We investigate the role of 12 shocks that drive the business cycles since the end of the 80s in the US and the Euro Area (EA). See the model description for more details.

Following Christiano, Motto and Rostagno (2014) the uncertainty associated to the financial sector plays a crucial role. The estimation and the quatitative analysis are provided by Dynare (Adjemian et al., 2011) and updated databases for the US and the Euro area are available online via DBnomics.

We show here the observed variables used in the estimation of the model.

We build the trajectory each variable would have followed if we feed the model with only one type of shock.

We show the historical decomposition of the observed variables used in the estimation (net of the average growth rate) over the sample period.

The bars represent the historical contribution of each of the shocks to the observed variables, that is the counterfactual values predicted by the model when all other shocks are set to zero.

We show the Forecast of all the observed variables used in the estimation for the next ten years (2016Q1-2025Q4).

The distribution of Forecast takes into account the uncertainty about both parameters and shocks. Shaded areas mark the uncertainty associated with our forecast, representing intervals between 2nd and 8th deciles, between 3rd and 7th and between 4th and 6th deciles.

For each observed variable in row, one column is the variance explained by the considered shock.

Numbers in each row may not add up to 100 as we ignore the correlation between the shocks when we add explained variances. Business cycle frequency is measured with HP filter (lambda = 1600).

We show the dynamic responses of variables in our model to a shock.

The table shows the prior and posterior distributions of estimated economic parameters and shocks.

The model introduces a financial accelerator mechanism and nominal rigidities in the context of a closed economy. The extensive presentation of the model can be found in Christiano, Motto and Rostagno (2014).

This description of the model defines preferences, technologies and market arrangements. It also allows to specify the 12 shocks that perturb the economy.

Households

There is a continuum of households in the economy who have access to capital markets.

  • They maximize their lifetime utility. Household preferences are separable in consumption and leisure, and it exists external habit formation on consumption.
  • The households hold two types of bonds (one-period bonds, and long-term bonds, 10 years) and perceived labor incomes.
  • There is a shock on the impatience of the households

Firms

Producers of the Final and the Intermediate Goods

  • Producers of the Final Goods
    • Representative and competitive final goods producers (price takers)
    • They combine intermediate goods
  • Producers of the Intermediate Goods
    • Monopolistic firms (price makers)
    • They produce with capital and labor
    • Only a fraction of these producers can adjust their prices (nominal rigidities)
    • There exist three types of transitory shocks
      • shock on markup
      • shock on the combination of labor-capital efficiency
      • shock on the investment price
    • There exists one permanent shock: the technological progress

Capital Producers and Entrepreneurs

  • capital producers

    • The representative producer of physical capital constructs end-of-period raw private physical capital
    • There is a shock on the efficiency to produce new investment goods
  • Entrepreneurs

    • Capital producers sell raw private physical capital to entrepreneurs who transform it into effective capital. This transformation rate is entrepreneur-specific.
    • To buy raw capital, entrepreneurs use their personal wealth and a loan obtained from a financial intermediary.
    • This business is risky
      • the raw capital is transformed into effective capital via a risky process
      • if the realized value of this transformation business is to low, the entrepreneur defaults because it cannot reimburse the loan.
    • Redistribution of assets
      • the net wealth of the entrepreneurs increases with the successful businesses
      • at each period, a fraction of this wealth is transferred to the households. This fractions is time-varying and is called the “equity shock”.

Financial Contract

  • The loan contract is characterized by agency problems subject to financial shocks
    • The agency problem is associated with the asymmetric information between the entrepreneur and the financial intermediary that makes costly checking the state of defaulting entrepreneur
    • The transformation rate of capital is observed by the entrepreneur after its purchases of raw capital.
  • Financial intermediary and risk shock
    • With the probability of no-default, the financial intermediary receives interest on its loan.
    • Otherwise, the financial intermediary gets a fix share of the assets of the bankrupt entrepreneur (the collateral), the complement of this share is used to pay the verification costs.
  • The “risk shock”
    • At each time, the standard deviation of the entrepreneur-specific shock is time-varying
    • An increase of the measure of the risk, which makes higher the cross-sectional dispersion between firm projects, induces larger financial frictions and thus higher spread

Monetary and Fiscal Policies

Central bank

  • The central bank sets the nominal interest rate according to a “Taylor rule”: the nominal interest rate increases with the inflation and the output-gap.
    • The objective of the central bank with respect to the inflation can change: the inflation target shock
    • There is a shock on this rule, the monetary shock
  • It could exist a gap between the long-term interest rate and the one implied by the model: the term structure shock

Government

  • The Government expenditures follow an exogenous process.
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