Unemployment Fluctuations in a SOE model with Segmented Labour Markets: the case of Canada

Unemployment Fluctuations in a SOE model with Segmented Labour Markets: the case of Canada Yahong Zhang March 17, 213 Abstract A distinct feature of recent financial crisis in Canada is that the job loss is not evenly distributed across industries. Manufacturing industries have been more affected than others: despite employing only about 2% of the total labour force, they account for over one-half of the total job loss during the financial crisis. To capture the labour market differences at the industry level, I introduce a segmented labour market structure to a medium-scale DSGE model with financial and labour market frictions. I estimate the model using Canadian data from 1991Q1 to 21Q4. I find that the degrees of labour and financial market frictions are indeed different between tradable and non-tradable sectors. Compared with the tradable sector, the elasticity of external finance for the non-tradable sector is almost 1 times higher; and the average wage contract is about 2 times longer. I also find the significant sectoral differences are mainly explained by sectoral specific technology and financial shocks. Overall, the technology and financial shocks in the two sectors explain more than a half of the fluctuations in unemployment in the Canadian labour market. JEL: classification: E32;E44; J6 Keywords: Segmented labour market; Unemployment; Financial frictions and shocks; 1

1 Introduction The recent financial crisis and the following recession have induced great interests in searching for the sources of unemployment fluctuations, particularly in exploring the importance of the frictions and shocks in the financial sector for explaining labour market dynamics. Recent works, Christiano, Trabandt and Walentin (211) and Zhang (211a and b), have applied Baynesian maximum likelihood method to estimate medium scale DSGE models to assess the contribution of a variety of shocks to unemployment fluctuations, with the focus on the contribution of financial shocks relatively to other shocks. Christiano, Trabandt and Walentin (211) find that domestic markup shock is the most important shock, explaining more than 2 per cent of unemployment fluctuations in the Swedish economy, and that financial wealth shock explains about 1 per cent; Zhang (211a and b) find that technology, investment and financial wealth shocks account for most of the unemployment fluctuations in the US and Canada, with financial wealth shocks explaining about 3 per cent of the fluctuations. In these studies, there is one aggregate labour market. However, economies consist of multiple sectors, and different sectors of the economy behave differently over the course of business cycles. In fact, one distinct feature related to the recent recession is that job loss is not evenly distributed across sectors. In Canada, during the financial crisis, unemployment rate rose from 6.3% to 8.6%, and total job loss amounted to 4,. Manufacturing industries have been more affected than others: despite employing only about 2% of the total labour force, they account for over onehalf of the total job loss. There is also a significant difference in employment dynamics between manufacturing and the services industries: employment in the manufacturing sector is almost 3 times as volatile as in the non-tradable sector. These facts point to significant differences in labour flows across Canadian industries. Shocks at the sectoral level may require resource to move from the contracting sectors to expanding sectors. If resources are not fully mobile between sectors, sectoral specific shocks will play an important role in shaping the movements in unemployment at the aggregate level. The standard one-sector, one-good models with one aggregate labour market are not equipped to address this issue since they assume away sectoral differences. In order to capture the sectoral differences, I introduce a segmented labour market structure into a multiple sector small open economy model with both financial land labour market frictions. I model the financial and labour market frictions in a similar way as Christiano, Trabandt and Walentin (211) and Zhang (211a and b): financial frictions are introduced a la Bernarke, Gertler and Gilchrist (1999) to finance capital acquisition, entrepreneurs in each sector need to pay risk premium in order to obtain external funds from financiers, and the risk premium depends on entrepreneurs balance-sheet positions; labour market frictions are modeled using Mortensen- Passiridis-Diamond framework which assumes that there are search frictions in the labour market and unemployment is an equilibrium outcome. The new feature of the model is the segmented labour market structure. There are two separate labour markets in the model: one for manufacturing industries (tradable sector), and one for services industries (non-tradable sector). The labour market

parameters are sector-specific. As a result, in one sector, the labour market may be tighter than the other (higher vacancy to unemployment ratio), and wage contract may be less sticky than the other. These features, from unemployed workers perspective, make the labour market in this sector less frictional, because it is easier for them to find jobs. In addition, the frictions related to labour mobility are modeled in the following way: For the workers who are willing to move across sectors, they have to be separated from jobs in one sector first to become unemployed. The separation rate is exogenously given. Once unemployed, they have the chance to search for jobs in the other sector and the probability of finding a job depends on the labour market tightness in that sector. I estimate the model using Canadian data from 1991Q1 to 21Q4. The main findings are as follows: First, given that none of the labour market variables is used in the estimation, the model performs particularly well in terms of matching the key features in the labour market: it not only matches the fact that aggregate unemployment is much more volatile than output; but also generates labour market dynamics differences in the sectoral level. In particular, the model is able to capture the fact that both employment and wages in the tradable sector are more volatile than that in the non-tradable sector. Second, the estimation results show that the degree of frictions in the labour and financial markets are indeed different for the two sectors: Compared to the tradable sector, the elasticity of external finance for the non-tradable sector is almost 1 times higher; and the average wage contract is about 2 times longer. Third, I find that unemployment fluctuations in the Canadian labour market are mainly driving by the technology shock in the non-tradable sector and financial wealth shocks in both sectors. Technology shock in the non-tradable sector is much more persistent than the tradable sector and explains almost 3 percent of the unemployment fluctuations in the Canadian labour market. Financial wealth shock in the tradable sector is more volatile but less persistent than in the non-tradable sector. Together, financial wealth shocks in the two sectors explain about 25 per cent of total unemployment variations. The paper is organized as follows. In the next section, I document some empirical facts regarding sectoral differences. In section 3, I describe the model. In section 4 I discuss the data and estimation strategy. In section 5, I present the estimation results and discuss the effect of the sectoral specific shocks on aggregate unemployment fluctuations. In section 6 I offer some concluding remarks. 2 Sectoral Difference: Some Empirical Facts 2.1 Output, employment and wage Throughout the paper, the tradable sector refers to manufacturing industries, and the non-tradable sector refers to the rest of the economy but excludes agriculture and natural resources. 1 The data used in this section and estimation are from the Statistics Canada. Output is measured by real GDP and expressed in per capita terms using the civilian population aged 15 and up. Wage is measured 1 The non-tradable sector includes utility, construction, wholesale and retail trade, transportation, information, finance and insurance, professional services, administrative and support, waste management, education and health and arts. 2

