We study two impediments to monetary policy transmission: (1) search friction in mortgage shopping (2) shadow banking. The first impediment weakens the mortgage refinancing channel of monetary policy. Many US mortgage borrowers do not refinance, despite seemingly having financial incentives to do so. We explore the role of search costs in explaining this inaction, focusing on the 2009-2015 period when mortgage rates declined. We estimate a dynamic discrete choice model of refinancing and search decisions using a panel data set, which includes information on the sequence of refinancing decisions and search intensity (the number of mortgage inquiries). We find that search costs significantly inhibit refinancing through two channels. First, higher search costs directly increase the cost of refinancing. Second, they also indirectly increase lenders’ market power and thus raise the offered refinance rates. We find that the indirect market power effect dominates. In chapter two, we study an additional source of market power coming from search friction: statistical discrimination by lenders, a tool to separate borrowers who differ in search intensity. We explore how statistical discrimination affects monetary policy transmission. We build and calibrate a general equilibrium model of the mortgage market with two types of borrowers who differ in the number of lenders they meet. If lenders meet refinancers with high current interest rates, they infer it is likely they did not search in the past and is not likely to search now. So, lenders infer these refinancers as non-shoppers and more likely to offer them high refinance rates. We find statistical discrimination significantly decreases the consumption response of non-shoppers to a monetary policy shock. In chapter three, we explore the monetary policy transmission when shadow banking co-exists with a regulated banking sector. We develop a model of banking in which both banks and shadow banks do liquidity transformation. The difference is that banks have access to the discount window to manage the liquidity risk while their balance sheet is regulated. Depending on the size of the shadow banking system, the effectiveness of changing the discount window rate may weaken as shadow banks and banks can become interchangeable.