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Labour and Product Market Reforms in General Equilibrium - Simulation Results Using a DGE Model of the Finnish Economy Juha Kilponen Bank of Finland
Antti Ripatti Bank of Finland
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Preliminary Draft February 2, 2005
Abstract
Using DGE model of the Finnish Economy (Aino model) we study the response of the economy to the reforms both in labour and in product markets. The reforms are two-fold. We assume that the wage mark-up, ie monopoly power of the wages setters is gradually reduced by 4 percentage points. At the same time, the degree of competition, ie the price margins, are exogenously reduced by 2 percentage points. These reforms imply a very favourable outcome of the economy. Both consumption and labour supply will permanently increase and the reforms are welfare enhancing. The public balances will improve giving room for 1.5 percentage point cut in income taxes. Our simulation exercises clearly demonstrate that such reforms may help in financing the future fiscal burden of ageing population.
Contents
1 Introduction
2 Consumers 2.1 General features . . . . . 2.2 Population dynamics . . 2.3 Preferences . . . . . . . 2.4 Aggregate labour markets 2.5 Consumption . . . . . .
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Aino model is a result of joint project by Juha Kilponen, Mika Kuismanen (ECB), Antti Ripatti and Jouko Vilmunen. We are also indebted to Juha Tarkka for plentiful of intensive discussions and guidance during the various stages of the model development project. We thank Jouko Vilmunen for useful comments on earlier versions of this manuscript. The usual disclaimer applies. Correspondence to
[email protected] or Bank of Finland, PO Box 160, FIN-00101 Helsinki, FINLAND.
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2.5.1 2.5.2 2.5.3 2.5.4
Assets . . . . . . . . . . Consumption of retirees Consumption of workers Wealth distribution . . .
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3 Public sector,pension fund and fiscal rule 15 3.0.5 Monetary policy . . . . . . . . . . . . . . . . . . . . . . . 18 3.1 Calibration of demand side . . . . . . . . . . . . . . . . . . . . . . 18
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4 Firms and Technologies 4.1 Domestic intermediate goods producer 4.2 Capital rental firms . . . . . . . . . . 4.3 Domestic retailers . . . . . . . . . . . 4.4 Exporter . . . . . . . . . . . . . . . . 4.5 Importing Firms . . . . . . . . . . . . 4.5.1 Aggregator . . . . . . . . . . 4.5.2 Foreign importers . . . . . . . 4.6 Parameter Values . . . . . . . . . . .
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5 Market Equilibrium
6 Product and Labour Market Competition in Finland 6.1 Estimation of the Mark-ups . . . . . . . . . . . . . 6.2 Simulation results . . . . . . . . . . . . . . . . . . 6.2.1 Labor market reforms . . . . . . . . . . . 6.2.2 Product and labour market reforms . . . . . 6.3 Sensitivity analysis . . . . . . . . . . . . . . . . . 7 Conclusions References
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1 Introduction
The future challenges in the Finnish economic policy are closely connected with fiscal policy, demo-graphic ageing and changes in production technology and technological development in general. For in-stance, demographic ageing will affect medium- and long-term macroeconomic development by affecting households’ decisions on consumption and labour supply, and, consequently, by affecting household wealth accumulation. It will additionally influence the distribution of wealth between generations. It will also lead to increased expenditure on social welfare and health. To the extent these services are funded out of the public purse, the growth in the proportion of elderly people will increase the tax burden on the workingage population and the public sector’s share of the national economy. If, in such a situation, the costs of servicing general government debt are also large, this will further restrict the scope for the active use of fiscal policy for short-term stabilisation
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and long-term growth objectives. At its worst, the ageing of the population could threaten the sustainability of public finances. If other factors remain unchanged, an ageing population will reduce labour supply across the country as a whole, and this in turn will be re-flected before long in rising wage levels, thus adversely affecting the international competitiveness of the economy. Demographic aging can also decisively alter the impact of monetary and fiscal policy on macroeconomic equilibrium. The purpose of this paper is to provide a quantitative view how some competitiveness policies as set up by Lisbon strategy can influence to public finances. In particular, we examine how the increase in competition both in the products markets and in the labour markets affect public finances. In preparing quantitative results we use recently developed DGE model of the Finnish economy, Aino. The model contains exogenously given mark-up in the domestic goods markets. This mark-up is given by the time-varying elasticity of substitution of different product brands. The mark-up temporarily varies also due to Calvo-type price rigidities. Similar structure holds for labour markets as well. Households have monopoly power with respect to their labour effort. The elasticity of substitution between various types of labour input gives the degree of competition and essential part of the mark-up. This elasticity of substitution is time varying. The model’s public sector is rich in terms of having various distortionary taxes. These include direct taxes on labour and capital and indirect taxes on consumption. Model economy is inhabited by two kinds of households: workers and retirees. The pension system is partly PAYG, in which pensions are transfers from workers to retirees. Since the model is new and, therefore, we are uncertain of the model properties, we put emphasis of the robustness of the results in terms of various parameter choices. Similar exercise for aggregated Europe has been done by Bayoumi, Laxton and Pesenti (2004a) and applied to Danish economy by IMF (2004) using a model variant of GEM (Bayoumi, Laxton, Faruqee, Hunt, Karam, Lee, Rebucci and Tchakarov 2004b). Their results are qualitatively similar to ours. However, some differences arise from the fact that unlike the GEM model, the Aino model has distortionary taxes. Aino model has already been used to study the effects of pure product market reforms in Bank of Finland (2004). In this paper, we extend the analysis with labour market reforms and provide sensitivity analysis. According to our simulation results the reforms that increase competition both in product and labour markets are welfare-enhancing. Both labour effort and consumption increase permanently. However, increasing competition is associated with an initial decline in private consumption. This is mainly due to the wealth effect caused by the temporary reduction in profits. In the balanced growth path the effect is, however, clearly positive. Employment increases over 1.5 per cent. Welfare improves almost as much when measured as consumption units. Public deficit is closed by a rigid income tax rule. This implies almost one percentage point decline both in income taxes and pension contribution rate. These are effects of 2 and 4 percentage point reductions in product and labour market mark-ups respectively. The effects of each reform are about the same size in terms of welfare equalising consumption. In order to check the robustness of these results, we experiment with changing some of the key structural parameters of the model. The results appear most sensitive to changes in elasticity of substitution between consumption 3
2 Consumers 2.1 General features
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and leisure. This is a crucial parameter affecting, not only the steady state level of consumption, but also on Frisch elasticity of labour supply. Rest of the paper is organised as follows. Sections 2–5 set up the model. Section 6 presents the simulation experiment in detail and discusses the results. The final section concludes.
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In Aino, in the spirit of general equilibrium theory, consumers make optimal decisions on consumption and labour supply. The theory does not describe any particular household, but only what happens on average. As is typical in modern macroeconomic models, consumers in Aino model seek to hold their life-cycle consumption as stable as possible. Consumers are viewed as being free from periodic credit constraints, and consumption decisions are thus neutral as regards risk considerations. Consumption decisions are, in contrast, influenced by household’s discounted wealth over their lifespan, ie, in addition to financial assets, by the expected present value of future labour income and income transfers. This life-cycle, or permanent income feature of households’ consumption behaviour loosens the relationship between consumption and current income. Consumers are assumed to try to infer or estimate by how much permanent or life-cycle income changes after a change in (current) income. Consequently, transitory changes in income will have only a small effect on their current consumption, whereas more persistent and, in the limit, permanent changes in income will change current consumption by a sizable amount. Individuals finite life-cycle consists of two distinct periods that are separated to the period of active working age and ”retirement”, as in Gertler’s (1999). As individuals live through these two distinct stages, they marginal propensities to consume and labour supply are affected by conditional retirement probability and conditional probability of death, as well as the fact that ”retirees” productivity is assumed to be lower than those of active working age. Individuals at active working age take account of their possible future retirement in their decisions on consumption and labour supply, and the constraints that become operative once they retire. In particular, the likelihood that the worker may lose part of his labour income due to retirement, induces her to discount the future income stream at higher rate than otherwise. This reduces consumption and increases saving. In this sense, active working age population saves for retirement. Similarly, finite lifetime makes the worker value the future less relative to present, as compared to infinite horizon case. The planning horizon of pensioners is shorter than active working age indviduals due to the constant periodic probability of death. Therefore, in the model, pensioners’ propensity to consume out of wealth is greater than that of the active working-age population. Under these assumptions, increased public consumption, financed eg by central government debt, will stimulate private consumption demand in the short term. Consumers will take into account the higher future taxes that will result from in4
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creased public consumption by increasing their savings in the medium term. The short-term expansionary effect of fiscal policy depends fundamentally on households’ saving propensity. The stronger household saving responds to changes in real interest rates, the weaker will the expansionary effect of fiscal policy be. Moreover, consumer heterogeneity means that higher income transfers to retirees boosts consumer demand, because the retired are more ready to consume than the working-age population. However, this has direct implications for labour supply, particularly when the increases in social security expenditure are financed by higher taxes. Increasing social security expenditure makes pensioners better off, but the long-term effect is to slow capital formation and hence weaken the economy’s production potential. In addition to these basic features of Gertler’s (1999) model few extensions have been made. First, we allow for distortionary taxes. Second, the labour markets are monopolistic and there are nominal rigidities that arise from Calvo type wage contracts. Third, individuals receive transfers from both the public sector (the state) as well as from pension funds. In modelling transfers, we have followed the general features of the transfers system in national accounts. Finally, Aino model’s supply side is rich and based on CES -production technology with with factor augmentation in the underlying technological progress. In Gertler (1999), the model is closed assuming competitive markets and Cobb-Douglas technology.
