Sources of the Business Cycle

Let us identify sources of the business cycle. First, we consider the result of variance decompo-sition that shows which kind of structural shock explains the variance of model concept. Table 3.7 summarizes the long term variance decomposition in three cases. What is common to all cases is that the investment adjustment cost shock plays a very important role in the business cycle. The difference in results in data rich environments is the role of measurement error and the labor supply shock. Especially, Case C is outputting quite peculiar results, so we think about it later.

The output fluctuations depend mostly on the variation of investment adjustment cost shock (46% for Case A and 40% for Case B). This shock is also the biggest fluctuating factor not only for investment but also for labor and wage. In fact, among the seven model concepts, the shock has acquired the first position of the four model concepts variations. A large amount of literature also pointed out the investment adjustment cost shock (or investment specific technology shock) plays a main role in explaining the business cycle. For example, see Sugo and Ueda (2008) and Kaihatsu and Kurozumi (2012b) in Japan, and Fisher (2006) and Justiniano and Primiceri (2008) in the U.S.

In particular, this shock is more important than the neutral technology shock (i.e. TFP shock).

TFP shock contribution is 18.6% in Case A (No. 2), but Case B is only 4.6% (No. 4). Contribution of demand shock to output still has a large preference shock (15% for Case A and 12% for Case B).

The monetary policy shock contributes 1.6% for both Cases A and B. However, it should be noted that this value is a contribution of the shock deviating from the policy rule, without reflecting on the contribution that the central bank endogenously responded to output.

Next, we consider the sources of inflation fluctuations. Similar to the results in Chapter 2, the majority of the inflation fluctuations are explained by noise of measurement error.⁶ The inflation variations explained by the measurement error is 70% for Case A and 65% for Case B. So, the model explained it by 30% in Case A and by 35% in Case B. In other words, it was 5% by which utilizing multiple information could further explain the inflation variation. But the contents are quite different. In Case A, 11% is TFP shock. This can be the result supported from this model as well as previous empirical results. Since it is 11% out of the 30%, it is correct by about 33% (as far as the model can explain) that inflation occurred because productivity declined, or deflation occurred because productivity rose. In Case B, the labor supply shock is the main source, accounting for 22%. It is 22% out of the 35%, so it is correct by 60% that inflation occurred because people did not want to work and the reservation wage went up, or deflation occurred because people wanted to work and the reservation wage went down. Also, this argument roughly holds for wage fluctuations in Case B (Instead, Case A explains wage variations mainly by the investment adjustment cost shock).

Finally, let us see the result of Case C. The explanatory power of inflation and wage fluctuations has increased dramatically (over 75%). Indeed, Case C contains wage and inflation fluctuations within the 90% credible interval in Figure 3.1. And the labor supply shock explained inflation fluc-tuation by 60% and wage flucfluc-tuation by 46%. Thus, Case C can explain them nearly 50% by the workers’ motivation. Certainly in Figure 3.2 (b), the i.i.d. labor supply shock showed the greatest fluctuation and oscillates 40% above and below the steady state. That is not all. Among the seven model concepts, only the investment caused the labor supply shock to fall to the top position (only 4% difference, the second position barely). In other words, if we seriously follow Case C, all business cycles will depend just upon the motivations of the workers.

6To explain the high-frequency behavior of inflation, it may be important to extend the model such as introducing financial friction and incorporating the influence of volatile fluctuations in asset prices. Then, we should verify how inflation fluctuations can be explained by the financial friction model. However, it should be noted that it is impossible to compare the fit with the data by the marginal likelihood in the SW model and the financial friction model when estimating the financial friction model by newly adding financial data.

3.6. RESULTS 103

Historical decomposition

Historical decomposition makes it possible to clarify the contribution of shock in more detail.

