A. Identifying assumptions and definitions

Following developments by Lechner (Reference Lechner2011) and Karlsson, Nilsson, and Pichler (Reference Karlsson, Nilsson and Pichler2014), we can analyze and test several identifying assumptions of the DID model.

(6) Definition of the average treatment effect (ATE)

Starting with Equation (1), we define the expected outcome for the treatment region versus the control group and for the pre-shock versus post-shock as follows:

(1)$$E\{ {Y_i^{T = t} {\rm \mid } \,D_i = d} \} = \beta _0 + \beta _1{\rm \;}d + \beta _2{\rm t} + \beta _3( {{\rm dt}} ) $$

$${\rm d} = \left\{{\matrix{ {0{\rm \;if\;control\;group\;}} \hfill \cr {1{\rm \;if\;treatment\;group\;( Three\;Lakes) \;}} \hfill \cr } } \right.$$

$$t = \left\{{\matrix{ {0{\rm \;if\;pre}\hbox{-}{\rm treatment\;period\;}( {01/2012-03/2014} ) } \hfill \cr {1{\rm \;if\;treatment\;period\;}( {04/2014-03/2015} ) } \hfill \cr } } \right., \;$$

with $Y_i^{T = t}$ Outcome (such as quantity, price, and income) and β ₀, β ₁, β ₂, β ₃ = parameters. Each coefficient can be interpreted as follows:

$$\hskip-30pt \bullet \hskip0.5pc\beta _0 = E\{ {Y_i^{T = 0} \, {\rm \mid } \, D_i = 0} \} $$

This is the expected outcome of the control group in the pre-treatment period.

$$\hskip-30pt \bullet \hskip0.5pc\beta _1 = E\{ {Y_i^{T = 0} \, {\rm \mid } \, D_i = 1} \} - \beta _0 = E\{ {Y_i^{T = 0} \, {\rm \mid } \, D_i = 1} \} -E\{ {Y_i^{T = 0} \, {\rm \mid } \, D_i = 0} \} $$

This is the difference in the outcome between the treatment and the control group in the pre-treatment period.

$$\hskip-30pt \bullet \hskip0.5pc\beta _2 = E\{ {Y_i^{T = 1} \, {\rm \mid } \, D_i = 0} \} -\beta _0 = E\{ {Y_i^{T = 1} \, {\rm \mid } \, D_i = 0} \} -E\{ {Y_i^{T = 0} \, {\rm \mid } \, D_i = 0} \} $$

This is the difference in the outcome for the control group in the treatment period compared to the pre-treatment period.

$$ \!\!\!\!\!\!\!\! \matrix{&\hskip-25pt \bullet \hskip0.5pc\ {\beta _3 = E\{ {Y_i^{T = 1} \, {\rm \mid } \, D_i = 1} \} -\beta _0-\beta _1-\beta _2 = } \hfill \cr & \qquad{{\rm \;}[ {E\{ {Y_i^{T = 1} \, {\rm \mid } \, D_i = 1} \} -E\{ {Y_i^{T = 0} \, {\rm \mid } \, D_i = 1} \} } ] -[ {E\{ {Y_i^{T = 1} \, {\rm \mid } \, D_i = 0} \} }} \cr & \hskip-135pt-E\{ {Y_i^{T = 0} \, {\rm \mid } \, D_i = 0} \} ]}$$

This is the difference in the outcome between the treatment group in the treatment period versus the pre-treatment period minus the difference in the outcome between the control group in the treatment period versus the pre-treatment period (Average Treatment Effect = ATE). Therefore, β ₃ is the coefficient of interest, which we will focus on for the results section of this paper.

B. Exogenous supply shock

According to economic theory, given constant demand, a negative supply shock will have a positive impact on price and a negative impact on quantity. Hail weather shocks, which are, by definition, exogenous, cannot be predicted in advance by a model, and accordingly, their impact can only be estimated ex-post. Our paper focuses on the effects of the exogenous supply-side shock, the hailstorm, which impacted the Three Lakes wine region. We would expect the resulting impact to be an automatic fall in the quantities of wine sold from the treatment region on the market and a price rise. This weather phenomenon could lead to a compensation effect, that is, a rise in demand for Swiss wines unaffected by the hailstorm, an increase in their quantities on the market, and a rise in their prices. We analyze this compensation effect in the Results section through the cross-price elasticity estimations for the wines of the Three Lakes and the other five Swiss wine regions, by color.

