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To analyse the impact of different amplification mechanisms on monetary policy robustness, the models considered here are similar in many respects but financial frictions. The suite of models includes the basic New Keynesian model, the financial accelerator model and the model with housing and collateral constraints (HCC). All the models are forward-looking, do not incorporate inflation persistence and account for nominal stickiness and monopolistic competition. In all the models monetary policy plays an active role in stabilizing economy because of short-term nominal inertia. All the models are allowed to be hit by monetary policy and TFP shocks. In what follows I briefly introduce the main characteristics of the models2_{. Equilibrium conditions and parameters’ calibration used for simulations are given}

in the Appendix.

3.2.1 Basic New Keynesian model

The basic New Keynesian model is a common reference in the monetary policy analysis. It is often used an a benchmark in macroeconomic literature, because it combines in itself par- simony, theoretical foundations, empirical relevance and practical usefulness. In its original version as suggested by Clarida et al. (1999) BNK does not incorporate any financial factors and accounts for purely forward-looking output and inflation; its dynamics is entirely due to exogenous processes without endogenous persistence and outcomes depending on agents’ expectations. The baseline BNK model features no capital and investment.

The version of the BNK model considered here is taken in its standard form as in Walsh (2010). Government spending is added to the model to introduce the demand side shocks, which are absent in the model formulation of Walsh. Thus, three types of exogenous dis- turbances are accounted by the BNK model here: monetary policy, TFP and government spending shock.

2_{Detailed exposition of the models considered is given in Walsh (2010), Christensen and Dib (2008) and Ia-} coviello (2005).

BNK model features a negative effect of interest rate on output. Current output depends on expectations of future consumption expenditure. Nominal prices are set based on future marginal costs; this indicates no inertia in inflation. Ultimately, inflation depends on move- ments in marginal costs, associated with variation in excess demand. The monetary policy rule that closes the model is presented in the next section. Gali (2008) and Walsh (2010) demonstrate that the efficiency is fully restored in the BNK model, when monetary policy aims to stabilize the economy’s average markup at its frictionless level.

3.2.2 Financial accelerator model

This model incorporates the financial accelerator mechanism developed in Bernanke and Gertler (1989). The borrowers and lenders are modelled explicitly and are incorporated into an otherwise standard New Keynesian setup with nominal stickiness and monopolistic com- petition. Frictions arise due to the agency problem caused by informational asymmetries. Specifically, the profitability of entrepreneurs, who borrow funds from risk-neutral banking sector, is a private information. The costly state verification setup suggested by Townsend (1979) is adopted, such that asymmetric information gives rise to agency costs, which are often referred to as monitoring costs, that the lenders need to pay to observe the ex-post en- trepreneurial productivity. In particular, when an entrepreneur cannot repay the debt, the lender pays verification cost as a share of entrepreneur’s assets and takes over her entire project. Bernanke et al. (1999) derive the optimal debt contract structure and show that the entrepreneurial debt payment is independent of realization of her idiosyncratic productivity. The model manifests the cost of external funds higher than the cost of internal funds, with the former related to borrowers’ net worth inversly. The dynamics of net worth follows the movements of the price of capital. Hence, the changes in the demand for capital affecting the price of capital trigger the movements of entrepreneurial net worth. As a result, the level of the external finance premium also changes, and this change reinforces the initial movements of the demand for capital, such that the demand side shocks are amplified.

Importantly, the role of the financial accelerator mechanism in driving the changes of demand for capital, and hence, investment, depends on the nature of the shock generating them. As demonstrated by Christensen and Dib (2008), the financial accelerator propagates and amplifies the effects of demand shocks, - like monetary policy, money demand and pref- erence shocks, - on investment. At the same time, the financial accelerator pushes down the response of investment to supply side shocks - for example, to technology and investment- specific shocks. As emphasized by Bernanke et al. (1999) and Christensen and Dib (2008), investment specific shock allows to explain important features of business cycle data, and hence is an important exogenous force driving the model.

Real distortions in the model imply that there is a trade-off for a policymaker between inflation and output stabilization.

3.2.3 Model with housing and collateral constraints

One of the sources of frictions in this model is the difference in discount rates of different agents: entrepreneurs, impatient (or liquidity-constrained) and patient (or unconstrained) households. As suggested in Iacoviello (2005), HCC model incorporates housing used by borrowers - entrepreneurs and constrained households - as collateral. Hence, this model accounts for an additional (as compared to the FA model) type of asset - housing, with house prices affecting the borrowing capacity of the debtors. This relationship constitutes a channel, via which the model’s endogenous propagation mechanism works beyond the conventional Bernanke et al. (1999) financial accelerator channel. Constrained households are assumed to have a strong preference for current consumption, such that growing hous- ing prices induce more than proportional rise of borrowing and consumption, which in its turn has an impact on aggregate output. Thus, the demand shocks are amplified in the HCC model. At the same time, inflation depresses the impact of supply shocks that induce negative correlation between output and inflation. So, the impact of supply shocks in this model is contracted in the same way as in the FA model. In addition to monetary policy and productivity shocks the HCC model accounts for cost-push shock, housing price shock and preference for housing shock.