The saving function

As mentioned in section 2.3, the reduced form of the saving function is estimated using data on household’s average monthly saving as inGuariglia(2001),Guariglia(2002),Rossi

(2009),Klemm(2012), andGiavazzi and McMahon(2012). 8

A major problem encountered when dealing with saving data is the likely mass point at zero, leading to non-linearity of the conditional mean. The sample considered in this paper is a clear example, with 51% of households reporting zero monthly savings.

A common approach in the applied literature is to estimate the conditional mean using a Tobit estimator. However, the Tobit estimator comes at the cost of some restrictive as- sumptions, namely normality and homoschedasticity. Using the OLS estimator on the log- transformed data is another possible solution, but would would translate in discarding a big fraction of the data. Transformations of the type ln(a + y) would not solve the problem in the latter case. They might solve the numerical one, but are likely to affect estimation in a non-sensible way.

In order to overcome these difficulties, the reduced form of the saving function is estim- ated using a Poisson Quasi Maximum Likelihood estimator. The choice of the estimator is driven by some characteristics of Poisson QMLE which make it an ideal candidate for the task: i) the estimator does not require the outcome to be Poisson-distributed in order to be consistent (Wooldridge,2010a;Cameron and Trivedi,2009) ; ii) it does a good job in deal- ing with big zero mass points (Silva and Tenreyro,2011). On top of that, Poisson QMLE is superior to other non-linear estimators in that it does not suffer the incidental parameters

8_{A common practice in the applied literature dealing with precautionary savings is to estimate reduced}

form equations where assets holdings are regressed on a measure of risk. BHPS data, however, do not contain information about the stock of wealth in a panel dimension. Information regarding wealth holdings and outstanding debt is available only for 1995, 2000 and 2005. This makes it difficult to compare wealth holdings among individuals who may have entered the labour market at different points in time. However, saving flows and stocks of wealth are, in principle, connected through the budget constraint.Guiso et al.

(1992) suggest that focusing separately on the effects of uncertainty on the flow of savings and on the stock wealth may serve as a double test of the theory of precautionary savings.

problem, and allows fixed effect estimation of the saving function. The assumption ne- cessary for the estimator to be consistent, other than non-negativity of the outcome, is an exponential parametrization for the conditional mean of the saving flow. The latter can be written as:

E(Sit|Zit) = exp (αTWs TWit+ αXsXit+ ci+ dt) (2.11)

One limitation of this approach is that it assumes that the observed zeroes in the data are actual zeroes (i.e. corner solutions) rather than the result of censoring. Since BHPS data only contains information about active saving, it is not possible to verify if individuals who report not to be active savers have actual negative savings. Classifying households with negative saving as non-savers might lead to understate or overstate the magnitude of the effect of temporary work. If households switch from positive/zero saving to negative saving when the head is in a temporary job, estimates of the saving equation will provide a lower-bound for the true consumption smoothing effect. If, instead, households react by decreasing the amount of outstanding debt, but remaining under the zero-saving threshold, misclassifying negative saving as zero will bias estimates against the existence of a precau- tionary motive. In this latter case, however, estimates of the consumption equations should be able to capture the precautionary response to the extent that the resources used to reduce the amount of debt are diverted from expenditures measured in BHPS data.

The vector Xit in the equation above includes the same set of individual and household’s characteristics used in the previous section. Additional regressors are a categorical vari- able for housing tenure, household earnings (log) , earnings of the household head (log), a dummy variable for benefit income in the household, a set of financial situation indicators controlling for financial constraints, and the same set of indicators for subjective expecta- tions about future economic conditions seen in section2.4 - which are added here to help controlling for standard life-cycle reason for saving.

head-specific fixed effects. As mentioned in the introduction, fixed effect estimation of the saving function is important for two main reasons. On the one hand, if selection into temporary jobs is guided by unobservable characteristics, like risk aversion, not fully ac- counted for by the set of covariates, fixed effects should mitigate the self-selection problem to the extent that these characteristics are time-invariant. On the other hand, fixed effects, along other major determinants of life-time income, should be able to account, at least partially, for permanent income. In this case, the inclusion of the current level of earnings should approximate the effect of the transitory component of income. This latter consider- ation will be further discussed when interpreting the results.