One important issue in this setup is the Three Lakes region's wine stocks, which could be used to compensate for the losses in wine production (due to the low harvest) and to maintain a constant supply and deliveries to the retail market. According to Switzerland's Federal Office for Agriculture, the Three Lakes region's stocks fell by 31.6% for white wines and 29.7% for red and rosé wines in 2013 (FOAG, 2016). These data are, however, limited as we did not have precise information for other distribution channels (HoReCa, wholesale, direct sales) to study their diversification effects. Our data (Nielsen, 2015) represent about one-third of the total volume of Swiss wines available in the country's market. With a lower wine supply available for the market due to the hail weather shock, we would expect producers to sell a greater share to their private consumers (direct sales) and perhaps restaurants (HoReCa) given the higher margins. On the other hand, only big wine producers have enough wine (usually 50–100,000 liters) to sell through retail market channels, and they usually have long-term contracts with distributors, which are difficult to terminate. Local consumers in the affected wine region could go directly to the grower, but, in general, the greater the physical distance, the less likely it is. A sensitivity analysis of these diversification effects is presented in the Results section.

C. Econometric model (baseline)

To identify whether sales of the treatment group (Three Lakes) wines significantly dropped in Switzerland's retail market after the weather shock, we use the following DID equation:

(2)$${\rm ln}( {{Outcom}{\rm e}_{i, t}} ) = \beta _0 + \beta _1{Trea}{t}_i + \beta _2{Pos}{t}_t + \beta _3( {{Trea}{t}_i\;{\ast\; Pos}{t}_t} ) + \varepsilon _{i, t}$$

Equation (2) is a random effect (RE) model, where we regress the Outcome_i,t (quantity, price, income) on the dummies Treat_i, Post_t, and (Treat_i ∗ Post_t), where, in more detail:

• • Treat_i is the time-invariant dummy that takes the value of 1 if the type of wine was affected by the weather shock (treatment group = Three Lakes) and 0 if it was not (control group);

• • Post_t is the individual-invariant dummy that takes the value of 1 if the observation came after the weather shock and 0 if it came before (cut-off date: April 2014);

• • Treat_i ∗ Post_t is the interaction variable between Treat_i and Post_t that takes the value of 1 if the observation was part of the treatment group and came after the cut-off point, and 0 otherwise.

The coefficient of interest is β ₃, which measures the difference in Outcome_i,t between the treatment and control groups after the treatment. In a fixed-effects model, coefficient β ₁ cannot be estimated due to the within transformation of the data. Equation (3) provides more detail, with the natural logarithm of the quantity of wine consumed as an independent variable:

(3)$${\rm ln}( {Q_{i, t}} ) = \beta _0 + \beta _3( {{Trea}{t}_i{\;\ast\; Pos}{t}_t} ) + S_{i, t}\theta + Z_t\gamma + u_i + \delta _t + \varepsilon _{i, t}$$,

where Q _i,t and S _i,t (along with vector parameter θ) are the quantity and vector of control time-variant variables (mostly climatic variables), respectively, where index i designates the type of wine, and t designates the time at which it was sold. Z_t (along with vector parameter γ) is a vector of the control individual-invariant variables (mostly economic variables), and u_i is the unobserved heterogeneity across individual AOCs. The latter term cancels out due to the within transformation in the fixed-effect model. δ_t is the time-fixed effect (at the monthly level) and ɛ_i,t the idiosyncratic error term. Note that in Equation (3), as opposed to Equation (2), the variables Treat_i and Post_t are not included in the model on their own (only through Treat_i * Post_t) due to the former's perfect collinearity with the individual FE (u_i) and the latter's perfect collinearity with the time FE (δ_t). Our regressions always use robust standard errors clustered at the individual level, which allows for autocorrelation and heterogeneity inside each cluster.