2.2 Population dynamics
Consumers are assumed to be borne as an active working age individual. Conditional on being an active worker in the current period, the probability of remaining one in the next period is ! while the probability of retiring is 1 ; ! . These transition probabilities are independent on individuals’ employment tenure, so that average tenure of active working age is 1;1 ! . Once an individual has retired she is facing a constant periodic probability of death (1 ; ). Given that the survival probability ( ) is assumed to be independent of retirement tenure, the average retirement period is 1 ! 1; . Regarding population dynamics, it is assumed that in each period (1 ; 1+nt )Nt new active working age individuals, are born. Given constant probabilities of retirement and death and that cohorts are large, retiree population (N tr ) then evolves according to
Ntr+1 = (1 ; !)Nt + Ntr
(2.1)
With some manipulations, it can be shown that ratio of retirees to whole population evolves according to
r 't NNt = 1 ;^ ! + 't^;1 (2.2) t Nt Nt ^t Nt =Nt;1. In the steady state, where N^t = N^ , and 't = ', this ratio where N becomes
' = 1^ ; ! : N ;
(2.3)
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2.3 Preferences
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In the steady state, active working age population and the retirees grow at the ag^ . Allthough we can allow for time-varying degregate population growth rate N mographic structure in general, we keep demographic structure unchanged in the ^t = N: ^ following simulations. Thus, in what follows, we assume that N
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Stochastic intertemporal decision problems are often solved recursively by constructing a sequence of value functions and decision rules. In order to obtain closed form decision rules, one needs to restrict attention to linear forms of value functions and specific type of uncertainty. Perhaps the most exploited case is the one where the agents face random interest rates (multiplicative uncertainty) but no uncertainty regarding endowments (additive uncertainty). Under these assumptions, agents preferences admit non-linearity across time and states of nature. In many situations, however, agents not only face uncertainty regarding, say, interest rate fluctuations, but also regarding endowments. In the framework of Von-Neumann and Morgenstern (VNM) utility theory, the general case of random interest rates with random endowments does not admit a closed-form solution, unless the agents preferences are linear accross the states of nature as well as through time. However, relaxing VNM axiom that agents are indifferent to the timing of the resolution of uncertainty, a much broader class of intertemporal stochastic decision rules can be obtained1. In particular, it is possible to present an intertemporal decision rule, where the decision can be broken into one regarding current decision, say, over consumption, and the one regarding the whole future sequence. Separation of decisions between current and future sequences is crucial since the decision rules can be constructed without contingency on entire history of the past decisions. This means that one can apply the maximum principle of dynamic programming to decision problems with recursive structure. Another important aspect is that a special class of so called recursive preferences, originally introduced by Epstein and Zin (1989) allows intertemporal elasticity of substitution and the relative coefficient of risk aversion to be represented by two different parameters2 . In the conventional time-additive and time-separable von Neuman Morgensterns expected utility preferences, one is restricted to present the individuals’ risk aversion parameter equal to the reciprocal of her elasticity of intertemporal substitution parameter. Risk aversion describes, say, consumers reluctance to substitute consumption across states of the world, where as the elasticity of intertemporal substitution describes the consumers willingness to substitute consumption across time. There is no particular reason why these two should be connected to each other (see for instance Hall (1988)). One popular parametric example of recursive preferences consists of the con1
For details, see Kreps and Porteus (1978,1979) In general, recursive preferences are defined in the nonstochastic environment by the assumption that, say, consumption ranking over future decisions is independent of the ranking over consumption bundles. These preferences can also capture the behavior where individuals prefer either early, or late resolution of uncertainty (for details, see for instance Weil (1990) and Farmer (1990)). 2
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stant elasticity aggregator:
Vt = fu(Ct)gc + fEt (Vt+1 )g ] c (2.4) The parameter c < 1 captures an intertemporal curvature of the preferences, while the parameter 1 captures the decision maker’s attitude toward risk. Commonly 1 ; is refered to as the coefficient of relative risk aversion. This parameter deter1
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c
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mines how an agent divides her current wealth across the available financial assets at any point of time. The special case of = 1 corresponds to a type of risk neutrality, where the agents are indifferent regarding risk, but still maintaining a non-trivial preference for the time at which consumption occurs (cf. Farmer (1990)).3 This special is analytically tractable, since it generates linear decision rules even with (idiosyncratic risk) to income, asset return and length of life. This is what we now assume4. As a result, special class of recursive preferences applied in AINO model can be summarised as follows:
Vtz = (Ctz )v (1 ; ltz )1;v ]c + z Et (Vt+1 ji)]c
1c
(2.5)
where
Et (Vt+1jw) = !Vtw+1 + (1 ; !)Vtr+1 w = (2.6) r r Et(Vt+1 jr) = Vt+1 = : (2.7) Vtz denotes an individual’s value function, and z = w r indicates whether the individual is at active working age w or retired r . C tz is consumption and 1 ; ltz denotes leisure. Thus, ltz denotes the fraction of time allocated to work. v denotes intratemporal elasticity of substitution between leisure and consumption, while c is curvature parameter which introduces consumption smoothing, as it captures the intertemporal curvature of the preferences. The retirees effective discount factor r is adjusted to take into account periodic probability of death, as finite lives implies effectively a shorter planning horizon. The willingness to smooth consumption over time implies a finite (constant) intertemporal elasticity of substitution = Ct =Ct+1 ) 1 ; @ log( @ log Rt+1 = 1;c . In the current setup of the model, perfect annuities market are introduced in order to eliminate the impact of uncertainty about time of death: Remaining wealth that retirees hold at the time of death are invested in mutual fund which in turn invests them in available financial assets at each period of time. Those surviving to the following period receive a return that is proportional to his contribution to the fund. For instance, if Rt is the gross return per unit invested by the fund, the gross return for a surviving retirees is Rt = at time t: Active working age individual, in turn, faces a potential risk of a decline in wage income. However, since individual’s preferences are over the mean of next period’s value function, and thus individuals care only the first moment of expected income, only a desire the smooth consumpion over time affects on consumption pattern in the face of idiosyncratic income 3 Since c is bounded above by 1, it follows that the risk-neutral decision maker prefer late resolution of uncertainty (for details see Kreps and Porteus (1978)). 4 Viitanen (2002) has estimated utility functions of the type using aggretate data on consumption and different assets for Finland.
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risk. Finally, a worker forms a certainty equivalent of his random utility as shown in equation (2.6). This implies that the worker takes into account the constraints that becomes operative after she retires.
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2.4 Aggregate labour markets
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In Aino, labour supply is determined endogenously via consumers’ optimal decisions on consumption and labour supply. Each individual has one unit of time which he may use to work or to enjoy leisure. Retirees as well as those at active working age may participate in the labour markets, yet retirees are less productive than active working age population. In addition, the labour market is imperfectly competitive due to the wage setting power of active working age population. It is assumed that those at active working age supply differentiated types of labour to the production sites, but their decisions are independent on specific labour and wage conditions at different locations. Workers pricing power at the labour markets mean that real wages will settle in the long-run at a level above the competitive equilibrium. Moreover, in the short term, real wages can depart from optimal level, due to the slow adjustment of nominal wages, reflecting the long duration and over-lapping nature of wage contracts. Following now standard approach in the literature it is assumed that only a fraction of workers can re-set their wage in each period. Fraction of workers that can re-optimise in each period is chosen randomly. Exogenous probabity q determines how often randomly chosen worker is allowed to re-set her wage. For those not being able to optimise in period t, the wage is adjusted using the steady state growth rate of wages. This steady state growth rate is denoted by w g: 5 More formally, behavior of aggregate wages is characterised by the following two equations
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WP (1 ; v) PtcCtw = 1 ; tWS t ; tt vL(1 ; 't)Nt ; Lwt ] q) wg E W + (1 ; q) wg W Wt = (1 +(1; t t +1 (1 ; q)2wg2) (1 + (1 ; q)2wg2) t;1
Wt =
(2.8) (2.9)
2 q (1 ; (1 ; q ) w g + (1 + (1 ; q)2 wg2)) Wt (2.10) where Ctw is consumption of active working age population and P tc is consumer price index, to be determined later on, L is inverse of wage mark-up, Nt is popWS ulation and Lw t denotes labour demand of active working age population. t t de-
notes labour income tax rate of working age population and t WP t denotes pension contribution rate. Equation for optimal wage W t is directly derived from active working-age individual’s intratemporal decision regarding labour supply, and taking into account individual labour demand constraint (2.12). Equation 2.9 is derived by applying the wage setting model of Rotemberg (1982). 5
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It would be easy to extend the model such that to allow partial or dynamic indexation of wages.
Given that active working age individuals and retirees have different productivities, we define aggregate effective labour supply index Lt as
Lt = Lwt + Lrt
(2.11)
(1 ; v) PtcCtr Lrt = 'Nt ; v W (1 ; tRS ) t
t
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Here 2 (0 1) denotes the productivity of a unit of labour supplied by a retiree. Labour demand of active working age population L w t is derived from (2.11) by assuming that retirees are always on their labour supply curve at prevailing wage (W ), and that domestic intermediate goods producer 6 is always on its labour demand curve7 . Retirees labour supply is determined by corresponding first order condition, written as (2.13)
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Ctr denotes retirees consumption and ' is a fraction of retireed population as in
(2.2). In solving the model’s steady state version, above labour demand/supply indices are made stationary by scaling them with N t while wage equations are scaled by labour augmenting technical change Lt and price level Pt to be determined later on. In modelling labour markets, we have not been particularly interested in exact institutional setup of the wage setting process in Finland. In the context of dynamic general equilibrium this would be formiddable task. This is due to the fact that the wage setting process in Finland is best characterised by a centralised wage bargaining where the confederations internalise, not only the general price level effects, but also the government’s budget constraint. Typically the so called monopoly union models fit to the situation where wage negotiations take place at industry level without internalisation of the price level effects nor government’s budget constraint. While this kind of modelling approaches have recently been developed in the context of dynamic general equilibrium models (see for instance Maffezoli 6
See section 4 for details. Each intermediate goods firm uses CES combination of differentiated types of labour. Workers labour demand index is given by 7
L = w t
where
Z
1
0
L (j ) dj w t
1
L
L
Lwt (j ) denotes the demand of type j worker.
Cost minimisation in the intermediate goods
producing sector implies that the demand of worker type j depends upon relative wage and aggregate labour demand index as follows:
; W t (j ) L (j ) = W (2.12) Lwt t where = 1+1 L is elasticity of substitution among differentiated labour inputs. W t (j ) denotes wage paid to worker type j and the wage index W is defined as w t
Wt =
Z
1
0
Wt (j )
L L +1
dj
1+LL
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2.5 Consumption
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2001, Ardagna 2002, ) , apparently they do not fit well to institutional setup in Finland. In Finland, the wage negotiations are typically centralised. Moreover, as it is well known by the arguments of Calmfors and Driffill (1988) centralised wage setting typically lead into outcomes that are closer to the competitive equilibrium outcomes when compared to decentralised wage setting systems. In Aino model, the distance of labour market’s equilibrium from competitive outcome in the longrun can be related with inverse of parameter L : This parameter can be thought of as capturing essential ”non-competitive” features of the wage setting process in Finland. Parameter q in turn can be calibrated such as to capture the fact that centralised wage contracts are typically signed for long-periods of time.
Both retirees and active working age individuals consume and save out of income derived from financial assets, labour and transfers received from the public sector. Given specific assumptions regarding preferences, population dynamics and constant periodic probabilities of retirement and death, there is no need to keep track of how assets and consumption are distributed among retirees and active working age population. Since marginal propensities to consume are the same for each individuals within the two groups, one can simply aggregate by summing accross individuals within the groups. Yet, since marginal propensities to consume out of wealth differ between the two groups, we must keep track on how financial assets are distributed between active working age population and retirees: aggregate private consumption, which is a sum of consumption of active working age individuals and retirees will depend upon evolution of this wealth distribution
2.5.1 Assets
There are different financial assets available for consumers : domestic bonds (ASt and APt ), issued by the public sector, foreign bonds A W t and stocks issued by F the domestic firms At . The domestic one period bonds pay a nominal return r t while the gross return of stocks is determined according to the profits of the firms in the model8 . Foreign bonds pay a return rtF : There is an exogenously determined risk-premium between domestic bonds and stocks issued by the domestic firms. Thus, we define
rtiAit = (1 + (1 ; tSt )rt)(ASt;1 + APt;1 ) + (1 + rtD )AFt + (1 + rtF )StAWt (2.14) where St is nominal exchange rate, rt denotes short-term nominal interest rate and rtF denotes corresponding foreign short term interest rate. tSt denotes tax rate at source . The share price, AFt is the nominal price (ex-dividend) of one equity share in period t. The factor defining the gross return of stocks is the profits of the firms Dt in the model. This gross return is defined as follows 1 + rtD = AFt+1 + (1 ; tKt ) Dt ]=AFt (2.15) 8
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See section 4 for details
where tK t denotes corporate tax rate. Profits, in turn are given as9
(2.16)
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Dt = Pt Yt ; WtF Lt ; Rt Kt (intermediate goods producers + Rt Kt ; PtI It (capital rental firm) + PtX Xt ; PtMRMtR ; PtX YtX (exporter) + (1 ; tCt )PtC CtT ; PtMC MtC ; Pt YtC (consumption goods retailer) + PtI ItT ; PtMI MtI ; PtYtI (Capital goods retailer)
This generates an important wealth channel in the model, making consumption and labour supply react directly to changes in the firms profits and profit margins.
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2.5.2 Consumption of retirees
A periodic budget constraint of a retiree born at time j and retireed at time k , and who survive at least until t + 1 is given by
rPj rWj rFj ArSj t+1 + At+1 + St+1 At+1 + At+2
rPj rWj F D rFj = 1 Rt (ArSj t + At ) + Rt St+1 At + Rt At+1 ]
rj rjk C rj + Wt (1 ; tRS t ) lt + Tt ; Pt Ct
(2.17) (2.18)
where Rth denotes after tax gross rate of return of corresponding asset:
Rt 1 + (1 ; tS )rt RtF = (1 + rtF ) RtD = 1 + rtD
A retiree chooses consumption and asset accumulation by maximising (2.5) subject to (2.18). Transfers Ttrjk are assumed to be distributed equally among retirees 10 . In the current setup of the model they are also indepent on retirees age or income. The retirees maximisation problem can be turned into dynamic programming problem, where consumption-saving decision is separable from the portfolio optimisation11. In order to find optimal consumption path, we thus simplify budget constraint into
rjk rjk rjk RS C rjk Arjk t+1 = (Rt = ) At + (1 ; tt )Wt Lt + Tt ; Pt Ct
(2.19)
where
Rt
J X = wrjk h=1
J X rjk = 1: h wht ht;1 Rt ;1 h=1
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See section ”Firms and Techology” for more details. Effectively in the model we separate between taxable and non taxable tranfers. Moreover transfers are distributed by the government or by the pension funds. Consequently, we define 10
P RT + T SRT ) + T SRNT : TtR (1 ; tRS t t t )(Tt 11
This is due to the fact that time and risk aggregators are linear homogenous.
