OBJETIVO GENERAL:

The aim of the empirical analysis is to investigate whether the household price risk aversion coef- cient is changing over time and then how time-varying price risk aversion aects the household food consumption pattern. This study provides an original contribution with respect to Belle- mare et al. (2013b), because the empirical analysis is microfounded and the price risk aversion parameter is allowed to change over time. To this end, the following empirical regression, which is derived from the above micro model, is used for estimation:

ln DEC = c jln PjtP + ln et+ ln dAijt (8) where the log of the indicator of dietary energy consumption (lnDEC), i.e. the amount of calories a representative farm household is assuming during the year, is employed as empirical counterpart

of the indirect utility function (Ramasawmy, 2012, 17), dAijt is the estimated household price

risk aversion (see below), et is the total expenditure, which proxies for the full income Yt of the

equation 6.

To control for possible sources of endogeneity between price risk aversion coecient Aijt, and

dietary energy consumption, DEC (e.g., it is possible that households with higher level of DEC, i.e. richer in terms of calories consumption, are less risk-averse toward food shortfall), the price

risk aversion coecient Aijt is not directly introduced as explanatory variable in the equation

8. Rather, a 2SLS approach is applied by rst instrumenting the risk aversion parameter ( dAijt)

through a rst stage regression, equation 9, and then including it as explanatory variable in the equation 8.

In order to instrument dAijt, the following rst-stage equation is estimated:

ln dAijt= jln Pj;t 1C + ln H + W1112+  (9)

where dAijt is the empirical counterpart of the price risk aversion parameter introduced by Belle-

mare et al. (2013b), PC

j;t 1 is the lagged value of the market price of the crop j, H a set of

household control variables and W1112 is equal to 1 if the observation refers to the survey wave

period 2011-2012, 0 if it refers to the waves 2009-2010 or 2010-2011.  the error term.

The lagged value of the market prices PC

j;t 1 is employed to control for the contemporaneous

endogeneity between the market prices, PC

j;t, and the price risk aversion coecient, Aijt.

Further instruments are the market prices of plantains, beans, cassava, maize, rice and sweet potatoes as well as the household size, the number of children and daughters, the literacy indi- cator, the attendance of the school, the gender and age of the household head (Dohmen et al., 2011; Moscardi and Janvry, 1977; Nielsen and Zeller, 2013) (D'Souza and Tandon, 2015, 14). The literacy of the household heads is proxied by a dummy, which is equal to 1, if they are literate, 0 otherwise. School attendance is dened by two dummy variables: the rst one refers to primary school, which is equal to 1 if the household head attended primary school, 0 other- wise; the second dummy concerns the attendance of secondary school, which is equal to 1 if the household head attended secondary school, 0 otherwise. The dummy variable for the gender of the household heads is equal to 1 if they are male, 0 if they are female.

The selection of instruments is based on a far-reaching literature and the relevance of the in- struments has been tested by various techniques: microeconomic models, econometric regression- based techniques, lottery-based, game-theoretical experiments, etc. (Dohmen et al., 2011; Moscardi and Janvry, 1977; Nielsen and Zeller, 2013; D'Souza and Tandon, 2015).

Take also into account that the equation 8 captures the impact of time-varying price risk aversion on household food consumption pattern, while the equation 9 allows to disentangle the variation of the price risk aversion coecient over time and to understand which household features have

a major impact on the price risk aversion coecient.

In this study, approaches of the previous literature are extended to detect the impact of these variables on the price risk aversion coecient, which assesses the relationship between the un- derlying market conditions and the household behaviour towards risk (Bellemare et al., 2013b). To this end, survey wave dummy variables are also introduced to detect changes of the price risk aversion over time. The inclusion of such time dummy allows to disentangle whether there was some break in the risk aversion parameter during the time period of the survey.

Note that in this empirical framework farm gate price PP

jt and market price PjC are included as

two dierent variables, because they are assessed at the dierent levels of the value chain of the crop j. The dierence between them depends on the structure of the value chain and can be due to several factors, like transport and transaction costs as well as market distorsions, which are not specically addressed in this study (Muratori, 2016). As it can be seen in the graph 1, high volatility of food prices occurred between 2009 and 2012. This situation allows to assess the impact of very volatile prices on the behaviour of farm households and, in particular, to study the changes of their risk aversion parameter over time in a comprehensive fashion.

Be also aware that in the price risk aversion matrix Aijt (Bellemare et al., 2013b), the Arrow

Pratt coecient of risk aversion, R, which proxies psychological risk preferences, is deducted.

