ijcrb.webs.com INTERDISCIPLINARY JOURNAL OF CONTEMPORARY RESEARCH IN BUSINESS Overdraft versus Collateral Constraint in the New Keynesian Model

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1 Overdraft versus Collateral Constraint in the New Keynesian Model + Wabekwa, Bundi *Fada, Kodun Abiah and Jonah, Udeme + Msc Financial Economics (University of Exeter, UK), Lecturer, Department of Accounting and Administration, Federal University Kashere, P.M.B 0182, Gombe State *MSc Finance & Banking in Emerging Economies (University of Reading, UK), Lecturer, Department of Business Administration, Gombe State University, P.M.B.127, Gombe State Msc Finance and Accounting (University of Wales, UK) Abstract Empirical evidence have shown that after an interest rate hike, credit constraints may become tighter, and a reduced ability to borrow could then force credit-constrained household to decrease durable consumption while the unconstrained increases durable consumption. We compared the collateral constraint model of Monacelli, 2009 by incorporation overdraft. We found that counterfactual problem in durable consumption under overdraft is short-lived and co-movement under collateral condition is more severe. This is evident from the sluggish decline in aggregate durable consumption. Following the argument of Monacelli (2009), the introduction of a borrowing constraint solves the co-movement puzzle. However, the introduction of overdraft of up to five multiples of annual wages facilitates in faster and better stabilisation of aggregate durables. This research shows that introducing other forms of heterogeneity between borrowers and lenders could be a promising way forward in solving the co-movement puzzle. Keywords: Monetary Policy, Durable goods and Overdraft constraint 1.0 INTRODUCTION There are many dimensions to monetary policy. Strategic questions such as defining and achieving price stability are often at the centre of debate among academics and policymakers. How monetary policy affects households behaviour and firms investment is another frequently discussed aspect. In such discourse, monetary policy is usually modelled very simplistically. It is described in terms of a single interest rate which is completely under the control of the monetary policy makers and at the same time is decisive for its influence on the private sector (Lacoviello, 2004). However, in reality the implementation of monetary policy is much more complicated. Modern theories of the monetary business cycle typically attribute central importance to new Keynesian models of monetary policy. The new Keynesian model featuring imperfect competition and price stickiness as central building blocks have recently become a workhorse reference for the analysis of business cycles and monetary policy. In the same vein Blanchard and Gali (2007) maintained that the New Keynesian model has emerged as a powerful tool for monetary policy analysis in the presence of nominal rigidities. Its adoption as the backbone of the medium-scale models currently developed by many central banks and policy institutions is a clear reflection of its success. COPY RIGHT 2013 Institute of Interdisciplinary Business Research 304

2 Goodfriend and King (1997) used this model to address several aspects of inflation targeting and strategy for interest rate policy. Recent work on the monetary transmission mechanism has emphasized some of the exceptional features of durable and non-durable goods in the monetary business cycle. An undesirable characteristic of the standard new- Keynesian models is that they tend to generate counterfactual co-movements between durable and non-durable consumption as pointed out by Barsky, (2003), House and Kimball (2007). Monacelli (2009) formalises the argument of Barsky et al (2007) by extending the standard New-Keynesian model to feature credit-constrained household, which in equilibrium borrow from households that are unconstrained. He reported that if a moderate degree of price stickiness is allowed in the durable sector, a positive co-movement is generated between durable and non-durable goods. Monacelli (2009) showed that the assumption on the degree of stickiness of durables becomes considerably less important once a collateral constraint on borrowing is initiated in the model. They also showed that credit market imperfections on the household s side could be relevant in accounting for the transmission of monetary policy shocks on durable and non-durable spending. The key idea is that, by affecting credit conditions for constrained household, monetary policy can have an impact on the intertemporal relative price of durables (the user cost), and therefore on the sectoral allocation of demand. 1.1 Paper Objective Empirical evidence have shown that after an interest rate hike, credit constraints may become tighter, and a reduced ability to borrow could then force credit-constrained households to decrease durable consumption while the unconstrained increases durable consumption. As a way of solving the counterfactual consumption behaviour in the durable goods sector, Monacelli (2009) incorporated collateral constraint in the new Keynesian model. Collateral constraint solves the counterfactual consumption behaviour only after several periods and hence, creates the need for improvement. The Objective of this paper is to device other better means of solving the counterfactual consumption behaviour between borrowers and lenders in the durable goods sector. 2.0 THE MODEL In the spirit of Monacelli, (2009), we assumed a closed economy populated by two types of infinitely lived households (constrained and unconstrained) and by firms. All household consume non-durable and durable goods. Perfectly competitive firms using labour as the only factor input produces both goods and households offer their labour services to firms. Prices of non-durables are sticky (Calvo, 1983). Policy makers set the interest rate in COPY RIGHT 2013 Institute of Interdisciplinary Business Research 305

