metadata: authors: 0: author: Diaz Sanchez, Jose Luis
count: Ireland
docna: 0: docna: Explaining the last consumption boom-bust
            cyclein Ireland : the role of news and noise shocks
docty: Policy Research Working Paper
subtopic: Labor Markets,Macroeconomic Management,Financial Sector Policy
teratopic: Private Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,Education
abstracts: cdata!: The objective of the paper is to explain
            the last boom and bust in consumption in Ireland by the
            failure of consumers to correctly distinguish permanent
            changes in productivity from temporary changes. It uses a
            business cycle model, where agents update their beliefs
            about long-run productivity using information -that they
            receive continuously- about the future state of the economy.
            The analysis finds that a large and prolonged disconnect
            between consumption and long-run productivity occurred in
            the years leading to the economic crisis, which led to --
            over-consumption -- for several quarters. A strong downward
            adjustment in 2008 followed when Irish consumers finally
            realized their mistake.
geo_reg_key: 80475,80461
repnme: repnme: Explaining the last consumption boom-bust
            cyclein Ireland : the role of news and noise shocks
display_title: Explaining the last consumption
            boom-bust cyclein Ireland : the role of news and noise shocks
listing_relative_url: /research/2013/06/17942511/explaining-last-consumption-boom-bust-cyclein-ireland-role-news-noise-shocks
topicv3: Current Account m1326278 1135,Financial Sector Development m1327681 1920,Labor Productivity m1504060 2756,Dynamic Stochastic General Equilibrium
            Models m1504539 3117
publishtoextweb_dt: 2013-06-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,Education
no_of_pages: 10
model_extractions: WPS6525 Policy Research Working Paper 6525 Explaining the Last Consumption Boom-Bust Cycle in Ireland The Role of News and Noise Shocks _Jose Luis Diaz Sanchez_ The World Bank Development Economics Vice Presidency Operations and Strategy Unit, June 2013
Policy Research Working Paper 6525

# **Abstract**

The objective of the paper is to explain the last boom and bust in consumption in Ireland by the failure of consumers to correctly distinguish permanent changes in productivity from temporary changes. It uses a business cycle model, where agents update their beliefs about longrun productivity using information—that they receive continuously—about the future state of the economy.

The analysis finds that a large and prolonged disconnect between consumption and long-run productivity occurred in the years leading to the economic crisis, which led to “over-consumption” for several quarters. A strong downward adjustment in 2008 followed when Irish consumers finally realized their mistake.

This paper is a product of the Operations and Strategy Unit, Development Economics Vice Presidnecy. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at jdiazsanchez@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Explaining the last consumption boom-bust cycle in Ireland: The role of news and noise shocks<sup>_∗_</sup>

## Jose Luis Diaz Sanchez

University of Paris 1 Pantheon-Sorbonne Paris School of Economics The World Bank

**Abstract**

The objective of the paper is to explain the last boom and bust in consumption in Ireland by the failure of consumers to correctly distinguish permanent changes in productivity from temporary changes. It uses a business cycle model, where agents update their beliefs about long-run productivity using information -that they receive continuously- about the future state of the economy. The analysis finds that a large and prolonged disconnect between consumption and long-run productivity occurred in the years leading to the economic crisis, which led to “over-consumption” for several quarters. A strong downward adjustment in 2008 followed when Irish consumers finally realized their mistake.

JEL classification: E21, E32.

Keywords: Business cycles, news shocks, long-run productivity. Sector Board: Financial Sector (FSE).

> _∗_ The views expressed in this article are those of the author and do not necessarily represent those of the World Bank. The author would like to thank Michal Andrle for very helpful comments and Blanchard, L’Huiller, and Lorenzoni for sharing their _Dynare_ code. Author’s e-mail: jdiazsanchez@worldbank.org.

<mark>1</mark>
# **1 Introduction**

Economic theory suggests that since productivity captures the capacity of the economy to produce income, an infinitely lived agent maximizing inter-temporal utility should base his consumption decisions on future productivity. Consequently, lack of understanding of this economic fundamental produces periods of “over” and “under-consumption”. Because agents cannot observe this macrovariable, they estimate it using not only observed productivity but also using information -that they receive continuously- which can or cannot affect productivity (income) in the future.

