with EC. Then, an increase in government consumption stimulates private consumption because of EC. The additional channel of EC to private consumption is depicted by the shift of labor demand to the right, which brings an improvement in unemployment. This channel is shown as (iv) in Figure 2(c). Furthermore, from equation (6), the increase in private consumption leads to a decrease of labor supply under nominal rigidities: The increase of private consumption decreases marginal utility of consumption $ \varphi_{t}^{c} $ . This raises the RHS in (6), that is, MRS between labor supply and consumption. On the other hand, real wage, the LHS in (6), is fixed due to nominal rigidities. Thus, to recover the equality of (6), members must work less (a decrease of labor disutility). This channel is shown as (v) in Figure 2 (c).

Suppose that the parameter $ \alpha_{g} $ in equation (10) is positive, which corresponds to the case with PPC. Then, an increase in government investment improves the productivities of private firms, which implies a decrease in marginal costs of private firms. Forward-looking private firms set their prices by taking future marginal costs into account under nominal stickiness. Thus, accumulation of PPC delivers a decrease in inflation, which triggers monetary easing policy. Therefore, the “crowd-out” effect will be weakened, which stimulates both private consumption and private investment. These effects are realized by the shift of labor demand to the right (shown as (iv) in Figure 2 (c)), which improves unemployment. It is worth noting that the channel through PPC has relatively longer effects than the channel through EC: Due to price adjustment sluggishness, the effect through the decrease in future inflation will be delayed but long-lasting.

Through the channels of non-wasteful fiscal expansions, aggregate labor supply and aggregate employment are determined at $ L^{\prime\prime} $ and $ H^{\prime\prime} $ , respectively. As a result, non-wasteful government spending may help unemployment to be reduced via fiscal stimuli.

Of course, the above illustration relies heavily on an extreme assumption that real wage stays at the same level. A rise of real wage leads to an increase in unemployment (and vice versa). The sluggishness of real wage adjustment depends on the strengths of price and nominal wage rigidities. It is also important how the monetary authority reacts to variations of inflation and output: An increase in private consumption through the channel of EC will cause inflation. If the central banker is a strong fighter of inflation, the increase in private consumption might be dominated by a crowding out effect from a monetary tightening policy.

Therefore, we need to estimate structural parameters to examine qualitatively and quantitatively the effects of non-wasteful fiscal expansions on unemployment in the Japanese economy. The next section describes our estimation methodologies.

## 3 Estimation Methodologies

We estimate parameters using Japanese macroeconomic quarterly data from 1980Q2 to 2012Q4. It should be noted that the estimation period includes zero-interest-rate policy periods. We argue about this point in section 4.4. This section provides a data description and illustrates how to implement the Bayesian estimation method.