Consequently, expectations about the reappearance and re-collapse of bubbles in the future do not influence decisions of the current young agents at all. Bubble assets last without depreciation as long as the economy remains in the bubble regime.

Equilibrium with no binding liquidity constraint

## Equilibrium with binding liquidity constraint

That is, capital is not only a factor of production, but also a means of providing liquidity to its owners.

Calibration

## Comparative Statics

High capacity utilization is justified by the cost of capital, which falls (lower right panel). Because the cost of a marginal increase in the capacity utilization rate is the market value of lost capital, the low cost of capital means that households raise the capacity utilization rate with less reluctance.

Fundamental Equilibrium

## Bubble Equilibrium

The ... first order condition regarding the demand for bubbling assets by savers is m~st+1. If the economy is in the fundamental regime, this equation is trivial because both sides are zero. Furthermore, the demand for bubble assets is zero in this case because the constraint (24) prohibits savers from buying bubble assets.

If the economy is in the bubble regime in period t, the equation is rewritten as. In other words, it is future marketability that justifies a positive price in the current period. This is an attractive feature of bubble assets, allowing savers to maintain the no-arbitrage condition.

That is, even though bubble assets do not provide dividends to their owners, savers … and are not strange to buy bubble assets and equity because bubble assets carry a greater liquidity premium. The second term in the numerator shows that, other things being equal, the emergence of bubbles increases investment.

## Comparative Statics

It can be seen that the economy grows faster in the bubble regime (red circles) than in the fundamental regime (red crosses) in the recurrent-bubble equilibrium. The upper left panel shows that more investment projects are financed in the bubble regime than in the fundamental regime. The utilization rate is higher in the bubble regime (left panel in the second row) because the price of capital is lower (right panel in the second row).

The price of capital is lower because liquidity service is lower in the bubble regime (the left panel in the third row). Households work harder in the bubble regime than in the fundamental regime (the left panel in the fourth row) as a result of intertemporal substitution. The red dots in Figure 6 show the unconditional mean of the growth rates in the recurring bubble equilibrium.

Moreover, in the equilibrium of recurring bubbles, the economy must tolerate changes in growth rates associated with changes in regimes. From Figure 6 we also learn that an objectively identical economy in the fundamental regime (zt = f) grows faster if it is in the fundamental equilibrium (blue line) than in the equilibrium of the repeating bubble (red crosses).

## E¤ects of a Regime Switch

The prediction of the model with non-repeating bubbles (stochastic bubbles with basic absorbing regime and initial condition z0 =f) is similar to the permanent bubble. Then, the economy starts to grow again, but the recovery from the crisis is very weak, indicating that our model generates superhysteresis after the bubble burst. That is, the creation of bubbles brings about a huge boom in the economy, followed by a steady steady growth.

A control switch in our model is similar to a news shock in the sense that it is neutral to the current technology. But unlike previous work in the news shock literature, our model is able to generate comovement to a regime switch without exotic utility functions, but only with variable capacity utilization. We suspect that our model can be adapted to accommodate additional regimes with bubbles that offer different levels of liquidity, but at the cost of losing tractability.

Specifically, some of the bubble assets in the economy depreciate, but new bubbles are also injected each period. These papers analyze the local dynamics around the bubble steady state, just as we did in the permanent bubble version of our model.

## Impulse Responses

Specifically, output, consumption, investment, hours worked, and capacity utilization increase more in the balloon regime than in the baseline regime. Namely, the size of the bubble increases when the economy in the bubble regime hits a positive productivity shock. With the increased liquidity provided by the balloons, the cost of capital does not rise as much as in the base regime.

As the cost of capital is lower, households are less hesitant to raise the capacity utilization rate, making the fluctuation in the bubble regime larger. In general, the responses are similar to those in the basic regime in the repeating bubble equilibrium. But the magnitudes of the responses are again larger in the bubble regime than in the baseline regime.

That is, the size of the bubble shrinks in the bubble regime after the shock, because. As the amount of liquidity provided by the bubble decreases, the price of capital does not decrease as much as it does in the fundamental regime.

