Discussion Paper

No. 2017-65 | September 25, 2017
What moves the Beveridge curve and the Phillips curve: an agent-based analysis


Understanding what moves the Phillips curve is important to monetary policy. Because the Phillips curve has experienced over time movements similar to those characterizing the Beveridge curve, the authors jointly analyze the two phenomena. They do that through an agent-based macro model based on adaptive micro-foundations, which works fairly well in replicating a number of stylized facts, including the Beveridge curve, the Phillips curve and the Okun curve. By Monte Carlo experiments the authors explore the mechanisms behind the movements of the Beveridge curve and the Phillips curve. They discovered that shifts of the Beveridge curve are best explained by the intensity of worker reallocation. Reallocation also shifts the Phillips curve in the same direction, suggesting that it may be the reason behind the similarity of the patterns historically recorded for these two curves. This finding may shed new light on what moves the Phillips curve and might have direct implications for the conduction of monetary policy.

JEL Classification:

C63, D51, E31, J30, J63, J64


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Cite As

Siyan Chen and Saul Desiderio (2017). What moves the Beveridge curve and the Phillips curve: an agent-based analysis. Economics Discussion Papers, No 2017-65, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2017-65

Comments and Questions

Anonymous - Referee report 1
October 19, 2017 - 08:40

I believe the topic of the paper is very interesting and the contribution seems relevant enough to be considered for publication by this journal. Indeed the joint analysis of the Phillips curve and the Beveridge Curve seems to be neglected as they are typically analysed in isolation.

The goal ...[more]

... of the paper is also clearly stated in the introduction, especially when they argue that their intention is to test the two hypotheses of “job market efficiency” and “worker reallocation”. Moreover, the authors also provide a complete description of the theoretic apparatus behind their approach. The choice of following the agent-based methodology seems the natural habitat for this kind of analysis. I also think that the authors carry out an extensive discussion of the results related to the Beveridge Curve and the Phillips curve and interesting insights emerge from such discussion.

However, I have identified a few major points that I think are necessary to tackle. Some of them do not necessarily imply any change in the model structure or in the paper, but the authors should still comment on them.

The most pressing issue is, in my opinion, that the model seems a replica of the model presented in Delli Gatti et al. (2011). The authors explicitly say that they rely on this framework but I have the feeling that the reader is left with no intuition about what differentiates this model from the original work by Delli Gatti et al. (2011). All the model equations are identical and even some parts of the paper are copied and pasted from the original work without even reporting them as a citation. I think this is an issue that should be properly tackled. The authors might also highlight the main contribution which, as far as I understand, relies on the ols procedure implemented towards the end of the paper.

Also, the calibration of the model deserves a bit more detailed explanation.

A second more specific aspect: the interest rate does not account for the financial fragility of the bank. Why? Moreover, instead of increasing the interstate rate, it is not clear why the bank does not stop lending at all to riskier borrowers.

Finally, is the model stock-flow consistent? The replacement procedure of firms and banks seems to suggest that the model is not SFC. Can the authors comment on in this?

As a minor point: I have found some typos here and there so the authors might want to go through the paper and fix them.

Saul Desiderio - Authors' answer to referee 1's comments
November 01, 2017 - 13:52

We are deeply grateful to the referee for the pertinent and insightful comments, which will be useful for future refinements of our work.

The referee has identified four critical points:

1) The similarities with Delli Gatti et al. (2011) (DG, henceforth);
2) Calibration;
3) Interest rates and credit ...[more]

... supply;
4) Stock-flow consistency.
Below we provide our answers to the four points.

1) The first issue concerns the originality of our work at three different levels: the model, the description of the model and the application of the model.

The referee's concern is that our model is the same as the one in DG. This is partly true because our work actually spawns directly from DG. In fact, whereas DG is a sophisticated methodological work, its sole application is just a co-movement analysis exercise. Hence, in order to fill this gap, the present paper was conceived some time ago, along with other works (in the meanwhile already published), both as an application and, in a sense, as a continuation of DG. Not surprisingly, therefore, our work inherited from DG most of the model and, in part, the description itself of the model.

However, the model in DG presents a weakness: newly hired workers get a higher wage than incumbent workers, which is patently an unrealistic feature. Hence, in the model we use in the present paper incumbent workers' wages are automatically updated to the level of the entrant workers' wage. This is the main modeling difference with respect to DG. In the paper we have not stressed much this new characteristic because we discovered that actually it does not bring about substantial differences in the results.

As far as the description of the model is concerned, the direct descent from DG and our carelessness perhaps lead us to a slight abuse of copy & paste from the original text without properly quoting. Hence, we acknowledge that a rephrasing of some parts of the paper may be in order.