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Ctr = t t Rt Art + Htr + Str ]
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rjk are chosen optimally before the realisation of The weights of single assets wht ;1 the state of the nature at period t: Since agents only care about mean of the next periods value function and that uncertainty is purely multiplicative, their maximisation problem yields standard first order conditions for consumption, labour and asset demands. First, it can be shown that total consumption by retirees yields (2.20)
where Htr and Str denotes discounted after tax values of labour income and transfers and t t is retirees marginal propensity to consume out of wealth: (2.21)
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Htr+1 r+ Htr = (1 ; tRS ) W L t t ^r t Lt+1 Rt+1 = r Str = Ttr + ^ Tt+1 . NRt+1 =
(2.22)
^ and total social security payments Since pensioner population grows at gross rate N ^ enters into discount factor. Discount factor are distributed equally among them, N of human wealth is similarly augmented with gross growth rate of retirees labour ^ rt+1 . In the steady state L^ rt+1 = L^ r = N: ^ supply L Retirees marginal propensity to consume out of wealth t t evolves according to following non-linear difference equation:
P^ c (1 ; tRS t ) t t =v = 1 ; ^t+1 (1 RS Wt+1 ; tt+1 )
!(1;v)
(Rt+1 =P^tc+1);1 t
t
t+1 t+1
(2.23)
^ t+1 Wt+1=Wt : The retirees marginal propensity where P^tc+1 Ptc+1 =Ptc and W to consume varies with expected real interest rate Rt+1 as well as with expected changes in real net wage income. As in standard Yaari (1965) and Blanchard (1985) models, likelihood of death (1 ; ) in (2.23) raises the retirees’ marginal propensity to consume. This can be seen easily by considering a case of logarithmic preferences at the limit where ! 1: In this case
=v = 1 ;
(2.24)
Notice that marginal propensity to consume depends also on intra-temporal substition v . Optimal consumption plan given by the equations 2.20-2.23, can then be combined with optimisation of portfolio weights w ht;1 : Taking the first order conditions of corresponding Euler equation with respect to portfolio weights gives us that
W^ t+1 (1 ; tRS t+1 ) c ^ Pt+1 (1 ; tRS t )
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!(1;v)c
Rt+1 P^tc+1
!;1
Rth+1 Ctr+1 =0 P^tc+1 Ctr
(2.25)
Since this condition must hold for every single asset, we have that in the deterministic version of the model,
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rtD rt = (1 ; ts) 1 + rt = 1 + rtF SSt+1 t
where the latter is a standard UIP condition.
2.5.3 Consumption of workers
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As regards to workers, a budget constraint of active working age population, born at time s is given by
ws WS WP ws ws C ws Aws t+1 Rt At + (1 ; tt ; tt )Wt Lt + Tt ; Pt Ct
(2.26)
and where Ttws denotes net transfers for the workers12 . A worker chooses consumption, labour supply and asset accumulation by maximising (2.5) subject to (2.26) and to the constraints that become operative once she retires. Intertemporal maximisation gives rise to a rather complicated Euler equation
Ctws
Pc
2
(1;v) t+1 Wt WS ; tWP )(1;v) R =P^ c (1 ; tt t+1 t+1 t+1 t PtcWt+1
= 4!Ctws+1
1;
1
WP (1 ; tWS t+1 ; tt+1 )
+ (1 ; !) ( t+1 ); Ctrs+1 1
;
!
1
(2.27)
1 ; tRS t+1
!1; 3 5
where t+1 > 1 is the ratio of marginal propensity to consume of the retirees to that of the active working age individuals. Moreover,
t+1 = !
1
1;
WP (1 ; tWS t+1 ; tt+1 )
1
; + (1 ; !) t1+1
1 ; 1 ; tRS t+1
!1;
(2.28)
Total consumption by active working age individuals can be expressed somewhat more conveniently in terms of consumption function:
Ctw = tRt Awt + Htw + Stw ] (2.29) where t is a marginal propensity to consume of active working age individuals. As in the case of retirees, this marginal propensity to consume out of wealth is a non-linear first order difference equation, which takes a form
t = 1 ; v 12
;
WP Wt P c 1 ; tWS t ; tt t+1 c Wt+1 Pt
!(1;v)
Rt+1 =P^tc+1 t+1
;1
t
t+1 (2.30)
Ttwj (1 ; tWt+1S ; tWt+1P )TtSW Tj + TtSW NTj :
13
Htw in (2.29) is a discounted sum of the wage bill of active working age individuals, i.e. Lt+ Wt+ : Stw is the sum across workers alive at t of the capitalised value of
social security.. Both of these measures take into account corresponding discounted values at the time of retirement. Formally,
Htw =
1 S WP 1;tW t+1 ;tt+1
1;
L^ wt+1 Rt+1 t+1
;
Htw+1
1; 1
+
(1 ; !) ( t+1 )
1
(1; tRS +1 )
1;
r Lwt Ht0+1
T
!
Rt+1 t+1
(2.31)
WP
+ 1 ; tWS Wt Lwt t ; tt 1; 1; 1; 1 1 1 w ! (1 ; ! ) ( ) N Str+10 W S W P t +1 RS t (1; t+1 ) 1; t+1 ; t+1 ) w w w St = Tt + ^ St+1 + Rt+1 t+1 NRt+1 t+1 t
DR AF
t
0 and where Str+1
'NSt t r
+1 +1
(2.32)
is a value of total income transfers including pensions per
Hr
r rt+1 denotes a value of human wealth per beneficiary at time t + 1 and Ht0+1 Lt+1 0 r working pensioner at time t + 1. Ht+1 is thus a measure of the aggregate value of human wealth during the retirement, but scaled by the number of working retirees. Presence of t+1 in the denominator of (2.31)-(2.32) shows how workers discount future income streams at a higher rate than at which the government can borrow, Rt : t+1 varies positively with the ratio of retirees marginal propensity to consume to an active working age individual’s marginal propensity to consume. It depends also positively on retirement probability and the the tax rates. This can be seen most easily by looking at the steady state value of in the special case where retirees and active working age inviduals face the same tax rate t. Then,
=
1
(1 ; t)
1;
! + (1 ; !) 1; ] 1
(2.33)
Enlarged discount rate of active working age population reduces the value of human wealth and social security relative to infinite horizon case. This in turn has a tendency to reduce working age individual’s consumption and increase saving. ^ augments the discount rate of the capitalised value of social security A factor N for the workers because with finite lives, a share of total social security entitlements of those currently alive declines over time as population grows. By similar ^ wt+1 enters into discount factor of human wealth13. Morever, notice that argument L in the special case with logarithmic preferences ( ! 1) marginal propensity to consume is constant, and it depends only on discount rate and intra-temporal substitution v:
t = 1 ; v 13
14
(2.34)
In case of non-stationary demographics structure, these equation need to be modified slightly.
2.5.4 Wealth distribution
Ar
T
Finally, let ft+1 Att+1 be a share of financial assets held by the retirees. After +1 some rather tedious algebra it can be shown that retirees share of financial wealth evolves according to14
ft+1=! = ft (1 ; t t = )RtAt =At+1 PS r r r r + (1 ; t ) WtLt +A Tt ; t t (St + Ht ) + (1 ;! !) t+1
(2.38)
Finally, aggregate consumption is obtained simply by summing up (2.20) and Ar (2.29), using ft+1 Att+1 and remembering that all the assets are eventually held +1 by the domestic consumers:
DR AF
Ct = t
1 ; ft
Rt At + Htw + Stw ] + t ft Rt At + Htr + Str ]
(2.39)
Consequently, transfers influence markedly on the evolution of the distribution of wealth, which in turn influences on aggregate consumption. Labour income taxes influence on consumption directly via the measures of human wealth and income transfers, but also indirectly through its effect on labour supply and distribution of assets between retirees and active working age population. Given that working age population discounts fugure income streams at higher rate than at which goverment can borrow, fiscal policy that postpones taxes into the future boosts up consumption in the short-run.
3 Public sector,pension fund and fiscal rule
The general government (public sector) is divided into to sectors, labeled as state RS and pension funds. The state collects taxes from labour income at rate t WS t tt C S capital gains at rate tFS t and consumption at rate tt : The state’s consumption Ct is devided into two components, where market goods C tSF are produced by the consumption goods retailer, while non-market goods Y tS are produced by the public 14
To see this, notice that retirees total assets evolve according to
r r c r w Art+1 = Rt Art + (1 ; tRS t )Wt Lt + Tt ; Pt Ct + (1 ; ! )At+1jt whereAw t+1jt denotes financial wealth accumulated by period t workers for period t + 1:
(2.35)
Awt+1jt Rt Awt + (1 ; tWt S ; tWt P )Wt Lwt + TtSW T ] + TtSW NT ; Ptc Ctw (2.36) A fraction of (1; ! ) of this accumulated wealth qualifies as retirees wealth, since this is a fraction of active working age population that retirees at the end of period t. The rest, ! of this financial wealth is held by the workers from period t to t + 1: Consequently, active working age individual’s total financial assets evolve according to
Awt+1 = ! Rt Awt + (1 ; tWt S ; tWt P )Wt Lwt + TtW ; Ptc Ctw
(2.37)
15
sector itself, using a simple linear production technology
YtS = St LSt
(3.1)
; (ASt ; ASt;1 ) (net lending)
T
The state also pays both taxable and non-taxable income transfers both to working age and to retirees. Iaddition, it issues one period goverment bonds A St that pay a gross return Rt . Each period, following budget constraint is satisfied
DR AF
w RS r = tWS t Wt Lt + tt Wt Lt (income tax revenues) + tSt rt(ASt;1 + APt;1 ) (tax at source) + tKt t (corporate income tax revenues) + tCt PtC CtF (indirect taxes) + tFS t Wt Lt (firms’ social security contributions) + PtO YtG ; WtF tS LSt (profits of the state’s firm) ; PtC CtSF ; PtO YtS (government consumption) ; PtI ItS (government investment)
(3.2)
; Tt (total net transfers) ; rtASt;1 (interest payments) where Tt denotes total net transfers, defined as ; SWT RS PR ; SRT Tt 1 ; tWS Tt + tt Tt + 1 ; tRS + TtSWNT + TtSRNT + TtSEU + TtSP t t Tt (3.3)
Public sector revenues must be in harmony with the expenditure caused by public consumption and investment, income transfers and interest expenditure on public debt. This is ensured in the model by the use of a fiscal policy rule. This sets the labour income tax rate so as to ensure that the long-term budget contraint is satisfied. The fiscal policy rule largely determines how quickly tax rates respond to changes in the state of the economy. Thus adjustment is typically assumed to be slow. Formally the fiscal policy rule is written in the following format:
S S s
tWS t = (At ; At;1 )=Yt ; A (1 ; 1=Y^t )]
(3.4)
where Y^t YYt;t 1 denotes gross growth rate of private production:(A St ; ASt;1 )=Yt is fiscal deficit expressed as a share of private production and As is an exogenous debt target of the state, expressed as a share of public debt over private production. is fiscal rule adjustment parameter which controls the speed of adjustment of labour income tax rate to deviation of public debt from its long-term target and fiscal deficit. In principle, higher the value of more concerned the state is on balancing its budget15 . 15
See for instance Railavo (2004) for the discussion on alternative fiscal policy rules and their stability properties.