3 response to inflation and output gap fluctuations. The new feature in this research is the replacement of overdraft with collateral constrained. This allows constrained household to secure credit not based on the value of their collateral but based on the value of their wages. The households are differentiated by their intertemporal discount factor : Patient ( u ) and Impatient ( c ). We further distinguished patient and impatient households and labelled relevant variables with subscript `u' and `c' correspondingly, as impatient households will simultaneously be, credit-constrained and patient households will remain unconstrained. The period utility of each type of household is identical: Where N jt denotes hours of labour of household type j c,u, and for every type of households X t denotes a CES consumption aggregator of form: Here, C t is a Dixit-Stiglitz (1977) aggregator of differentiated non-durable goods, and D t denotes consumption of durable goods, 0 is the share of durable goods in the composite consumption index, and 0 is the elasticity of substitution between services of non-durable and durable goods. The differentiated goods are indexed by z 0,1 and the Dixit-Stiglitz aggregator for consumption goods is defined as: The corresponding price index for consumption goods is given by Where P c,t and P d,t denote prices of consumption goods and rental price of housing respectively and the composite price index is determined as: The households are indifferent between buying new or existing stock of durable goods. Demand for each of the consumption goods is given The stock of durables is updated as follows: Where d t denotes expenditures on durable goods COPY RIGHT 2013 Institute of Interdisciplinary Business Research 306

4 2.1 HOUSEHOLDS Credit Unconstrained Consider an economy with a representative household at time t that maximises a discounted sum of expected utilities: 0 is the intertemporal elasticity of substitution of aggregate expenditure, is the disutility of labour. The budget constraint of unconstrained consumer is Where W ~ ut represents the value of the household's end of the period portfolio, A ut represents beginning of period financial wealth and T ut represent government transfers. W ut is nominal wage rate. Consumption spending consist of spending on non-durable and durable goods, priced P c,t and P ~ d,t correspondingly. D t 1 are dividends realised at the beginning of the new period. We define stochastic discount factor Q t,t 1 with the property that the price in period t of any portfolio with random value A ut 1 in the following period is given by: We also specify a limit on borrowing to prevent `Ponzi schemes': Credit Constrained The utility maximisation problem of credit-constrained households is the same as for credit-unconstrained households, However, the system of constraints is different. Credit constrained households face the budget constraint (written in real terms using the same notation as above) Where R t D is interest rate faced by the constrained household, Note that this rate is not necessarily the same rate as for unconstrained households. t A is an aggregate cost that the household has to bear when arranging new debt contracts. Financial intermediaries determine the maximum amount of borrowing. i.e, a ct is exogenous for the household. 2.2 INTERMEDIATE GOODS FIRMS An intermediate good producing firm in each sector employs two types of labour - those who are constrained and those who are unconstrained. For each type of labour, wages are equalised across all firms. All firms belong to the unconstrained households; therefore, their discount factor is used to evaluate profits. COPY RIGHT 2013 Institute of Interdisciplinary Business Research 307

5 Parameters Value (Collateral) Value (Overdraft) Production of Non-durable Goods Profit optimisation problem is standard. A firm chooses employment and prices to maximise profit: Subject to: Production constraint Demand constraint And price rigidity Table 1: Calibration and Solution Method Description Stead/baseline state value Overdraft multiple on annual wages 0 5 Rate of durable down payment u Patience rate of the Unconstrained c Patience rate of the Constrained Elasticity of Substitution between services of durable and Non-durables Share of durable goods in the composite consumption index Elasticity of labour supply 1 1 Probability of not resetting prices Preferences of hours worked 1 1 Durable goods depreciation rate COPY RIGHT 2013 Institute of Interdisciplinary Business Research 308

