Lithuania in the euro area: monetary transmission and macroprudential policies

This article develops a two-country monetary union new Keynesian general equilibrium model with housing and collateral constraints calibrated for Lithuania and the rest of the euro area. Within this setting, and following the recent entry of Lithuania in the European Monetary Union, the aim of the article is twofold. First, it studies how shocks are transmitted differently in the two regions, considering the recent common monetary policy. It then analyzes how Lithuanian macroprudential policies should be conducted in the context of the EMU. The proposed macroprudential tool is a decentralized Taylor-type rule for the LTV which responds to national deviations in output and house prices. Given the features of Lithuania’s housing market, common shocks are found to be transmitted more strongly in this country than in the rest of the euro area. In terms of macroprudential policies, results show that the optimal policy in Lithuania with respect to the euro area may have a different intensity and that it delivers substantial benefits in terms of financial stability.

a tiny part in the decision-making. Furthermore, some specific characteristics of the housing market in Lithuania can result in the single monetary policy being transmitted in the Lithuanian economy in a way that is different than in other countries.
The Lithuanian housing market has certain particularities that make it different from the markets in the country's euro area partners. One of these differences pertains to mortgage contracts. Housing loans (and loans to nonfinancial corporations, NFCs) in Lithuania are almost exclusively made at variable interest rates (set for fixed periods of up to 1 year), which are quick to respond to changes in borrowing costs in the financial markets. 1 At the beginning of 2013, about 70% of new loans to households were issued at flexible interest rates. In 2014 and 2015, the proportion increased to more than 80% (in 2015 the share of flexible rate loans for both households and NFCs reached 90%). 2 In the big countries of the euro area, however, the majority of households take mortgages at a fixed rate. 3 For France and Germany, the ratio of flexible-rate loans is pretty low, around 12% and 15% respectively, while in Spain it reaches 82%. This high heterogeneity is reflected in the average percentage of 45% for flexible-rate mortgages in the euro area (the corresponding percentage of fixed-rate loans is therefore 55%).
Another issue of concern, now that Lithuania is part of the euro area, is how to correctly implement policies to promote financial stability, in cooperation with the other members. The economy of Lithuania has suffered from the same financial stability problems stemming from the crisis as other countries. Like other economies, it has been trying to recover ever since, and it has in fact fully recovered in terms of economic activity. The banking sector, in any case, is now far better prepared to withstand such turbulences than at the outset of the most recent economic downturn. Recent Financial Stability Reviews (Bank of Lithuania 2013Lithuania , 2014Lithuania , 2015 have stressed that despite the growth of the domestic economy and the improved financial health of the private sector, credit activity was subdued in 2014 and in the first half of 2015. However, irrespective of the better preparedness of the banking sector to withstand shocks, the overall conditions remain challenging. It is of the utmost importance not only that the banking sector be capable of absorbing the previous shocks, but also that it be adequately prepared to face any new systemic risks and to ensure sufficient credit availability for the real sector under the least favorable conditions. As a new member of the euro area, Lithuania has to implement its macroprudential policies in the context of its new economic setting, interacting with the other monetary union members that indeed share the same monetary policy. The Bank of Lithuania pursues macroprudential policy at the national level and monitors, assesses, and does its best to limit the macroprudential risk for the stability of the domestic financial system; in doing so, it has the possibility to cooperate with the European Central Bank (ECB) and other national and international institutions. One of the Bank of Lithuania's intermediate objectives is to mitigate excessive credit growth and too high leverage.
The article begins by illustrating monetary policy transmission in Lithuania in the context of the euro area and then proposes the implementation of a macroprudential tool, based on the loanto-value (LTV), 4 that aims at maximizing welfare. 5 The basic modeling setup constitutes a twocountry new Keynesian dynamic stochastic general equilibrium (DSGE) model with financial frictions. In each country, there is a group of individuals who are credit constrained and need housing collateral to obtain loans. Countries trade goods, and savers in each country have access to foreign assets. Within this setting, the article considers how macroprudential policies should be conducted in Lithuania in the context of the euro area. It proposes, as a macroprudential tool, a decentralized Taylor-type rule for the LTV that responds to national credit deviations from the steady state. It also includes the common monetary policy with a Taylor rule, consistent with the ECB target of price stability, with interest-rate smoothing for the setting of interest rates by a single central bank.
Results show that common shocks are transmitted more strongly in Lithuania than in the rest of the euro area, given that Lithuania has variable-rate mortgages and a higher LTV cap than its European partners. With respect to macroprudential policies, it is found that the optimal policy is that Lithuania may have a different intensity in its LTV setting than the rest of the euro area, given that monetary policy is more effective in this country. In addition, the LTV rule is found to be welfare enhancing for the entire monetary union, although there is a welfare trade-off between borrowers and savers. This is because, on the one hand, macroprudential policies bring a more stable financial system, and on the other hand, monetary policy may be less effective, and inflation volatility can increase.
The article is organized as follows: The next section briefly addresses the author's main contribution, linking it to the recent literature. The model is then described, followed by a presentation of the parameter values and then of the dynamics of the model. The sixth section analyzes optimal macroprudential policies before concluding.