Table 1: Standard Deviations: tradable vs non-tradable Output Employment Wage Tradable.348.186.15 Non-tradable.88.66.61 Relative volatility 3.95 2.81 1.71 using index of average hourly earnings. All the three series are logged and detrended using an HP filter with smoothing parameter 16. Figures 1-2 plot the output, employment and wage for the tradable and non-tradable sectors for the sample period 1991Q1 to 21Q4, and they clearly show all three variables are more volatile in the tradable sector than that in the non-tradable sector. Table 1 provides the standard deviations of output, employment and wages for the two sectors. The relative volatility in the third row is computed by normalizing the standard deviations of the three variables in the tradable sector to their non-tradable counterparts. Table 1 further quantifies the difference in volatilities across the two sectors: output in the tradable sector is about 4 times as volatile as that in the non-tradable sector; employment is about 3 times, and wage is about 2 times. 3 The Model I consider a small open economy which consists of three sectors: tradable, non-tradable and imported-goods sectors. Labour markets for the tradable and non-tradable sectors are segmented. In each labour market, employment agencies post vacancies and hire workers seeking jobs in that sector. The sector-specific employment agencies supply labour services to the entrepreneurs in that sector, who produce sector-specific intermediate goods using labour services and capital. Since entrepreneurs need to borrow to finance capital purchases, they are subject to financial frictions. Entrepreneurs supply intermediate goods to retailers in each sector, which produce final goods. A representative household with a large family structure has a fraction of its members are unemployed, the rest are either employed in the tradable or non-tradable sector. The household consumes, saves both in domestic bonds and foreign bonds, pays tax and receives profits from retailers in each sector. In addition, there are capital producers, a government that balances the budget, and a central bank that implements a simple interest rate rule. In what follows, I describe the role of each agent in the model. 3.1 Household Each member in the household consumes, holds both nominal domestic bonds B t and foreign bonds Bt which are denominated in foreign currency, receives dividends from retailers Π t, and pays taxes T t. At time t, a fraction of household members are employed, n t, and a fraction of household members are unemployed u t = 1 n t. For the employed household members, n T t of them are employed in the tradable sector, and n N t of them are employed in the non-tradable sector. For the 3

unemployed household members, u T t of them search for jobs in the tradable sector, and u N t of them search for jobs in the non-tradable sector. The employed family members earn nominal wages Wt T and Wt N respectively. The unemployed members receive unemployment benefits ub t. Following Andolfatto (1996) and Merz (1995), family members are assumed to be perfectly insured against the risk of becoming unemployed. Thus consumption is the same for each family member. The budget constraint for the representative household is where both W T t P t c t + B t + e tb t κ t R t and W N t + T t W T,t n T,t + W N,t n N,t + ub t (1 n t ) + R t 1 B t 1 + e t R t 1B t 1 + Π t, (1) are determined by Nash bargaining between employment agencies and workers. The labour supply n T t and n N t are determined by a search and match process. e t is nominal exchange rate. The return on the foreign bonds, κ t R t, depends on the foreign interest rate R t and a country-specific risk premium κ t, which is assumed to be an increasing function of the net foreign-debt-to-gdp ratio: κ t = exp ( υ e t B t P t y t where υ >, y t is real GDP and B t is the total level of indebtedness of the economy. Given the budget constraint equation (1), the representative household chooses c t, B t, and Bt to maximize the lifetime utility with E t= β t u(c t ), c 1 σ t u(c t ) = µ t 1 σ, where c t is consumption of final goods in period t and where µ t is a preference shock which follows The first-order conditions yield: log µ t = ρ µ log µ t 1 + ɛ µ t, ɛ µ t i.i.d. N(, σ 2 ɛ µ). ), [ ] Rt λ t+1 µ t+1 λ t µ t = βe t, (2) π t+1 [ ] R λ t µ t = βe t κ t s t+1 λ t+1 µ t+1 t, (3) s t πt+1 where π t = P t /P t 1 is the CPI inflation rate and s t = e t Pt /P t is the real exchange rate, where is a foreign price index. Equations (2) and (3) imply the uncovered interest rate parity (UIP) P t 4

condition: 3.2 Employment agencies R t κ t R t = e t+1 e t. Following Christiano, Trabandt and Waletin (211), I model employment agencies as intermediaries between the representative household (who supply labour) and entrepreneurs (who demand labour to produce wholesale goods). 2 The labour market is modeled using a standard search framework. On the one hand, the employment agencies post vacancies, and bargain wages with workers; on the other hand, they combine labour supplied by households into homogeneous labour services and supply them to entrepreneurs at a competitive price. The labour market is segmented. Employment agencies in the tradable sector (non-tradable) only post vacancies in the tradable (non-tradable) sector. Unemployed workers need to decide which sector jobs to search. Unemployed workers seeking for tradable sector jobs are denoted as u T,t, and those seeking for non-tradable sector jobs are denoted as u N,t. In equilibrium, searching for jobs in each sector gives the same expected payoff. In the beginning of period t, in each sector i, employment agency j employs n i,t (j) workers, and posts v i,t (j) vacancies to attract new workers. The total number of vacancies and the number of employed workers are denoted as v i,t = v i,t (j)dj and n i,t = n i,t (j)dj. The number of unemployed workers at the beginning of period t is u t = 1 n t = 1 n T,t n N,t = u T,t + u N,t. The number of new hires m i,t is given by a standard Cobb-Douglas aggregate matching technology m i, t = µ i,m u σm i,t v1 σm i,t. For an employment agency, the value of adding another worker at time t is the price of selling one unit of labour service p l i,t, minus the wage cost wn i,t (i) p i,t and vacancy costs κ i x 2 i,t(j) 2, plus the continuation value of a filled vacancy: J i,t (j) = p l i,t wn i,t(j) p i,t κ i, 2 x i,t(j) 2 + (ρ i + x i,t (j))βe t Λ t,t+1 J i,t+1 (j), where x i,t (j) is the hiring rate for employment agency j, and ρ i is the probability of a match that survives to the next period. The value of employment, V i,t (j), is V i,t (j) = w i,t (j) + βe t Λ t,t+1 [ρv i,t+1 (j) + (1 ρ)u i,t+1 ], 2 This leaves the equilibrium conditions associated with the production of wholesale goods unaffected, although the labour market is frictional. 5