6 3.0 DISCUSSION AND FINDINGS The foundation of this research is based on the work of Monacelli (2009). However, we made an extension to their findings by replacing collateral constraint with overdraft and we further compared impulse responses on consumption behaviour of Monacelli s collateralised household with overdraft constrained household. From figure 1 and 2 below, notice that an exogenous productivity shock in the economy leads to increase in production. Productivity shock means that labour suddenly becomes more efficient and firms now produce more output. As a result, firms find it optimal to shade jobs in order to maximise expected profit. Wages of the remaining labour force in active employment goes up to compensate them for higher productivity. Note that productivity shock only occurred in the non-durable sector. Although, the durable sector did not experience hike in labour productivity, firms in that sector have to pay higher wages in order to align itself with the non-durable sector. Note that wages is assumed to be mobile and so wages are equalised across all firms. Prices are set as mark up on marginal cost. As such, decline in labour demand reduces marginal cost and fall in marginal cost results to fall in prices. The reason for this is quite intuitive; as more workers get laid-off, firms spend less on wages. Note that labour is assume to be the only factor input and recall that wages of the retained workforce rises to compensate them for additional efficiency. Therefore, as labour declines, marginal cost falls notwithstanding the rise in nominal wages of the remaining labour force. This is because labour demand falls more proportionately than the increase in nominal wages. For firms to sell more output, they have to reduce prices in order to encourage demand. Note that fall in prices increase the purchasing power of wages. Thus, as prices fall, real wage of both households increases. Notice that a welfare-maximizing monetary policy maker raises interest rate in the immediate aftermath of a shock and later reduces it below baseline. Note that the price of durable goods is assumed to be flexible and that of nondurable goods, sticky. Due to price rigidity in the non-durable sector, prices does not decline instantaneously when marginal cost falls, it declines at random interval with a certain probability and remain fixed with a certain probability and therefore, aggregate price changes slowly. Although, the impulse responses to the productivity shock in non-durable sector under the overdraft condition are similar to those in the collateral condition. However, there are important differences in the sluggishness of adjustment COPY RIGHT 2013 Institute of Interdisciplinary Business Research 309

7 and in magnitude of responses. Similar to the collateral condition, productivity shock in the non-durable sector results to fall in marginal cost. Quantitatively, both wages and unemployment rises relatively higher under overdraft constraint condition. This allows the constrained consumers to increase consumption of non-durables relatively more under overdraft comprared to collateral condition thereby maximixing their utility as they do not need to accumulate durable goods to increase consumption. Therefore, they reduce the consumption of durables relatively more under overdraft. The reason for this is quite intuitive;- the credit negotiating ability of the constrained under overdraft does not depend on the value of their stock of durables unlike in the collateral condition. Therefore, they do not need to accumulate durables. Under overdraft, lower price contributes to higher real wage and lower real wages increases the purchasing power of wages and therefore allows the constraint to consume more non-durable goods. Now, we need to understand whether the enormous rise in interest rate by the central bank is reasonable. The rationale for the subastantial rise in interest rate is basically to ensures low price but this makes borrowing costly. Note that debt accumulates to approximately the same level as in the case of collateral but debt rises faster under the overdraft condition. This ensures increased availability of resources to be spent on consumption when prices are still relatively lower (due to price rigidity in the non-durable sector). If interest rate would be lower, then debt would become enormously too high, i.e. in later periods it will require servicing and so overall utility will not be maximised. So, it is in the need to keep debt under control that the central bank to raise interest rate too high. On the other hand, looking at the speed of adjustment, the economy reacts noticeably faster under overdraft than under collateral. This is intuitively clear. Unlike overdraft, when we need to adjust impluse responses, we need to change the value of collateral (provided that prices react with similar speed). Collateral could adjust only slow. However, under Overdraft condition, we only need to adjust wages which is a quicker process they adjust as quick as prices. Notice that the pattern and magnitude of changes in durable consumption in response to interest rate fluctuation differs under both condition. In the aftermath of the shock, aggregate durable consumption under collateral condition increases slightly more than under overdraft condition as prices rises. As interest rate falls and touches its baseline, durable consumption of the unconstrained falls and converges to baseline under both conditions. However, as interest rate crosses its baseline, their durable consumption crosses steady state where it is negative under the collateral condition. Notice that durable consumption of the unconstrained COPY RIGHT 2013 Institute of Interdisciplinary Business Research 310

