While effects of measurement error can sometimes be benign, this is often not the case when estimating causal effects. Two specific examples include estimation of (i) the average causal effect when confounders are measured with error and (ii) the natural indirect effect when the exposure and/or confounders are measured with error. Methods adjusting for measurement error typically require auxiliary information such as external data or knowledge about the measurement error distribution. Here, we propose methodology relying on no such information, and instead show that when the relationship between the error-prone confounders and the outcome is linear, one can recover consistent estimation of these causal effects using what we refer to as synthetic instrumental variables. These are functions of only the observed data that behave as instrumental variables for the error-prone confounders. We estimate the average causal effect of maternal protein intake on child neurodevelopment as well as the component of this effect that is mediated by lead using data from Bangladesh. Here, protein intake is calculated from food journal entries, and is thought to be highly subject to measurement error.