where w i,t (j) is the real wage. The value of unemployment, U i,t, is U i,t = ub t + βe t Λ t,t+1 [s l i,t+1v i,t+1 + (1 s l i,t+1)u i,t+1 ], where ub t is the unemployment benefit, s l i,t+1 is the probability of finding a job next period, and V i,t is the average value of employment for a new worker at time t. 3 The workers surplus for having a job at employment agency j, H i,t (j), is H i,t (j) = V i,t (j) U i,t. Given that it implies that U T,t = U N,t, βe t Λ t,t+1 s l T,t+1H T,t (j) = βe t Λ t,t+1 s l N,t+1H N,t (j). Thus, for an unemployed worker, the expected payoff of searching for either sector jobs must be equal. In equilibrium, a lower job finding rate in one sector must be compensated by a relatively higher surplus of having a job in that sector. Employment agencies and workers negotiate a nominal wage w n i,t(j) to maximize the joint product of the workers surplus H i,t (j) and the employment agencies surplus J i,t (j). However, every period, each employment agency only has a fixed probability 1 λ to negotiate with workers. Thus, the Nash bargaining problem between employment agencies and workers is s.t. max H i,t (j) η J i,t (j) 1 η, w n i,t(j) = w n i,t with probability 1 λ = w n i,t 1π with probability λ, where π is the steady-state inflation rate. The equation for the real wage w i,t derived from this staggered contracting is: t w i,t = η(p l i,t + κ i 2 x2 i,t(i)) + (1 η)( b + s i,t+1 βλ t,t+1 H i,t+s+1 ) +λρβe t Λ t,t+1 t+1 w i,t+1. (4) The first term of equation (4) is the worker s contribution to the match, and the second is the worker s opportunity cost. These are conventional components for Nash bargaining solutions for wages. The third term is from the staggered multi-period contracting. Finally, the aggregate real wage w i,t can 3 See Gertler and Trigari (29) for details about the average value of employment. 6

be expressed as w i,t = (1 λ)w i,t + λπ 1 π i,t w i,t 1. 3.3 Entrepreneurs There are entrepreneurs in both the tradable and non-tradable sectors. Following Bernanke, Gertler and Gilchrist (1999), entrepreneurs are risk-neutral and have a finite life. In each sector i, at each period t, entrepreneur j uses capital k i, t and labour services l i,t to produce wholesale goods y i, t using a Cobb-Douglas technology: where z i,t is the technology shock which follows y i,t (j) = z i,t (k i,t (j)) α (l i, t (j)) 1 α. log z i,t = ρ z,i log z i,t 1 + ɛ z i t, ɛ z i i,t i.i.d.n(, σ2 ɛ z i). Entrepreneurs purchase capital at price q i,t from capital producers, using both their own net worth N i,t and bank loans. Bank loans can be from domestic market, B i,t, or from international market B i,t. 4 Entrepreneurs can default due to idiosyncratic shocks. Since only entrepreneurs observe the realization of the idiosyncratic shocks, the optimal loan contract in Bernanke, Gertler and Gilchrist (1999) is such that entrepreneurs pay a risk premium on loans. Thus for domestic loans, the external finance premium, s(.), depends on the entrepreneur s balance-sheet position. At the aggregate level it can be characterized by ( ) qi,t k i,t+1 rp i,t = s, (5) N i,t+1 where rp (.) > and rp(1) = 1. Equation (5) expresses that in each sector, the external finance premium increases with leverage. For the loans from the international market, the entrepreneurs are subject to country-specific risk premium κ i,t : ( κ i,t = exp υ i e t B i,t q i,t k i,t+1 N i,t where υ i > is a parameter determining the relative size of b i,t (j) and b i,t(j) for each sector. The one-period profit function for entrepreneurs j is: 4 IMF country report (28) suggests that a quarter of financing of Canadian corporations is raised in the U.S. Data source from Statistic Canada also suggests the same. The survey of suppliers of business financing suggests that in 28, almost 2 per cent of the total debt is foreign debt. For the manufacturing industries, the fraction is even higher close to 3 per cent. Although there is a slight decrease after 28, foreign debt remains a significant portion of total debt financing for Canadian corporations, especially for manufacturing industry. ), 7