Transforming Equation (3) and deriving ln(Q_i,t) with respect to I_i,t (which denotes Treat_i * Post_t) gives us:

$$\displaystyle{{\partial Q_{i, t}} \over {\partial I_{i, t}}} = e^{{\rm ln}( {Q_{i, t}} ) }{\rm \;\ast\; }\beta _3\Leftrightarrow \displaystyle{{\partial Q_{i, t}} \over {\partial I_{i, t}}} = Q_{i, t}{\rm \;\ast \;}\beta _3$$

We therefore obtain the semi-elasticity parameter β ₃, that is to say, the percentage change in quantity relative to an absolute change in the interaction variable I_i,t:

$$\beta _3 = \displaystyle{{\displaystyle{{\partial Q_{i, t}} \over {Q_{i, t}}}} \over {\partial I_{i, t}}}$$

D. Econometric model (extension)

This subsection extends the Equation (3) model by allowing β ₃ to vary over time (β^t):

(4)$${\rm ln}( {Q_{i, t}} ) = \beta _0 + \beta _3^t ( {{Trea}{t}_i{\;\ast\; Pos}{t}_t} ) + S_{i, t}\theta + Z_t\gamma + u_i + \delta _t + \varepsilon _{i, t}$$

Autor (Reference Autor2003) analyzed the effects of increased employment protections on firms’ use of temporary workers by including both leads and lags in a DID regression:

(5)$${\rm ln}\left( {Q_{i,t}} \right) = \beta _0 + \mathop \sum \limits_{t = -q}^{-1} \beta _3^t \left( {{Trea}{t}_i{\rm \;*\;}\delta _t} \right) + \mathop \sum \limits_{t = 0}^m \beta _3^t \left( {{Trea}{ t}_i{\rm \;*\;}\delta _t} \right) + S_{i,t}\theta + Z_t\gamma + u_i + \varepsilon _{i,t}$$

We set t = 0 as the start of the treatment (cut-off date) with q leads $\mathop[\sum \nolimits_{t = -q}^{-1} \beta _3^t ({Trea}{t}_i{\rm \;*\;}\delta _t)]$, which analyzes pre-trend characteristics, and m lags $\mathop[\sum \nolimits_{t = 0}^{m} \beta _3^t ({Trea}{t}_i{\rm \;*\;}\delta _t)]$, which analyzes the treatment effect changes (if any) over time after the treatment (see also Jacobson, LaLonde, and Sullivan (Reference Jacobson, LaLonde and Sullivan1993) for event study models).

The idea is to interact the time dummies (δ_t) with the treatment indicator (Treat_i) for the pre-treatment and treatment periods. It is important to leave out one of the treatment periods if we wish to get a saturated model. The estimated coefficients between the treatment and control groups in the pre-treatment period should be statistically insignificant to prove the common trend assumption (Karlsson, Nilsson, and Pichler, Reference Karlsson, Nilsson and Pichler2014). The interaction dummies after the treatment indicate whether the weather shock effect is fading, staying constant, or increasing over time. Due to the important disturbance to the monthly-frequency data, we also aggregated specifications for time and treatment interactions by trimester and semester. The results of this analysis are presented in the Robustness Checks section.

A. Placebo pre–post treatments

This robustness check's goal is discarding the fact that no other anticipated or postponed effects occuring in the Three Lakes region. In Table 4's Specification (1), we created a placebo pre-treatment effect by anticipating the cut-off date of one year, namely in April 2013. As expected, we did not find any significant statistical results. This confirmed that no pre-treatment effects occurred. We also created a placebo post-treatment effect—Specification (2)—by moving the cut-off date to one year later in April 2015. As expected, even though this coefficient became positive, we found no significant statistical results. This seems to confirm that the treatment effect was fading.

Table 4 Placebo pre–post treatment regressions (quantity)

Notes: *** p < 0.01, ** p < 0.05, * p < 0.1; clustered robust standard errors (individual) in parentheses; FE = fixed effect (individual).