LITERATURE REVIEW AND OUR CONTRIBUTION
This article links the policy-making issue to different strands of the literature. An extensive literature shows that institutional consumption, financial, or housing market heterogeneity can endanger the optimality of the European Monetary Union (EMU) as a currency area (Maclennan, Muellbauer, and Stephens 1998;Rubio 2014); (Task Force, 2009). The model constitutes a twocountry version of the seminal article by Iacoviello (2005), which introduced a financial accelerator that works through the housing sector, in the flavor of Aspachs and Rabanal (2010). However, it introduces cross-country housing-market heterogeneity, as in Rubio (2014). The article is also related to the recent literature on macroprudential and monetary policies in Iacoviello-type models, such as in the aforementioned Kannan, Rabanal, and Scott (2012) or Carrasco-Gallego (2013, 2014). However, it explores the issue in a twocountry setting, as in Brzoza-Brzezina, Kolasa, and Makarski (2015). The novelty of this article is its special application to the case of Lithuania in a two-country framework with respect to the rest of the euro area. There is also some literature looking at the response of the Lithuanian economy to a common ECB rate shock. In particular, Stakėnas and Stasiukynaitė (2016), through an empirical structural VAR, look at the responses of GDP, HICP (excluding energy), and credit to nonfinancial institutions and households in Lithuania (and to GDP and HICP only for the euro area) due to a 100 bp increase in the Euribor. Their results are in line with some previous studies, such as Errit and Uusküla (2014) and Georgiadis (2015), which concluded that the response to a monetary policy shock coming from the euro area is quite substantial.

MODEL SETUP
The present discussion considers an infinite-horizon, two-country economy inside a monetary union. The home country is denoted by LIT and the rest of the union by EUR. Households consume, work, and demand real estate. There is a financial intermediary in each country that LITHUANIA IN THE EURO AREA provides mortgages and accepts deposits from consumers. Each country produces one differentiated intermediate good, but households consume goods from both countries. For simplicity, housing is a nontraded good. Labor is assumed to be immobile across the countries. 6 Firms follow a standard Calvo problem (after Calvo 1983). In this economy, both final and intermediate goods are produced. Prices are sticky in the intermediate-goods sector. Monetary policy is conducted by a single central bank that responds to a weighted average of inflation in both countries. Analogous to the setting of the interest rate, there is a rule for the setting of the LTV, which serves as a macroprudential measure. Housing-market heterogeneity is allowed for across the countries.

The Consumer's Problem
There are three types of consumers in each country: unconstrained consumers, constrained consumers who borrow at a variable rate, and constrained consumers who borrow at a fixed rate. The proportion of each type of borrower is fixed and exogenous. 7 Consumers can be constrained or unconstrained in the sense that constrained individuals need to collateralize their debt repayments in order to borrow from the financial intermediary. Interest payments in the next period cannot exceed a proportion of the future value of the current house stock. In this way, the financial intermediary ensures that borrowers are going to be able to fulfill their debt obligations in the next period. As in Iacoviello (2005), constrained consumers are assumed to be more impatient than unconstrained ones. 8 There is a financial intermediary in each country. The financial intermediary in each country accepts deposits from domestic savers, and it extends both fixed-and variable-rate loans to domestic borrowers.