π i,t (j) = B i,t(j) + e tbi,t(j) + p w P t P i,ty j i,t + q i,t(1 δ)k i,t (j) t p l B i,t 1 (j) e i,tl i,t (j) R t 1 rp i,t 1 R t Bi,t 1(j) P t 1κ i,t 1 t P t q i,t k i,t+1 (j), (6) where p w i,t is the relative price for the wholesale goods in sector i, and p l i,t is the labor service price. The entrepreneur j chooses l i,t (j), k i,t+1 (j), b i,t (j) and b i,t(j) to maximize E t= β t π i,t (j). The first order conditions yields: and l i,t (j) : p w y i,t (j) i,t l i,t (j) = pl i,t, (7) k i,t+1 (j) : q i,t + E t β[p w y i,t+1 (j) i,t+1 k i,t+1 (j) + q i,t+1(1 δ)] =, (8) Define the expected return on capital in each sector as b i,t (j) : 1 E t β[ R trp i,t π t+1 ] =. (9) b i,t(j) : 1 E t β[ s t+1rt κ i,t ] =. (1) s t πt+1 E t r k i,t+1 = E t[p w i,t+1α yi,t+1 k i,t+1 + q i,t+1 (1 δ)] q i,t. In each sector, the expected return on capital must equal to the expected costs of external finance E t r k i,t+1 = E t β[ R trp i,t π t+1 ]. The demand for foreign debt for each sector is determined by E t ri,t+1 k = E t β[ s t+1rt κ i ]. s t πt+1 Finally, the aggregate net worth in each sector is given by N i,t+1 = γ i,t η e i (r k i,tq i,t 1 k i,t R t 1rp i,t 1 π t b i,n,t 1 s trt 1κ i,t 1 b s t 1 π i,t 1), t 8

where η e i is the survival rate of entrepreneurs for each sector. γ i,t is a financial wealth shock, an exogenous shock to the survival probability of entrepreneurs in sector i. It follows an AR(1) process: log γ i,t = ρ γ log γ i,t 1 + ɛ γ t, ɛ γ i,t i.i.d. N(, σ2 ɛ z). For the entrepreneurs that are going out of business, they consume their residue equity: ce i,t+1 = (1 γ i,t η e i )(r k i,tq i,t 1 k i,t R t 1rp i,t 1 π t b i,t 1 s trt 1κ i,t 1 rp i,t b s t 1 π i,t 1), t The aggregate demand for labour services is relatively simple. Given that the aggregate production function is constant returns to scale, y i,t = k i,t α (z i,t l i,t ) 1 α, the aggregate labour demand equation can be written as p w i,t(1 α) y i,t l i,t = p l i,t, where l i,t is the labour services supplied by employment agencies in sector i, (1 α) y i,t l i,t is the marginal product of labour services, p w i,t is the relative price for wholesale goods and p l i,t is the relative price for labour services. 3.4 Capital producers Capital producers use investment goods to produce new capital purchased from entrepreneurs. At the end of the period t, they buy investment goods I t, at real price p I,t = P I,t /P t to produce sectorspecific capital that can be used by entrepreneurs at time t + 1. Capital production in each sector is assumed to be subject to an investment-specific shock, τ i,t, which follows an AR(1) process log τ i,t = ρ i,x log τ i,t 1 + ɛ τ i,t, ɛ τ i,t i.i.d.n(, σ 2 ɛ τ i ). Following Christiano, Eichenbaum and Evans (25), we assume that capital producers in sector i = {T, N} face investment adjustment costs S(I i,t, I i,t 1 ), such that in steady state S = S = and S >, and ξ i > is an investment adjustment cost parameter. The production of each capital stock yields the following time-t profit function The aggregate stock of capital evolves as follows: Π i t = q i,t I i,t τ i,t q i,t I i,t S(I i,t, I i,t 1 ) p I,t I i,t. (11) K i,t+1 = I i,t τ i,t I i,t S(I i,t, I i,t 1 ) + (1 δ)k i,t. (12) 9

3.5 Sectoral good producers There are sectoral good producers in all three sectors: tradable, non-tradable and imported good sectors. The sectoral good producers in the tradable and non-tradable sectors buy tradable, nontradable input from entrepreneurs, and those in imported good sector buy foreign homogeneous intermediate inputs, and differentiate them slightly into z i,t (j) and sell the product at price p i,t (j). The final good for each sector i, z i,t, is the composite of individual variety, [ 1 z i,t = ] ε y i,t (j) ε 1 ε 1 ε dj. The price index that minimizes the sectoral good producers cost function is [ 1 p i,t = ] 1 p i,t (j) 1 ε 1 ε dj. Following Calvo (1983), in each period, only a fraction 1 ν i of retailers reset their prices, while the remaining retailers keep their prices unchanged. The retailer chooses p i,t (j) to maximize its expected real total profit over the periods during which its prices remain fixed: [( ) ] E t Σ i=ν p pi,t (j) i,t+i y i,t+i (j) mc i,t+i y i,t+i (j), p i,t+i where mc i,t is the real marginal cost, which is the price of wholesale goods relative to the price of sectoral final goods (p i,w,t /p i,t ). The real marginal cost for imported intermediate goods is e t Pt for a given nominal exchange rate, e t, and foreign price level, Pt. p t,i βi c t+i /c t is the stochastic discount factor. Let p t be the optimal price chosen by all firms adjusting at time t. The first-order condition is: ( ) ε Et p s= i,t = νs p 1 s,t+smc i,t+1 y i,t+i ( p i,t+i ) ε ε 1 E t s= νs p 1. s,t+sy i,t+i ( p i,t+i ) 1 ε The aggregate price evolves according to: p i,t = [ν i p 1 ε i,t 1 + (1 ν i)(p i,t) 1 ε ] 1 1 ε. Retailers in the tradable sector produce goods for domestic use, zt,t d, and exports, ze T,t, so that z T,t = zt,t d +ze T,t. Following Obstfeld and Rogoff (1995), we assume the producers currency pricing behavior in the manufacturing sector. Thus, the law of one price holds for exported domestic goods. However, due to the presence of nominal rigidities in the import sector, exchange rate movements are partially passed through to domestic prices. The aggregate foreign demand function for exports 1