16
; (APt ; APt;1 ) (net lending)
T
Pension funds are taken out of the public sector and treated as a separate fund16 which transfers some of the income from the working-age population to the retired. The fund collects pension contributions from the private sector – from companies and employees. Since the pension fund is distinquished from the state, their operate in the model by having their own periodic budget constraint and budget balancing rule. The pension fund consumes CtP and invests ItP in each period, as well as distributes social security transfers including pensions to the retirees T PRt . It receives pension contributions from the private sector, as well as small transfers T tSP from the state. The pension fund also accumulates its financial assets A Pt that are assumed to be hold by the private sector. Each period, therefore, following periodic budget constraint holds for the pension fund:
DR AF
F G G = tFP t Wt Lt + L ] (social security contributions of employer) w SW + tWP t Wt Lt + Tt ] (social security contributions of employee) + TtSP (transfers from the state)
(3.5)
; TtPR (total transfers paid to retirees) ; PtO CtP ; PtI ItP (consumption and investments) ; rt APt;1 (interest payments)
SW denotes those transfers where tFP t is employer’s pension contribution rate T t from the state to workers that are treated as labour income, TtSP are transfers from the state to pension funds and finally T tPR denote pensions and other transfers from pension funds to retirees. These slight complications regarding treatment of income transfers arise from the fact that we want to mimic at least partly the actual transfers observed and accounted in the national accounts system. Consumption and investments of the pension funds are exogenously determined. Furthermore, it is assumed that in the long-run steady state pension fund can have some ”debt target”, which is eventually achieved by adjusting employeers (or employers) pension contribution rate accordingly. In the current version of the model, this ”pension contribution rule” follows the same logic as the fiscal rule. 16
Finnish statutory pension system is approximately 20 per cent funded. Otherwise functions as decentralised pay-as-you-go (PAYG) system. Pension funds are private but they are jointly liable for payment of pensions (eg in the case of insolvency). Beneficiaries may not influence to the management of funds or amount of savings, mainly due to the fact that contribution rates, etc, are administred. In national accounts, these funds are classified as a part of general government. Besides the statutory earnings-related pension scheme there is also a national pension scheme covering all citizens; and increasingly popular non-statutory pension schemes that are partly tax deductable. From the modelling point of view, we consider the funded part of the pension system as normal private savings and the PAYG part as a transfer from workers to pensioners. Hence, the ”pensions” — are treated as part of the social security transfers.
17
3.0.5 Monetary policy
3.1 Calibration of demand side
T
Monetary policy reflects Finland’s small share in euro area. According to capital key the share of Finnish economy is approximately 1.5 percent that of the euro area. Consequently the feedback from the Finnish economy to euro area level is very modest. A reasonable approximation is that the euro area policy rate is exogenous for Finnish economy and foreign exchange rates17 are fixed. Therefore, the model assumes that St = St;1 .
DR AF
Untill very recent applications of Bayesian estimation techniques to large-scale DGE models18 , many structural parameters in micro-founded models like Aino used to be calibrated or by using traditional GMM techniques. In the current version of Aino, many parameters in the supply side has been estimated using the GMM and cointegation techniques, while the demand side parameters has been largely calibrated. This is clearly somewhat unsatisfactory, given rapid development and availability of Bayesian estimation techniques. Nevevertheless, in the current version of the model, parameters affecting demographics has been calibrated such as to fit approximately demographich structure in the near future, where retirees share to whole population, here defined as 15 ; 74 years old is roughly 25 %. This has required to set periodic probability of retirement and death as given in table (1). Corresponding retirement and active working age periods are then roughly 12 and 48 years. Annual net growth rate of population has been set to :16%: These demographich assumptions reflect roughly the situation Finland is facing during the following decade. In order to fit the participation rates observed we have set the relative productivity of ”retirees” to be 33 % of that of active working age, while wage mark-up has been set to 25%: This wage mark-up is somewhat lower than that observed in Europe on average (30 %) Intra-temporal substitution has been set to 0:855 and inter-temporal elasticity of substitution has been set as high as :5. Both intra and inter-temporal substitution rates are on a high side, but has been necessary to in order to obtain reasonabe calibration of the steady state values of the model. In order to illustrate how the current version of Aino model meets the recent data, we use the data from 1995-2003 and calculate annual averages of several macro economic variables. The reason for not using longer time span is that Finland experienced major structural changes during the 1990s recession and we thus want to fit the balanced growth path of Aino closer to current economic environment. Table (2) summarises some relevant macro economic variables expressed either as a percentage of private production or in case of labour market and demographic variables, as a percentage of whole population. The model’s initial steady state In the data we approximate the currency basket S t according to export weights of the following countries: Germany, Italy, UK, USA, Sweden and Japan. See Ripatti and Viertola (2004) for details. 18 See for instance Smets and Wouters (2003a, 2003b,2003c). 17
18
v
! 1=L N^
Explanation Intra-temporal subsitution Inter-temporal substitution probability of surviving probability of remaining in active workforce relative productivity of retirees wage mark-up population growth rate, p.a.
Value
:855 :5 0:979836 0:99478 0:32 25% 0:16%
Method Calibrated Calibrated Calibrated Calibrated
T
Parameter
Calibrated Calibrated Calibrated
Table 1: Calibration of Demand Side
DR AF
reflects partially an expected demographic change in the near future. In particular, there is higher private consumption share, which shows up also in higher import share. In addition, statutory pension contibution rate is higher than in the data, reflecting an assumption of higher pensions during the following decade. % shares
Name
Variable
Private production(in efficiency units) Imports (% of priv.prod.) Exports (% of priv.prod.) Consumption (% of priv.prod.) Private consumption Public consumption Investment (% of priv.prod.) Private investment Public investment Employment rate Capital share in efficiency units Retirees (% share of tot. pop.) Income tax rate, % Pension contribution rate, %
Y M X C CH CG I I8 IG L K '
ws wp
The data 1995-2004
:193 44:6 55:6 103:6 72:4 31:3 27:5 23:3 4:0 58:2 2:57 :18 32 4:4
Steady-state
0:217 67:1 64:0 105:5 86:2 29:3 29:4 25:4 3:8 57:8 2:7 :25 32 6:6
Table 2: Steady state shares and the data
4 Firms and Technologies
The particular challenge for the component of Aino that describes corporate behaviour — ie the supply component — is to describe the major changes in the structure of the economy that occurred in the 1990s: eg the dramatic decline in the labour share, the rapid improvement in average capital productivity and the growth in price margins. Being a growth model, Aino has been built around the conventional assumption that economic growth depends ultimately on the efficiency and 19
DR AF
T
volume of labour input.19 Hence, the model does not explain the causes of technological development and hence growth in labour productivity. In Aino, the temporary sources of growth and slump can be of many different types. Capital-augmenting technological advances are important in explaining the 1990s phenomenon whereby, despite rapid growth in output, investment recovery was, historically speaking, slow. According to Aino, this was because considerably more output was extracted from the existing capital stock eg via the rearrangement of labour input. Moreover, changes in the structure of output correspond in the model to changes in the parameters describing technological development. In the 1990s, output growth was strongest in sectors that required little in the way of productive capital per se. The structure of Aino also makes it possible to take into account temporary changes in consumer preferences. Such changes can be seen in eg growing demand for domestic products relative to imported goods irrespective of any movements in relative prices. In Aino, the corporate sector comprises five imaginary firms. A key role is played by domestic producers of intermediate goods, who combine capital and labour inputs to produce domestic intermediate goods. Capital and labour inputs are technological complements in the production technology of these firms. Domestic producers of intermediate products operate in monopolistic product markets. Thus, they have pricing power in relation to their products. Such power is a consequence of the products’ imperfect substitutionability and is determined outside the model. The model assumes that not all firms are able to constantly reset their prices at the corresponding optimal level (Calvo pricing). Therefore, some prices are sticky and do not immediately adjust to the underlying flex price optima. The friction associated with pricing forces companies to factor in their pricing decisions perceptions of how they expect their cost factors — eg capital costs, pay costs, changes in production technology, competitive factors — to develop in the future. In the model, such things as anticipated future pay rises already affect current prices, factor demands and output volume. Domestic producers of intermediate products purchase their capital inputs (capital services) in a competitive capital market (from companies providing capital services) in which capital is freely for sale and transferable for use by other companies. An alternative to changes in the physical capital stock is to change the capacity utilisation rate. The cost here is that more intensive capital utilisation also speeds up capital depreciation. This leads before long to a need for more investment. Capital utilisation also causes other costs: interest costs must be paid to the capital financer, and building up the capital stock also requires time and physical resources. Because it takes time to build up the physical capital stock, when deciding on an investment companies must take into account what the economic operating environment will be like by the time the investment has matured into functioning production capacity. The optimal investment decisions in the real world described above together with the pricing feature make firms’ behaviour forward-looking. In this respect, Aino emphasises, in line with modern macroeconomic theory, the importance of expectations in the behaviour of economic agents. Taking expectations into account has a crucial effect on how Aino is used in making forecasts. This is because the 19
Technically speaking, long-term economic growth depends on the pace of development in labour-augmenting technology and the pace of growth in labour input.
20
DR AF
T
model’s outcome also fundamentally reflects an assessment of economic agents’ expectations.20 Domestic intermediate products are used in the production of final products. Companies producing consumer goods combine domestic and foreign intermediate product inputs. Capital goods and services producers and producers of goods and services for export also operate in a similar way. All three types of final producer operate in competitive product markets in which they take the market price for their products as given in their own decision-making. Thus, they only decide their own output volumes and the intermediate products they will use within the limits set by their production technology. Because of this, total imports depend on consumption, investment, exports and the relative prices of imports. In Aino, the impact of relative prices is estimated to be fairly strong. This means eg that if the prices of imported intermediate products (import prices) rise strongly relative to the price of the domestic intermediate product, the final producer will to a large degree substitute the imported input with domestic input. An exception to this is that in the manufacture of goods for export the domestic and foreign intermediate product inputs are rarely interchangeable, but rather complement each other. For example, the assembly of mobile phones requires Finnish know-how and imported parts. In contrast to many other models, Aino is consistent in respect of how different sectors’ internal input demand, prices and output volumes are interlinked. Nominal import prices are assumed to be sticky in a manner corresponding to domestic prices, ie Calvo pricing is applied here as well. It is also assumed that, in the short term, exchange rate pass-through to import prices is incomplete. This is due to the fact that some international companies price their products in accordance with demand in the specific market area. Table 3 serves as a road map to the supply side of the whole Aino model. The remaining of this section is organised as follows. We first introduce an aggregator that generates demand function for each intermediate goods producer and the timevarying degree of competition, ie mark-up. The key firm, domestic intermediate goods producer is introduced in the subsequent section. Capital markets are studied in the subsection that follows. Retailers, ie final goods producers are studied in subsections 4.3-4.4. Subsection 4.5 describes the behaviour of importers. Final section discusses the parameter values of the supply side. 20
Among other means, economic agents’ future expectations are traditionally measured by barometer surveys. These can be used in selecting parameter values for the model. There is also fairly plentiful indirect data available on the future expectations of economic agents. An appendix to the Bank of Finland’s winter forecast (Bank of Finland Bulletin 1/2004) (‘Deriving growth and inflation expectations from financial market prices’) describes how growth and inflation ex-pectations can be estimated from bond and share prices. For many products, eg oil or electricity, there are markets where future trade volumes and prices can be agreed in advance. The prices on these futures markets indicate almost directly economic agents’ expectations regarding the future prices of these products. The oil price -assumptions in the present forecast are based partly on these price expectations. Similarly, the forecast’s interest and exchange rate assumptions are derived directly from financial market instruments. It is, however, impossible to get comprehensive data on economic agents’ expectations, particularly in respect of macroeconomic variables.
21
Table 3: Goods Markets Structure in Aino Labour supply
Capital rental firm
Kt = Ut KtpSS
Lt (j )
T
kk SSS kkk k SSS k Domestic intermediate kk SSS kkk K SSSSS goods producer kkkkk L(j )
h ; ; ; L ; i;1= K Yt(j ) = t Kt + (1 ; ) t Lt (j ) )
u
Y (j )
Aggregator
Yt =
hR 1 0
i;1=zt
RRR RRR Y X RRR RRR RRR
DR AF
ll Consumption goods lllllll l lll Y C h retailer ll
Yt(j )zt d j
;
v
C CtT = C CY t Yt
;C
i 1 ; C ;C ; C +(1 ; C ) CM M t t
(
Exporter
;
F Xt = X CY t Yt
YI
O
h
;X
; X i; 1X +(1 ; X ) RtMtR ;
O
Investment goods retailer
X 1 h ; I I i; I ; ; ; I I ItT = I IY + (1 ; I ) IM t Yt t Mt MR
MC
I Foreign M
MtC
O
MtI
countries
MtR
4.1 Domestic intermediate goods producer
The composite domestic intermediate good is produced by the continuum of firms, who face in a monopolistic competition. The intermediate goods Y t (j ) are aggregated to the composite good by the following aggregator
Yt =
Z
1
0
Yt (j );zt d j
;1 z t
:
The parameter zt 2 ;1 1) determines the elasticity of substitution 1=(1 + zt ). For non-positive values of zt the intermediate goods are gross substitutes. Perfect substitutability, and, consequently, the perfect competition, is obtained by letting zt approach ;1 so that in this case the elasticity of substitution approaches infinity. We allow for time variation in the elasticity of substitution. The cost minimization implies the following conditional demand function for the individual good j (j 2 0 1])
Yt(j ) = PPt (j ) t
22
; 1+1 z t
Yt
(4.1)
and the price index for the composite domestic intermediate good
Pt =
Z
1
0
Pt(j )
z t 1+ zt
dj
1+z zt t
:
(4.2)
h ;
Yt(j ) = Kt Kt
;
T
Domestic intermediate goods, Y t (j ), are produced by producers who face monopolistic competition. They take the production technonology and the factor augmenting technical trends as exogenously given. The production function is of the CES type and take the specific form of constant-returns-to-scale21.