Unconstrained Consumers (Savers)
Unconstrained consumers in LIT maximize, as in Equation (1): Here E 0 is the expectation operator, β 2 0; 1 ð Þ is the discount factor for savers, and C u t , H u t , and L u t are consumption at t , the stock of housing, and hours worked, respectively. j represents the weight of housing in the utility function. 1= η À 1 ð Þ is the aggregate labor-supply elasticity. Consumption is a bundle of domestic and foreign-produced goods, defined as: where n is the size of LIT.
The budget constraint for LIT is as in Equation (2): where P LITt and P EURt are the prices of the goods produced in countries LIT and EUR, respectively, Q t is the housing price in LIT, H u t is the stock of housing, and W u t is the wage for unconstrained consumers. B u t represents domestic bonds denominated in the common currency. R LITt is the nominal interest rate in LIT. Positive bond holdings signify borrowing, and negative signify savings. However, as will be seen, this group will choose not to borrow at 32 M. RUBIO AND M. COMUNALE all: they are the savers in this economy. D t are foreign-bond holdings by savers in LIT, who indeed have access to the international financial market. R t is the nominal rate of foreign bonds, which are denominated in euros. As is common in the literature, stationarity of net foreign assets is ensured by introducing a small quadratic cost of deviating from zero foreign borrowing, ψ 2 D 2 t . Savers obtain interest on their savings. S t and F t are lump-sum profits received from the firms and the financial intermediary in LIT, respectively.
Dividing by P LITt , the budget constraint can be rewritten in terms of goods LIT as in Equation where π LITt denotes inflation for the goods produced in LIT, defined as P LITt =P LITtÀ1 : Maximizing Equation 1 ð Þ subject to Equation 3 ð Þ; the first-order conditions for the unconstrained group are obtained in Equations (4), (5), (6), (7), and (8): Equation 4 ð Þ equates the marginal rate of substitution between goods to the relative price. Equation 5 ð Þ is the Euler equation for consumption. Equation 6 ð Þ is the first-order condition for net foreign assets. Equation 7 ð Þ is the labor-supply condition. These equations are standard. Equation 8 ð Þ is the Euler equation for housing and states that at the margin the benefits from consuming housing have to be equal to the costs.
Combining Equations 5 ð Þ and 6 ð Þ, a nonarbitrage condition is obtained between home and foreign bonds, as in Equation (9) Since all consumption goods are traded and there are no barriers to trade, it is assumed in this article that the law of one price holds, as in Equation (10): where variables with a star denote foreign variables and P Ã LITt is the foreign price of goods produced at home.

Constrained Consumers (Borrowers)
Constrained consumers in LIT are of two types: those who borrow at a variable rate, and those who do so at a fixed rate. The difference between them is the interest rate they are charged. The variable-rate constrained consumer faces R LITt , which will coincide with the rate set by the central bank. The fixed-rate borrower pays R LITt , derived from the financial intermediary's problem. The proportion of variable-rate consumers in LIT is constant and exogenous, and is equal to α LIT 2 0; 1 ½ . Constrained consumers are more impatient than unconstrained ones; that is, e β<β in terms of the discount factors for borrowers and savers respectively. Constrained consumers face a collateral constraint-the expected debt repayment in the next period cannot exceed a proportion of the expectation of tomorrow's value of today's stock of housing, as in Equations (11) and (12): where Equations 11 ð Þ and 12 ð Þ represent the collateral constraint for the variable-and fixed-rate borrower, respectively. k LITt can be interpreted as the loan-to-value ratio in LIT. Note that in such models with collateral constraints, the LTV is typically considered exogenous. At the macroeconomic level, LTVs partly depend on exogenous factors such as regulation. This parameter is usually calibrated to match the average (market) LTV in the country analyzed. 11 However, in this model, it can vary depending on economic conditions, as a macroprudential policy variable. 12 The setting of the fixed interest rate, R LITt , follows Rubio (2011). It is assumed that there is a financial intermediary in each country that accepts deposits from savers and extends both fixedand variable-rate mortgages to borrowers. For the two types of mortgage to be offered, the fixedinterest rate has to be such that the intermediary is indifferent between lending at a variable or a fixed rate. R LITt will be an aggregate interest rate that contains information on all the past fixedinterest rates associated with past debt. Each period, this aggregate interest rate is updated with a new fixed interest rate that is an average discount average of all future variable interest rates.
The problem for the variable-rate borrower is presented without loss of generality, since for the fixed rate it is symmetrical. Variable-rate borrowers maximize their lifetime utility function as in Equation (13): ; subject to the budget constraint (in terms of good LIT) as in Equation (14): and subject to the collateral constraint in Equation 11 ð Þ. Note that variable-rate borrowers repay all debt every period and acquire new debt at the current new interest rate. This assumption implies that the interest rate on variable-rate mortgages is revised every period for the whole stock of debt and changed according to the policy rate. 13 To make the problem for fixed-rate borrowers symmetrical and analogous to existing models with borrowing constraints, the same debt-repayment structure is assumed for this type of borrower. Obviously, fixed-rate contracts are not revised every period. However, to make the model more realistic, but still tractable, the fixed-interest rate will be such that a revised fixed rate will be applied only on new debt, keeping constant the interest rate applied to existing debt. In this way, the structure of the model is reconciled with the fact that fixed-rate contracts are long-term.
The first-order conditions for these consumers are as in Equations (15), (16), (17), and (18): These first-order conditions differ from those of unconstrained individuals. In the case of constrained consumers, the Lagrange multiplier on the borrowing constraint λ cv t À Á appears in Equations 16 ð Þ and 18 ð Þ. As in Iacoviello (2005), the borrowing constraint is always binding, so that constrained individuals borrow the maximum amount they are allowed, and their saving is zero. The problem for consumers is analogous in country EUR.