Since the mid-1990s to roughly the mid-2000s, strong increases in labor productivity were coupled with a sharp rise in Irish consumption. However, since around the mid-2000s, while labor productivity remained roughly stable, consumption not only continued its ascendant path, but experienced even higher growth. In 2008, a sharp adjustment in consumption occurred while labor productivity remained stable. If agents base their consumption decisions only on observed labor productivity, there should not be such instability in the relationship between these two variables. It seems then that information about future changes in productivity has played an important role in consumption decisions in Ireland.

The aim of this paper is to explain the last boom and bust in Irish consumption by the idea that a large part of the information about the future received by Irish consumers did not have the expected permanent effects on productivity. In particular, our initial intuition is that because of strong increases in labor productivity from mid-1990s to mid-2005, and because of positive signs received about the future, Irish agents believed that the stabilization of labor productivity that occurred in the mid-2000s was only temporary. Consequently, they “overestimated” future productivity, leading to a period where Irish agents consumed at levels above what economic fundamentals (in this case long-run productivity) suggested. When they realized their mistake, they immediately and strongly adjusted consumption expenditures downwards.

To give empirical support to our intuition, we built on the business cycle with news shocks proposed by Blanchard et al. ( _forthcoming_ ) (henceforth BLL) where agents form their beliefs about future productivity (and hence future income) based on information about the future which sometimes is news, sometimes just noise. Thus, agents face a signal extraction problem that can potentially lead to large disconnects between consumption and economic fundamentals.<sup>1</sup> We find that errors in consumers’ beliefs about future productivity were substantial during the last 15 years in Ireland. In particular, Irish consumers’ behavior reacted with an important delay to changes in this variable during the mentioned period. The most important consequence has been the large disconnect between the considered economic fundamental and consumer beliefs since 2005. Indeed, since that date, long-run productivity started a descent trajectory, while agents still were estimating increases in this macro-variable. A strong adjustment in

> 1This analysis would not be possible in a typical model with news shocks where agents perfectly anticipate changes in productivity. See Lorenzoni (2011) and Milani (2012) for a survey of the news shocks literature.

2
consumption occurred in 2008 when agents finally realized that they were “overconsuming”.

Blanchard et al.( _forthcoming_ ) and L’Huiller (2012) find qualitatively the same results as our paper using US data. They both find first a slow learning for consumers about changes in the permanent component of productivity. Second they find an overshooting of their beliefs -on long-run productivity in the first paper, and on permanent productivity in the second- around 2005, followed by a sudden downward adjustment in 2008.

The paper continues as follows. Section II presents the basic version of the BBL model. Section III describes the estimation methodology and presents the recovered shocks and states from the estimation. Section IV concludes.

# **2 The BLL basic model**

## **2.1 The model**

We consider a framework where productivity is driven by two disturbances: a permanent and a transitory shock. A key assumption in this model is that consumers do not observe the two shocks separately, but only the realized level of productivity. The permanent shock introduces uncertainty about the economy’s long-run fundamentals. The presence of the transitory shock implies that consumers cannot back out the permanent shock from productivity observations, thus creating a signal extraction problem. We assume that consumers have access to an additional source of information, as they observe a noisy signal of the permanent component of productivity. This adds a third source of fluctuations, a shock to the error term in the signal, which is called in Lorenzoni (2009) and Blanchard et al. ( _forthcoming_ ) a “noise shock”, and which has the features of aggregate demand shocks, i.e. the shock increases output only temporarily. Consumers solve their signal extraction problem, form expectations about future productivity, and choose spending based on these expectations. Finally, we assume the existence of nominal rigidities in the economy, which implies that spending determines output in the short-run. We explicitly list below the specific assumptions of the model.