; i;1= + (1 ; ) LtLFt ;
(4.3)
DR AF
The factors of production include homogenous capital 22 , Kt , and non-homogenous L 23 labour, LFt (j ). K t and t denote time-varying capital and labour-augmenting technical progress respectively, which are unobservable to the econometrician. They are common for all firms. The elasticity of technical substitution is given by 1=(1 + ), where is the substitution parameter in production function. refers to share parameter. The cost minimization implies the following real marginal costs
"
# 1+
1+ 1 Rt WtF 1+ MCt (j ) = 1+1 1+ (4.4) + (1 ; ) Pt(j )
Kt Pt(j )
LtPt(j ) where Rt denotes the nominal rental price of capital services and WtF = (1+ tFP t + FS 24 25 tt )Wt represents nominal labour costs . In the steady-state , prices, P (j ), are determined by mark-up, over marginal costs P (j ) = MC (j ):
Mark-up is given by
= ; 1z :
(4.5)
Note, that the mark-up is not unity in the steady-state case since the steady-state elasticity of substitution 26 between the intermediate goods is generally finite. The first order conditions with respect to labour and capital services are loglinear. They are given by
log ; {z t ; Kt} +(1 + )(yt ; kt ) = rt ; pt |
(4.6)
; pt
(4.7)
tK log(1 ; ){z; t ; Lt} +(1 + )(yt ; lt) = wtF | tL
21 According to Ripatti and Vilmunen (2001) this seems to be reasonable assumption for post 1980 data. 22 Capital is rented from capital rental firms, “leasing firms”. 23 We do not specify their stochastic properties at this stage. See Ripatti and Vilmunen (2001) for further discussion about their properties and estimates using aggregate Finnish data. S 24 F P tt and tF t denote firms pension and social security contributions respectively 25 The symbols without time subscript denote the steady state values. 26 The elasticity of substitution is =( ; 1) in terms of .
23
T
where rt is the log of nominal rental rate of capital services, w tF nominal wages and pt output prices. Due to the monopolistic competition in the market for output, the time-varying slope of the demand curve, t log(t ), enters to the first order conditions. Note also that t log t for each type of s in the model. The dynamics of the price level Pt (j ) of producer j arises from the assumption that a firm changes its price level when it receives a random “price-change signal” (Calvo 1983, see). Probability of receiving a price change signal is given by 1 ; ( 2 0 1]). It is constant. Since there is continuum of intermediate producers, 1 ; also represents the share of producers that has received such a signal and, consequently, got an opportunity to change their prices. The average time between price changes is given by 1=(1 ; ). Let Pt (j ) denote the price level set by those intermediate goods producers that received the “price-change signal” in period t. With probability s the price Pt (j ) is still in effect at date t + s (s 0). The producer’s problem is the following
DR AF
1 X sM max E t tt +s t+s Pt (j ) fP (j )g
(4.8)
s=0
t
where the momentary profits are given by
t+s Pt (j ) = Pt(j ) ; MCt+s (j ) Yt+s(j ) = Pt(j ) ; MCt+s (j )
1 Pt (j ) ; 1+ zt
Pt+s
(4.9)
The first order condition is given by
1 P1 s 1+ z t E M P Pt(j ) = t t s=0P tt+s t+s Yt+1szMCt+s(j ) : 1+ t s Et 1 s=0 Mtt+s Pt+s Yt+s
(4.10)
Following the formulation (4.2) of the price index of intermediate goods, the aggregate price level evolves according to the following equation of motion
"
z t 1+ zt
Pt = Pt;1 + (1 ; )Pt(j )
z t 1+ z t
# 1+z zt t
:
(4.11)
The first term on the right hands side reflect the prices set by the those firms that have not received a “price-change signal”, ie the price is inherited from the previous period. The second term is the price level set by those firms that have received a “price-change signal”. It is determined by equation (4.10). Linearization
We linearize the pricing equations (4.10) and (4.11) in the standard way. Note however, that we need to allow the time-varying mark-up. Assuming symmetry of the firms we obtain the following aggregate pricing equation for the intermediate goods producer
pt = M Et pt+1 + (1 ; )(1 ; M ) t + mct ; pt] :
(4.12)
Inflation is determined by the expected inflation and changes in the slope of the demand curve and the real marginal costs. 24
Yt+s:
4.2 Capital rental firms
;
T
Capital is homogenous factor of production that is owned by firms that rent capital to producers of domestic intermediate goods. It operates under perfect competition. The capital rental firms may choose between physical capital accumulation K tp or a higher utilization rate Ut with Kt = Ut Ktp;1 (Ut 2 0 1]). Physical accumulation generates real adjustment costs in the form of lost capital stock, whereas the capital utilization rate affects the depreciation of the capital stock. Capital accumulation is given by
Ktp + aK Ktp Ktp;1 Ktp;2 = Ktp;1 1 ; D(Ut )] + It
(4.13)
DR AF
where aK () denotes the adjustment costs of physical capital stock. The depreciation factor D (Ut ) (D () 2 0 1]) is an increasing function of the capital utilization rate, D0 (Ut ) > 0. The capital rental firm maximizes its expected discounted profits
max E fU gfI g t t
1 X
t
s=0
Mtt+s Kt+s
subject to capital accumulation equation (4.13) and the definition of capital services. The momentary profits are given by
Kt =Rt Kt ; PtI It =Rt Ut Ktp;1 ; PtI fKtp + aK (Ktp Ktp;1 Ktp;2 ) ; Ktp;1 1 ; D(Ut)]g:
(4.14)
The price index of investment goods is the price index of the domestic investment good retailer, PtI . Since the firm is owned by households, the future profits are discounted using the nominal stochastic discount factor (pricing kernel) Mtt+s = sU 0 (Ct+s)PtC =U 0 (Ct)PtC+s] (PtC refers to price index of composite consumer goods). Optimal level of capacity utilization is given by the following first order condition wrt Ut
Rt = PtI D0(Ut )
(4.15)
which relates the rental price to the marginal depreciation of the capital stock. The first order condition wrt capital stock Ktp is given as follows
; PtI Et 1 + aK1 (Ktp Ktp;1 Ktp; 2 ) + Et Mtt+1 Rt+1 Ut+1 ; PtI+1 aK2 (Ktp+1 Ktp Ktp;1 ) ; (1 ; D(Ut+1)) ; Et Mtt+2 PtI+2aK3 (Ktp+2 Ktp+1 Ktp) = 0:
(4.16)
Due to the end-of-period timing of physical capital stock 27 , the accumulated physical capital is in use in the following period. Hence, it is the expected following period’s rental rate that governs the current period investment decision. 27
This is a usual way to measure the capital stock in the national accounts.
25
Parametrics We define the adjustment cost function as follows
;
1 Ktp ; 2 Ktp;1 2 : 2 Ktp;1
T
aK (Ktp Ktp;1 Ktp;2) =
This formulation of adjustment costs allow for hump-shaped responses of investments to various shocks. The depreciation factor is paremeterised as follows (see Baxter and Farr (2001))
D(Ut) = 0 + 1 +1 Ut1+ 2 : 2
DR AF
It has the rust-and-dust part, 0 , and the wear-and-tear part: the second summand on the right-hand-side. The parametric version of (4.16) is as follows:
; PtI Et
Ktp ; 2 Ktp;1 1 + 1 Ktp;1 " (
+ Et Mtt+1 Rt+1 Ut+1 ; PtI+1 ; 1(1 + 2)
Ktp+1 ; 2 Ktp Ktp
p p2 ; 1 ( Kt+1 ; p 22 Kt ) ; 1 ; 0 ; 1 +1 Ut1++1 2 2 (Kt ) 2 ; Et Mtt+2 PtI+2 12 Kt+2 K; 2 Kt+1 = 0: t+1
!#)
(4.17)
and, that of the (4.15)
Rt = U 2 : PtI 1 t
(4.18)
The usual ‘investment equation’ can be obtained by substituting (4.6) and (4.18) into (4.17). Consider the case that this substitution is done and the resulting equation is linearised. The resulting equation contains the ‘fundament’ part corresponding (4.6) and the dynamic part that contains leads and lags of k t . The parameters 1 and 2 — related to adjustment cost function — determine the coefficients of leads and lags of kt . The coefficient of the ‘fundament’ part is essentially determined by the parameters in depreciation function, 1 and 2 , and the elasticity of technical substitution .
4.3 Domestic retailers
The economy is inhabited by two retailers. The first one is specialized for consumer goods and the other one for capital goods. They combine domestic intermediate input — produced by the intermediate goods producers — and imported goods and services and operate under perfect competition. This means that they 26
DR AF
T
do not produce any value-added and can be considered as aggregators, which represent how consumers or capital rental firm (and public sector) substitute between domestic and foreign intermediate goods and services. The domestic intermediate goods used in the production of consumption and investment goods are labelled as YtC and YtI respectively. The imported goods we label as MtC and MtI . We alCM IY IM low time-varying factor augmenting technical progress, CY t , t and t , t to reflect the changes in the preferences related to the consumption or investments of tradables and non-tradables. Since the technology is CES type, we introduce substitution parameters C and I .28 The retailers sell their products both to the private sector and to the general government. The output of the consumption goods retailer consist of the private consumption, and public purchases 29 , CtT CtH + CtSF . Same holds for the investment goods retailer, t It8 + ItG . Since general government is divided into pension funds and other general government, we disaggregate public investments as follows: ItG = I P + I S . The price indices of the retailers are in market prices, ie prices faced by consumers. The consumption goods retailer pays indirect taxes 30 , measured as a share of the nominal output, tC . The profits of the consumption goods retailer are
(1 ; tCt )PtC CtT ; PtYtC ; PtMC MtC :
(4.19)
The technologies — or, rather, aggregators — of the retailers are given as follows
h ;
C CtT = C CY t Yt
ItT
;C
i C ; C ;C ;1= + (1 ; C ) CM M t t
(4.20)
h ; ;I ; IM I ;I i;1=I I IY I I = Y + (1 ; ) M : t
t
t
t
(4.21)
Cost minimization implies the following price indices P tC and PtI
2
1 PtC = (1 ; tCt );1 4(C ) 1+ C PCYt t
2
PtI = 4(I )
1 1+ I
Pt
IY t
C 1+ C
+ (1 ; C ) 1+ C tCM t
I
1+ I
+ (1 ; I )
MC 1+CC P
1 1+ I
1
MI 1+I I P t
IM t
3 5
3 5
C +1 C
(4.22)
I +1 I
:
(4.23)
The elasticities of substitution are given by 1=(1 + C ) and 1=(1 + I ) respectively. Public purchases here means the national accounts item of general government consumption, from which the public value added, ie mainly salaries, is subtracted. 30 In our terminology we include VAT, etc. taxes and subsidies in to the measurement of indirect taxes. 28 29
27
and the conditional factor demands
; = C CY t 1+
C C
; IY 1+I I I I Y =
t
t
Pt
(1 ; tC )PtC
Pt PtI
1 1+ I
ItT
1 1+ C
CtT
(4.25)
1
1+ C PtMC CtT (1 ; tC )PtC 1 ; IM 1+I I PtMI 1+ I T I I It : Mt = (1 ; ) t PtI
MtC
; 1+ = (1 ; C ) CM t
C C
(4.24)
T
YtC
(4.26) (4.27)
DR AF
In the estimation of the elasticity of substitution between imported consumption goods and domestic intermediate products we rely on the first order condition with respect to imported goods. Its log-linear version may be written as follows
M C C C log(1 ; C ) + C (cTt ; mCt ; CM t ) = pt + mt ; pt ; ct ; log(1 ; tt ):
(4.28)
Note that the right-hand-side of the above equation is the share of imports to the value of consumption. For positive values of C the inputs are gross-compelements and for negative values gross-substitutes. This form highlights the difference in the graphical investigation. We rely on the cointegration techniques in the estimation of the elasticity of substitution 1=(1+ C ). This requires an assumption that C t is stationary. Our point estimate for the parameter C is -0.7731 (with standard error 0.049) that implies elasticity of substutution 4:4. This implies that the elasticity of substitution deviates significantly from zero and from the unity 31. Figure 1 depicts relative factor prices and the estimatated technical trends. Note that, here as in the case of intermediate goods producers, we are not able to identify the share parameter C . This is due to the fact that it cannot be distinguished from the constant term in the technical trends. We calibrate this parameter to correspond the intermediate good’s factor share. It is 0.87. The estimation of the elasticity of substitution between imported investment goods and domestic intermediate goods relies on the similar first order condition as (4.28). The estimated elasticity of substitution is smaller in the case of investment goods. Our estimate is 2:2, which is given by the estimate of I = ;0:538 with the standard error of 0:183. This means that the factors are gross-substitutes. The calibrated value of the share parameter I is 0:67
4.4 Exporter
Exporter is a firm that combines domestic intermediate input, Y tF , and imported materials32 , MtR to produce export good, Xt in competitive markets. We allow 31 32
28
Unit elasticity of substitution corresponds the Cobb-Douglas aggregator. This includes energy, other raw materials, and industrial intermediate inputs.