of manufactured goods is ( zt,t e et P T,t = ϖ P t ) ν Y t, (13) where Yt is foreign output. The elasticity of demand for domestic manufactured goods among foreigners is ν, and ϖ > is a parameter determining the fraction of domestic manufacturedgoods exports in foreign spending. 3.6 Aggregate final goods producers There is a representative firm that acts in a perfectly competitive market and uses sectoral output to produce final consumption and investment goods, x j t, with j = {C, I}, according to the following CES technology: x j t = [ (ω j T ) 1 ) ν j (z ν j 1 d,j ν j T,t ( ) 1 + ω j ν j N ( ) z j ν j 1 ν j N,t + ( ) ω j 1 ν j F ( z j F,t ) ν j 1 ν j ] νj ν j 1, (14) where ω j T, ωj N, and ωj F denote the shares of domestically-used tradable, non-tradable, and imported composite sectoral goods, z d,j N,t,zj N,t,zj F,t, respectively, in the final good, where ωj T + ωj T + ωj F = 1, and ν j > is the elasticity of substitution between sectoral goods. p j t = [ (ω j T ) 1 ν j ( ) p j 1 νj ( ) 1 T,t + ω j ν j N ( ) p j 1 νj ( ) 1 N,t + ω j ν j F ] ( ) p j 1 ν 1 j 1 ν j F,t. (15) 3.7 Government The government is assumed to balance its budget, where g t follows an AR(1) process, g t = T t, log g t = (1 ρ x ) log g ss + ρ x log g t 1 + ɛ g t, ɛ g t i.i.d.n(, σ 2 ɛ g). 3.8 Monetary policy rules The central bank adjusts the nominal interest rate r n t according to a simple interest rate rule: r n t r n = (rn t 1 r n )ρr (( π t π )ρπ ( y t y )ρy ) 1 ρr e ɛm t, where r n, π and y are the steady-state values of rt n, π t and y t, and ε m t that follows i.i.d. N(, σ ε m). ε m t is a monetary policy shock 11

ρ π, ρ y and ρ r are policy coefficients chosen by the central bank. 3.9 Rest of the world Given that Canada is a small open economy, I assume that domestic developments do not affect the rest of the world. However, the foreign economy has an impact on the Canadian economy. Following Dib, Mendicino and Zhang (28), for simplicity, I assume that the foreign output, foreign interest rate, and inflation exogenous and follow AR(1) processes. 3.1 Aggregation and equilibrium The resource constraint is z t k α t l t 1 α = c t + i t + g t + κ N 2 x2 N,tn N,t + κ T 2 x2 T,tn T,t + ce T + ce N. Furthermore, for the labour market, l T,t = n T,t, and 4 Estimation 4.1 Calibrated values l N,t = n N,t. I use Bayesian techniques to estimate the model for the Canadian economy. I use and the data sample spans from 1991Q1 to 21Q4. Some parameters need to be calibrated to match the salient features of the Canadian economy, Table 2 reports these parameters and their calibrated values. For most of the parameters that govern the sectoral shares, I use the calibrated values in Dib, Mendicino and Zhang (28). The calibrated value for the discount factor, β, is set to.99, which implies an annual steady-state real interest rate of 4 percent which matches the average observed in the estimation sample. The curvature parameter in the utility function, γ, is set to 2, implying an elasticity of intertemporal substitution of.5. The capital shares in the production of tradable and non-tradable goods, α T and α N, are set to.35 and.3, which are close to the values suggested by Macklem et al. (2). The capital depreciation rate, δ, is assumed to be common to both tradable and non-tradable sectors and set to.25, a value commonly used in the literature. The shares of tradable, non-tradable, and imported goods in the production of consumption good, ωt C, ωc N, and ωf C, equal.1,.57 and.33, respectively, to match the average ratios observed in the data for the estimation period. Since the share of imported good in the production of the investment good is higher than that in consumption good production. I set ωt I, ωi N, and ωi F equal to.2,.4 and.4, respectively. 12

The parameter measuring the degree of monopoly power in the intermediate-goods markets, θ, is set to be equal to 6, which implies a 2 percent markup in the steady-state. Based on Dib (23), both the elasticity of substitution between tradable, non-tradable and imported goods in the production of final consumption goods, ν C, and the elasticity of demand for domestic manufacturedgoods among foreigners, ν, are set equal to.8. The elasticity of substitution between tradable, non-tradable and imported goods in the production of final investment goods, ν I, is set equal to.6, implying that imported goods are less substitutable in producing investment than against the consumption good production. The steady-state gross domestic and foreign inflation rates, π and π, equal 1.48 and 1.52, respectively, which are the historical averages over the estimation sample for Canada and the U.S. Following Dib, Mendicino and Zhang (28), I calibrate the parameter υ to match a foreign-debtto-gdp of about 3 percent as in the data. The parameters determining the steady-state leverage ratios for tradable and non-tradable sectors, k T and k N, are set to.7 and.6, respectively, which is suggested by King and Santor (28). In calibration, the following functional form is used for the external finance premium: ( ) χ qt k t+1 s t =, (16) N t+1 where χ is the elasticity of the external risk premium with respect to leverage and χ >. χ can be viewed as a reduced-form parameter capturing financial market frictions. For most of labour market parameters, I use values from Zhang (211a and b). The bargaining power parameter, η, is set to.5, which is commonly used in the literature. The elasticity of matches to unemployment, σ m, is set to.5, the midpoint of values typically used. Following the suggestion of Zhang (28), the job-separation rate, 1 ρ, is set to.9, matching the average job duration of 2.8 years in Canada; the job-finding rate s l is set to.927, matching the fact that one-third of the unemployed workers find jobs within one month. I normalize the mean of market tightness to 1, which implies that the value of µ m in the matching function equals the quarterly job-finding rate. Following Gertler, Sala and Trigari (28), I express b, the steady-state flow value of unemployment, as b = b(p l + κ 2 x2 ), (17) where b is the fraction of the worker s contribution to the job. Following Shimer (25), I set b to.4. There are several new parameters that arise from the fact that the labor market is segmented and entrepreneurs can borrow from both domestic and foreign lenders. The survival rate of jobs in tradable sector, ρ T, is set to.94, which is taken from Tapp (211). The steady-state unemployment rate for tradable sector u ss,t, and the ratio of employed workers in tradable sector is set to θ are set to.19 and.2 respectively to match the data. I use debt allocation data from survey of suppliers of business financing to calibrate υ T and υ N. This survey suggests that from 28 to 21, the average ratio of foreign debt to total debt is 25% for tradable sector; and 17% for non-tradable sector. I 13