8 under overdraft condition remains on its baseline when interest rate is below baseline. Now let us see why these happen: Under the collateral condition, as durable prices rises, the unconstrained reduce durable consumption. As durable prices falls afterwards, they reduce durable consumption. However, the case is different under overdraft condition. As interest rate falls until it reaches baseline, durable prices falls and the unconstrained durable consumption converges to baseline. However, as interest rate becomes negative, durable prices falls but the unconstrained does not reduce durable consumption further beyond baseline. This is because, they as owners of firms are experiencing increasing marginal cost and despite that, they still reduce prices as interest rate falls. Secondly, aside stabilising prices, the effect of changes in interest rate determines the debt negotiating ability of the constrained households under the collateral condition. At a high interest rate, the unconstrained enjoys high interest on lending. However, the constrained cannot secure credit due to low relative prices. Therefore, they reduce durable consumption following a monetary contraction and increase it thereafter as interest rate falls. Similarly in the same vein, durable consumption of the constrained rises and converges to baseline under both conditions as interest rate falls. As interest rate crosses its baseline where it is negative, their durable consumption crosses steady state from above where it is positive under the collateral condition. On the contrary, durable consumption of the constrained remains on its baseline even as interest rate falls below baseline under overdraft condition. Let us see why these happen; as prices increase, movement in the relative prices of durables strengthens the collateral constraint effect by increasing the value of collateral. Hence, the constrained increase durable consumption even as durable prices rise. They do this to ensure high stock of durable in order to facilitate increased ability to negotiate for credit in future even when collateral value eventually falls. On the other hand, the constrained households are not too concerned about the acquisition of durable under overdraft condition unlike under collateral. This is because their ability to secure credit is not tied to the value of their stock of durables. Notice interest rate rises higher and prices converge to steady state faster under overdraft compared to collateral condition. Although non-durable consumption stabilises at almost the same time under both conditions, durable consumption converges faster to steady state under overdraft condition. The magnitude of fluctuation is larger under overdraft condition but the speed of convergence to steady state is quicker. COPY RIGHT 2013 Institute of Interdisciplinary Business Research 311

9 Figure 1: Overdraft Condition Source: Calibration Solution from MATLAB Scientific Software COPY RIGHT 2013 Institute of Interdisciplinary Business Research 312

10 Figure 2: Collateral Condition Source: Calibration Solution from MATLAB Scientific Software 4.0 CONCLUSION After an interest rate hike, credit constraints may become tighter, and a reduced ability to borrow could then force credit-constrained household to decrease durable consumption while the unconstrained increases durable consumption. However it takes longer time for prices to be stabilised under collateral condition. Overall we observed an important quantiatative/qualitative differences in the size of inflation /price adjustment, real wage and unemployment. The economy is also quicker to control under overdraft condition and counterfactual movement in the durable goods sector under collateral condition is more severe. In addition, overdraft condition encourages the constrained households to demonstrate higher labour productivity. This is evident from the sluggish decline in aggregate durable consumption. However, despite the counterfactual movement in the consumption of durable goods between both households, monetary policy is still able to stabilise the economy. This research shows that monetary COPY RIGHT 2013 Institute of Interdisciplinary Business Research 313

11 policy is able to reconcile the co-movement problem in the durable goods sector. Following the argument Monacelli (2009), the introduction of a borrowing constraint solves the co-movement puzzle. However, the introduction of overdraft of up to five multiples of annual wages facilitate in the better stabilisation durable consumption. 5.0 RECOMMENDATION In order to maintain sustainable price stability using the interest rate mechanism as an instrument of monetary policy, we recommend monetary policy makers incorporates overdraft constraint of up to 1/5 of annual wages. This means the ability to borrow should not be based on the value of collateral, which is price sensitive. Rather, it should be based on the amount of annual wages. This will go a long way in solving the counterfactual consumption behaviour in the durable goods sector and will further be more effective in stabilising aggregate consumption. COPY RIGHT 2013 Institute of Interdisciplinary Business Research 314

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