Figure 1: Relative price of imported consumption goods and the technical trend 3.00
ct − mtC Import share
2.4
2.50
T
2.75
λ tCM λ tCY
2.3
2.25 2.00
2.2
1975
1980
1985
1990
1995
2000
1975
1980
0.2
1990
1995
2000
pt − ptC
0.15
ptM − ptC
1985
DR AF
0.10 0.05
0.1
0.00
0.0
−0.05
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
All variables are in logs. Means and ranges are adjusted in graphs with two lines.
XM time-varying factor-augmenting technical progresses, XY t and t to reflect the increase in the effiency of factor usage. Since the technology is CES type, we introduce a substitution parameter X . Consequently, the technology — or the exports aggregator — is given as follows
Xt =
h
; XM R ;X i;1=X X + (1 ; ) t Mt :
; F ;X X XY t Yt
Cost minimization implies the following price index P tX
"
; X 1+1 X
PtX =
Pt
XY t
X =(1+X )
;
+ 1;
X 1+1 X
PtR
XM t
X =(1+X ) #(X +1)=X (4.29)
and the conditional demand functions for inputs
Pt PtX
YtX
; = X XY t 1+
MtR
; 1+ = (1 ; X ) XM t
X X
X X
1+1 X
Xt
MR 1+1 X P t
PtX
Xt :
(4.30) (4.31)
In the estimation of the elasticity of substitution between domestic intermediate input and imported raw materials, we rely on the same approach as in the case of domestic retailers. We assume that the imported-input-augmenting technical change 29
Figure 2: Relative price of imported investment goods and the technical trend i t −m t I Import share
1.75
λ tIM λ tIY
1.50
1.50 1.25
T
1.25
1.00 1.00
0.75
0.75 1975
1980
1985
1990
1995
2000
p t I −p t C
0.3
1975
1980
1985
1995
2000
p t −p t C
0.10
0.2
1990
DR AF
0.05
0.1
0.00
0.0
−0.05
−0.1
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
All variables are in logs. Means and ranges are adjusted in graphs with two lines.
may contain a deterministic linear time trend. This trend captures the deepening of the intra-industry trade. It also means — with a positive slope — that the share of imported raw materials in the production of exports has increased steadily. This is simply a local approximation since this share cannot expand forever. Our estimate for the elasticity of substitution is 0:45. The estimated X = 1:217 with the standard error of 0:378. Not surpricingly, the point estimate suggest that the imported raw materials and the domestic intermediate input are gross-complements in the production of exported goods and services. The calibrated value of the share parameter X is 0:51.
4.5 Importing Firms
This subsection relies on Ripatti and Viertola (2004). Imported goods and services are used by the retailers and the exporter in the Aino economy. They combine imported and domestically produced intermediate goods to produce final consumption, capital and exported goods. The consumer goods and services (including 5 per cent of imported energy) are used by the consumption goods retailer, capital goods and services are used by the capital goods retailer, and the exporter uses energy and intermediate goods in producing exported goods. Each of these retailers operates under perfect competition in their output markets. We derive a model for import prices of the imports by main use, ie for the retailer sector. We follow the approach derived by Betts and Devereux ((1996),(2000)) 30
Figure 3: Relative price of imported raw materials and the technical trend in exports x t −m t R Import share
1.00
λ tXM λ tXY
1.5
T
1.0 0.75
0.5
0.50
0.0
1975
1980
1985
1990
1995
2000
1980
1985
1990
1995
2000
p t −p t X
p tMR −p tX
0.2
1975
0.1
DR AF
0.1
0.0
0.0
−0.1
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
All variables are in logs. Means and ranges are adjusted in graphs with two lines.
and applied to Finnish aggregate import data by Freyst¨atter (2003). We assume that a fraction of importers price their product in local (Finnish) currency and rest of importers in producer (in their own) currency. Their pricing contains identical frictions in the form of Calvo (1983), ie they may change their price only in the case of receiving a random price-change-signal. Their cost functions are identical too. The aggregation of the pricing behaviour over these two types of importers yields an import price Euler equation where import prices depend on expected future import price inflation, current and expected future changes in foreign exchange rates and on the real marginal costs of the importers. For each group of import products we introduce three sets of firms: an importer (aggregator), foreign importers pricing their products in the Finnish currency (FCP firms), and foreign importers pricing their products in their own currency (PCP firms). We introduce the following notation, M is the aggregate imported good with an aggregate price level P , the prices related to FCP firms are denoted by P F and to PCP firms by P P . Quantities are M F and M P respectively. In log-linearization, small letters denote the log-deviations of the variables from the steady-state, ie x t = log Xt ; log X , where letter without a time subscript denotes the steady-state value. In purely atemporal equations we ignore the time subscripts. The foreign discount ? . factor between periods t and t + k is denoted by Rtt +k
31
4.5.1 Aggregator
M=
Z ! o
M F (j );dj +
Z
1
!
T
An importing firm aggregates the products of the foreign importing firms (FCP and PCP firms). The goods are produced in a number of varieties or brands defined over a continuum of unit mass. Brands of goods by FCP firms are indexed by j 2 0 ! ) and those of PCP firms by j 2 ! 1]. Aggregate imports, M , is then defined as
M P (j );dj
;1=
:
(4.32)
The aggregate price index is the defined as follows
P=
Z ! 0
P F (j ) 1+
dj +
Z 1 !
SP P (j ) 1+
dj
1+
(4.33)
DR AF
where S is foreign exchange rate in foreign currency, eg EUR/USD. Assuming symmetric equilibria and log-linearising the price equation (4.33) around the steadystate yields
pt = !pFt + (1 ; !)pPt + (1 ; !)st:
(4.34)
One may give ! an interpretation as the share of the firms that price their products in local (Finnish) currency. These are firms that do not have the opportunity immediately adjust their prices when foreign exchange rates move. The cost-minimazation implies the following demand functions
M F (j ) =
F ; 1+1 P (j )
M P P ; 1+1 P M (j ) = SPP (j ) M:
(4.35) (4.36)
It does not matter whether the importer operates inside or outside the Finnish borders, since it does not produce any value-added. Therefore, it does not influence to the accounting system of the whole Aino model.
4.5.2 Foreign importers
Foreign importers operate outside Finnish borders. They face imperfect competition in their output markets. This means that they take into account the demand functions (4.35) and (4.36) in their pricing decisions. We assume that all FCP and PCP firms share the same cost function C (j ), which is assumed to be homogenous of degree ? . one in output. They also share the same stochastic discount factor R tt +k The dynamics of the price level Pt (j ) of importer j arises from the assumption that a firm changes its price level when it receives a random “price-change signal” (see Calvo 1983). Probability of receiving a price change signal is given by 1 ; ( 2 0 1]). It is a constant and identical to all (both FCP and PCP) firms. Since there is continuum of firms, 1 ; also represents the share of firms that has received 32
1 X sR? i P i(j ) max E t tt+k t+k t fP i (j )g t
s=0
where it+k
i
T
such a signal and, consequently, got an opportunity to change their prices. The average time between price changes is given by 1=(1 ; ). Let Pti (j ) i = F P denote the price level set by those firms that received the “price-change signal” in period t. With probability s the price Pti (j ) is still in effect at date t + k (s 0). Firms’s problem is the following
i = F P
(4.37)
Pt (j ) i = F P is momentary profits of a firm type i.
FCP firms
Given the momentary profits of FCP firm
DR AF
Ft+k PtF (j )] = PtF (j )MtF+k (j ) ; St+k Ct+k (j )MtF+k (j ) F ; 1+1 = PtF (j ) ; St+k Ct+k (j )] Pt (j ) Mt+k : Pt+k
the first-order-condition of the profit maximizing problem (4.37) is given by
1 P1 s ? 1+ M S MC (j ) E R P 1 PtF (j ) = ; t k=0 P1tt+k t+k t+k 1 t+k t+k ? P 1+ Mt+k Et k=0 sRtt +k t+k
(4.38)
where MC (j ) = C 0 (j ). The aggregate price level PtF evolves according to the following equation of motion
PtF
n ; 1+ F 1+ o 1+ F + (1 ; ) Pt (j ) = Pt;1
:
(4.39)
Assuming symmetric equilibrium and log-linearising the equations (4.38) and (4.39) gives the Euler equation for FCP firms
pFt = R? Et pFt+1 + (1 ; )(1 ; R ) (st + mct ; pFt ): ?
(4.40)
PCP firms
Given the following momentary profits of PCP firm
Pt+k PtP (j )] = St+k PtP (j )MtP+k (j ) ; St+k Ct+k (j )MtP+k (j ) P ; 1+1 S t +k Pt (j ) P Mt+k : = Pt (j ) ; St+k Ct+k (j )]St+k Pt+k
the first-order-condition of the profit maximizing problem (4.37) is given by
1 P1 s ? 1+ R S P E M MC (j ) PtP (j ) = ; 1 t k=0P1 tt+k t+k t+k t+1 k t+k ? St+k P 1+ Mt+k Et k=0 sRtt +k t+k
(4.41)
33
where MC (j ) = C 0 (j ). The aggregate price level PtF evolves according to the following equation of motion
1+
1+ o 1+
+ (1 ; ) St PtP (j )
:
(4.42)
T
n ;
StPtP = StPtP;1
Assuming symmetric equilibrium and log-linearising the equations (4.41) and (4.42) gives the Euler equation for PCP firms
pPt = R? Et pPt+1 + (1 ; )(1 ; R ) (mct ; pPt ): ?
Aggregation
(4.43)
DR AF
Using the aggregation equation (4.34) and Euler equations (4.40) and (4.43), we obtain the aggregated import price equation
pt
?) (1 ; )(1 ; R (st + mct ; pt ) t pt+1 + + (1 ; !)( st ; R? Et st+1 ):
=R? E
(4.44)
This is the theoretical equation we base our estimation. Parameters of interest are , R? and !. In the our model code we follow the version by Christiano, Eichenbaum and Evans (2003), where the firms that do not get the Calvo signal and cannot reoptimise may index their prices on past inflation. The resulting equation is as (4.44) except that the difference operator is replaced by the double difference operator. This generates more inertia to the import price inflation.
4.6 Parameter Values
The parameter estimates are given in table 4. We estimate the parameters of the production functions using cointegration methods (Johansen 1995). The parameters related to the capital stock’s adjusment costs, depreciation function and import prices are estimated using GMM. For detailed description of estimation strategies, see Ripatti and Vilmunen (2004). Generally, cointegration methods work reasonably in most cases. The deep recession in early 1990s makes it difficult to estimate the elasticity of technical substitution between capital and labour and the elasticity of substitution in consumption goods retailer’s production function. GMM yields plausible parameter estimates when proper set of instruments is chosen but it seems that the standard error suffers from multicollinearity of instruments.