## Existence Condition

Because the cost of capital is relatively high, households are reluctant to raise the capacity utilization rate, making the decline in investment and labor hours greater in the bubble regime than in the fundamental regime. The first term on the right-hand side of equation (26) is the payout each investor pays for the investment. This implication is in line with the previous work on bubbles; if we further assume equal to = 0, the …first term on the right-hand side collapses to g, and g > r is the well-known dynamical ine¢ciency condition for the existence of bubbles in OLG models.

By making the first term on the right smaller, a larger value makes it harder to support calling. In other words, sufficient friction in the financial market is needed to ensure that the economy is in a bubble equilibrium. All other things being equal, bubbles persist (mb is positive) when liquidity constraints are tight, the rental price of capital is high, and/or the investment (and hence growth rate) in the bubble regime is high.

But people consider the possibility of the bubble bursting if they are in the bubble regime, and assess their assets accordingly. For example, in the case of complete depreciation, the price of shares in the bubble regime is stable.

## A Regime Switching World

The timing of regime changes in our model looks different from the estimates of alternative regime change models. Importantly, the estimated model captures the rise of the housing bubble in the early 2000s and its subsequent collapse in 2008–2009. This is most likely a result of the short duration of this bubble and the fact that the housing bubble emerged quite nearby.

The top right panel of Figure 10 shows the …ltered path of the price of the bubble (in red the HP-…ltered trend). It plots the expected value calculated from the probability of the economy being in the bubble regime for a period times the price of bubble assets realized if the economy is in the bubble regime for the same period. However, with the arrival of the Great Moderation era (mid-1980s), the price of the bubble became more volatile.

Despite the moderating effect of the underlying regime, there is still a role for less volatile shocks to account for the Grand Moderation. Similarly, the episode of high volatility during the 2008-2009 recession calls for greater concern, particularly on the demand side of the economy.

## A Permanent-Bubble World

Interestingly, both the estimated probabilities and the bubble price correctly capture the housing boom episode. As a trend across the entire sample, we observe that the bubble price has been falling since the 1960s. Namely, because periods of high valuation are associated with periods of faster growth in our model, the growth slowdown of recent decades can be partly attributed to the smaller size of the bubbles.

Although there is very little debate about real estate and information bubbles, it is less clear where the bubbles originated before 1980. An obvious candidate for the 1970s is loose monetary policy (the Burns-Miller dove regime, assessed in Fernandez-Villaverde, Guerron-Quintana, and Rubio -Ramirez (2015)). Interestingly, Contessi and Kerdnunvong (2015) report luxury stock and housing markets (based on cyclically adjusted earnings ratios and cyclically adjusted rent price ratios) over the period 1965:Q3–1968Q4.

Shiller (2015) also noted an example of a high price-to-earnings ratio that occurred in January 1966 and called it the "Kennedy-Johnson Peak."

A Bubbleless World

## Three Models Side-By-Side

Mayer-Foulkes (2005): “Het effect van financiële ontwikkeling op convergentie: theorie en bewijs”, The Quarterly Journal of Economics. M.(2014): “Long-Term Damage from the Great Recession in OECD Countries”, Working Paper 20185, National Bureau of Economic Research. King (1984): “Time-Separable Preferences and Intertemporal- Substitution Models of Business Cycles”, The Quarterly Journal of Economics The optimale hoeveelheid geld”, in Models of Monetary Economies, uitg.

Kerdnunvong (2015): "Asset Bubbles: Detecting and Measuring Them Are Not Easy Tasks," The Regional Economist, (July). “Minimal State Variable Solutions for Markov-Switching Rational Expectations Models,” Journal of Economic Dynamics and Control Frontiers in Structural Macroeconomic Modeling. Estimation of dynamic equilibrium models with stochastic volatility,"Journal of Econometrics Insider-outsider labor markets, hysteresis and monetary policy," Economics Working Papers 1506, Department of Economics and Business, Universitat Pompeu Fabra.

Moore (2012): "Liquidity, Business Cycles, and Monetary Policy,"Working Paper 17934, National Bureau of Economic Research. 2009): "Bursting Bubbles: Consequences and Cures,"Upubliceret manuskript, University of Minnesota. 1987): "Con...dence and the Real Value of Money in a Overlapping Generations Economy," The Quarterly Journal of Economics.

Model with no binding constrains

Fundamental Model

Recurrent Bubble Model