Therefore, Aijt does not provide any information whether the household psychological risk pref-

erences change over time after the occurrence of some price shocks. Nevertheless, it is possible to have an insight in the variations of the psychological risk preferences due to the occurence of price shocks, by analysing the residuals  of the rst-stage regression 9. Indeed, the residuals

 are the left-over, after the relationship between price risk aversion parameter Aijt and a set

of variables, which proxy the availability and eciency of risk-bearing institutions, is estimated. Therefore, although the residuals  entail much noise, they represent a rough indicator of the

empirically estimated household psychological risk aversion, bR, as well as they can be employed

as dependent variable in the following regression, which is estimated within a xed eect model:

b

R = H + W1112 (10)

This approach allows to investigate whether the household psychological risk preferences, R change over time and which factors determine such a variation. The above described model includes both the behaviour of net sellers and net buyers. Nevertheless, it is likely that the behaviour of two groups of farm household is dierent after the occurrence of a price shock. To

deal with this issue, the equation 9 is extended with a market position dummy variable, MPhjt,

which is equal to 1, if the farm household is a net seller of a given crop j, 0 otherwise:

ln dAijt= jln Pj;t 1C + ln H + W1112+ MPhjt (11)

The equation 11 allows to disentangle whether there is dierence in the reaction to price shocks between net seller and net buyer farm households.

Data

The approach is based on the data collected by the Ugandan Statistical Oce and the World Bank team within the framework of the Living Standard Measurement Study (LSMS) (World Bank, 2015).

Such database applied to this method allows to draw consistent conclusions, which can be gener- alized to the population of Uganda, because its sampling design warrants representativeness at national and sub-national level (Himelein, 2012). Moreover, the database is integrated with data on calories intake of food, which are collected from International Network of Food Data Systems (FAO, 2015).

The panel database concerns households which consumed or produced the major staple crops in Uganda, like beans, cassava, maize, plantains, rice and sweet potatoes during three survey waves, taking into consideration the following years 2009-2010, 2010-2011 and 2011-2012. Data were prepared to allow the estimation of the magnitude and the sign of the variables of interest. Due to the particular structure of the agricultural survey data, several sheets of the Living Standard Measurement Study were merged in order to obtain necessary information for the analysis.

The collected database provides information about consumption and production behaviour of 3284 households which harvested or consumed the above mentioned staple crops during the LSMS survey waves 2009-2010, 2010-2011 and 2011-2012 or at least in one of them.

This leads to the construction of two dierent databases, a balanced and an unbalanced panels which are both used for the analysis. In the unbalanced panel database all 3284 households are taken into account for the estimation, while the balanced one consists of 2491 households, since some observations are missing for one or two years.

In order to compute dietary energy consumption (DEC), calories intake for kilogram is taken from the International Network of Food Data Systems (FAO, 2015). In particular, I distinguished calories data between the dierent food items and their processing status, for instance if they are dry or fresh.

Another important issue with respect to data preparation concerns the conversion of non- standard measurement units, like cups, buckets, etc., widely used in the context of rural agri- culture, into kilograms. Conversion factors were taken from (World Bank, 2011) and (Woittiez et al., 2013).

The reported farm gate and market prices, given for the specic measurement units provided by the respondents (for instance, a sack or a cup), were converted in prices per kilogram of crop. If market prices were missing, they were replaced by the average market price of the specic crop. Instead, farm gate prices were not imputed and therefore there are many missing values for this variable. The reason of the dierent approach with respect to the missing values of the two prices is due to the fact that the farm gate price received by the farmers can vary in a signicant way across regions, along seasons and due to the market access available to the farm household. Farmers cannot easily switch from one buyer to the other, because they are quite dispersed across the country and live often in remote areas. On the contrary, consumers, mostly living in urban environment, can more easily switch from a seller to the other in order to obtain a better price for kilogram of crop, given the same quality level of the purchased product. The kilogram-equivalent quantities and the calories intake for kilogram are also used for the

computation of the yearly dietary energy consumption.

Moreover, information about actual income earned by the household members is dicult to ob- tain because of the reticence of respondents to declare such data and the prevalence of informal business activities. In order to have a reliable estimate of the household income, the expenditure approach is followed. Household nancial capability is based on total expenditures, i.e. all ex- penses for consumption, non-durable, durable goods and for taxes and other fees. Such outlays are reported for dierent time horizons and therefore all of them are converted on a 365-days basis to get total yearly expenditures.

