (ref. 26). Farm profits are defined as the total value of farm production minus all costs plus subsidies received minus taxes paid. They are normalized by the total agricultural area used in the year to give farm profits per hectare. Yields are calculated as the crop produced in the year divided by the area of crop planted. The five crops considered in this paper constitute around 25% of the value produced by European farms, with the remainder coming from meat and dairy production and other grain, fruit and vegetable crops. Weather data are monthly averages averaged over a growing season defined by the observed planting and harvest date for each region using the SAGE crop calendar data set^{27, 28, 29}. For the profits per hectare regression we use a standard March–September growing season definition. We create balanced data sets by retaining only those observations with data for the whole period 1989–2009. This prevents possible confounding of the estimation by gradual entry of eastern European countries into the data set after the mid-1990s. Additional details on the construction of the data set and control variables are given in the Supplementary Information.

We estimate equation (1) using ordinary least-squares regression, weighting by the square root of farm area to reduce heteroskedasticity and to make results more representative of the average growing area. Standard errors were estimated using 500 block-bootstraps, blocking at the country by 2-year level to account for heteroskedasticity, within-country spatial autocorrelation, and temporal autocorrelation at one-year lag. The estimated response functions can be used to calculate the expected damages from climate change with (equation (2)) and without (equation (3)) adaptation. These responses are shown diagrammatically in Supplementary Fig. 1 and, given a shift in climate from to can be estimated for each observation as:

where the βs are the parameter estimates obtained from the equation (1) regression. These response curves are combined with climate model projections for the period 2030–2049 under the A1B scenario using a 13-member ensemble from the ENSEMBLES project⁷. The projections from this ensemble and the equations for decomposing ensemble projection uncertainty are described in the Supplementary Information. The ensemble we use pertains to a single emission scenario but scenario uncertainty constitutes only a small fraction of total uncertainty in climate projections at regional levels by 2040 and therefore is unlikely to affect our conclusions³⁰.