Final-Goods Producers
In LIT, there is a continuum of final-goods producers that aggregate intermediate goods according to the production function in Equation (19): where ε > 1 is the elasticity of substitution among intermediate goods. :

Intermediate-Goods Producers
The intermediate-goods market is monopolistically competitive. Following Iacoviello (2005), intermediate goods are produced according to the following production function in Equation (20): where t represents technology. It is assumed that log t ¼ ρ log tÀ1 þ u t , where ρ is the autoregressive coefficient and u t is a normally distributed shock to technology. γ LIT 2 0; 1 ½ measures the relative size of each group in terms of labor. 14 L c t is labor supplied by constrained consumers, defined as α LIT L cv t þ 1 À α LIT ð Þ L cf t . The first-order conditions for labor demand are as in Equations (21) and (22): 15 where X t is the markup, or the inverse of marginal cost. The price-setting problem for the intermediate-goods producers is a standard Calvo-Yun case. An intermediate-goods producer sells goods at price P LITt z ð Þ; and 1 À θ is the probability of being able to change the sale price in every period. The optimal reset price P OPT LITt z ð Þ solves the following in Equation (23): The aggregate price level is given as in Equation (24): Equations 23 ð Þ and 24 ð Þ and log-linearizing are used to obtain the standard forward-looking Phillips curve. 16 The firm problem is similar in EUR.

Aggregate Variables and Market Clearing
Given α LIT ; the fraction of variable-rate borrowers in LIT, aggregates can be defined across constrained consumers as the sum of variable-rate and fixed-rate aggregates, so that

Monetary Policy
The model closes with a Taylor rule, with interest-rate smoothing for interest-rate setting by a single central bank, as in Equation (25): 18 0 ρ 1 is the parameter associated with interest-rate inertia. 1 þ ϕ π ð Þ measures the sensitivity of interest rates to current inflation. ε R;t is a white-noise shock process with zero mean and variance σ 2 ε . R is the interest rate in steady state. This rule is consistent with the ECB's primary objective of price stability.

Macroprudential Policy
A Taylor-type rule is considered as an approximation for a macroprudential policy for the loanto-value ratio. In standard models, the LTV ratio is a fixed parameter that is not affected by economic conditions. However, regulation of LTV ratios can be thought of as a way to moderate credit booms. When the LTV (cap) ratio is high, the collateral constraint is less tight. Since the constraint here is binding, borrowers will borrow as much as they are allowed to. Lowering the LTV tightens the constraint and therefore restricts the loans that borrowers can obtain. Recent research on macroprudential policies has proposed Taylor-type rules for the LTV ratio so that it reacts inversely to such variables as the growth rates of GDP, credit, the credit-to-GDP ratio or house prices. 19 For the purposes of the model, it was decided to make the rule more parsimonious. thereby allowing the LTV ratio to react to borrowing. This will help for a further study on LITHUANIA IN THE EURO AREA the interactions with monetary policy. These rules can be a simple illustration of how a macroprudential policy could work in practice. Here it is assumed that there is a macroprudential Taylor-type rule for the LTV ratio, such that it responds to deviations of credit from its steady state. 20 A decentralized macroprudential policy is considered in which each country can implement its own rule, represented by Equations (26) and (27): where k SSLIT ; b LIT are the steady-state values for the LTV ratio and borrowing in LIT. ϕ k LIT ! 0 measures the response of the LTV to deviations of borrowing from its steady state. This kind of rule would be countercyclical, delivering a lower LTV ratio in credit booms, therefore restricting the credit in the economy.