Table 2: Calibration of the parameters Param. Definition Values β discount factor.99 γ inverse of intertemporal substitution of consumption 2 ν C elasticity of substitution between sectors, consumption.8 ν I elasticity of substitution between sectors, investment.6 θ intermediate good elasticity of substitution 6 α T capital share, tradable.35 α N capital share, non-tradable.3 δ T capital depreciation rate, tradable.25 δ N capital depreciation rate, non-tradable.25 ωt C share of tradable good, consumption.1 ωn C share of non-tradable good, consumption.57 ωt I share of tradable good, investment.2 ωn I share of non-tradable good, investment.4 υ parameter of country-specific risk premium.41 k T steady-state leverage, tradable.7 k N steady-state leverage, non-tradable.6 π steady-state domestic inflation rate 1.48 π steady-state foreign inflation rate 1.52 ρ aggregate survival rate of jobs.91 ρ T survival rate of jobs in tradable sector.94 s l aggregate job-finding rate.927 η bargaining power of workers.5 b parameter for unemployment flow value.4 σ m elasticity in matches to unemployment.5 u ss,t steady-state unemployment rate for tradable.19 θ ratio of employed workers in tradable sector.2 14

Table 3: Estimation Results: Foreign Shock Processes Prior Posterior Coef. Description Density Mean Std Mode Autoregressive parameters ρ R Foreign interest rate B.6.1.965 ρ π Foreign inflation B.6.1.625 ρ y Foreign output B.6.1.83 Standard deviations σ R Foreign interest rate I.5 2..13 σ π Foreign inflation I.5 2..25 σ Y Foreign output I.5 2..8 calibrate υ T and υ N to match these ratios. 4.2 Data and priors Bayesian techniques are used to estimate the model. Since the dynamics of the key variables for the rest of the world are exogenous to the Canadian economy, I assume that foreign output, inflation and nominal interest rate all follow an AR(1) process and estimate the parameters governing these processes separately. Following the literature, I assume foreign shocks autoregressive coefficients to follow a beta distribution with mean.6; and the standard deviations of the shocks to follow an Inverted Gamma distribution with mean.5 percent and standard deviation 2. I use U.S. quarterly real GDP per capita for foreign output, federal funds rate in quarterly term for foreign interest rate, and the quarter to quarter growth rate of the GDP deflator for foreign inflation. Foreign output is logged and HP-filtered. Foreign nominal interest rate and inflation are demeaned. Table 4 reports the priors and the modes for the posterior distribution. Taking the estimated foreign shocks as given, I then estimate the main model using nine series of quarterly Canadian data from 1991Q1 to 21Q4: output in tradable sector, output in non-tradable sector, consumption, investment, government spending, nominal interest rate, inflation, risk premium and real exchange rate. Output is measured by real GDP. Consumption is measured by real expenditures of non-durable goods, semi-durable goods and services. Investment is measured by the sum of business gross fixed capital formation, investment in inventories and real expenditure of durable goods. Data on these real variables are expressed in per capita terms using the civilian population aged 15 and up. The nominal interest rate is measured by the overnight rate in quarterly terms. Inflation is the quarter-to-quarter growth rate of the core CPI. Risk premium is measured by difference between business prime lending rates and nominal interest rate. The real exchange rate is measured by multiplying the nominal U.S./CAN exchange rate by the ratio of U.S. to Canadian prices. The series of tradable output, non-tradable output, consumption, investment, government spending and real exchange rate are logged and detrended using an HP filter with smoothing param- 15

Table 4: Estimation Result: Behavior Parameters Prior distribution Posterior distribution Mode Mean 5 percent 95 percent Risk premium elas., T χ T gamma (.5,.2).15.18.8.29 Risk premium elas., N χ N gamma (.5,.2).218.212.187.255 Calvo wage, T λ T beta (.75,.1).545.579.424.79 Calvo wage, N λ N beta (.75,.1).832.816.73.91 Calvo price, T ν T beta (.75,.1).734.683.57.84 Calvo price, N ν N beta (.75,.1).569.567.513.611 Calvo price, F ν F beta (.75,.1).957.951.936.973 Inv. adj. cost, T ξ T norm (1,.5) 1.56 1.159.424 2.369 Inv. adj. cost, N ξ N norm (1,.5).81.92.38.128 Taylor rule inertia ρ r beta (.5,.25).641.613.553.78 Taylor rule inflation ρ π gamma(.5,.5).478.518.394.592 Taylor rule output gap ρ y norm (.125,.15).3.4 -.2.9 Table 5: Estimation Results: Shocks Processes eter 16. The series of domestic nominal interest rate, inflation, and risk premium are demeaned. There are twelve behavioral parameters to estimate: the elasticity of the external risk premium for both tradable and non-tradable sectors χ T and χ N ; the investment adjustment cost parameter for both tradable and non-tradable sectors ξ T and ξ N ; the Calvo price parameters for both tradable, nontradable and imported good sectors ν T, ν N and ν F ; the Calvo wage parameters for both tradable and non-tradable sectors λ T and λ N ; and the Taylor rule parameters ρ π, ρ y and ρ r. I also estimate the first-order autocorrelations of all the exogenous shocks and their respective standard deviations. For most of the priors, I follow the literature. I use Beta distributions for all parameters bounded in the [,1] range. This applies to the shocks autoregressive coefficient, whose mean I set to.6. The parameters of nominal rigidities for price and wages are also assumed to follow a beta distribution with mean.75, which corresponds to changing prices and wages every 4 quarters on average. Gamma and Inverted Gamma distributions are assumed for parameters that are supposed to be positive. The priors on the investment adjustment cost and risk-premium elasticity are in line with previous literature. For the standard deviation of the shocks I assume an Inverted Gamma distribution with mean.5 percent and standard deviation 2. The prior assumptions on the monetary policy parameters allow for a range of interest-rate inertia between and 1, and a positive response to inflation. I use a normal distribution for the reaction to output in order to allow for a negative response. The priors are reported in Tables 4 and 5. 16