So, the main contribution of our paper, which can be better highlighted in the text as suggested by the referee, is indeed the sensitivity analysis and the theoretical insights that it conveys. In our opinion this is not of little importance, because models become really interesting only when they are used as analytical tools in order to investigate specific issues.

2) We do not describe in detail the calibration procedure because the model basically is not calibrated on real data using a formal procedure. What we did was to choose by trial and error a parameterization such that the model output looked somewhat realistic and comparable with various statistics computed on U.S. data. Nonetheless, our model can replicate satisfactorily a number of stylized facts even without calibration. We want to point out, though, that calibration is still a thorny issue for AB models, which in fact are seldom brought to real data. Various complicated calibration procedures have been proposed, but none so far enjoys broad consensus among practitioners. This research area is active but still far from reaching solid and practical solutions.

3) The interest rate determination rule we have implemented in the model is based on the vast 'external finance premium' theoretical literature. In this literature the interest rate increases with the borrower's financial conditions. Of course, more complicated models, where also the lender's financial conditions play a role, can be conceived. But the need for keeping the model as simple as possible pushed us to use a simple rule for the interest rate. Whether this is enough, simulation results should tell us.

In addition, the external finance premium theory partly answers also the second part of the referee's question, which is why banks do not stop lending to risky borrowers altogether. The idea is that the higher the borrower's risk, the higher the interest rate charged by the bank, and so in principle the lower the credit demand by the borrower. Hence, a situation in which the lender stops lending may also be interpreted as a situation in which the lender does not stop lending and contemporaneously charges an infinite interest rate.

Nonetheless, in our model banks’ losses indeed cause the credit supply to decline, even though this happens at the expenses of all firms, not just of the riskier ones. Thus, in future refinements of the model more sophisticated mechanisms for the credit supply (and demand) may well be implemented.

4) The referee's guess is right: the model is not stock-flow consistent. The size of the capital of the new entrant is determined on the basis of the firm size distribution at the end of each period (technically it is the truncated mean of the size of active firms). As for the source of the initial capital, we implicitly assume that the government pours money into the new firm (or the new bank) by issuing public debt that is bought by an un-modeled central bank. Basically, there is a government engaged in some sort of countercyclical expansionary fiscal policy financed by monetized debt.

In principle, soon or later the government should pay back the public debt to the central bank, but for simplicity we assume that this never happens, which on its turn can be justified if the government has seigniorage power. So interpreted, therefore, our model can be indeed regarded as SFC (conditional on an extreme countercyclical fiscal policy, of course).

In future works our model should definitely become truly SFC without relying on an extreme Policy in order to increase its degree of realism. Nonetheless, we believe that SFC is more important when the model is used to assess Policy (monetary policy, in particular, when balance sheets and nominal variables play a crucial role); in our case, as long as simulation results are quite realistic, the lack of SFC is of lesser importance.

Anonymous - Referee report 2
November 20, 2017 - 09:19

The paper builds an agent-based model to analyse the joint dynamics of the Beveridge curve and of the Phillips curve. The model built by the authors is similar to other agent-based models proposed in the literature (e.g. Fagiolo et al., 2004, Riccetti et al., 2014). The authors show that the ...[more]

... model is able to jointly reproduce the main regularities of the labor market, including the Phillips curve, the Beverage curve and the Okun's law. They also perform a sensitivity analysis with parameters of the model capturing central aspects of labor market dynamics such as search costs, contracts' length, etc. In particular, they relate changes in these parameters to changes in either the location or the slope of the Phllips and Beveridge curves. The analysis reveal some interesting and - sometimes counterintuitive patterns - like for instance a Phillips curve that becomes steeper as search costs in the market decrease.

The paper is well written and the subject is highly relevant. In addition, the analysis is competently made. Accordingly, I am quite favourable to the publication of the paper. I have just some comments that authors should take into account

Please provide estimations also of the relation between price inflation and the unemployment rate. The Phillips curve is usually shown using the former variable. There is no reason to show only the relation between wage inflation and unemployment.
The explanation of the relation between the parameter M and the slope of the Phillips curve at page 22 is not very clear and it should be improved.

-Continuing on my previous comment, I also think that the authors put too much emphasis on the role of wage competition among firms in order to attract workers. However, the model used by the authors, a general disequilibrium model. Accordingly, the effects of lower search frictions on wage inflation can also due to feedbacks coming from the goods market. For instance, lower search costs can also reduce frictional unemployment, and thus generate higher demand for goods and thus higher prices and then (e.g. via the minimum wage) higher wages in the labor market. The role of feedbacks and of interactions among different markets should be taken into account also in the explanation of the other results discussed in Section 4.