Welfare Measure
In order to provide a measure for welfare, how cross-country asymmetries affect welfare is numerically evaluated for a given policy rule and for technology shocks. As discussed in Benigno and Woodford (2012), two approaches have recently been used for welfare analysis in DSGE models: characterizing the optimal Ramsey policy; and solving the model using a second-order approximation to the structural equations for a given policy and then evaluating welfare using this solution. As in Mendicino and Pescatori (2007), the latter approach is taken to be able to evaluate the welfare of the three types of agents separately. 21 The individual welfare for savers and borrowers in LIT is defined, respectively, as in Equations (28) and (29): Following Mendicino and Pescatori (2007), social welfare in LIT is defined as a weighted sum of the individual welfare for the different types of households as represented by Equation (30): The welfare of borrowers and savers is weighted by 1 À e β and 1 À β ð Þ; respectively, so that the two groups receive the same level of utility from a constant consumption stream. Everything is symmetrical for EUR.

M. RUBIO AND M. COMUNALE
Total welfare is defined as a weighted sum of the welfare in the two countries, as in Equation (31): In order to make the results more intuitive, welfare changes are presented in terms of consumption equivalents. The welfare evaluated when the macroprudential policy is not active is used as a benchmark and compared with the welfare obtained when the policy is implemented. 22

PARAMETER VALUES
Parameters are calibrated to reflect the economy of Lithuania and of the rest of the euro area. Some of the parameters are standard and are common for both economies, and some others will be specifically calibrated for each country. Tables 1 and 2 present a summary of the parameter values. Discount factors are set to be common in both economies, following the standard values in the literature. The discount factor for savers, β , is set to 0:99 . 23 The discount factor for borrowers, e β , is set to 0:98 . 24 The steady-state weight of housing in the utility function, j , is set to 0:12 and 0:14, in the euro area and Lithuania, respectively. This parameter pins down the ratio of housing wealth to GDP, since the latter in the steady state is a function of this parameter. 25 It was set as η ¼ 2 , implying a value of the labor supply elasticity of 1: 26 For the loan-to-value ratio, a steady-state value of 0.68 and 0.78 is considered for the euro area and Lithuania, respectively, taking the LTV ratio observed in the data. 27 The labor-income share of  unconstrained consumers, γ , is set to 0:7 . 28 A value of 6 is picked for ε , the elasticity of substitution among intermediate goods. This value implies a steady-state markup of 1:2 . The probability of not changing prices, θ , is set to 0:75 , implying that prices change every four quarters on average. The Taylor rule parameters were ρ ¼ 0:8 and ϕ π ¼ 0:5: The first value reflects a realistic degree of interest-rate smoothing. 29 ϕ π is consistent with the original parameters proposed by Taylor in 1993. α, the proportion of variable-rate mortgages, was considered to be 0.45 and 0.82, in the euro area and Lithuania, respectively. The size of Lithuania is considered to be 0.35%. 30 A technology shock was a 1% positive technology with 0.9 persistence. 31 Tables 1 and 2 present a summary of the parameter values.

SHOCK TRANSMISSION
This section studies the dynamics of the model by showing impulse-responses to a monetary policy shock, a technology shock, and a house-price shock, abstracting from macroprudential policies, and using the parameter values shown in the previous section. Given the structural differences between Lithuania and the rest of the euro zone, a monetary policy shock coming from the ECB will potentially be transmitted in a different way in Lithuania. Other shocks (e.g., technology and housing demand), even if they are common, will have different impacts on the two economies and will have to be accommodated by the single monetary policy. Figure 1 presents impulse responses to a monetary policy shock representing a decrease in the interest rate by the ECB. The common monetary policy shock is transmitted to the two economies in different ways. Although the effects on house prices and inflation are very similar for Lithuania and the rest of the euro area, the effects on borrowing differ. In particular, note that in Lithuania the increase in borrowing is stronger than in the rest of the euro area. Lithuania is an economy in which rates are variable, as opposed to the big countries of the EMU. Therefore, the same drop in the policy rate is transmitted in a direct way to the borrowing rate, causing credit to increase sharply. On the other hand, the LTV in Lithuania is also larger than in the rest of the euro area. This creates a higher financial accelerator, and thus the same changes in the interest rate and house prices affect the collateral constraint by more, making borrowing more sensitive to monetary policy changes. This stronger increase in credit creates an extra increase in consumption demand in Lithuania.

