This paper deals with a problem of censored data in the household demand analysis when budget survey data is used. Micro-data, in contrast with aggregated data, usually contains a significant portion of zero observations (no consumption recorded) that leads to censoring of data and potential selectivity problem resulting in biased estimates if inappropriate econometric model is used. We review different treatment methods available in the literature that control the selectivity problem. Concretely, it is Tobit model, Two-part model, Double-hurdle model, Sample selection model with three different estimators - FIML, Heckman two-step, and Cosslett's semi-parametric estimator. On the empirical example we indeed show that firstly the treatment methods are necessary also for small levels of censoring and secondly the choice of treatment method matters even for different products within the same dataset. We compare performance over the above single-equation demand models together with OLS. The household demand is analysed for 13 different food products with high variety of level of censoring. We found that the Heckman two-step procedure and Cosslett's semi-parametric estimators performed best among all examined techniques in our case and that these two estimators yield similar estimates of income and own price elasticities. The Two-part model performs equivalently but the estimation results differ from the Heckman two-step and the Cosslett's estimator. The OLS estimates are biased and perform poorly together with Tobit model with weak performance.