Prior distribution Posterior distribution Autoregressive parameters Mode Mean 5 percent 95 percent Technology, T ρ z,t beta (.6,.2).771.777.686.864 Technology, N ρ z,n beta (.6,.2).969.948.9.995 Preference ρ e beta (.6,.2).893.883.822.939 Investment, T ρ τ,t beta (.6,.2).666.579.333.935 Investment, N ρ τ,n beta (.6,.2).869.872.766.94 Government ρ g beta (.6,.2).777.76.674.871 Financial,T ρ γ,t beta (.6,.2).667.587.26.923 Financial, N ρ γ,n beta (.6,.2).779.772.696.855 Standard deviations Technology, T σ ɛ z,t invg (.5,2).173.181.158.29 Technology, N σ ɛ z,n invg (.5,2).4.41.36.46 Monetary σ ɛ m invg (.5,2).3.34.25.39 Preference σ ɛ e invg (.5,2).1.12.82.118 Investment,T σ ɛ τ,t invg (.5,2).23.56.15.68 Investment,N σ ɛ τ,n invg (.5,2).61.64.5.75 Government σ ɛ g invg (.5,2).57.59.51.66 Financial,T σ ɛ γ,t invg (.5,2).82.56.15.68 Financial,N σ ɛ γ,n invg (.5,2).3.64.5.75 I use Dynare 3.65 to estimate the model and use Metropolis-Hastings algorithm to perform simulations. The total number of draws is 1, and the first 2 percent draws are neglected. A step size of.36 results in a acceptance rate of.27. The log data density is 252.59. 5 Results 5.1 Estimates Table 4 reports the mode, the mean and the 5 and 95 percentiles of the posterior distribution of the behavioral parameters. The estimates indicate significant heterogeneity across sectors. In the follows, I focus on the estimates of parameters that reflect the sectoral differences. The estimates of risk premium elasticity parameter, χ T and χ N, are quite different for the two sectors: χ T is estimated to be.15; while χ N is estimated to be.22. 5 The external finance costs are 1 times more responsive to balance-sheet positions in the non-tradable sector, suggesting that the degree of financial frictions is higher for the firms in the non-tradable sector. The staggering wage contract parameters, λ T and λ N, are estimated at.55 and.83 respectively, suggesting that wages remain unchanged on average about 2 quarters in the tradable sector and about 6 quarters in the non-tradable sector. The sectoral difference is also captured by the sticky price parameters. For the tradable sector, ν T, is estimated to be.73, implying that the expected price duration is 3.7 quarters. For the non-tradable sector, ν N is estimated at.57, suggesting the the expected price duration is 2.33 quarters. The estimates of the rest of the parameters are also consistent with the existing studies in the literature. 5 The estimated values reported in this section are the modes of the posterior distribution. 17

Table 5 reports the mode, the mean and the 5 and 95 percentiles of the posterior distribution of the shock processes. The estimates also suggest significant heterogeneity across sectors. For example, the technology shock in the tradable sector is almost 4 times as volatile as that in the nontradable sector (1.73 versus.4). The financial wealth shocks are quite different for the two sectors as well: the shock in the tradable sector is about 3 times as volatile (.82 versus.3) as that in the non-tradable sector, although it is less persistent (.66 versus.77). Among all the shocks, the technology shock in the non-tradable sector is estimated to be most persistent, with a coefficient of.97. The preference shock is the most volatile, with a coefficient of.1. 5.2 Fit of the model I first examine how well the model economy is able to account for the overall volatility in the data. Table 6 reports the standard deviations (normalized relative to output) for the nine key variables. Overall, the model appears to capture well the basic features of the data. The model comes quite close in terms of matching the volatility in aggregate investment i, risk premium rp; it captures almost half of the relative volatility in consumption c, real exchange rate s, and inflation π. The model also captures about 4 percent of the relative volatility in nominal interest rate r. For the key labour market variables, the model is able to capture the fact that unemployment is much volatile than output, although it slightly overestimates the relative volatilities for both employment and unemployment. Table 6: Standard Deviations for the Key Macro Variables: Model vs. Data y c i r π rp s u n Data 1.56 4.4.45.52.9 3.29 5.51.63 Model 1.37 4..18.29.7 2.73 7.32.76 I next study whether the model economy is able to capture the sectoral differences in output, employment and wages observed in the data. For each variable, I normalize the standard deviations in the tradable sector to these in the non-tradable sector and report the relative volatilities in the data and model in Table 7. In the data, output in the tradable sector is about 4 times as volatile as that in the non-tradable sector. The model is able to capture half of it (2.9 vs 3.95). The model is also able to capture about 4 per cent of the relative volatility in employment. For real wage, the model comes very close to the data, although it slightly overestimates its value (1.98 vs 1.71). Table 7: Relative Volatilities: Model vs. Data Output Employment Wage Data 3.95 2.81 1.71 Model 2.9 1.14 1.98 18