Impulse Responses to a Technology Shock
When there is a common technology shock, demand increases in a similar way in both countries ( Figure 2). In the same way, inflation decreases both in LIT and EUR and reduces the interest rate. The main difference comes on the financial side. Given that Lithuania has a higher LTV than the rest of the euro area and the interest rate is variable, borrowing increases by more in Lithuania following the fall in the common policy rate. As in the previous case, the increase in mortgaged houses is higher in Lithuania. For this kind of shock, a slightly larger increase in house prices is observed in Lithuania, with respect to the rest of the euro area.

Impulse Responses to a House Price Shock
Figure 3 describes impulse responses to a house price shock both in Lithuania and the rest of the euro area. As can be seen from the figure, the house price shock is stronger in Lithuania, causing credit to increase by more there. This creates strong effects on mortgaged houses and on consumption. In the rest of the euro area, the effects are similar but weaker.

OPTIMAL MACROPRUDENTIAL POLICY
The discussion in this section searches for the macroprudential policy that is optimal in the sense that it maximizes the country's welfare. It is assumed that macroprudential policy is taken at a national level and that both countries take the ECB policy as given when deciding on their macroprudential policies. Table 3 presents the optimized parameters for the macroprudential rules, in particular the ones described in Equations 26 ð Þ and 27 ð Þ. Taking monetary policy as given, the parameters that maximize welfare in each country are searched simultaneously. 32 The first row in Table 3 corresponds to the optimal macroprudential policy in the rest of the euro area. In the second row, Lithuania optimizes its macroprudential policy to maximize its welfare. 33 As can be seen, the optimal policy in Lithuania may have a different intensity, compared to the rest of the euro area. This is mainly due to the variable rates that predominate in Lithuania. In the rest of the euro area, with fixed rates, monetary policy is less effective and macroprudential policies can compensate for this fact. Table 4, using the optimal parameters just described above, presents the gains in terms of the welfare (in consumption equivalents) that implementing this optimal rule represents. As in Ascari and Ropele (2009), this makes it possible to find the constant fraction of steady-state consumption that would have to be transferred to the agent if there were a welfare loss under the new parameterization. 34 Here a positive value of consumption units represents a welfare increase; that is, how much the agent would pay in units of consumption in order to be better off. A negative value means that welfare is decreasing; that is, by how much an agent should be compensated in units of consumption. The benchmark is the case in which there are no macroprudential policies in place.
As may be observed from Table 4, macroprudential policies enhance welfare in both regions. In models with collateral constraints, macroprudential policies deliver welfare gains because of the externality coming from the constraint. In models of this kind, the collateral constraint is always binding, and, therefore, borrowers are not able to smooth consumption as savers do. Thus, a policy that enhances financial stability brings them a more stable scenario with a more stable consumption path. 35 However, as is usual in this kind of model, there is a trade-off   between borrowers and savers. Savers are worse off with macroprudential policy because, in this model, the sticky-price assumption creates a distortion that affects them. Since they are the owners of the firms, ideally they would like to live in a world in which there is price stability, the goal of monetary policy. If monetary policy loses effectiveness with the presence of macroprudential policies, savers may not like the policy. 36 In the aggregate, the economy benefits from macroprudential policies, but the gain comes from the borrower's side. Table 5 displays both macroeconomic and financial volatilities to further our understanding of where the welfare gains come from. The standard deviations for output, inflation, and borrowing are calculated for Lithuania and the rest of the euro area. The benchmark is the case in which there are no macroprudential policies in place (first column). It is then possible to see how these volatilities change when one considers the optimized parameters obtained in Table 3 (second column of Table 5). As can be seen, when the macroprudential policy is introduced, the economy benefits from a more stable economy, in terms of both output and borrowing. 37 This comes at the expense of larger volatility of inflation in the model, because of the differences that may arise between macroprudential and monetary policies in the context of supply-side shocks. 38

