B.1 Data and moment restrictions

First, we calibrate the capital depreciation rate δ using annual using consumption, investment, government consumption, and fixed asset depreciation data for the U.S. from 1947 through 2016. Since our model economy is closed, we measure GDP as the sum of consumption, investment, and government consumption. Over the sample period, we compute an average annual ratio of fixed asset depreciation to GDP of about 13.8%, an average ratio of investment to GDP of about 17.0%, and an average GDP growth rate of about 3.2%. Then using the following steady state relationship from the neoclassical growth model:

we compute an implied annual capital depreciation rate of about 10.9% and set δ equal to about 0.027.

Next we use quarterly consumption, investment, government consumption, and hours data from the US from 1947:Q1 through 2017:Q4 to compute an implied TFP series. We deflate consumption, investment, and government consumption by the GDP deflator. We use the investment data to compute an implied capital stock for the US using the method of perpetual inventory. See Dejong and Dave (2011), Chapter 11 for a description of the method. We then compute a TFP series using a Cobb-Douglas production function with a capital share of income α set to 0.35.

We then apply a HP filter to log TFP and log government consumption and estimate AR(1) models for each of the filtered series. We estimate via OLS an autocorrelation coefficient on log TFP ρ_Z to be about 0.79 and we estimate the standard deviation of the shock to log TFP σ_Z to be about 0.0067. We estimate an autocorrelation coefficient with OLS on log government consumption ρ_G to be about 0.89 and we estimate the standard deviation of the shock to log government consumption σ_G to be about 0.014. Figure 9 shows scatter plots of log TFP and log government consumption against their own lagged values and prediction lines implied by the OLS results.

Figure 9:

Left panel: Scatter plot of log TFP against log TFP lagged one period. Right panel: Scatter plot of log government consumption against log government consumption lagged one period. Both series are HP-filtered.

We also compute an average ratio of government consumption to GDP of about 20% and we use this value to calibrate the steady state level of government consumption G¯ in the model.

We use monthly data from June 1964 through November 2017 to compute average values for the inflation rate, the nominal interest rate, and the T-bill rate. We compute an average annual PCE inflation rate of about 3.5% and an average annual 3-month T-bill rate of about 4.9%. So we require that in the steady state gross quarterly inflation Π be about 1.0085 and gross nominal interest Rⁿ be about 1.012. Together these restrictions imply a calibrated value of the household’s subjective discount factor β of about 0.997.

Next, we impose a restriction on the deposit rate. In our model, deposits pay interest and we do not distinguish between different deposit types. However, in practice banks offer several kinds of deposits including demand deposits, small time deposits, and savings account deposits. Historically, Regulation Q in the US prevented banks from offering interest on demand deposits and so an interest rate like the 3-month CD rate will overstate historic interest paid to deposits as a group. Therefore we create a statistic for measuring the average deposit rate taking into account that only a fraction of deposits pay interest.

We measure total deposits as:

and we measure the interest on instruments in M2 minus M1 by the 3-month CD rate. We assume no interest paid on checkable deposits. Our measure of the deposit rate is then given by the weighted average:

Our calculation implies an average annual deposit rate of about 4.5% so we require that the quarterly deposit rate in the model R^D equals about 1.011 in the steady state.

From March 2006 to January 2018, the average worker in the US worked about 34.3 hours per week and so we require that the steady state share of household’s available time devoted to labor H equal about 20%. Using quarterly data on outstanding debt and equity of nonfinancial firms in the US, we compute an average leverage ratio for the country of about 29% and we use this to restrict the value of (QK − N)/N. Our value is about 21 percentage points below what BGG use, but the difference has no meaningful effect on our overall calibration and simulated results.

Finally, we compute the average excess reserve to deposit ratio from January 1959 through August 2008 to be 0.051%. We deliberately exclude post-August 2008 data because of the dramatic change in the excess reserve-deposit ratio that began in September 2008. Also, in order to remain consistent in our definition of deposits, we compute this ratio using our measure of total deposits described above and not simply checkable deposits.

In Table 4 we summarize the moments that we use to calibrate the model.

B.2 Additional parameter values

We set the Cobb-Douglas production function parameter α to 0.35. We set the elasticity of substitution between retail goods ϵ so that the gross markup of retail goods over wholesale goods is 1.25 Altig et al. (2005). Like SGU, we set the Calvo-pricing parameter θ to 0.8 so that the nominal price of the average retail good remains fixed for 5 quarters. We follow BGG and set ψ – the elasticity of the steady state price of capital Q with respect to the steady state investment to capital ratio – to 0.25. We also follow BBG by setting Ω equal to 0.01 × (1 − α)⁻¹ so that the entrepreneurial wage is 1 percent of output in the steady state.

For the monetary policy rule, we set the coefficient on the lagged nominal interest rate ρ_r to 0.9, the coefficient on inflation ϕ_π to 1.5, and the coefficient on output deviations ϕ_y/4 to 0.5. Like BGG, we require an annual entrepreneurial default rate of 3%. We accomplish the restriction by setting F(ω¯|σω2)=0.03/4. We set the required reserve ratio to 0.01 reflecting the fact that our broad measure of deposits includes instruments like savings account deposits which are not subject to a reserve requirement. We use the parameter estimates from CMR to calibrate the autoregressive coefficients and standard deviations of the shocks monetary policy v_t, and the shock to the proportion of firms that default each period σ_ω,t.

Since σ_σ,t, our shock to the variance of σ_ω,t, does not have a counterpart in CMR – or in any other model of which we are aware – we select an autocorrelation coefficient of 0.9 and suppose a variance 1. We set the banker’s preference parameter ξ_Φ to 20 for the main simulations and explore in Figure 3 how changing ξ_Φ affects the predictions of the model.