In order to develop comparison some controls were introduced. Such dummies indicate whether the household head is male, whether he or she is literate and attended primary or secondary school. The number of children (members younger than 18 years) in each household and their gender, household size and the age of the household head were also computed and included in the panel database.

Following the equation 7, all parameters for the calculation of the the price risk aversion coe-

cient Aijt were separately computed.

By merging the household production and consumption database for the above mentioned crops and taking the dierence between the yearly kilogram-equivalent harvested and the kilogram- equivalent consumed quantity, the yearly marketable surplus for each crop and household was obtained.

If quantity produced and consumed of a given crop were missing and then the marketable sur- plus could not be computed, it is not straightforward, whether the missing values are due to zero production and consumption or whether the respondent was not able to reply to the question. To avoid to spoil the dataset, in this case missing values of marketable surplus were not replaced.

The budget share of marketable surplus of commodity jt = P

P

jtMj

Yt was also added to the

database. The price risk aversion matrix evaluates the impact of the underlying market con- ditions on the household behaviour towards risk: in particular, it includes the amount of the marketable surplus, the value of the market prices, the budget share of the revenues from the sale of each commodity, the cross-price elasticity between the marketable surplus of dierent commodities, the income elasticity of marketable surplus and the Arrow-Pratt coecient of rel- ative risk aversion (Turnovsky et al., 1980) (Bellemare et al., 2013b).

The Arrow-Pratt coecient of relative risk aversion is estimated from the data, by computing the second derivative of the dietary energy consumption with respect to the quantity of consumed crops (Arrow, 1971). The Arrow-Pratt coecient is estimated by a two-steps static panel model: in the second stage the quantity of consumed crops is regressed on the tted value of DEC, derived from the rst stage computation. The choice of the xed or random eects strategy is based upon the results of the Hausman test. Result of the estimation with respect to the Arrow-Pratt coecient of relative risk aversion is 1.0277, which is within the range of credible values found in the literature (Bellemare et al., 2013b, 886) (Friend and Blume, 1975) (Chavas and Holt, 1990) (Hansen and Singleton, 1983) (Saha et al., 1994).

In this empirical analysis the utility function V (PP

jt; Yt; Aijt) is given by the dietary energy con-

sumption (DEC). This function turns quantity of crops consumed into calories available to the household.

Besides, a specic database is created to estimate the income and cross-price elasticity of the marketable surplus of each commodity. The elasticities are computed through a static panel

model, which used the results of the Hausman test also in this case.

With all information included in the database, the price risk aversion coecient Aijt is com-

puted for each combination of household, crop and year. Then, this parameter was added to the database.

Since endogeneity between risk aversion coecient and dietary energy consumption was detected in several specication tests, a set of instruments to be employed in the IV regression was derived from the microfounded model or taken from the literature: some of the instrumental variables are the market prices of plantains, beans, cassava, maize, rice and sweet potatoes. Moreover, there are some instruments which describe the main household features like the household size, the number of children and daughters, the literacy indicator, the attendance of the school, the gender and age of the household head (Dohmen et al., 2011), (Moscardi and Janvry, 1977) (Nielsen and Zeller, 2013) (D'Souza and Tandon, 2015, 14).

The literacy of the household heads is proxied by a dummy, which is equal to 1, if they are literate, 0 otherwise. The attendance of the school is dened by two dummy variables: the rst one refers to primary school, which is equal to 1 if the household head attended primary school, 0 otherwise; the second dummy concerns the attendance of secondary school, which is equal to 1 if the household head attended secondary school, 0 otherwise.

Moreover, the dummy variable for the gender of the household heads is equal to 1 if they are male, 0 if they are female. Finally, a survey wave dummy variable was introduced, which as- sumes value 1 over the 2011-2012 period, and value 0 if the wave is 2009-2010 or 2010-2011. The inclusion of such time dummy allows to disentangle whether there was some break in the risk aversion parameter during the time period of the survey. A summary of the dummy variables is provided in table 2.

The selection of the instruments is based on a far-reaching literature: indeed, several articles verify the relevance of the above mentioned variables as determinants of risk preferences, by ap- plying microeconomic models, econometric regression-based techniques, lottery-based and game- theoretical experiments (Dohmen et al., 2011), (Moscardi and Janvry, 1977) (Nielsen and Zeller, 2013) (D'Souza and Tandon, 2015).

All variables other than the dummy indicators were converted in logarithms, so that the coe- cients of the all estimated regressions can be directly interpreted as elasticities.

Estimation Results