CONCLUDING REMARKS
This article develops a two-country DSGE model with housing to study the implications of the entry of Lithuania into the euro area. One of the countries is calibrated to reflect the Lithuanian economy, while the other one represents the rest of the euro area.
The discussion begins by examining how common shocks are transmitted in different ways in the two regions. In particular, results show that common shocks (monetary policy, technology, or house-price shocks) are transmitted in a stronger way in Lithuania than in the rest of the euro area, given that Lithuania has variable-rate mortgages and a higher LTV ratio than its European partners.
How macroprudential policies should be conducted in this context is examined next. Macroprudential policies are approximated as a rule for the LTV setting that responds to deviations of credit from its steady state. The optimal macroprudential policy for Lithuania is found to have a different intensity in its LTV setting than the rest of the euro area, given that monetary policy is more effective in Lithuania. It is also found that the LTV rule is welfare enhancing for the entire monetary union, although there is a welfare trade-off between borrowers and savers. Two factors explain this: on the one hand, macroprudential policies bring a more stable financial system, but on the other, monetary policy may be less effective and inflation volatility can increase.  (2014) on data from ECB. They report the share of flexible-rate mortgages among the oldest active mortgages related to the household main residence. 4. In the model, the LTV ratio will be calibrated to match the average (market) LTV in steady state.

