RDP 2011-04: Assessing Some Models of the Impact of Financial Stress upon Business Cycles 5. Business Cycle Characteristics of the Models

5.1 The GOZ Model

To assess the business cycle properties of the GOZ model we simulate data from it and apply the BBQ cycle-dating procedure to the simulated data. Because the real variables in the GOZ model are log deviations from a constant growth path we need to add back a trend growth term to the simulated data to get a series on the level of GDP that can be used to determine the business cycle. We use the growth rate assumed by GOZ. Table 1 contains the cycle output along with what we would get when BBQ is applied to quarterly per capita US GDP data over the period 1973:Q1–2009:Q4.[8] The Smets-Wouters results are found by using the parameters estimated by GOZ; in other words, they show the business cycle properties of the model when the financial accelerator mechanism is excluded.[9]

Table 1: Business Cycle Characteristics – Data, SW and GOZ Models
Data SW model GOZ model
Durations (qtrs)
Expansions 13.6 13.3 14.8
Contractions 4.8 4.5 4.2
Amplitude (%)
Expansions 9.2 8.9 9.0
Contractions −2.8 −1.9 −1.6
Cumulative amplitude (%)
Expansions 132.4 99.2 107.9
Contractions −8.1 −7.0 −5.2

The SW and GOZ models both show a good match to the business cycle characteristics, and overall the differences between them are not great. If one looks at the outcomes for investment, these remain broadly the same, although perhaps surprisingly, the amplitude of the average investment expansion is less in the GOZ model. Thus the presence of a financial accelerator does not seem to have had a great effect upon business cycle outcomes, although it should be noted that these are averages and credit may be important in particular cycles.

Some experiments can be conducted here. Doubling the standard deviation of the credit supply shocks in the GOZ model has a very small effect upon the cycle. It is necessary to make much bigger changes in order to have an impact, well outside the range of values of the external finance premium that have been observed. Thus, quadrupling the standard deviation reduces expansion length to 14.6 quarters and increases the amplitude of recessions, although only to −1.7 per cent. But it does this by producing premia of 1,000 basis points (and more). At that level the probability of a recession is around 0.43, but one might think that this is rather low for such an extreme external finance premium. Doubling the coefficient χ in Equation (5), which governs the sensitivity of the external finance premium to the entrepreneur's net worth, has little impact on the business cycle characteristics.

5.2 The Iacoviello Model

Using the parameter values provided in Iacoviello (2005) we simulate data from his model. Because Iacoviello ‘detrended’ the per capita GDP data with a band-pass filter before estimating the parameters of his model, the simulated data does not correspond to the level of GDP, which is necessary for business cycle dating. To recover the latter from the filtered data is a non-standard problem.[10] Consequently, we decided to work with the filtered data, that is, to investigate the growth cycle rather than the business cycle. Table 2 therefore contains the growth cycle in output from the IAC model and from the data (found with the BBQ program), over Iacoviello's estimation period of 1974:Q1–2003:Q4. Clearly the fit on durations is quite good, but the amplitudes of growth cycle expansions and recessions are considerably smaller in the model than in the data. The growth cycles are fairly symmetric as the asymmetry in the business cycle comes from the fact that there is positive long-run growth and that has been filtered out here.

Table 2: Growth Cycle Characteristics – Data and Iacoviello Model
Data Iacoviello model
Durations (qtrs)
Expansions 5.7 5.5
Contractions 4.8 5.5
Amplitude (%)
Expansions 5.4 4.5
Contractions −5.2 −4.5
Cumulative amplitude (%)
Expansions 23.2 16.1
Contractions −18.1 −16.5


Alberto Ortiz kindly provided us with a Dynare program that simulated an updated version of the model they use, and some of their data for the period 1973:Q1–2009:Q4. The parameter values set in that code are the posterior mean and are different to those reported in their paper, in part due to a shorter estimation period being used, namely 1985:Q1–2009:Q4. As this is quite short for cycle dating we focus on the longer sample when comparing the models to the data. If instead the shorter sample was used then expansions would be longer and contractions less severe. [8]

Using the parameters from Smets and Wouters (2007), the results are not that different. [9]

Landon-Lane (2002) studies this problem for the Hodrick-Prescott filter. We attempted to reconstruct the data by inverting the band-pass filter via a Moore-Penrose generalised inverse. Although an experiment with actual data seemed to recover the levels correctly, when applied to simulated data the growth rate in the reconstructed output series had negative serial correlation, which is contrary to actual US GDP data. Such negative serial correlation induces long expansions, as it implies a rapid bounceback from any negative growth rate. Hence we were finding that the Iacoviello model was producing very long business cycle expansions, although this might have been an artifact of our inversion procedure. [10]