B. Placebo control regions

Table 5 shows the results from our five placebo treatment regions. This analysis is important for demonstrating that the common trend assumption (Karlsson, Nilsson, and Pichler, Reference Karlsson, Nilsson and Pichler2014) is not violated by one of the five control regions. One example of a violation of that assumption could be a significant supply shock in one of the treatment regions. In this regression model, we removed the Three Lakes region and treated each control region in turn as a placebo treatment region against the four remaining controls. As expected, we found no statistically significant results, and this model seemed to show that there were no significant supply shocks for any of the control regions in the same treatment period framework chosen for the Three Lakes.

Table 5 Placebo control regions regression (quantity)

Notes: *** p < 0.01, ** p < 0.05, * p < 0.1; clustered robust standard errors (individual) in parentheses; FE = fixed effect (individual).

C. Regressions for different configurations of the control group

This robustness check's goal is to change the control group's specification, removing one of the five regions at a time from each regression. The region's sizes varied a lot in terms of the quantity of wine they sold. Therefore, it is important to check whether removing one region from the regression would change the results significantly. Table 6 shows that this baseline specification did not significantly change our regression results (between –21.9% and –25.8% compared to –22.8% baseline regression results). This demonstrated that the baseline model was stable, with statistically significant results at the 1% level. Another robustness check (not presented) was to create two synthetic control groups, one closer to (Valais, Vaud, and Geneva) and one farther away from (Ticino and German-speaking Switzerland) the Three Lakes region. These results showed negative effects of 23.0% for the first and 23.5% for the second synthetic control, both at the 1% significance level.

Table 6 Regressions for different configurations of the control group (quantity)

Notes: *** p < 0.01, ** p < 0.05, * p < 0.1; clustered robust standard errors (individual) in parentheses; FE = fixed effect (individual).

D. Regressions by color type

Finally, Table 7 presents three different cross-color specifications regressing the treatment region's wines (All, White) with the control wines (All, Red, and Rosé). The proportions of red, white, and rosé wines in each wine region vary strongly. This is an additional robustness check that considers this heterogeneity by testing whether the color of a wine can influence the baseline regression results (presented in Table 3). The results all remained significant at the 1% level and relatively stable compared to the baseline results, varying between –23.6% and –27.7%.

Table 7 Regressions by color type (quantity)

Notes: *** p < 0.01, ** p < 0.05, * p < 0.1; clustered robust standard errors (individual) in parentheses; FE = fixed effect (individual).

E. Extension of the regression results

This robustness check's goal was to go beyond the pre-treatment and treatment design by analyzing the hail shock at higher frequency periods (semesters, trimesters, and months). Letting $\beta _3^t$ in Equation (5) vary over time allowed us to analyze the trend in more detail and with more precise time trends. Figure 5 shows the interactions between time dummies and treatment groups over time, aggregated at the semester level. We noted that the pre-trend interactions were statistically insignificant and quite regular. The dotted vertical line indicates the date of the weather shock (June 2013). The dashed vertical line shows the 2013 vintage's arrival on the retail market (at the April 2014 cut-off point). The solid vertical line represents the end of the 2013 vintage's effect (March 2015), as the new 2014 vintages, unaffected by the weather shock, were entering supermarkets. It is very interesting to note that $\beta _3^t$, even though statistically insignificant, had a negative sign between the dashed and solid vertical lines. Meanwhile, after the 2013 vintage effect, the estimated coefficients became positive again, supporting the negative shock effect of the treatment region's wine sales in the treatment period under evaluation.

Figure 5. Estimated shock effect over time (by semester).

Source: Author's illustration using data from Nielsen (2015).

For more details, Table 8 gives all the estimated lead and lag interaction coefficients for the semestrial frequency specification. The semestrial-frequency specification seemed to be the most convincing one for analyzing a time-varying $\beta _3^t$, better than the trimestral frequency specification and far better than the monthly frequency specification, which gave less clear visual evidence.Footnote ⁸

Table 8 Leads and lags (semester)

Notes: *** p < 0.01, ** p < 0.05, * p < 0.1; clustered robust standard errors (individual) in parentheses; FE = fixed effect (individual).