ACKNOWLEDGMENTS
However, the market LTV can vary depending on economic conditions and may be different with respect to the imposed LTV cap set by authority. When the LTV cap is high, the collateral constraint is less tight. Moreover, since the constraint in this model is binding, borrowers will borrow as much as they are allowed. Lowering the LTV tightens the constraint and therefore restricts the loans that borrowers can obtain. 5. Here we follow Angelini et al. (2014), who assume that the loss function in the economy also contains financial variables. Therefore, it is used here as a proxy for financial stability, which is seen as the actual aim of macroprudential policy (Galati and Moessner 2011). 6. This is a standard simplifying assumption, since the focus of the article is on financial markets. The fact that labor mobility has been a factor within the euro area is acknowledged, but it is not covered here. This is especially true for Lithuania, where it resulted in a labor shortage and a significant emigration. 7. According to the European Mortgage Federation, the type of mortgage contracts across a country responds, to a large extent, to institutional or cultural factors that are beyond the scope of the present model. In the short run, the proportion of each type of mortgage contract can fluctuate, but, typically, it does not imply a change in the fixed-or variable-rate category of the country. 8. This assumption ensures that the borrowing constraint is binding in the steady state and that the economy is endogenously split into borrowers and savers. 9. The variables in small letters are taken divided by P LITt : 10. The log-linearized version of this equation could be interpreted as the uncovered interest-rate parity. 11. Due to data availability, we use the average new loans' LTV at origination. 12. It has to be taken into account that in reality, macroprudential LTV caps are not always binding. Even a stable LTV cap inherently has a countercyclical effect, because it is less binding after a crisis but is LITHUANIA IN THE EURO AREA likely to become more binding as credit and housing prices pick up during the financial cycle (Matkėnaitė, Ramanauskas, and Reichenbachas 2016). 13. This assumption is consistent with reality, in which variable-interest rates are revised very frequently and changed according to an interest-rate index tied to the interest rate set by the central bank. 14. It can be seen as labor-income share and proxy for the differences in debt to GDP. 15. Symmetry across firms makes it possible to avoid index z: 16. The Phillips curve is defined asπ LITt ¼ βπ LITtþ1 À e kx t þ u LITt ,wherex is 1/real marginal cost and e k ¼ ½ð1 À θÞð1 À βθÞ=θ: 17. An endogenous supply of housing could be easily introduced in a two-sector version of this model. However, the qualitative results would not change for the demand side of the model, which is the focus of this article. For two-sector models, see, for example, Iacoviello and Smets (2006) or Iacoviello and Neri (2010). 18. This type of rule is also used in other monetary-union models. See Iacoviello and Smets (2006) or Aspachs and Rabanal (2008). Furthermore, as shown in Iacoviello (2005) and Rubio and Carrasco-Gallego (2013), a rule that only responds to inflation enhances the financial accelerator. 19. With a macroprudential orientation, Kannan, Rabanal, and Scott (2012) also examine a monetary policy rule that reacts to prices, output, and changes in collateral values with a macroprudential instrument based on the LTV; Funke and Paetz (2012) consider a nonlinear version of a macroprudential rule for the LTV. 20. The authors have also experimented with rules that react to output and house prices, and results for the dynamics of the model are similar. The first variable would correspond to the objective of the macroprudential regulator to moderate booms in the economy that could lead to an excessive credit growth. Drehmann et al. (2010) also point out that the deviations of credit from its long-term trend are very good indicators of the increase in systemic risk, which is the focus of macroprudential attention.
As for house prices, given collateral constraints, they are the key causal variable for the dynamics of loans to households and appear to correspond to the actual behavior of policymakers (Angelini, Neri, and Panetta 2012). 21. Dynare software was used to obtain a solution for the equilibrium implied by a given policy by solving a second-order approximation to the constraints, then evaluating welfare under the policy using this approximate solution, as in Schmitt- Grohé and Uribe (2004). See Monacelli (2006) for an example of the Ramsey approach in a model with heterogeneous consumers. 22. This follows Ascari and Ropele (2009). 23. Since the seminal article by Kydland and Prescott (1982), the literature on DSGE models consider a calibrated value of 0.99 for the discount factor as the standard value for this parameter. 24. Lawrance (1991) estimated the discount factors for poor consumers at between 0.95 and 0.98 at quarterly frequency. 25. Following Iacoviello and Neri (2010), this article uses 1.2, a value that reflects the ratio of housing wealth to GDP across most industrialized countries, as a proxy for the euro area. The ratio is higher, though, in Lithuania. 26. Microeconomic estimates usually suggest values in the range of 0 and 0.5 (for males). Domeij and Flodén (2006) showed that in the presence of borrowing constraints, this estimate could have a downward bias of 50%. 27. Note that the macroprudential LTV cap in Lithuania since 2011 has been 85%, which is higher than the average LTV in the last decade. 28. This value is in the range of the estimates of Iacoviello (2005) and Iacoviello and Neri (2010) for the United States, and Campbell and Mankiw (1991) for the United States, Canada, France, and Sweden. Therefore, it is taken as valid for most of the countries of the euro area. 29. See McCallum (2001). 30. Even though Lithuania is such a small country, the two-country setting is still desirable, so as to be able to study the interaction between policies in Lithuania and the rest of the euro area and, potentially, centralized versus decentralized policies.
31. This high persistence value for technology shocks is consistent with what is commonly reported in the literature. Smets and Wouters (2002) estimated a value of 0.822 for this parameter in Europe; Iacoviello and Neri (2010) estimated it as 0.93 for the United States. 32. As in Angelini et al. (2014), given that regulations are not microfounded here, a positive approach is adopted throughout the article. Second-order values should not be taken as normative. That is, taking the presence of the macroprudential regulator as given, the effects of the regulation on the economy are studied. 33. This follows Angelini et al. (2014) in which it is assumed that the loss function in the economy also contains financial variables, namely borrowing variability, as a proxy for financial stability. Then there would be a loss function for the economy that would include not only the variability of output and inflation but also the variability of borrowing: L ¼ σ 2 π þ λ y σ 2 y þ σ 2 b , where σ 2 π ; σ 2 y and σ 2 b are the variances of inflation, output, and borrowing. λ y ! 0 represents the relative weight of the central bank to the stabilization of output. 34. The consumption equivalent measure for the saver, as in Ascari and Ropele (2009), is given by 1 À exp½ð1 À βÞðV u;new À V u;old , and analogously for the other agents. 35. In other words, if the financial system is very unstable and the asset prices (house prices in this framework) are very volatile, borrowers' consumption will also be very volatile, since it depends on the value of the collateral. 36. Allowing for fiscal redistribution would bring a Pareto improvement. However, fiscal mechanisms are not considered in this article. The aim here is to stress the impact of optimal macroprudential policies for agents and within the two countries. 37. Note that this macroprudential policy involves only a short-term output cost, since the policy does not represent a change in the steady state. Welfare benefits are long-term. 38. See Rubio and Carrasco-Gallego (2015) for a detailed explanation of the policy conflicts.