-page 14. Please provide more explanations about the Keynesian origins of fluctuations in the model. Claiming that there is excess supply is not enough to claim that the model is Keynesian.

Page 7. Please use a label different from "preferential attachment". The preferential attachment works just for the largest firm and not for the others. Also it is not clear why the same search scheme is not applied also to other firms in the queue (e.g. consumers first visit the largest, then the second largest, and so on and so forth).

Saul Desiderio - Authors' reply to referee 2
November 27, 2017 - 14:34

We are deeply grateful to the referee for her/his careful analysis and remarks, which will be taken into account in future revisions of our paper.

Below our replies to the issues raised.

1) The referee suggests to present also the price version of the Phillips Curve and to ...[more]

... better explain the relation between the slope of the curve and parameter M (i.e. search costs).
Providing the estimate of the Phillips curve in the price version is quite easy. More difficult is to provide an answer to the second issue, as we do not know where our explanation is not clear. So, what we can do is to just try to explain it again in a more succinct way.
Lower search costs indeed increase wage competition as workers can choose from a wider array of employers. This increases wages per se. Additionally, firms paying higher wages have an advantage in hiring workers over the other firms that can be exploited better when wage competition is higher. Hence, when wage competition increases (lower frictions) high-wage firms have a higher chance to hire workers than their competitors. But this implies that for a given number of newly hired workers (or a given decrease in unemployment), the percentage of those hired by high-wage firms will be, ceteris paribus, higher. This will cause the average wage to grow faster (with respect to a situation with lower wage competition).
Again, to better grasp the intuition behind our reasoning we suggest to think of this mechanism also in the opposite situation, that is when search costs increase: when competition is lower firms are on the same footing, that is higher wages do not increase the chance to hire more and, therefore, for a given number of newly employed workers there will not be a higher proportion of workers hired by high-wage firms. So wages will grow more slowly.
We can also use a zoological analogy to support our argument: if food competition is tougher, only bigger and stronger animals will eat and survive. Consequently, the average size of surviving animals will grow. But if competition for food is less intense, then also smaller and weaker animals will have their share of food and survive, causing the average size of surviving animals to grow less.
Anyway, we acknowledge that ours is only one possible interpretation of the results (see point 2 below).

2) The referee also hints at a consumption demand-driven explanation of wage inflation, claiming that our explanation gives too much importance to the role of wage competition.
We thank the referee for pointing out the possibility of an alternative explanation, which is reasonable and, moreover, is perfectly consistent with our Keynesian interpretation of business fluctuations (see also point 3 below). So, we agree with the referee that the role of feed-backs among different markets should be stressed more. However, the referee's reasoning is not totally correct because the minimum wage is not indexed to inflation (in our model). Maybe the higher demand for consumption goods just increases labor demand and, as a consequence, wages.

3) The referee demands to better explain our claims about the Keynesian nature of fluctuations.
In our model fluctuations are not determined by exogenous aggregate shocks but by the overall internal functioning of the model itself. In particular, fluctuations seem to be driven by endogenous changes in aggregate demand as peaks in unemployment correspond to peaks of unsold inventories (not reported in the paper, see pg. 14). What we can see from simulations basically is that whenever excess supply occurs on the consumption goods market, excess supply shows up also on the labor market. In addition, these imbalances are not reduced by relative prices adjustments (in fact, imbalances are persistent over the all simulation). According to the post-Walrasian disequilibrium approach, which our model closely relates to, such a situation is the distinctive feature of Keynesian unemployment, as opposed to 'Walrasian' unemployment where excess demand on one market corresponds to excess supply on another market. This explains why we regard unemployment and fluctuations as Keynesian.

4) Finally, the referee asks why the 'preferential attachment' mechanism (which moreover is suggested to be renamed) is not applied to all the firms in the queue.
Because of search costs, each period consumers can visit only a small number of firms. Hence, they are exposed to the risk of buying from expensive producers. In order to try to minimize this risk, every period the consumer explores the market in search of lower prices by selecting at random some of the firms. The drawback of such behavior is to select 'popular' firms that quickly exhaust all their produce. As a consequence, the consumer is exposed also to the risk of being rationed. At this point the preferential attachment mechanism enters into play in order to try to minimize this second kind of risk. Thus, the mechanism applies only to the first largest firm because of the consumer's need of balancing between two contrasting risk types.
Incidentally, we use the term 'preferential attachment' simply because we do not have a better one.