Productivity _at_ (in logs) is the sum of two components, the permanent _xt_ , and the transitory component _zt_ : The permanent component follows a unit root process: The transitory component follows a stationary process: The coefficients _ρx_ and _ρz_ are in [0,1[, and _εt_ and _ηt_ are independently and identically distributed (i.i.d.) draws from a normal distribution with zero mean and with variances _σε_<sup>2and</sup><sup>_σ_</sup> _η_<sup>2.</sup> 3
In addition to observing the realized productivity level _at_ each period, consumers receive a noisy signal ( _s_ ) about the permanent component _xt_ : where _vt_ are also i.i.d. draws from a normal distribution with zero mean and with variance _σv_<sup>2.</sup> We assume that consumers set consumption (in logs) _ct_ equal to their long-run productivity expectations: where _Et_ is the expectation conditional on the consumers information at date _t_ , i.e., conditional on current and past values of _at_ and _st_ .

We simplify the determination of output by assuming that consumption is the only component of demand, and that output is fully determined by the demand side. Thus, output (in logs) is equal to consumption _yt_ = _ct_ . Finally, we assume a linear production function in labor, so that the labor input _nt_ adjusts to produce _yt_ , given the current productivity _at_ , and then _nt_ = _yt_ - _at_ .

We now solve for consumption ( _ct_ ). Using (2) we can compute the expected value of cumulative productivity in the long-run: We replace _a_ with _x_ in (5), since the transitory component disappears in the long-run and, rearranging the equation above, we get consumption: Finally, to complete the solution of the model, we need to solve the consumers’ signal extraction problem to express the expectations of _xt_ and _xt−_ 1 in terms of current and lagged values of the shocks ( _εt_ , _ηt_ , _vt_ ). This is done in the next sub-section using standard Kalman filtering.

# **2.2 Solving the consumers’ signal extraction problem**

We define the state vector _Xt_ = ( _xt, xt−_ 1 _, zt_ )<sup>_′_</sup> , the shock vector _Vt_ = ( _εt, ηt, vt_ )<sup>_′_</sup> , and the vector of consumers’ observations _St_ = ( _at, st_ )<sup>_′_</sup> . The notation _Xt/t_ represents the agents’ expectation _E_ [ _Xt/St, St−_ 1 _, .._ ].

We use the Kalman filter to express the agents’ expectations _Xt/t_ in recursive form as: 4
where the matrix of Kalman gains K depends on the variance parameters _εt_ , _ηt_ and _vt_ . In particular, when the variances parameters are large, _st_ and _at_ are less precise signals of _xt_ and agents take longer to adjust their expectation _xt/t_ to the true value _xt_ (see Lorenzoni 2009 for more details).

Since _Xt_ = _AXt−_ 1 + _BVt_ and that _St_ = _CXt_ + _DVt_ , we can re-write the dynamics of _X_ as:<sup>2</sup> _t/t_

# **3 Results**

## **3.1 Maximum likelihood estimation**

After having solved in the previous section the consumers’ Kalman filter to obtain the dynamics of consumers’ expectations, we proceed to estimate the parameters of the model. The equations describing the equilibrium are the ones included in the vectors _Xt_ , _Xt/t_ , and the equation of the endogenous state (6). The variables observed are _ct_ and _at_ . We use _Dynare_ for maximum likelihood estimation.

The consumption series is constructed by dividing real consumption by population. The labor productivity series is constructed by dividing employment by real GDP. Both series are taken in logs. An important issue we have to confront is that, contradictory to our model, productivity and consumption have different growth rates over the sample. This difference reflects factors left out of our simple model such as changes in participation rate, or changes in saving rate (likely linked with the deterioration of the Irish current account during most of the studied period), or changes in the capital-output ratio. Consequently, we remove the drift in the consumption-to-productivity ratio applying the first-differencing filter to both series.

Our dataset spans the period 1997Q1 to 2011Q4. The series for Real GDP, Real Personal Consumption Expenditures, and Employment are from the OECD database. Population data comes from Eurostat and the Central Statistics Office (CSO). Figure 1 plots the data series.

## **3.2 Recovering shocks and states**

Figure 2 shows the recovered shocks from our structural estimation. We remark that permanent productivity shocks are much smaller compared to the size of noise and transitory productivity shocks.<sup>3</sup> This result highlights the major signal

> 3The high autocorrelation of the permanent shocks is a consequence of the difficulty to identify the precise quarter when the permanent change in productivity occurs.

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