5 Market Equilibrium
All the markets are in equilibrium at each point of time. The capital goods market is in the equilibrium if the supply of capital services by the capital rental firm equals 34
DR AF
T
Table 4: Parameters of the Supply Side Parameter Value Std.err. Method -19.37 26.24 GMM a M 0.978 1.70 GMM 1 55.47 198.07 GMM 2 1.47 24.41 GMM 2 13.29 120.46 GMM -0.25 88.63 GMM 7.80 384.43 GMM 0.75 119.35 GMM 0.0125 Derivedb 0 0.010 Derived 1 0.034 Derived 2 13.29 Derived 0.724 Historical data 1=(1 + ) 0.58 Derived 0.1 Calibrated C -0.5 Calibrated C 1=(1 + ) 2 Derived C 0.87 Calibrated I -0.538 0.183 Cointegration 1=(1 + I ) 2.2 Derived I 0.67 Calibrated X 1.22 0.38 Cointegration 1=(1 + X ) 0.45 Derived X 0.51 Calibrated C I R R =R =R =M Calibratedc C 0.88 Calibratedc C 0.6 Calibratedc ! I 0.95 Calibratedc I 0.3 Calibratedc ! X 0.6 Calibratedc !X 0.9 Calibratedc W 1.24 Cointegration
is restricted to lie between 0:95 and 0.9999. The estimate of M The steady-state depreciation coefficient is estimated as the average of depreciation coefficient from the capital accumulation equation. c Preliminary estimates exist. a b
35
to the demand for capital services by intermediate goods producers.
Z
1 0
Kt (j )dj = Kt :
(5.1)
W R LLW t = Lt + Lt F G G LLF t = Lt + t Lt :
T
Similarly the demand of labour equals its supply. There is extra complication due to the fact that we measure the labour supply (LLW t ) in the worker’s unit and labour demand (LLF ) in the private sector employment units as follows t (5.2) (5.3)
Since these are measured in different units they are not equal at the equilibrium. In terms of heads (number of employed), the labour supply equals labour demand, ie LSt = LDt as follows:
DR AF
R LSt = LWt + LRt = LLW t + (1 ; )Lt G G LDt = LFt + LGt = LLF t + (1 ; t )Lt :
(5.4) (5.5)
In the intermediate goods sector the demand for intermediate goods by the retailers and exporter equals total supply:
YtC + YtI + YtX = Yt:
(5.6)
Stock markets clear when the supply shares equals the demand for shares. This implies that
tD = 1:
(5.7)
Markets for final goods clear when
CtSF + Ct = CtT ItG + It = ItT
(5.8) (5.9)
PtX ; M = X (5.10) t t St PtW where PtW is the aggregated export price of competing economies and M t aggreW
gate imports of export markets. Markets for non-market goods clear when the supply of non-market goods, YtG equals pension funds’ consumption, C tP , and other general government’s consumption of non-market goods, C tSNM :
CtP + CtSNM = YtG:
(5.11)
When market clearing conditions (5.1) – (5.11) hold, then the workers’ and pensioners’ budget constraints (2.26), (2.18), the general government budget constraint (3.2) and pension fund’s budget constraint (3.5) imply the following accumulation of foreign assets
StAWt = (1 + rtF )St AWt;1 + TtSEU + P| tX Xt ; PtMRMtR ;{zPtMC MtC ; PtMI Mt}I trade balance
(5.12)
where the lower line defines trade balance. The current account is given by St (AW t ; AWt;1 ), the factor income account by rtF St AWt;1 and the transfers account by TtSEU . 36
6 Product and Labour Market Competition in Finland
Reduction of price margin.
Reduction of slack in the use of input factors.
DR AF
T
Increase in competition implies inversely decrease in the mark-up. It reduces the ability of intermediate goods producers and workers to exploit their market power by restricting the supply of intermediate goods and labour effort. Therefore, in Aino model it directly scales up supply of intermediate goods and labour supply. Augmented competition also adds up — within the limits of elasticity of substitution — factor demands, ie employment, capital and consumption. Price and wage levels are directly declined. Høj and Wise (2004) discuss possible channels through which the reforms may operate:
Competitive environment stimulates productivity growth.
Since technological change in Aino model is exogenously given we can only take into account the first channel. Therefore, our estimates of the potential benefits of increased competition lie on the conservative side. Nicoletti, Bassanini, Ernst, Jean, Santiago and Swaim (2001) models the interlinkages in regulations and technological growth. Hence, there exist a possible future extension to our approach by modelling the linkage between the price mark-up and labour-augmenting technological change. Currently these measures are assumed to be orthogonal in Aino model. Martins, Scarpetta and Pilat (1996) estimates product mark-up for various OECD countries and industries. In manufacturing, the mark-up in Finland is among highest (1.24) in OECD countries where as in some other industries it is on or below the average level (1.19-1.36). The manufacturing industry consists mainly of large exporting firms that are large in their output markets. Consequently, they might have market power and pricing-to-market behaviour in particular in their domestic markets that are fairly small with respect to their level of production. Høj and Wise (2004) lists in very detailed manner possible restrictions in product market competition Finland. They also provide estimates of macroeconomic effects of increased competition. According their estimate, based on the empirical work by Nicoletti et al. (2001), “if Finland moved towards best practice for product market liberalisation in the OECD, then the employment rate could increase by another 1/4–1/2 percentage point” (page 36). This quantitative estimate is at the same magnitude as the scenario in Bank of Finland (2004), where the product market mark-up was assumed to decline 1=2 percentage point in the long-run. The resulted long-run employment growth was estimated to be 0.2 percent in the long-run. It is, however, very difficult to compare their assumption of the decline in the mark-up to the microeconomic estimates of Høj and Wise (2004). Nicoletti et al. (2001) and Jean and Nicoletti (2002) argue that lack of competition in product market typically correlates with the lack of competition in labour
37
6.1 Estimation of the Mark-ups
T
markets.33 The existence of mark-ups in product markets gives rise to economic rents. That may induce rent seeking behaviour by labour unions leading to markups in in labour markets. Therefore these are generally not independent.
DR AF
The degree of product market competition collapses to time-varying parameter t ;1=zt in pricing equation (4.12). It is the inverse of elasticity of substitution parameter in various brands on domestic intermediate goods. It might capture effects such as competition regulation, horisontal collusion in product markets, public ownership of domestic firms, differences in product stardards, etc. The model setup has a drawback in the way that imperfect competition is limited to intermediate goods producer only. The final good producers operate under perfect competition in their product markets. Consequently, we cannot, for example, limit the mark-up changes to domestic markets only. The export markets is influenced too. 34 This create some difficulties in interpreting the simulation results as the existence of the mark-up in exports market generally increases domestic welfare due to higher profits of exporting firms. One way to construe our simulation exercise is to assume that corresponding product mark-up changes are performed abroad as well. The estimation of product mark-up, t , in pricing equation (4.12) is based on the approach developed by Ripatti and Vilmunen (2001) and applied in the context of Aino model by Ripatti and Vilmunen (2004). In relies on the factor demand and pricing equations of the intermediate goods producers, ie equation (4.6), (4.7), and (4.12) respectively, and on the capital adjustment costs and depreciation function, (4.17) and (4.18). If the paremeters of those equations were known, and we would assume perfect foresight, the unobserved capital-augmenting technical change K t , L labour-augmenting technical change t and price mark-up t could be computed using these equations. As an estimate of the elasticity of technical substitution, 1=(1 + ), between capital and labour, we use value 0:58 that is close to estimate by Jalava, Pohjola, Ripatti and Vilmunen (2005) for post-war period. The rest of the parameters are as reported in table 4. It seems that the perfect foresight assumption is heroic in the sense that the resulting estimates of the unobservables are very volatile. Therefore we smooth and extrapolate them using Kalman filter techniques and unobserved trend component model. Figure 4 depicts various measures of private sector firms’ profits. Profits and t are model based measures, whereas gross-operating surplus is a national accounts measure. All of them share similar level shift, allthough the timing of the shift varies. A possible explanation of this level shift is the huge structural change in manufacturing after the deep recession and the rise of ICT industries. All of this creates some confidence to our estimate of t . In recent years the smoothed values 33
The measure of wage premia in the above-mentioned studies is based on the characteristics of the workers, working conditions and firms. Therefore, it does not directly correspond our labour market mark-up measure. 34 The GEM model by Bayoumi et al. (2004b) allows for imperfect competition in various components of final goods and is able to make this breakdown.
38
Figure 4: Private sector profit measures and t
30
Profits/output Gross−operating surplus/output ϒt
T
35
25
20
15
DR AF
10
5
1975
1980
1985
1990
1995
2000
2005
Means and ranges are adjusted. Left scale corresponds Profits/output line. Profits is the model’s profit measure, gross-operating surplus is obtained from national accounts and t is based on our own calculations.
of t have been on the level 1:08. This is fairly small value compared to, for example, estimates by Martins et al. (1996) that reports 1:24 for manufacturing. The actual level of t depends, in particular, on the choice of exogenously given risk premia in stock returns. As described above, the parameters of production function, pricing and adjustment costs in investments also play a crucial role here. Therefore our estimate is tentative but consistent with data and other parameters in the model. One may also defend this estimate in the light of microeconomic evidence. Kilponen and Santavirta (2004) find that the average price-cost margin in Finnish industry is roughly 8%, when using microdata from annual Industrial Statistics surveys. This data cover essentially all Finnish manufacturing plants employing at least 5 persons, up to year 1994, and from 1995 on plants owned by firms that employ no less than 20 persons. The rate and the size of decline in mark-up is more important than the level estimate of t itself. In our simulation experiment we assume that t declines from 1:078 to 1:06. In relative terms this is rather substantial increase in the level of competition. We also assume that there is persistence in the transition to lower mark-up. We try to mimic the goals of Lisbon Agenda so that 80 percent of the decline has achieved by 2010. The level of competition in labour market is given by the parameter L in equation (2.8). 1=L determines the premium over the marginal rate of substitution between consumption and leisure. It captures factors like bargaining power of labour
39
6.2 Simulation results
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unions, and the unionisation rate, minimum wage legislation, unemployment benefits, hiring and firing costs, immigration policies etc. Given the calibrated level of product market mark-up, t = 1:078, we calibrate rest of the model parameters to produce steady state that is relatively close to average data between 1995-2004. This implies that the labour market mark-up is at the level 25 percent, ie L = 0:8. In the following simulations we assume that this mark-up declines 5 percentage points (L = 0:833). As in the product mark-up case, we assume that 80 percent of this reduction is reached in 2010.