5.3 Sources of unemployment fluctuations Table 8 reports the forecast error variance decomposition based on the mode of the model s posterior distribution for 9 key macroeconomic variables, including unemployment, output for both the tradable and non-tradable sectors, employment for the tradable and non-tradable sectors, consumption, investment, nominal interest rate, inflation and real exchange rate. Fluctuations in unemployment are primarily driven by domestic technology and financial wealth shocks. Together these two types of shocks account for more than half of the variations in unemployment (54%). Notice although the tradable sector is only about one quarter of the size of the non-tradable sector, the financial shock in the tradable sector accounts for about the same fraction of the fluctuations (12%) in the aggregate unemployment rate as that in the non-tradable sector. The rest of the variations in unemployment are explained by foreign shocks (29%), monetary policy shock (9%), preference shock (5%), and investment-specific shocks (3%). Technology and financial wealth shocks are also the most important shocks explaining output and employment fluctuations at the sectoral level. For the tradable sector, about 85% of the variations in output, and 56% in employment are accounted by the sector-specific technology and financial wealth shocks. For the non-tradable sector, we observe a similar pattern: about 5% of the variations in output and 34% in employment are explained by the technology and financial wealth shocks. Financial wealth shocks in the two sectors also contribute significantly to the other key macro variables. Financial wealth shocks in the tradable sector account for about 31% of the volatility in consumption, 1% in investment, 5% in nominal interest rate and 38% in inflation; financial wealth shocks in the non-tradable sector explain about 64% of the variations in investment and 1% in inflation. The financial wealth shocks seem to crowd out the investment-specific shocks, which have limited importance for all the variables. For the rest of the shocks, technology shocks in the non-tradable sector also contributes significantly to consumption (2%). Monetary policy shocks contribute significantly to inflation (32%). Foreign interest rate shocks are important in explaining for the variations in exchange rate (76%). 5.4 Model dynamics Given the importance of the sectoral specific technology and financial wealth shocks in explaining the movements in aggregate unemployment, in this subsection I discuss how the key variables of the model economy response to these two types of shocks. I use the technology and financial wealth shocks in the tradable sector as an example. Figure 3 illustrate the responses of the key variables in the model to a one-standard-deviation increase in financial wealth in the tradable sector. The solid line in each panel illustrates the response of the respective variable in the sector where the shocks occurs (tradable sector); and the dotted line reports the responses of the same variables in the other sector (non-tradable sector). The last 19

Table 8: Variance Decomposition of the Key Variables Tech. Tech. Fin. Fin. Money Invest Invest Govern. Prefer. Int. rate Inflation Output shock shock shock shock shock shock shock shock shock shock shock shock T N T N T N foreign foreign foreign U rate 2.13 27.16 12.42 12.12 8.62.2 2.83.2 5.42 28.95.4.1 Output, T 69.96.39 15.55.85 6.2.2.69.15 2.35 3.81.6.15 Output, N 6.1 3.39 9.46 21.44 6.3.1 1.2.13 3.9 21.11.3.11 Empl,T 32.6 2.31 24.39 5.3 1.64.3 1.61.3 4.44 17.86.25.81 Empl,N 7.84 24.4 13.71 1.36 8.71.2 3.4.18 4.24 27.3.4.16 Cons 1.45 19.39 31.12 8.47 3.53.1 1.9.8 27.7 6.37.1.5 Inv 7.61 3.66 9.6 64.27 5.6.4 5.44.16 1.64 2.27.3.2 Int. rate 3.4 14.35 5.26 7.44 2.94.1 2.98.83 12.97 4.66.1.12 Inf 2.14 6.8 37.79 1.1 32.43.1 2.1.56 7.63 1.27.1.6 Exch. rate.68 2.36 7.79.57 5.94.2.25 5.72 76.14.33.2 2

two panels report the responses of aggregate employment and unemployment. A positive financial wealth shock increases entrepreneurs net worth in the tradable sector. On one hand, in the tradable sector, the rise in net worth pushes down the external finance premium, leading entrepreneurs to increase their demand for capital. However, the rise in demand for capital is not accompanied by a rise in demand for labour (although labour demand rises in the initial periods). Instead, entrepreneurs in the tradable sector substitute labour services with capital, and the demand for labour services declines. Hiring rate in in the tradable sector declines after the initial rise, leading the decline in employment. On the other hand, in the non-tradable sector, the hiring rate and employment rise. This is because the rise in capital demand from the tradable sector push up the capital prices, forcing the entrepreneurs in the non-tradable sector to face a higher leverage. Risk premium rises significantly in the non-tradable sector given that the value of elasticity of external finance is very high χ N =.22. The demand for capital drops. Entrepreneurs in the non-tradable sector substitute capital with labour, thus the demand for labor rises in the non-tradable sector. The rise in hiring rate in the non-tradable sector not only absorbs the unemployed workers from the non-tradable sector, but also attracts unemployed workers in the tradable sector. Both unemployment rates in the tradable and non-tradable sectors drop, leading a decline in aggregate unemployment rate. Figure 4 shows the response of the model to a positive technology shock in the tradable sector. On the one hand, output in the tradable sector rises after the shock. Different from the case with the financial wealth shock, the rise in output demands more labour services instead of capital. Hiring rate rises and the tradable sector employs more workers. On the other hand, the rise in labour demand drives up wages, leading a decline in labour demand in the non-tradable sector. More unemployed workers in the non-tradable sector moves to the tradable sector to look for jobs, causing the initial rise in unemployment rate in the tradable sector. The movement in the aggregate unemployment rate is mitigated by the fact that the decline in employment in the non-tradable sector partly cancels out the rise in the tradable sector.. 6 Conclusions Are sector-specific shocks important in shaping unemployment fluctuations in the Canadian labour market? The analysis of the paper suggests that they are. In this paper I introduce a segmented labour market structure into a small open economy model with financial and labour market frictions. Estimation results suggest that there are a lot of heterogeneity across sectors: compared to the non-tradable sector, prices are more rigid but wages are more flexible in the tradable sector, and external finance costs are less responsive to firms balance-sheet position. In addition, shocks are different at the sectoral level. The technology shock is more persistence in the non-tradable sector, and it accounts for almost 3 per cent of the unemployment fluctuations in the Canadian labour market. Financial wealth shocks in both tradable and non-tradable sectors contribute significantly to the movements in unemployment. Together, they explain about 25 per cent of the variations in unemployment. 21