Accumulating the contribution of all the shocks will be a model concept. The discrepancy between the model concept and the data is the measurement error. In other words, it is a task to confirm details of the model concept seen in Figure 3.1 in detail. It should be noted that this contributes not only to the current contribution but also to the inertia of the past shocks. Historical decomposition is also examined centered on Cases A and B.

Figure 3.4 depicts the historical decomposition of output (real GDP data). Sources of the output fluctuations are investment adjustment cost shock and preference shock in both cases. In a data rich environment, labor supply shock is added to them.

Let us pay attention to around the bubble era in the early 1990s. The boom is primarily due to the positive contribution of the preference shock and the investment adjustment cost shock (through the negative shock, see Figure 3.2 (a), (b)). In a data rich environment, the labor supply shock is pulling out the output, so that reservation wage had increased during the bubble period due to positive labor supply shock (increase in labor disutility), which has pushed the economy down (See also historical decomposition of real wage in Figure 3.6 (b)).⁷ The collapse of the bubble occurs prior to the fall of the preference shock. After that the negative contribution of the investment adjustment cost shock begins. But we should care about the difference in shock’s inertia (preference shock inertia is about 50%, and investment adjustment cost shock is about 70%).

In the meantime, the monetary authority had made a negative contribution by monetary tight-ening so as to suppress overheating of the bubble since 1989, and monetary easing since 1991 when the bubble collapsed (see also Figure 3.9 (a) (b) ). Hence, the central bank plays a major contri-bution to stabilization. On the other hand, the fiscal authority is extremely small in contricontri-bution to output, regardless of repeated fiscal stimuli after the collapse of the bubble economy (obvious result from the variance decomposition in Table 3.7).

Of course, the results could differ as the models are different. But the result that investment adjustment cost shock is the main source seems quite robust regardless of the model. Sugo and Ueda (2008) also reached the same conclusion, but it is natural because the same model (the SW model) is estimated (though estimation method is different). By the way, what is the investment adjustment cost shock? (Similarly, what is the investment specific technology shock?) We know that it is a shock on the cost function of investment goods production, but what exactly should we imagine?

One interpretation is that the shock corresponds to an amplified investment fluctuations due to the agency cost, as pointed out by Justiniano and Primiceri (2008b). Kaihatsu and Kurozumi (2014a,b) incorporated a financial friction into the SW model and examines the impact of the unanticipated firm’s net worth deterioration to output fluctuations. They found it was the main source of the business cycle in the U.S. (Kaihatsu and Kurozumi 2014a) but not in Japan (Kaihatsu and Kurozumi 2014b) and again, they concluded the Japan’s lost decade was caused by an unexpected decline of the investment specific technology.

Inflation is the same fluctuation factor as the output, but in Case A, TFP shock is also a major factor. Instead in Case B, the labor supply shock matters. At the beginning of the bubble era, inflation was caused by positive preference shock and negative investment adjustment cost shock. In

7Kobayashi and Inaba (2006) and Otsu (2011) provided the evidence that wage fluctuations through the labor mar-ket friction (called as labor “wedge”) had a key role on output fluctuations by applying the business cycle accounting (BCA) to Japanese data.

Case B, an increase in reservation wage due to a rise in labor disutility will add to the explanatory factor of inflation. On the other hand, in Case A, the deflation pressure can be confirmed by the increase in TFP.

It should be noted that investment adjustment cost shock seems to be a supply shock from the name, but according to this result, this is a demand shock. The decline in the adjustment cost of investment means the improvement of productivity of investment goods. This implies right shift of investment goods supply curve, which lowers investment goods price. This alone is a supply shock.

However, the decline of the invest goods price simultaneously triggered demand for investment goods by households. Thus, the right shift of investment goods demand curve also arises at the same time. Looking at the historical decomposition, the adjustment cost shock has made a positive contribution to both output and inflation. In other words, the investment adjustment cost shock is a demand shock.

Finally, monetary tightening after 1989 and monetary easing after 1991 have little effect and are not the main cause of inflation fluctuations.