DR AF
As in the standard theoretical models of imperfect competition, we expect that declining market power of the workers shows up in an increasing output. Part of this increasing output is due to increasing private consumption in the domestic economy. Another part is due to the fact that lower production costs(due to declining real wage) in the economy translate into lower level price level, which in turn means higher exports and depreciating the real exchange rate. Higher production also requires higher steady state capital stock, which in turn boosts investments. Moreover, higher domestic investments and private consumption requires further increase in import volumes. The magnitudes of these effects depend on the degree of substitutability of domestic and private production. The effects of private production in the long-run depend crucially upon the response real wage, and thus labour supply on declining market power. This response in turn crucially depends upon elasticity of substitution between leisure and consumption. Moreover, increasing efficiency of the domestic economy translates into lower income tax rate. Given that taxes in the Aino model are distorting, additional efficiency gains is achieved through lower income tax rate translates. In particular, lower income tax rates, ceteris paribus, lead into higher labour supply. The dynamic, or short and medium run effects of increasing competition depend such issues like adjustment costs of capital and intertemporal subsitution. Given distorting taxes in the Aino model, short and medium term effects also crucially depend upon speed of fiscal adjustment. The speed of fiscal adjustment can be controlled through parameter in equation (3.4)
6.2.1 Labor market reforms
In order to assess the magnitudes of these various effects, the table (5) shows how an anticipated gradual decline in the wage mark-up translates into percentage deviations of several macroeconomic variables from their corresponding steady state values. The table (5) also shows the share of total effect that is achieved after 5 years. In general, the model simulations suggest small, but rather reasonable effects on the macroeconomic equilbrium. Private production increases in the long 1.2 % with associated increase in private investment, and private consumption and employment. Real exchange rate depreciation is rather modest in comparison to in40
After 10 years 0.78 0.27 1.02 .39 .76 -.48 -.08 -.03 .66 -7.4 -3.9 .71
Long % of total effect run after 5 years 1.24 41.0 1.23 8.7 1.08 76.5 1.08 15.3 0.98 55.7 -.24 184.77 -.7 12.0 -.18 0.65 .44 0 n.a. -4.0 80.0 0.33 22.3 0.47
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After 5 years 0.51 0.11 .83 .16 .55 -.45 .0 -.01 .45 -2.6 -3.2 .47
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Private Production, % Private Consumption, % Private Investment, % Capital Stock, % Employment, % Real Wage, % Income tax rate, % points Pension contrib. rate, % points Real exchange rate, % Debt to output ratio, % points Wage mark-up, % Export to import ratio, % points Welfare, %
After 2 years 0.21 -.01 .47 .04 .25 -.24 .0 .0 .20 -.4 -1.8 .20
Table 5: AINO estimates of the increasing labour market competition in the Finnish Economy creasing consumption and investments. Yet, there is a moderate improvement in export to import ratio in the long-run. Fiscal adjustment shows up in very modest short and medium term decline in income tax rate, but rather larger adjustment of debt to GDP ratio. Once the economy has reached a new equilibrium however, noticeably lower income tax rate is required for maintaining balanced budget. Similarly, required pension contribution rate settles about -0.2 percentage point lower value. Finally, and most importantly. there is an improvement in the Aino model’s consumer welfare of about 0.5 %. Looking at the short- and medium run adjustment, it is evident from the table that increasing competition in the labour markets translate relatively rapidly into investment hike, while consumption responds with considerably delay. Moreover, there is a hump-shaped response of real wage, such that in the medium term real wage over-reacts to declining market power of the wage setters. This is reflected also in private consumption which shows a modest decline during the first 2 years of the simulation. Faster initial reaction in real wage also implies that increase in employment contributes more to the increase in private production that does the increase in the capital stock. A sluggish increase in capital stock reflects the real adjustment costs of capital. Similarly consumption slow response reflects relatively high intertemporal substitution of the Aino model’s consumers.
6.2.2 Product and labour market reforms
In many situation, regulatory reforms in the product markets are ssociated with declining wage mark-ups in the labour markets. In the next simulation we combine gradually declining wage mark-up with gradually declining price mark-up. As in the previous simulation, we assume that roughly 80 % of the total 2 percentage
41
After 10 years 1.98 0.22 3.99 1.74 1.44 1.73 .2 -.16 1.73 -2.4 -3.9 -1.78 1.74 n.a
Long % of total effect run after 5 years 2.92 46.25 2.47 -27.33 3.65 104.78 3.65 23.5 1.71 67.0 2.77 37.8 -.7 -27.2 -.7 6.4 1.59 77.0 0 n.a. -4.0 80.0 -1.85 80.0 .86 102.5 1.22 n.a
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After 5 years 1.35 -.23 3.82 .86 1.14 1.05 .2 0 1.22 1.03 -3.2 -1.47 1.16 n.a
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Private Production,% Private Consumption,% Private Investment,% Capital Stock,% Employment,% Real Wage,% Income tax rate,% points Pension contr. rate, % points Real exchange rate,% Debt to GDP ratio, % points Wage mark-up, % Price mark-up, % Export to import ratio,% points Welfare, %
After 2 years 0.51 -0.67 2.78 .26 .54 0.39 .1 0 .59 2.18 -1.8 -.82 .58 n.a
Table 6: AINO estimates of the increasing labour and product market competition in the Finnish Economy, (level effects point decline in the price mark up is achieved after 5 years. The results are reported in table (6) First, the Aino model’s simulations suggest considerabe efficiency gain for the economy, once the adjustment process is completed. There is roughly 3 percent increase in private production. The largest part of this increase in production possibilities comes from an increase in the capital stock of about 3.7 percent. Declining price mark up is translated relatively faster to production prices and to consumer prices than to nominal wages, resulting an increasing real wage of 2.8 percent in the long-run. Increasing real wage attracts more workers to the labour markets, thus increasing employment of about 1.7 % in the long run. Regarding consumption, we observe an initial and rather prolonged decline in consumption level. This is due to the wealth effect as the firms profits are driven down in the short and medium run. Moreover, since nominal interest rate remains constant, and the economy’s rate of inflation is temporary driven down, there is temporary increase in the real interest rate. Higher real interest rate contributes to initial decline in consumption. In the long run, however, as increasing real wage and economy’s capital stock translates into higher accumulated wealth, consumers consumption possibilities eventually improve of about 1.7 percent relative to baseline. This is also translated into a considerable welfare increase of about 1.2 percent when measured in consumption units. In the long-run fiscal situation improves, leading into 0.7 percentage point decline in income tax rate. Similarly, there is a 0.7 percentage point decline in pension contribution rate. Finally, export to import ratio improves along depreciating real exchange rate and improved price competitiveness of the domestic products. Short-run and medium run dynamics reveal how the economy adjust to the new equilibrium. One interesting feature arises from fiscal adjustment. Namely, in the 42
6.3 Sensitivity analysis
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short-run income tax rates are driven up, as well as debt to output ratio. This is mainly due to the fact that initial drop in consumption drives down revenues from indirect tax. In order to finance government consumption, transfers and investments, there is a need to compensate these lost revenues by increasing the tax revenues from wages, hence temporarily increasing the income tax rate and borrowing from the households.
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General equilibrium models like Aino, has a number of structural and preference parameters which importantly shape the dynamic and long-run effects. In this section we discuss how the results would change if some of these crucial parameters would be altered. First, we change the intertemporal elasticity of substitution from 0.5 to 0.7 thus reducing the income effect of consumption 35. This change in parameter has more significant effects in the short-and medium run than in the long-run. It turns out that in the long-run higher intertemporal elasticity of substitution tends to downplay the effects of increasing competition in the product and labour markets to output, consumption and capital stock. For instance, level of consumption is now 2.25 % higher, instead of 2.47 % after adjustment to increasing competition has been completed. Only the long-run response of real wage is slightly magnified with higher intertemporal elasticity of substitution. Lowering the elasticity of substitution between labor and capital by 0.1. from 0.72 to 0.62 has also rather marginal effects on simulation results. Increasing competition results slightly smaller effects on output, consumption and capital stock For instance, as a result of increasing competition in the labor and product markets, the level of capital stock goes up by 3.5 % in comparison to 3.7 % in the standard simulation. In the Aino model, the Frisch elasticities of labour supply for workers and pensioners are 0.15 and 0.31 in the standard calibration of the model in the long-run 36 . The value for workers is at the bottom range of international microeconomic studies, which report the values from 0:15 ; 0:32:37 . Kuismanen (2005a, 2005b) has estimated compensated labour supply elasticities using Finnish Labor Force survey data. Depending on the data sample and the methods used, his estimates range from 0.08 to 0.30. 35
Higher intertemporal elasiticity of substitution reduces the labour supply of pensioners. We have thus re-calibrate the labour productivity of pensioner to 0.375.. 36 Given Cobb-Douglas form of intratemporal utility the steady state values of Frisch elasticities of labour supply for workers and retirees can be calculated as
FW = FR =
(
1
(1;tW S ;tW P ) W 1; C W
(
1
(1;tRS ) W 1; C R
; 1)
; 1)
37
However, in comparison to standard Real Business Cycle literature the workers’ labour supply elasticity is on low side. For instance Bayomi, Laxton and Pesenti (2004) uses the value 0.33 in the standard calibration of GEM to Euro area.
43
After 5 years 1.28 -.31 1.06 1.13 .48 -2.4 -3.2 -1.47
After 10 years 1.98 0.25 1.43 1.74 .18 -8.2 -3.9 -1.78
Long-run 2.92 2.47 1.71 2.77 -.7 0 -4.0 -1.85
Percentage of total effect after 5 years 43.79 -12.59 62.0 40.65 -27.2 n.a. 80.0 80.0
T
Private Production,% Private Consumption,% Employment,% Real Wage,% Income tax rate,% points Debt to GDP ratio, % points Wage mark-up, % Price mark-up, %
After 2 years 0.44 -0.78 .47 0.45 .41 1.54 -1.8 -.82
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Table 7: AINO estimates of the increasing labour and product market competition with faster fiscal adjustment Increasing Frisch elasticity of labour supply is likely to magnify the effects of increasing competition both in the labour and the product markets. We have thus experimented by decreasing the value of intratemporal substitution parameter from 0:855 to 0:8. This requires re-calibration of the pensioners relative productivity to 0:6 in order to keep pensioners labour supply within observed range. As a result of this this re-calibration, workers’ Frisch elasticity of labour supply increases to value 0:23, while pensioners Frisch labour supply elasticity remains at roughly 0:3. With these new values of elasticities we find that the effects of increasing competition are now roughly 30 % higher than in the standard simulation (see table 6). For instance output and private consumption increase in the long-run by 3:97 % and 3:51 %. Similarly, employment increases now by 2:45% in comparison to 1:71% in the standard simulation. Finally, these larger effects show up also in markedly higher increase in utility. Utility increase measured in units of consumption is 1:73% in the long-run. As a final check of the robustness of our results, we make fiscal adjustment considerably faster. This is achieved by inreasing the value of parameter in the fiscal adjustment equation from 0:02 to 0:1: As expected, faster fiscal adjustment leads into more pronounced increase in income tax rate in the short and medium run. Faster adjustment of income tax rate, in turn, implies less pronounced increase in debt to output ratio in the short run. Faster fiscal adjustment results slightly more pronounced decline in consumption in the short-run when compared to the case with slow fiscal adjustment. This is associated with somewhat less pronounced increase in employment but more pronounced increase in real wage. Finally, faster fiscal adjustment has only very minor effects on private investment and capital stock (not reported). The table (7) summarises some of the results with faster fiscal adjustment. Finally, figure (5) compares the dynamic adjustment paths under standard simulation and under fast fiscal adjustment.
44
7 Conclusions
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T
According to Høj and Wise (2004), Finnish economy suffers from stagnation in decreasing competition barriers in product markets. Finnish labour markets can be characterised as highly centralised. Finnish economy will face a dramatic demographic change in forthcoming decades leading to substantial rise in old-age dependency ratio. The ageing population will increase fiscal burden substantially. Product and labour market reforms may form a possible avenue for reliefing this burden. We use recently developed Aino model of the Finnish economy to give a quantitative evaluation of the macroeconomic effects of the increased product and labour labour competition. Aino model contains explicit parameters relating to degree of competition in product and labour markets. We simulate the response of the model’s economy to changes in these parameters. Our estimate for the baseline level of product market mark-up is 8 percent and for labour market mark-up 25 percent. We simulate 2 percentage points decline in product mark-up and 4 percentage points decline in wage mark-up. The decline is gradual in these mark-ups so that 80 percent of the shock is passed in 5 years. This time frame corresponds the time frame of Lisboa strategy that aims completing reforms by 2010. We test the robustness of our simulation results to some key parameters of the model. These include various parameters such as fiscal adjustment and labour supply elasticities. Each of our choice of mark-up shocks gives roughly same magnitude in welfare improvements. Welfare rises 1.2 percent in the long-run when measured in consumption units. Consumption, investments, employment and production rises and prices decline in the long-run. There is, however, initial slump in consumption due to the wealth effect of the contracted profits and due to the rise in real interest rate. The increased efficiency gives room to decrease income tax rate and employees’ pension contribution by 0.7 percentage points each. This change in tax rates keeps the long-run public debt to GDP ratio at constant baseline level. Contrary to Høj and Wise (2004) we cannot offer any particular practical recommendation. They are beyond the scope of a macro model like Aino. For the same reason it is hard to say whether the size of the assumed decline in mark-up is big or small. Cross-country comparisons using the same methodology and model structure would possibly validate our choices. Finally, product market competition and technological changes are not necessarily independent (Nicoletti et al. 2001). Our experiment does not take into account this interdependence. Positive correlation between these would imply even greater positive responses. Hence, in this respect our estimates of the benefits of the product and labour market reforms might be conservative.
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Figure 5: Labour and Product Market Reforms: Dynamic Adjustment Paths under Different Assumption of Fiscal Adjustment
5
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Note: Horisontal axis is in quarters. Dashed line corresponds to our benchmark case and solid line to the case of faster fiscal adjustment.
46
[References to be completed]
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